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Technical and Economic Assessment of a 500W
Autonomous Photovoltaic System with LiFePO4 Battery
Storage
João Filipe Esteves Carriço
Thesis to obtain the Master of Science Degree in
Electrical and Computer Engineering
Supervisor: Prof. José Paulo da Costa Branco
Examination Committee Chairperson: Prof. Rui Manuel Gameiro de Castro
Supervisor: Prof. José Paulo da Costa Branco
Member of Committee: Prof. João José Esteves Santana
Prof. Carlos Alberto Ferreira Fernandes
November 2015
II
III
Acknowledgments
I would like to express my gratitude and appreciation to the supervisor of this work, Professor Paulo
Branco for giving me this opportunity, his guidance, persistency and encouragement. It would not be
possible without his contribute. I would like to thank all my family, specially my mother, father and sister
for all the patience and support and a very special thanks to my girlfriend Inês Freire who gave me
strength. Finally, to all my colleagues and friends who listened, advised and made their questions mine
contributing to a better research.
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V
Abstract
The access to electricity in some African countries is still very poor. For isolated villages where the
distance to the major cities is higher than hundreds of kilometres and the number of populations is very
low, it is not economically viable to build a connection to the electrical grid. Autonomous photovoltaic
(PV) installations are the key for future full autonomy of the household at a low infrastructure cost. More
particularly, this thesis studies and tests the behaviour and efficiency of a low-cost isolated
(autonomous, off-grid or stand-alone) photovoltaic (PV) system with the novel Lithium Iron Phosphate
(LiFePO4) battery storage, for the rural area near Luena in Angola. The system (solar panel, batteries,
controller and inverter) is designed having in mind the required household load and energy available
from the sun. These determined the sizing of the PV panels’ nominal power, LiFePO4 battery pack
storage capacity, the energy monitoring system as well as the power of the inverter.
In this context, the autonomous solar energy production system was developed for a nominal power of
500W. It was configured considering the load diagram of a typical rural house in order to achieve a high
lifespan of LiFePO4 batteries with less maintenance as possible. The experimental tests were made
under real conditions with the relevant electrical parameters being measured and logged along the day.
These tests have shown that, although the system ensures the energy supply effectively between the
months of February to November, during the rainy season the system should be complemented with a
second source of alternative energy.
Keywords
Autonomous/Off-grid PV system, Angola, system efficiency, LiFePO4
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VII
Resumo
O acesso à eletricidade em alguns países africanos é ainda muito precário. Em vilas isoladas onde a
distância às grandes metrópoles é superior a algumas centenas de quilómetros e o número de
habitantes é pequeno, não é economicamente viável construir uma interligação à rede elétrica. Os
sistemas fotovoltaicos autónomos são a chave para pequenas habitações autossuficientes em termos
energéticos a um preço de infraestruturas reduzido. Em particular esta tese estuda e testa o
comportamento e eficiência de um sistema isolado de custo reduzido com as recentes baterias de Lítio-
Ferro-Fosfato (LiFePO4) para a zona rural de Luena em Angola. O sistema (painéis solares, baterias,
controlador e inversor) é dimensionado tendo em vista a energia necessária ao abastecimento dos
consumidores e a energia solar disponível. Estes irão determinar os valores de potência nominal dos
painéis, a capacidade do “pack” de baterias de lítio, do sistema de gestão de energia assim como a
potência nominal do inversor.
Neste contexto, o sistema de produção elétrica autónomo foi desenvolvido para uma potência nominal
de cerca de 500W. O sistema foi configurado tendo em consideração o diagrama de carga típico destas
pequenas habitações rurais, de forma alcançar o maior tempo de vida útil das baterias de LiFePO4 com
a mínima manutenção possível. Os ensaios experimentais foram realizados em condições reais com
todos os sinais elétricos relevantes medidos e gravados ao longo do dia. Estes mostraram que, apesar
de o sistema assegurar o abastecimento energético de forma eficaz entre os meses de Fevereiro a
Novembro, durante a época das chuvas o sistema deverá ser complementado com uma segunda fonte
de energia alternativa.
Palavras-chave:
Sistema fotovoltaico autónomo, Angola, rendimento, LiFePO4
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Contents
Acknowledgments .................................................................................................................................. III
Abstract .................................................................................................................................................... V
Resumo ................................................................................................................................................. VII
Contents ................................................................................................................................................. IX
List of Figures ....................................................................................................................................... XIII
List of Tables .........................................................................................................................................XV
List of Symbols ................................................................................................................................... XVII
List of abbreviations ............................................................................................................................. XIX
1 Introduction ...................................................................................................................................... 1
1.1 Motivation and problem definition ............................................................................................ 1
1.2 Objectives ................................................................................................................................ 2
1.3 Thesis structure ....................................................................................................................... 3
2 Autonomous PV Systems – Actual Panorama ................................................................................ 5
2.1 Photovoltaic Systems Types ................................................................................................... 6
2.1.1 Grid-tied Systems ............................................................................................................ 7
2.1.2 Off-Grid Systems ............................................................................................................. 8
2.1.3 Hybrid Systems ................................................................................................................ 9
2.2 Solar Radiation ...................................................................................................................... 10
2.2.1 Direct and diffuse radiation on a tilted plane ................................................................. 10
2.2.2 GHI, DNI ........................................................................................................................ 11
2.2.3 Angle definition .............................................................................................................. 11
2.2.4 Solar radiation measuring instruments .......................................................................... 15
2.3 Angola Case-Study ................................................................................................................ 16
2.3.1 Introduction .................................................................................................................... 16
2.3.2 General Overview .......................................................................................................... 16
2.3.3 Solar Resource .............................................................................................................. 18
2.3.4 Temperature and sunshine hours .................................................................................. 19
2.3.5 Energy sector scenario .................................................................................................. 20
2.3.6 Energy consumption costs ............................................................................................ 22
2.4 Conclusions ........................................................................................................................... 23
3 Photovoltaic Energy Systems Constitution .................................................................................... 25
3.1 Electrical Loads ..................................................................................................................... 25
3.1.1 Refrigerator .................................................................................................................... 26
3.1.2 Lighting .......................................................................................................................... 27
3.1.3 CRT TV .......................................................................................................................... 28
3.2 PV Panels .............................................................................................................................. 28
3.2.1 Working Principle ........................................................................................................... 29
3.2.2 Electrical parameters ..................................................................................................... 30
X
3.3 Energy Storage - LiFePO4 Batteries ..................................................................................... 31
3.3.1 Cell Operation ................................................................................................................ 33
3.3.2 State of Charge (SOC) and Depth of Discharge (DOD) ................................................ 34
3.3.3 Battery pack initial balancing ......................................................................................... 35
3.4 Batteries Management System ............................................................................................. 37
3.4.1 Safety Functions ............................................................................................................ 38
3.4.2 Cell Balancing ................................................................................................................ 38
3.4.3 SOC estimation .............................................................................................................. 44
3.5 Autonomous or Off-Grid Inverters ......................................................................................... 44
Pure sine wave inverters ............................................................................................................... 45
3.6 Cables .................................................................................................................................... 48
3.7 PV System Efficiency ............................................................................................................ 49
3.8 Conclusions ........................................................................................................................... 50
4 Autonomous PV System – Project ................................................................................................ 51
4.1 Loads ..................................................................................................................................... 51
4.1.2 Experimental loads power ............................................................................................. 53
4.1.3 Daily consumed energy ................................................................................................. 53
4.2 PV Panels Production Capacity ............................................................................................. 54
4.3 PV array sizing ....................................................................................................................... 55
4.4 Batteries ................................................................................................................................. 55
4.5 Autonomous or Off-Grid Inverter ........................................................................................... 56
4.6 Regulator ............................................................................................................................... 58
4.7 DC Cables ............................................................................................................................. 58
4.8 Protection – DC Switch and DC Fuses ................................................................................. 58
4.9 Prototype costs ...................................................................................................................... 59
4.10 Economic analysis of the off-grid PV system ........................................................................ 61
4.11 Conclusions ........................................................................................................................... 62
5 Experimental Results ..................................................................................................................... 63
5.1 Electrical parameters measurement ...................................................................................... 63
5.2 The Autonomous PV Experimental Set-up ............................................................................ 63
5.3 Initial Charging of the Cells .................................................................................................... 65
5.4 Bottom vs Top Balancing ....................................................................................................... 67
5.5 The Autonomous PV Run – Lisbon, Portugal ........................................................................ 69
5.6 Reserve Days ........................................................................................................................ 74
5.7 Comparison Methods ............................................................................................................ 74
5.8 Operation in the remaining months of the year ..................................................................... 77
5.9 Autonomous PV Run – Luena, Angola .................................................................................. 79
5.10 Conclusions ........................................................................................................................... 84
6 Conclusions and Future Prospects ............................................................................................... 87
6.1 Conclusions ........................................................................................................................... 87
6.2 Future Work ........................................................................................................................... 89
7 Bibliography ................................................................................................................................... 91
XI
8 Appendix ........................................................................................................................................ 95
8.1 National Instruments NI-USB6008/9 Data Acquisition Device .............................................. 95
8.2 Current Transducer LA-25-NP Datasheet ............................................................................. 97
8.3 Power Logger Fluke 1735 ..................................................................................................... 99
8.4 Tektronix TDS 2001/2012C Oscilloscope ............................................................................. 99
8.5 Data logging ......................................................................................................................... 100
8.5.1 Voltage log ................................................................................................................... 100
8.5.2 Current log ................................................................................................................... 101
8.6 CALB SE130AHA Battery Cell Datasheet ........................................................................... 104
8.7 Suntech polycrystalline STP225 – 20/Wd PV panels Specifications .................................. 105
Solar Cell Electrical Model ........................................................................................................... 106
8.8 TUV Solar Cable .................................................................................................................. 109
8.9 BMS Off-Grid 123 Electric ................................................................................................... 109
8.10 Livre Pure Sine wave Inverter 1500W ................................................................................. 111
8.11 KENTT 201E Refrigerator Datasheet .................................................................................. 112
8.12 Sony KV-14LT1E 13’’ Color TV Datasheet ......................................................................... 114
8.13 IST Meteorological station ................................................................................................... 115
8.14 Temperature Logger Tiny Tag Talk 2 – TK-4014 ................................................................ 115
8.15 Economic Evaluation Indicators .......................................................................................... 115
8.15.1 Net Present Value (NPV) ............................................................................................. 115
8.15.2 Internal Rate of Return (IRR) ....................................................................................... 116
8.15.3 Payback Period ............................................................................................................ 116
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XIII
List of Figures
Figure 2.1 - Global cumulative growth of PV Capacity (Source IEA) ...................................................... 5 Figure 2.2 - Grid-tied PV system block diagram ...................................................................................... 7 Figure 2.3 - Block diagram of an isolated PV system – Inverter connected to the regulator .................. 9 Figure 2.4 - Block diagram of an isolated PV system – Inverter connected to the battery ..................... 9 Figure 2.5 - Block diagram of a hybrid isolated PV-Wind system with energy storage ........................ 10 Figure 2.6 - Incident radiation on a tilted surface (source: adapted from The Irradiation Data, Andres Cuevas) ................................................................................................................................................. 10 Figure 2.7 - Angles of a tilted surface (source: adapted from ITACA website) ..................................... 12 Figure 2.8 - Solar rays on a) geographical and b) panels referential .................................................... 13 Figure 2.9 - Solar irradiance measuring instruments – a) pyranometer and b) pyrheliometer (source: NREL and IBPSA-USA website) ........................................................................................................... 15 Figure 2.10 - Campbell-Stokes sunshine recorder (source: WeatherBug blog) ................................... 16 Figure 2.11 - Africa and Middle East Global Horizontal Irradiation average annual sum between 04/2004 and 03/2010 [10] .................................................................................................................................... 17 Figure 2.12 - Angola Global Horizontal Irradiation (GHI) map [10] ....................................................... 18 Figure 2.13 - Daily mean solar radiation averages in Luena, Angola (source: PVGIS Climate-SAF database 2001-2012) ............................................................................................................................ 19 Figure 2.14 - Average temperatures in Luena, Angola [30] .................................................................. 20 Figure 2.15 - Angola electrical sector intervenients [33] ....................................................................... 20
Figure 3.1 - Autonomous PV System electric block diagram ................................................................ 25 Figure 3.2 - EU energy efficiency labels (source: which.co.uk website) ............................................... 27 Figure 3.3 - Fluorescent Lamp Lighting block diagram (source: next electronics website) .................. 27 Figure 3.4 - Sony TV operating current ................................................................................................. 28 Figure 3.5 - Multi-junction cell (source: solar cell central) ..................................................................... 29 Figure 3.6 - Exothermic reaction evolution with temperature [45] ......................................................... 32 Figure 3.7 - LiFePO4 simplified cross section cell [46] .......................................................................... 33 Figure 3.8 - LiFePO4 typical cell charging curve [49] ............................................................................ 34 Figure 3.9 - Parallel cell charging with power supply ............................................................................ 35 Figure 3.10 - LiFePO4 balancing time [48] ............................................................................................ 37 Figure 3.11 - BMS block diagram (adapted from “The Electropaedia” website) ................................... 37 Figure 3.12 - Types of balancing [51] .................................................................................................... 39 Figure 3.13 - Passive vs active Cell Balancing (Source: Texas Instruments) ....................................... 39 Figure 3.14 - Passive switched shunting resistor balancing (based on [51]) ........................................ 41 Figure 3.15 - Example of a passive cell balancing circuit TI BQ77PL900 [52] ..................................... 41 Figure 3.16 - a) Bottom balancing and respective b) after charging ..................................................... 42 Figure 3.17 - a) Top balancing and b) after discharging ....................................................................... 42 Figure 3.18 - Passive cell balancing based on voltage [52] .................................................................. 43 Figure 3.19 - Block diagram of a sine wave inverter (adapted from Texas Instruments) ..................... 45 Figure 3.20 - Inverter output waveform and corresponding harmonics ................................................ 45 Figure 3.21 - Inverter efficiency characteristic a) Xantrex Prosine off-grid inverter efficiency curve for 1000 and 1800W 24V system (source: Xantrex) and b) 1500W Livre Inverter ..................................... 47 Figure 3.22 - Cable losses ..................................................................................................................... 48 Figure 3.23 - Off-grid PV system connection diagram .......................................................................... 49
Figure 4.1 - KENT 201E refrigerator load diagram (1h) ........................................................................ 52 Figure 4.2 - Total daily load diagram ..................................................................................................... 53 Figure 4.3 - Refrigerator a) starting and b) operating current ............................................................... 57
Figure 5.1 - a) Autonomous PV system testing bench and b) system components ............................. 64 Figure 5.2 - Battery pack and BMS monitoring boards ......................................................................... 64 Figure 5.3 - Battery pack voltage during discharge on a constant resistive load of 6Ω a) without and b) with initial balancing ............................................................................................................................... 65
XIV
Figure 5.4 - Cell’s voltage during discharge on a resistive load of 6Ω a) without and b) with initial individual charging ................................................................................................................................. 66 Figure 5.5 - Discharge at approximate 0.06C current rate or 8A (3.3Ω resistor) .................................. 67 Figure 5.6 - Discharge on a resistive load of 6Ω a) bottom and b) top balancing ................................. 67 Figure 5.7 - Charge at constant current I=6A with a) bottom and b) top balancing .............................. 68 Figure 5.8 - PV installation site and sun trajectory in March 2015 ........................................................ 69 Figure 5.9 - Total solar irradiance incident on a horizontal (red) and 35º tilted plane (black) on 14th March 2015 with clouds .................................................................................................................................... 70 Figure 5.10 - PV (blue) and battery pack voltage (black) on 14th March 2015 ...................................... 71 Figure 5.11 - Battery pack voltage on 14th March 2015 ........................................................................ 71 Figure 5.12 - PV panel output power on 14th March 2015 .................................................................... 73 Figure 5.13 - PV module temperature and efficiency on 14th March 2015 ............................................ 74 Figure 5.14 - Global horizontal irradiance measured at IST meteorological station (red) and PVGIS global clear-sky irradiance (black) ......................................................................................................... 75 Figure 5.15 - Global irradiance incident on the PV panel plane calculated from experimental GHI (red) and PVGIS database (black) ................................................................................................................. 76 Figure 5.16 - Monthly global irradiation average and temperature on a 35º tilted plane [26] ............... 77 Figure 5.17 - Global horizontal irradiation in a) Angola and b) Portugal [10] ........................................ 80 Figure 5.18 - Monthly average global irradiation on a β=35º plane in Lisbon, Portugal (blue) and β=19º in Luena, Angola (black) [26] ................................................................................................................. 81 Figure 5.19 - Monthly average temperatures in Lisbon, Portugal (blue) and Luena, Angola (black) [26, 30] .......................................................................................................................................................... 81
Figure 8.1 - LA 25-NP current transducer characteristic ....................................................................... 99 Figure 8.2 - Connecting a Differential Voltage Signal [NI USB-6008/6009 User Guide] .................... 100 Figure 8.3 - LabVIEW Signal Express Monitor / Record interface ...................................................... 100 Figure 8.4 - LabVIEW Signal Express Playback interface .................................................................. 101 Figure 8.5 - LEM LA25-NP equivalent circuit according to datasheet parameters [58] ...................... 102 Figure 8.6 - Experimental setup to obtain LA-25 NP characteristic .................................................... 103 Figure 8.7 - Experimental characteristic test of the LEM LA25-NP ..................................................... 103 Figure 8.8 - Equivalent electrical model of a solar cell a) three parameters and b) five parameters [59] ............................................................................................................................................................. 106 Figure 8.9 - Stationary characteristic I(V,G) of a photo-diode exposed to solar light [59] .................. 107 Figure 8.10 – BMS 123 a) dashboard and b) system settings ............................................................ 110 Figure 8.11 - Inverter characteristic with a resistive load .................................................................... 111 Figure 8.12 - Capacitor-start motor a) connections and b) phasor diagram at starting [60] ............... 112 Figure 8.13 - Single-phase equivalent circuit with core losses [61] .................................................... 113
XV
List of Tables
Table 2.1 - PV module prices in 2012 in European countries [5] ............................................................ 6 Table 2.2 - PV systems combinations ..................................................................................................... 7 Table 2.3 - Average annual GHI, GTIopt and D/G in some Angola cities [10, 26] ................................ 19 Table 2.4 - Annual sunshine hours and climate conditions for different Angola regions [30, 31] ......... 20 Table 2.5 - Normal low voltage electricity tariff in Angola (single phase) [33] ....................................... 22
Table 3.1 - Battery technologies comparison [42, 43, 44] ..................................................................... 32 Table 3.2 - Balancing topologies comparison [51] ................................................................................ 40 Table 3.3 - Comparison of Balancing Algorithms [48] ........................................................................... 43 Table 3.4 - Typical actuation voltage levels of off-grid pure sine wave inverters and PWM regulators 47
Table 4.1 - Loads electrical experimental parameters .......................................................................... 53 Table 4.2 - Experimental dairy loads energy ......................................................................................... 53 Table 4.3 - Irradiation on Luena, Angola [26] ........................................................................................ 54 Table 4.4 - Pure sine wave inverter price and specifications ................................................................ 60 Table 4.5 - Total system cost ................................................................................................................ 60
Table 5.1 - Energy of the discharge tests in Figure 5.3(a) - unbalanced and Figure 5.3(b) - balanced cells ........................................................................................................................................................ 65 Table 5.2 - Energy and mean daily efficiency of the different components .......................................... 72 Table 5.3 - Statistical test results .......................................................................................................... 76 Table 5.4 - Autonomous PV system average technical data ................................................................ 77 Table 5.5 - Monthly average vs 14th March irradiation ......................................................................... 78 Table 5.6 - Estimated energy available to the loads ............................................................................. 78 Table 5.7 - Percentage of days of full and empty battery [26] ............................................................... 79 Table 5.8 - Radiation comparison between Angola and Portugal (source: PVGIS climate-SAF Europe and Africa maps database 2001-2010) [10, 57, 26] .............................................................................. 80 Table 5.9 - Global irradiation in Luena, Angola and Lisbon, Portugal on the horizontal and optimal inclined plane [10, 26, 30]..................................................................................................................... 81 Table 5.10 - Estimated energy available to the loads in Luena, Angola ............................................... 82 Table 5.11 - Percentage of days of full and empty battery [26] ............................................................. 83
XVI
XVII
List of Symbols
A – Amp
𝐴 – PV surface azimuth angle
𝐴𝑆 – Solar azimuth angle
𝐶 – Cell Capacity
D – Daylight saving time
EOT – Equation of Time (min)
𝐸𝑑 ≡ 𝑊𝐷 – Daily energy required by the loads
𝐸𝐼𝑁 – Energy received (in)
𝐸𝐿𝑜𝑎𝑑𝑠 – Energy of the loads
𝐸𝑂𝑈𝑇 – Energy delivered (out)
𝐸𝑃𝑉 – Energy produced by the PV panels
𝑓𝑠 – Sampling rate
𝐺 – Solar Irradiance (W/m²)
𝐺𝑏 – Beam radiation
𝐺𝑏_ℎ𝑜𝑟𝑖𝑧 – Incident (beam) radiation component perpendicular to the ground horizontal plane
𝐺𝑏_𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑡 – Maximum incident (beam) radiation
𝐺𝑏_𝑚𝑜𝑑𝑢𝑙𝑒 – Module (beam) radiation or radiation incident on the tilted plane
𝐺𝑑 – Diffuse radiation
𝐺𝑔𝑙𝑜𝑏𝑎𝑙 – Global radiation
𝐺𝑟 – Reflected radiation
𝐻ℎ – Irradiation on horizontal plane (Wh/m²/day)
𝐻𝑖 – Solar Irradiation (kWh/m²)
𝐻𝑜𝑝𝑡 – Irradiation on optimally inclined plane (Wh/m²/day)
𝐼𝑛 𝐷𝐶 𝑆𝑤𝑖𝑡𝑐ℎ – Nominal current of the DC switch
𝐼𝑅𝑀𝑆 – Root mean square current
𝐼𝑏𝑝1, 𝐼𝑏𝑝2, . . , 𝐼𝑏𝑝𝑁 – Cell’s by-pass current
𝐼𝑝𝑎𝑐𝑘 – Current circulating in the battery pack
𝐼𝑟𝑒𝑔_𝑚𝑎𝑥 – Maximum regulator current
𝐼𝑧 – Admissible current on the cables
LCT – Local Clock Time (h)
LiCoO2 – Lithium Cobalt Oxide
LiCoPO4 – Lithium Cobalt Phosphate
LiFePO4 - Lithium Iron Phosphate
LL – Local Longitude (°)
LSTZ – .Longitude of Local Standard Time Meridian (°)
𝑚 – the diode ideality factor
XVIII
mmf – Magnetomotive force
𝑁 – Day of the year
NiCd – Nickel-Cadmium
NiMH – Nickel-metal hydride
𝑃𝐽𝑜𝑢𝑙𝑒 – Joule losses on the cables
𝑃𝑃𝑉 - Power produced by the panel(s)
𝑃𝑅 – Power dissipated in a resistor (Joule Power)
𝑃𝑖𝑛𝑗𝑒𝑐𝑡𝑒𝑑 - Power at the end of the cables terminals, injected in the batteries
𝑃𝑖𝑛𝑣_𝑚𝑖𝑛 – Minimum inverter power
𝑃𝑙𝑜𝑎𝑑𝑠,𝑝𝑒𝑎𝑘 – Peak power of the loads
𝑅 – Resistance
𝑅𝐷𝑆𝑂𝑁 – Transistor resistance
𝑅𝐵𝑎𝑙 – On-Board resistor in parallel with the cell at passive balancing
𝑆 – Incident radiation or sun ray vector
𝑡𝑎𝑟𝑖𝑓𝑓 – Electrical tariff (€/kWh)
𝑡𝑠 – solar hour (h)
𝑈𝐵𝐴𝑇,𝑇𝑜𝑡 ≡ 𝑈𝐷𝐶 – Total battery DC voltage (V)
𝑈𝑅𝑀𝑆 – Root mean square voltage (V)
V – Volt
W – Watt
Wh – Watt-hour
𝑊𝐵𝑎𝑡,𝑇𝑜𝑡 – Total energy of the batteries
𝑊𝐷 ≡ 𝐸𝑑 – Daily energy required by the loads (Wh)
𝛼 – Solar altitude or solar elevation angle (º)
𝛽 – Surface inclination angle (°)
𝛽𝑜𝑝𝑡 – Optimal inclination angle (°)
𝜃𝑖 – Incidence angle (°)
𝛿 – Declination angle (°)
∆𝑇𝑠 – Sampling time
∆𝑈 – Cables Voltage drop
𝜂𝐵𝐴𝑇 – Battery efficiency (%)
𝜂𝐵𝑀𝑆 – BMS efficiency (%)
𝜂𝐵𝑀𝑆+𝐵𝐴𝑇+𝐼𝑛𝑣 – BMS, batteries and inverter efficiency
𝜂𝑃𝑉 – PV panels efficiency
𝜂𝑖𝑛𝑣 – Inverter efficiency
𝜂𝑙𝑜𝑠𝑠𝑒𝑠 – Cable losses factor
𝜂𝑠𝑦𝑠𝑡,𝑎𝑢𝑡 – Autonomous/Off-grid system efficiency
𝜙 – latitude (°)
𝜔 – hour angle (°)
XIX
List of abbreviations
AC – Alternating Current
AM1.5 –Spectral Distribution of Solar Radiation
BMS – Battery Management System
CC – Constant Current
CFL – Compact Fluorescent Lamps
CPV – Concentrated Photovoltaics
CRT – Cathode Ray Tube
CSP – Concentrated Solar Power
CV – Constant Voltage
DAQ – Data Acquisition
DC – Direct Current
DEEC – Department of Electrical Energy and Computers
D/G – Beam vs Diffuse Radiation Ratio
DIF – Diffuse Horizontal Irradiance/Irradiation
DOD – Depth of Discharge
DNI – Direct Normal Irradiance/Irradiation
EDEL – Empresa de Distribuição de Electricidade de Luanda
ENDE – Empresa Nacional de Distribuiçao de Electricidade
ENE – Empresa Nacional de Eletricidade
EOT – Equation of Time
EU – European Union
GAMEK – Gabinete de Aproveitamento do Medio Kwanza
GER – Gabinete de Energias Renováveis
GHI – Global Horizontal Irradiance/Irradiation
IEA PVPS – International Energy Agency Photovoltaic Power Systems
IRR – Internal Rate of Return
IRSE - Instituto Regulador do Sector Energético (Energy Sector Institute Regulator)
IST – Instituto Superior Técnico
LCT – Local Clock Time
LFP - Lithium Iron Phosphate (LiFePO4)
LL – Local Longitude
LSTZ – .Longitude of Local Standard Time Meridian
MBE – Mean Bias Error
MINEA – Ministério da Energia e Águas
MPPT – Maximum Power Point Tracking (or Tracker)
NOCT - Normal Operating Cell Temperature
NPV – Net Present Value
OCV – Open Circuit Voltage
XX
Op Amp – Operational Amplifier
OV – Overvoltage
PFC – Power Factor Correction
PV – Photovoltaic
PVGIS – Photovoltaic Geographical Information System
PRODEL – Empresa Nacional de Produção de Electricidade
RELOP – Associação de Reguladores de Energia dos Países de Língua Oficial Portuguesa (Portuguese
Official Language Energy Regulators Association)
RMSE – Root Mean Square Error
RNT – Rede Nacional de Transporte (National Transport Grid)
SOC – State of Charge
SR – Switched Shunt Resistor
STC – Standard Test Conditions
THD – Total Harmonic Distortion
UPS – Uninterruptible Power Supply
USD – Unites States Dollar
Wp – Watt-peak
1
1 Introduction
In the rural areas of developing countries, the access to electricity is still very deficient. This happens
once the distances involved are very large and do not justify the investment for supplying small
populations. The focus on rural electrification aims to give people better living conditions at low cost,
with the certainty that there will be no short or medium term return, but those conditions will make all the
difference on the development of that country.
This work aims to create a final solution that is actually possible to use immediately, add value and solve
these issues improving the living standard of people. The fully autonomy depends on the energy storage,
its efficient management and control is the key to ensure a long operation period.
Photovoltaic (PV) systems are a convenient solution for having a clean and reliable source of energy
and also provide electricity in locations where it is not possible to connect to the conventional electricity
grid or the connection has a high cost. The decrease of photovoltaic panels manufacturing cost make
autonomous photovoltaic systems more beneficial over the years. Consequently, PV installations have
been growing significantly in many countries over the past years. The use of PV installations meets then
economic, environmental and social causes. It is imperative to provide access to energy to ensure
socioeconomic development in the world’s poorest and developing countries. Although its relatively high
cost, autonomous/isolated or off-grid PV systems gradually expands with government economic support
and private investments.
Energy production is the basis for the working time capacity of an autonomous system which additionally
requires energy storing, in other words, batteries. Within the range of available chemical types, lithium
type has high electrochemical potential which makes it one of the most reactive of metals. These
properties give lithium the potential to achieve very high energy and power densities in many
applications such as automotive and photovoltaic. Lithium Iron Phosphate (LiFePO4) have some
advantages compared with other lithium battery types, having a very stable thermal behaviour. For this
reason they are object of study and also the best ways of using this type of cells.
This is the context of this study, more particularly PV isolated systems with LiFePO4 storage to supply
residential buildings in Angola and all the related elements necessary for its operation.
1.1 Motivation and problem definition
Electrical energy is a fundamental good for the development and well-being of a society. Africa is a
continent with a low rate of access to electricity, so it is important to develop solutions to improve life
conditions of the populations without harming the environment. Despite its huge natural resources
(mostly hydric potential), Angola is a country inserted in this context, with a per-capita consumption
2
below the average in Africa [1]. It is estimated that in Angola less than 20% of the population has access
to energy [2]. The power grid is still very limited supplying only the big cities. There are groups of diesel
generators that run on local networks to supply industries located in remote places, with problems of
continuous electricity supply. The prolonged drought affects river flows which in turn require electricity
production to stop. Also the dependence of the price of diesel fuel and its transportation costs, which
despite being relatively low compared with European countries, are continually growing due to the
decrease of natural resource reserves.
LiFePO4 have some advantages compared with other lithium battery types but some working constrains.
Lithium cells tend to have different state of charge (SOC) when used in groups (connected in series or
parallel) and submitted to several charge/discharge cycles. Enumerating some of the reasons, this could
happen due to external temperature differences, cell’s impedance differences or capacity manufacturing
differences. The SOC of each cell individually is not detected by any SOC measuring instruments. The
strategy to have the SOCs as close as possible is to do what is called balancing which should always
depend on system application and is generally done by a Battery Management System (BMS).
Protecting a single cell has a certain complexity, protecting a battery (a series string) is harder: cell
voltages do not divide equally, temperatures vary, etc. The higher the protection the higher the system
cost, for this reason the project is a balance between costs and capabilities as usual.
The electrical needs in developing countries is constantly growing which sets new horizons for energy
isolated systems.
1.2 Objectives
This thesis aims on the use of autonomous photovoltaic systems with LiFePO4 batteries to supply
individual or collective residential buildings in rural areas, more particularly at Luena zone in Angola.
The main objectives are the following:
1. Definition of the energy pathways in an autonomous photovoltaic home system (recognition the
involved elements);
2. Identification of the typical consumers profile on a small residential building in Angola. Based
on this, project the nominal values of each element that constitutes the system regarding the
typical consumers profile;
3. Cost–benefit analysis of the system in study by verification and analysis of total experimental
system efficiency results.
4. Study and test the behaviour of the novel LiFePO4 batteries under load when used in group as
a battery pack; Identify the best balancing typology for LiFePO4 batteries using the available
measuring equipment;
3
1.3 Thesis structure
This thesis is constituted by six chapters organized in the following sequence:
In Chapter 1 is done a general overview of the work;
In Chapter 2 the different types of autonomous photovoltaic systems are introduced, basic solar
radiation concepts and the contextualization of Angola and the introduction of economic
indicators;
In Chapter 3 is introduced the photovoltaic system and the various features of the components
necessary for its implementation;
In Chapter 4 is made the project of the components is done accordingly to the objectives;
In Chapter 5 is done the experimental study system elements behavior and its efficiency;
In Chapter 6 is made a summary of the conclusions drawn from work and some proposals for
future developments;
4
5
2 Autonomous PV Systems – Actual Panorama
The thermic conversion of the solar radiation can be used in several applications from water heating
(concentrated solar thermal, also known as concentrated solar power - CSP) to electricity production
(electrical) since the discovery in 1954 by Bell Labs who found that silicon doped with certain impurities
was very sensitive to light. As a result emerged the first solar modules that allowed a practical application
and with an energy conversion efficiency around 6% in laboratory. Photovoltaic (PV) technology is an
active solar system type based on the photoelectric effect, converting light into electrical energy through
photovoltaic cells that in turn form a photovoltaic panel. Nowadays, the most established solar PV
technologies are crystalline silicon-based systems. Silicon terrestrial module efficiencies cells reach
22.9% at Standard Test Conditions1 (STC) in laboratory [3]. Each cell generates a Direct Current (DC)
power of about 1.5W (0.5V and a 3A current) and the number of cells depends on the panel technology
[4]. A PV System consists of several PV panels connected in series and parallel forming what is called
a string. Photovoltaic modules power is usually between 50W and 315W. This systems may be
connected to the grid (grid-tied) or be isolated (off-grid) and are basically constituted by controllers,
batteries and inverters so they may feed the consumers. With the correct maintenance the durability is
higher than 20 years, making this a very reliable source of energy.
The global PV capacity grew 49% a year on average since 2003 as illustrate in Figure 2.1. Decentralised
systems represent approximately 60% of the global market, while centralised systems are close to 40%.
The share of off-grid installations is very small compared to grid-tied, once grid-tied systems expanded
in large scale from 2000 to 2013. However, like PV technologies in general off-grid systems are
expanding, especially in developing countries with high solar exposure. [5] [6]
Figure 2.1 - Global cumulative growth of PV Capacity (Source IEA)
1 Cell temperature, 𝜃𝑟 = 25°𝐶 ≡ 𝑇𝑟 = 298.16 K; Incident radiation, 𝐺𝑟 = 1000 𝑊/𝑚2; Spectral Distribution of Solar
Radiation AM1.5 - Total solar spectral irradiance distribution (direct and diffuse) at sea level, clear sky day, at an inclined plane at 37° tilt toward equator facing the sun, an absolute air mass (AM) of 1.5 (solar zenith angle 48.19°S)
6
As with other investments, prices tend to be smaller as the investments in photovoltaic systems expand.
In autonomous systems, batteries represent the largest share of investment usually greater than 40%
and can raise the cost of Watt-peak (Wp) to twice of a grid-tied system. The photovoltaic panels
constitute about 15-20% of the investment and the inverter another 20%. The remaining stands for the
control system and other costs. Additionally, the price is difficult to define as it depends on location, size,
and component specifications regarding the consumer’s needs. With data from 2013, a survey of system
prices in International Energy Agency Photovoltaic Power Systems (IEA PVPS) European reporting
countries2 showed the system prices in the off-grid sector (<1 kW), irrespective of the type of application,
typically ranged from about 2.7 to 20 USD/W. This means that a 500W system may cost between 1250
and 10.000 USD [5].
Data from selected IEA PVPS reporting countries showed that the price evolution of PV modules and
small-scale systems (<1 kW) has been decreasing specially since 2007. Table 2.1 specifies that different
PV technologies module prices varies from 0.5 to 1.54 USD/W in European countries. This represents
a price between 112.5 to 346.5 USD for a 225W PV panel. In 2012 some manufacturers have reported
losses which resulted in a price increase. The future trend is a price stabilisation of about 1 USD/W for
PV modules and 2.5 USD/W3 for residential systems [5].
Table 2.1 - PV module prices in 2012 in European countries [5]
Country USD/W
Austria 0.5 – 0.72
Denmark 0.72 – 1
France 0.96
Germany 0.92
Italy 0.67 – 0.87
Netherlands 1.39
Spain 0.73
Sweden 1.54
Switzerland 0.86 – 1.08
2.1 Photovoltaic Systems Types
In terms of PV systems network connectivity, there are currently two types: grid-tied systems and
isolated or autonomous systems with and without battery energy storage. In some literature [4] [7] [8]
[9], the hybrid systems with several energy sources (PV, diesel generators, wind, etc.) are considered
a third type; however due to the hybrid definition is more correct to portray it as a category. Table 2.2
shows different possible combinations of PV systems that are further explained in more detail. The
electrical loads may be Direct Current (DC) or Alternating Current (AC) power depending on application,
however only AC loads go in line with the context of this work. There may also be found grid-tied systems
with energy storage, the batteries work as a backup of energy in case the grid fails, Uninterruptible
2 Austria, Denmark, France, Italy, Spain, Sweden and Switzerland 3 Battery costs are not included
7
Power Supply (UPS), however this solution makes the installation more expensive and therefore used
only in very specific cases.
Table 2.2 - PV systems combinations
Types of PV systems Energy storage No energy storage Hybrid
Grid-tied X X X
Autonomous/Off-grid X X X
2.1.1 Grid-tied Systems
In grid-tied systems, the connection to the electric grid allows the sale of electricity to the power
distribution companies and the feeding of the loads. The generated energy is injected directly in the grid.
Therefore, batteries and regulators are not necessary, what makes the system simpler and less
maintenance.
Figure 2.2 represents the main equipment of a grid-tied system with AC loads (the protection elements
are not represented). Purchase and sell back energy meters may be, in some cases, substituted by bi-
directional meters. A power inverter makes possible the connection to the grid and the connection of the
consumers is done at the grid side node.
Medium power grid-tied inverters use a Maximum Power Point Tracker (MPPT) to optimize PV panels
performance. This device constantly adjusts the input of a DC/DC converter (accordingly to the actual
irradiance and temperature) which selects the voltage output based on a simulated model. Selecting an
output voltage the current automatically adjusts and its value depends on the IV curve of the panel
(Figure 8.9). In many countries there are several incentive policies for small home systems sell your
energy to the grid with advantageous rates.
PV
Consumers
Energy meter:
Sell back
Energy meter:
Purchase
Grid
PDC
PACInverter Isolation Transformer
DC/DC Converter
MPPT
Figure 2.2 - Grid-tied PV system block diagram
Another recent solution that is being implemented is the connection of the inverter directly to consumers’
houses circuit for immediate consumption. This is done using an inverter for each panel – Microinverter4.
A photovoltaic system typically includes several panels wired together in series/parallel, with their total
4 Inverter used for a single panel that automatically synchronizes with the grid
8
DC output going to a central “string” inverter. This design has a few significant weaknesses. First, if the
inverter goes down, the whole system is down. Second, at any given moment, each solar panel may be
producing different amounts of power depending on shading, age, wear, and other factors. In the central
configuration, the overall system performance is dragged down by the weakest link. A string inverters
has to go with the average of the array rather than optimizing the outputs of each panel.
Microinverters are dedicated to a single PV panel and use the MPPT algorithm for each panel
individually, optimizing the overall system output regardless of minor shading issues and other variations
among individual panels. The connection of this type of inverters to consumers’ houses circuit allows
power reduction required from the network and consequent energy cost reduction for consumers without
the need of a producer contract, thus being autonomous (off-grid system).
2.1.2 Off-Grid Systems
The term isolated, autonomous or off-grid system owes its name due to the lack of any connection to
the electrical grid. In an isolated system without energy storage and DC or AC loads, consumers utilize
immediately the electric energy produced by the photovoltaic module. The investment in this type of
system is lower compared to systems with energy storage elements incorporated. However, the supply
to consumers is only possible during energy production hours. For example, a very common application
is water pumping systems.
Autonomous PV systems with energy storage are constituted by a string of PV panels, a solar
regulator/controller to monitor the batteries’ voltage levels and a battery pack. The energy produced by
the PV panels is delivered to the loads, and the surplus energy is stored in the batteries. The stored
energy may be used during the night when there is no solar radiation. Consequently, the batteries must
have enough capacity to feed the load during the night and/or in low solar radiation days. The regulator
has the ability to cut-off the PV and also cut-off the consumers supply accordingly to the battery voltage
levels. The use of DC loads only may avoid the use of an inverter. Inverter efficiency and consumption
in stand-by reduces the amount of available power to the loads. However, the use of DC loads is not
very usual and this equipment is always more expensive than AC equipment. Using only AC loads is a
cheaper solution and has more interest in terms of project.
Two configurations are possible – connect the inverter to the solar regulator (Figure 2.3) or directly to
the batteries (Figure 2.4). The use of an off-grid inverter is required when using AC loads. Solar
regulators are usually projected for currents up to 50A. In case of loads without high current peaks, the
inverter may be connected to the regulator as shown in Figure 2.3.
9
PV
DC Loads
Battery
Pack
Solar Reg.
PDC
PAC
PDC
AC Loads
Inverter
Figure 2.3 - Block diagram of an isolated PV system – Inverter connected to the regulator
Figure 2.4 - Block diagram of an isolated PV system – Inverter connected to the battery
AC loads are usually constituted by electrical motors, lights, TVs and other equipment with high starting
currents that produce prohibitive currents on the DC side. These peaks may reach 100A in the battery
pack and going through the regulator. To avoid such currents in the solar regulator, a direct connection
of the inverter to the batteries is a possible solution, as shown in Figure 2.4. With this configuration, the
regulator may connect/disconnect the PV panels and the DC loads. The inverter acts like a regulator
being the under-voltage protection for the batteries thus disconnecting the AC Loads. In this case, the
efficiency of the inverter has to be taken into account once it might be working at 20% of its nominal
power once an oversizing is necessary due to power peaks. The two different typologies choice depend
on the cut off parameters of the inverter and regulator nominal current.
2.1.3 Hybrid Systems
Hybrid systems consist of a combination of several energy sources in photovoltaic applications.
Diesel/gas generators, wind power and other sources may be used besides PV panels. This systems
need more complex control and protection circuits and are generally used for medium to high power
applications. For example in PV/Diesel medium power systems, the generator should work only when
the batteries reach the low voltage level and shuts down when the batteries are charged.
Figure 2.5 shows a hybrid isolated system with PV and wind energy sources. Different from configuration
in Figure 2.4, this configuration allows the charge of the batteries during the day and night. Wind
generators are always AC power, so the wind regulator makes possible the connection to the batteries
in DC current.
PV DC Loads
Battery Pack
Solar Reg.
PDCPDC PAC
AC Loads
Inverter
10
PV
Consumers
PAC
Battery Pack
Wind Generator
Solar Reg.
Wind Reg.
PDC
PDC
PAC
Inverter
Figure 2.5 - Block diagram of a hybrid isolated PV-Wind system with energy storage
For autonomous PV systems, there are no regulations in many countries, giving some freedom to their
implementation. Autonomous PV systems with electric energy storage based on LiFePO4 battery pack
is the focus of this work, being studied in more detail. Particular care is the requirement to ensure the
batteries and the power plant to have the longest possible useful lifetime.
2.2 Solar Radiation
Before analysing some data is important to make a brief introduction to the concepts of solar radiation.
Sunlight is part of the electromagnetic radiation given off by the Sun. The visible spectrum is constituted
by infrared, visible and ultraviolet light. The incident solar power per unit area, 𝐺, is the solar irradiance
and is measured in 𝑊 𝑚2⁄ . The solar energy incident per unit area, 𝐻𝑖 , is designated irradiation and is
measured in 𝑘𝑊ℎ 𝑚2⁄ . Only a part of the solar radiation hits the earth surface and this radiation is
classified in two different types regarding its way of incidence: direct and diffuse [4].
2.2.1 Direct and diffuse radiation on a tilted plane
When the surface under study is tilted with respect to the horizontal, the total irradiance on the tilted
surface is the direct (beam) normal radiation projected onto the tilted surface, plus the diffuse plus the
reflected radiation on the tilted surface. Figure 2.6 illustrates the types of radiation for a tilted surface
being the reflected radiation a particular case of diffuse radiation. Note that if the surface is not tilted the
reflected radiation component does not exist as explained below. [4, 10, 11]
Figure 2.6 - Incident radiation on a tilted surface (source: adapted from The Irradiation Data, Andres Cuevas)
11
Direct or Beam radiation 𝐺𝑏, is the quantity of solar radiation received directly from the sun. Diffuse
radiation 𝐺𝑑, is the sunlight received indirectly being scattered by atmosphere particles (clouds, fog,
dust, etc.). There is also a particular case of the diffuse radiation if the focusing surface is tilted relatively
to the horizontal plane: Albedo or reflected radiation 𝐺𝑟, is the radiation reflected in any non-atmospheric
element and is calculated as the ratio between the amount of reflected radiation and received radiation.
If the radiation is referred as “horizontal” or “tilted”, it means that the receiver plane is a horizontal plane
or a tilted plane relatively to the horizontal plane, respectively. Global Insolation, Total Irradiance or
Global Irradiance/Irradiation on a tilted surface is the sum of direct and diffuse radiation that focus on a
surface [12, 13]:
𝐺𝑔𝑙𝑜𝑏𝑎𝑙 = 𝐺𝑏 + 𝐺𝑑 + 𝐺𝑟 (2.1)
The global radiation is the most important parameter for evaluation of solar energy potential of a
particular region and the most basic value for PV simulations.
2.2.2 GHI, DNI
Global Horizontal Irradiation (GHI) is the sum of the solar radiation energy (direct and diffuse) that hits
one square meter in a horizontal plane in one day. Global Tilted Irradiation at the optimal inclination
GTIopt, is the same as GHI but for a tilted surface facing north (south hemisphere) at the optimum
inclination angle 𝛽𝑜𝑝𝑡. Another radiation sometimes seen in the literature and project software is the
Direct Normal Irradiance/Irradiation (DNI) which is the quantity of solar radiation received by a surface
that is perpendicular (normal) to the direction of the sun rays. Typically, the amount of irradiance
annually received by a surface may be maximized by keeping it normal to incoming radiation. This type
of radiation is usually important for CSP and concentrated photovoltaic installations (CPV)5.
2.2.3 Angle definition
The angle of the sun rays on the PV surface influences the amount of solar energy produced. This angle
is called angle of incidence, 𝜃𝑖, and is the angle between the sun rays and the normal to the PV panel
surface. The optimal angle 𝛽𝑜𝑝𝑡, refers to the fixed module inclination angle at which PV modules should
be oriented in order to maximize power (annual mean value). This angle depends mainly on the
installation geographical position (latitude) due to the variation of the sun altitude angle (𝛼) in the sky
across the year. The greater the location latitude (furthest from the equator) the lower the solar altitude
and more oblique the incident sun rays. The normal to the centre of the Earth is also referred as local
zénite. The solar azimuth angle 𝐴𝑆 is the angle between the horizontal projection of the sun vector 𝑆 and
the north direction. The panel azimuth angle 𝐴, is the angle between the horizontal projection of the
normal to the panel 𝑁 and the north direction (convention adopted in this work). The convention
N=±180º, S=0º, E=-90º, W=90º is also usually used in the northern hemisphere once at solar noon the
5 CPV use lenses and curved mirrors to focus the sunlight onto highly efficient multi-junction solar cells
12
sun is directly south in the northern hemisphere. Figure 2.7 shows the referred angles of PV panel’s
orientation [4, 7, 10].
The solar irradiance is usually measured at meteorological/radiometric stations on a horizontal plane as
global and diffuse irradiance, however the panels are often tilted and the data on inclined surfaces is
not available [13]. Due to their very different dependences on the tilted irradiance, the direct and the
diffuse components of the global irradiance must be considered separately [14]. The direct and reflected
radiation can be computed with good accuracy using simple algorithms but the diffuse component is
more complex and has to be estimated with different models requiring the information of global and
direct radiation incident on a horizontal surface [12, 13, 15].
Figure 2.7 - Angles of a tilted surface (source: adapted from ITACA website)6
𝑆 – Incident radiation or sun ray vector;
𝜃𝑖 – Angle of incidence between the DNI and the normal to PV surface;
𝛽 – Angle of inclination of the surface from the horizontal;
𝛼 – Solar altitude or solar elevation angle;
𝐴 – PV surface azimuth angle.
The monthly average daily radiation calculation method was first developed by Liu and Jordan [16] and
refined by Klein [17] where the diffuse radiation is considered isotropic (distributed uniformly all over the
sky). However, for the daily efficiency calculation purposes of this work, the diffuse irradiance is not
considered, once it usually corresponds to less than 10% of the total irradiance in clear sky days.7
Besides, the diffuse component decreases with the tilt angle. At the same time, the ground diffuse part
of irradiance increases, but is a small portion of the total irradiance [14]. Regarding this, the beam
6 http://www.itacanet.org/the-sun-as-a-source-of-energy/part-3-calculating-solar-angles/ 7 calculated using the Liu and Jordan model [16]
13
radiation incident (normal) to a fixed tilted surface 𝐺𝑏_𝑚𝑜𝑑𝑢𝑙𝑒, may be calculated accordingly to the
following expressions [4, 18, 19]:
a)
b)
Figure 2.8 - Solar rays on a) geographical and b) panels referential
𝐺𝑏_𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑡 =𝐺𝑏_ℎ𝑜𝑟𝑖𝑧sin 𝛼
(2.2)
𝐺𝑏_𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑡 represents the maximum beam radiation from the sun and is illustrated in Figure 2.8 a). It
changes during the day and year and gather information about the position of the sun in the sky (its
zenith and azimuth angles). 𝐺𝑏_ℎ𝑜𝑟𝑖𝑧 is the usually measured radiation component perpendicular to the
ground horizontal plane as Figure 2.8 a) vectors relationship examples. The solar angle 𝛼 [º], may be
defined by:
𝛼 = sin−1(sin 𝛿 sin𝜙 + cos 𝛿 cos𝜔 cos𝜙) (2.3)
where 𝜙 is the latitude [º], ω is the hour angle [º].
The declination angle 𝛿, is the angle between a line joining the centers of the sun and the earth to the
equatorial plane. It is zero at the vernal an autumnal equinoxes and has the value of approximately 23.5º
at the summer solstice and -23.5º at the winter solstice. The declination angle is usually considered
constant for 24h [20]. The expression for 𝛿 in degrees is given by [21]:
𝛿 = 23.45° × sin (2𝜋
365(284 + 𝑁)) (2.4)
where 𝑁 is the day of the year. The hour angle in degrees:
14
𝜔 = 15(𝑡𝑠 − 12) (2.5)
where 𝑡𝑠 is the solar hour [h]. It may be calculated from civil time using the following equation [11]:
𝑡𝑠 = 𝐿𝐶𝑇 +𝐸𝑂𝑇
60−𝐿𝐿 − 𝐿𝑆𝑇𝑍
15− 𝐷 (2.6)
where LCT is the local clock time in hours, LL is the local longitude, LSTZ is the longitude of the meridian
of the reference hour both in degrees8, D is the daylight saving time parameter (equal to 1 (hour) if the
location is in a region where daylight savings time is currently in effect, or zero otherwise). EOT is the
equation of time in minutes. It represents the difference between the medium solar hour and the real
solar hour and may be approximated by:
𝐸𝑂𝑇 = 0.258 cos 𝑥 − 7.416 sin 𝑥 − 3.648 cos 2𝑥 − 9.228 sin 2𝑥 (2.7)
where 𝑥 in degrees is given by:
𝑥 =360°(𝑁 − 1)
365.242 (2.8)
where N is the number of days since the begging of the year.
The irradiance on a tilted planes varies significantly with its orientation (azimuth and inclination angle)
and the vector N is defined to gather this information. The incidence angle 𝜃𝑖, between the sun vector
and the normal to any tilted surface, is exposed on Figure 2.8 b) and is given by the relation:
cos 𝜃𝑖 =𝐺𝑏
𝐺𝑏_𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑡=𝐺𝑏_𝑚𝑜𝑑𝑢𝑙𝑒𝐺𝑏_𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑡
(2.9)
Defining the incidence angle in terms of the date, hour and localisation:
cos 𝜃𝑖 = (sin 𝛿 sin𝜙 + cos 𝛿 cos𝜙 cos𝜔) − cos 𝛿 sin𝜔 sin 𝛽 sin𝐴
+ sin𝛽 cos𝐴 (sin 𝛿 cos𝜙 − cos 𝛿 sin𝜙 cos𝜔) (2.10)
reminding that A is the PV surface azimuth angle as defined in Figure 2.7 Substituting (2.2) in (2.9), the
radiation incident on a tilted surface finally results as:
𝐺𝑏_𝑚𝑜𝑑𝑢𝑙𝑒 =𝐺𝑏_ℎ𝑜𝑟𝑖𝑧sin 𝛼
cos 𝜃𝑖(𝛽) (2.11)
Note that this method has a mathematical limitation for low solar angles once that result in a division by
close to zero values.
2.2.3.1 Optimal Angle
The optimal angle varies throughout the year and an energy gain up to 12% is possible when the panels
are tilted this angle [22]. The most accurate way to determine it is to make measurements on site once
8 Note that west longitudes are negative, and time zones west of GMT are negative as well
15
it depends on the local weather and climate conditions [14]. Previous studies show that, if local and
weather and climatic conditions are not considered, the optimal fixed angle of PV modules depends only
on geographical latitude, 𝜙. Considering only the direct radiation the optimal tilt angle is calculated by
𝜙 − 𝛿, knowing that the declination angle is zero at the equinox (22 March and 23 September) and
±23.45° at the solstices (21 June 22 December). There are other proposed paths to calculate the optimal
angle in the literature [23, 24, 25]. The weather and climate effect is considered in PVGIS9 data [26] in
the next chapters. PVGIS tool is explained in more detail in 2.3.3.
2.2.4 Solar radiation measuring instruments
Hourly or daily global, beam and diffuse radiation measurements are very important to get reliable data.
This data is used to estimate the energy available at the PV panels plane at a given place. For this
measurements two types of measuring equipment exist: pyranometers and pyrheliometers.
a)
b)
Figure 2.9 - Solar irradiance measuring instruments – a) pyranometer and b) pyrheliometer (source: NREL and IBPSA-USA website)
A pyrheliometer or actionometer (Figure 2.9 b) measures the direct beam solar radiation (small portion
of the sky around the sun) at normal incidence in W/m². The instrument is mounted on a tracking
mechanism with the thermopile detector at the end of the tube which converts heat to an electrical signal.
The aperture angle of the instrument is 5.7° so the detector receives radiation from the sun and from an
area of the circumsolar sky two orders of magnitude larger than that.
A pyranometer or solarimeter (Figure 2.9 a) measures the total irradiance (beam and diffuse) from all
the hemisphere (180º field of view) on a planar surface by a thermopile sensor in W/m². The sensor may
be coupled to a shade disk, ring or sphere that follows the position of the sun in the sky “blocking” the
beam radiation. With this accessory only the diffuse radiation is measured. Depending on the instrument
accuracy and reliability, the International Standard ISO9060 defines three different categories for
pyranometers: second and first class instruments (1-2% accuracy), and secondary standard instruments
(maximum uncertainty of 3%) [27, 28].
The hours of bright sunshine is the time in which the solar disc is visible and is usually used for long-
term averages of solar radiation. For this measurements the Campbell-Stokes sunshine recorders use
9 Photovoltaic Geographical Information System
16
a solid polished glass sphere as a lens, concentrating the incident light to two photoelectric cells
represented on Figure 2.10. One is shaded from beam radiation and one exposed to it. With no beam
radiation the two sensors read a close radiation level. When beam radiation is present the output levels
are widely apart.
Figure 2.10 - Campbell-Stokes sunshine recorder (source: WeatherBug blog)
2.3 Angola Case-Study
2.3.1 Introduction
The case study presented in this chapter is Angola – a country on the west coast of Africa in a tropical
zone in the latitude range of 6 to 17ºS and 12 to 23ºE longitude range. More particularly, the rural interior
zone of Luena at 11º47’31.3’’S and 19º54’30.1’’E is studied in more detail. In order to contextualize this
work as well as possible in the Angolan energy sector reality, it is important to assess the energy
scenario and the solar availability in this country.
2.3.2 General Overview
Most communities in Africa don’t have access to electricity, thus the use of individual generators, mostly
diesel is very common. These generators are used due to the low cost of oil, but high emissions and
noise are down factors. Africa is a continent with high solar potential due to high sun exposure between
latitudes of 14 to 30º N (all of the Sahara zone) and 14 to 30° S latitude band (Namibia zone), as
represented in Figure 2.11. Only the areas of this latitude in the Americas, Middle East and Australia
have the same solar potential on the planet. For this reason and due to the continued fall in prices of
PV panels, photovoltaic technology is becoming a viable alternative in this continent.
Angola is a country with a large energy gap, 250 kWh/per capita, which places it behind the average
per-capita consumption in Africa [1]. It is estimated that in Angola less than 20% of the population has
access to energy, and within these consumers 75% live in the capital [2]. According to the Angolan
ministry of energy and waters, there is a need for implementation of solar photovoltaic systems in rural
zones, for electrification of social infrastructure, including schools, medical centres and administrative
buildings [29]. The need for approval of legislation to encourage the use of renewable energy
technologies is another of the plans for the development of "green" energy in Angola. In this context, PV
autonomous systems are a more clean and environmental friendly solution.
17
Figure 2.11 - Africa and Middle East Global Horizontal Irradiation average annual sum between 04/2004 and 03/2010 [10]
Angola has a lower price of electricity due to its high hydric potential and hydroelectric plants. Since the
end of the civil war in 2002, generating capacity expanded to 1,160 MW in 2007, of which 67% was
hydroelectric and 33% was diesel-generated. There are three main transport zones, north, center and
south and some small isolated systems. Capanda dam on the Kwanza River near the northern town of
Malange in 2004, with two turbines produces 260 MW following a 112 million USD investment, which
doubled its capacity to 520 MW. Northern Angola has the 180 MW Cambambe dam on the Kwanza
River, which supplies Luanda, and the 18 MW Mabubas dam on the Dande River. The Biópio hydro
plant on the Catumbela River and several small thermal plants serve the central provinces. The 51 MW
Matala dam on the Cunene River, which started rehabilitation in 2007, is the main source of electricity
in the southwest. Angola's internal electricity grid is weak and poorly integrated, with much power lost
in transmission, common power outages, worsened by poor maintenance and below-cost tariff
structures. [2]
Although the climate of Angola is tropical, it is not characterised as such due to the influence of three
factors:
The cold Benguela current along the southern coast;
The relief in the interior zones;
The influence of the Namibe desert on the southwest.
With two very clear seasons: the dry season (cacimbo), with less amount of cloudiness and lower
temperatures from May to September, and the rainy season with up to 70% cloudiness especially along
the ocean coast and higher temperatures from September to May. The shortest day is on June 21rst
solstice and the longest on December 21rst solstice10.
10 http://www.timeanddate.com/
18
Angola has a tremendous potential of both wind and solar resources. Being a developing country with
a population of 21.47 million people in 201311, Angola offers great promise and opportunity for launching
renewable energy products.
2.3.3 Solar Resource
There are some databases and web tools to assess the solar resource and PV systems performance.
SolarGIS and PVGIS are two of those tools and will be used as a reference in this work. SolarGIS is a
high resolution solar radiation database developed from Meteosat MSG data available for Europe, North
Africa, and Southwest Asia [10]. PVGIS is a free solar radiation web application that uses satellite
images (Meteosat) and ground measurements to calculate the solar radiation at the surface of the earth.
CM-SAF is the most recent PVGIS database representing a total of 12 years of data from the first
generation of Meteosat satellites (Meteosat 5-7, known as MFG), there are data from 1998 to 2005 and
from the second-generation Meteosat satellites (known as MSG) there are data from June 2006 to
December 2011. The algorithms differ between MSG and MFG. The spatial resolution is 1.5 arc-minutes
(about 3km right below the satellite at 0° N, 0° W). The coverage extends from 35° S to 58° N and from
18° W to 55° E. It is available for Europe, Africa, Mediterranean Basin and more recently expanded to
cover south-west Asia [26].
In Angola the global solar irradiation is above 2000kWh/m²/year especially in the interior and south areas
accordingly to SolarGIS maps in Figure 2.12.
Figure 2.12 - Angola Global Horizontal Irradiation (GHI) map [10]
11 The world bank (http://data.worldbank.org)
19
Table 2.3 - Average annual GHI, GTIopt and D/G in some Angola cities [10, 26]
𝑳𝒐𝒄𝒂𝒕𝒊𝒐𝒏 𝑮𝑯𝑰 [𝒌𝑾𝒉 𝒎𝟐 𝒚𝒆𝒂𝒓⁄⁄ ] 𝑮𝑯𝑰 [𝑾𝒉 𝒎𝟐 𝒅𝒂𝒚⁄⁄ ] 𝑮𝑻𝑰𝒐𝒑𝒕[𝑾𝒉 𝒎𝟐 𝒅𝒂𝒚⁄⁄ ] 𝑫/𝑮
Luanda 1900 5430 5490 0.42
Luena 2100 5870 6100 0.33
Huambo 2200 5890 6140 0.33
Lubango 2300 6090 6380 0.29
Namibe 2200 6370 6540 0.28
Table 2.3 represents the averages irradiances at the horizontal (GHI) and Tilted (GTI) plane. D/G is the
annual ratio of the total radiation arriving at the ground which is due to diffuse radiation. GTI and GHI
are the most important radiations to projects using PV panels and when tilted to the optimum angle
some annual mean gains may be observed relatively to the horizontal position. For this reason GTIopt is
the radiation to consider.
Regarding Angola climate characteristics, Figure 2.13 represents the daily average GHI and GTI
(irradiation) for each month in Luena city. According to this database the optimal inclination for Luena
area is 19 degrees (annual mean). [26]
Figure 2.13 - Daily mean solar radiation averages in Luena, Angola (source: PVGIS Climate-SAF database 2001-2012)
Luena registered the lowest values in the rainy season from November to March and the highest in the
dry season from April to October. This result goes in line with the rest of the country. The annual GHI
average is 5870 Wh/m²/day and the GTIopt is 6100 Wh/m²/day resulting in a gain of 3.92% at the
optimally inclined plane.
2.3.4 Temperature and sunshine hours
The geographical position of Angola provides a radiation of 10 to 12 hours per day during the entire
year. Table 2.4 shows some annual mean climate conditions for Angola regions. The annual mean
sunshine hours ranges from 2200 to about 2400 hours and the mean temperatures from 19 to 25ºC.
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec0
1
2
3
4
5
6
7
8
Month
Irra
dia
tion [kW
h/m
2/d
ay]
GHI
GTIopt
20
Table 2.4 - Annual sunshine hours and climate conditions for different Angola regions [30, 31]
Location Alt. (m) Climate Min / Av. / Max Temp. (ºC) Sunshine hours
Luanda 74 Subtropical thorn woodland 22 / 25 / 28 2340
Luena 1357 Subtropical moist forest 14 / 21 / 28 2464
Huambo 1700 Subtropical moist forest 12 / 19 / 26 2401
Namibe 44 Subtropical desert 17 / 21 / 33 2230
The dry season has more than 260 hours of sunshine per month and the rainy season reduces to 150-
160 hours [32]. In Figure 2.14 is represented the monthly average temperatures in Luena, Angola. The
lower temperatures are registered in the dry season between May and September (Tmin=9ºC,
Tmed=18, Tmax=26ºC). The higher temperatures between September and March occur at the cloudy
season when the days are longer.
Figure 2.14 - Average temperatures in Luena, Angola [30]
2.3.5 Energy sector scenario
In Angola, the government institution responsible for the energy sector is the Ministry of Energy and
Water (MINEA – Ministério da Energia e Águas) with the public investments plans being made by the
Ministry of Planning and the coordination of the Energy National Commission by the Ministry of Finance
(Figure 2.15).
Figure 2.15 - Angola electrical sector intervenients [33]
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec5
10
15
20
25
30
35
Month
Irra
dia
tion [kW
h/m
2/d
ay]
Tmax
Tmed
Tmin
Generation
MINEA
Responsible Ministry of Planning
IRSE
Regulator
Ministry of Finance
ENE, SOCEL and GAMEK
ENE and GAMEK ENE and EDEL
Transport Distribution
21
To accelerate the energetic situation in Angola, on 20th November 2014, an executive decree was
signed by José Eduardo dos Santos to extinguish two national companies of the energy sector and
create three new ones. The objective is to create companies dedicated exclusively to each of the sectors
of production, transport and distribution. Empresa Nacional de Electricidade (ENE) and Empresa de
Distribuição de Electricidade de Luanda (EDEL) were replaced by two new power companies – Empresa
Nacional de Produção de Electricidade (PRODEL) responsible for the exploration of the production
power plants and Empresa Nacional de Distribuição de Electricidade (ENDE) which operates
exclusively on the commercialization and distribution of electrical energy. Besides this, Rede Nacional
de Transporte de Electricidade (RNT) was also created which operates on the transport sector. [34]
This sector is regulated by the Electrical Sector Regulator Institute (IRSE – Instituto Regulador do Sector
Energético operating four national companies: Socel, GAMEK – Gabinete de Aproveitamento do Medio
Kwanza and Luanda Electricity Distribution Company (EDEL). ENE is the biggest generation player,
operates most of the National Transport Grid (RNT) and also distribution outside Luanda. In Luanda the
distribution is taken by EDEL. In the production sector GAMEK is responsible for the implementation
and management of the biggest hydroelectric dam in the country – Capanda Central – in the north of
the country with 520MW of installed capacity [33, 35].
The legislation for the energy sector in Angola is governed accordingly to the General Law of Electricity,
Law nº 14A/96 of 31st May 1996, which establishes the legal regime for energy production, transport,
distribution and utilisation. The population’s electricity needs is ensured by the Public Electric System
constituted by the National Transport Grid (RNT) and the set of installations of production and
distribution associated to it. IRSE is the public regulator entity with the duty of monitoring and
implementing the General Law of Electricity, preparing studies and projects principles of the relationship
between the different sector agents. The approval of concessions, as well as their assignment is the
responsibility the Council of Ministers. The National Department of Renewable Energy (Direcção
Nacional de Energia Renováveis) is the MINEA department with the objective of promoting and
developing renewable energy projects in the country. The realisation, promotion, evaluation,
implementation and monitoring actions of the renewable energy sector are executed by the Renewable
Energy Cabinet (GER - Gabinete de Energias Renováveis) accordingly to the Executive Order Nº
134/09 Republic Diary Nº 226 Series I of 30th November 2009.
The 1st phase of the implementation of the new policies started after 2009 and ended in June 2011 with
the installation of 63 grid-tied solar systems with 3-5 kWp. The 2nd phase began with the launch of the
competition for the installation of 244 systems in 47 locations in 12 provinces: Bengo, Bié, Huíla,
Huambo, Kuando Kubango, Luanda, Lunda Norte, Lunda Sul, Malange, Moxico, Uíge and Zaire [29]. A
Programme of Activities named “ENERCAP SunLighting™ Africa – Programme to replace kerosene
lamps with micro PV LED systems in the sub-Sahara” region is currently in the process of validation
covering a number of African countries, including Angola. In a 2012 Bloomberg article, Angola revealed
its plans to invest in about 130 solar projects, although there was no information regarding the size or
22
technology. There is also a CDM project in the feasibility stage, providing a total of 0.730 MW from 70
solar PV villages (grid connected). Furthermore, a capacity building programme conducted by Econ
Pöyry emphasizes a large potential for solar PV in the south of the country, where hydropower resources
are more limited. The study includes a 3 MW solar plant in Tombua, with potentially further solar plants
being installed in Namibe and Benguela. [2]
In Angola there is no regulation for microgeneration once the politics related to renewable sources and
decentralised production were taken only after 2009 in order to take the signed international
commitments on the reduction of CO₂. Having this in consideration in this work, it is considered the price
of the electricity tariff and the price of the fuel to produce the equivalent power to access the economic
viability of an autonomous systems and its payback period.
2.3.6 Energy consumption costs
The electric tariff in Angola is regulated and established accordingly to the Executive Decree nº 118/06
of 14th August 2006 represented in the next table:
Table 2.5 - Normal low voltage electricity tariff in Angola (single phase) [33]
Electricity tariff in 2015 Electricity tariff in 201512
3.35 kwanza/kWh 0.0265 €/kWh
The tariff for the active energy does not express the real cost of energy, which should be many times
higher. Besides, this tariff ensures only 20% of the costs of the system and should increase in the next
years due to the foreseen electrical grid expansion programme [36].
12 Based on a rate of 1€=123.677 AOA on 9th Jun 2015 (www.xe.com)
23
2.4 Conclusions
This chapter presented the different types of photovoltaic systems with special focus on isolated
autonomous systems. An introduction to different types of radiation and context of the work on the
African continent was made. As to radiation concerns, it was specified the proposed measurement
method that will be used to calculate on the experimental chapters. In order to reduce the complexity,
diffuse radiation is neglected once this is less than 10% of the total radiation incident on the panels on
a clear day. Also the reflected radiation on the ground is neglected for simplification.
Angola has a high solar potential with high average irradiance and sunshine hours rates, near 2000
kWh/m²/year and 2300h respectively. The energy sector is expanding and the government is
encouraging renewable energies and grid interconnection, living room for this systems in that country
and in many others in Africa. The cost of energy is very low nowadays, however in the next years the
tariff is expected to be updated and the price should increase to support infrastructure expansion costs
which will make this systems economically more interesting.
24
25
3 Photovoltaic Energy Systems Constitution
Isolated PV systems main objective is to feed electrical loads. They are basically constituted by five
elements: a set of PV modules (production), batteries (storing), a regulator to manage the state of charge
of the batteries (control), an inverter to convert DC to AC current (conversion) and loads (consume).
Each of this elements is going to be seen in detail next.
The off-grid PV system has the following architecture:
PVAC
Consumers
PAC
Battery Pack
BMS
PDCPDC Inverter
Figure 3.1 - Autonomous PV System electric block diagram
The straight lines represent a direct connection and the dashed lines the control unit. The panels and
the inverter work at the nominal voltage of the batteries and the BMS monitors each cell or the whole
battery pack electrical parameters. It actuates on the relays opening and closing the circuit, if the
batteries go over or undercharging respectively. The inverter has also its own protection, like short-
circuit, under and over voltage; however, it should be ensured that the inverter and BMS actuation
voltages do not conflict.
A feasibility analysis of the system is made by customer’s need of power by studying the capacity
required for storage and power generation.
3.1 Electrical Loads
The purpose of an autonomous PV system is to cover the demand of remote consumers. The
characterization of load depends on several factors, being power and working time the main factors for
a long-term working. In order to perform a correct project of the system, it is important to know the
consumption of the loads as precisely as possible. Regarding this, whenever possible, an experimental
measurement of daily loads consumption at the installation site should be made.
In this work, the electrical load for a rudimentary house in the countryside of Angola consists of:
1) 100W nominal power refrigerator;
2) 13’’ CRT TV;
3) 60W Incandescent Lamps or equivalent.
26
The refrigerator is the most critical of the loads, as it stores the essential goods. The system should be
projected to ensure its correct operation for the longest time possible. In order to meet the basic needs
of a house, the refrigerator should have both refrigerator and freezer compartments. The power of this
device is the key element for the dimensioning and should be as low as possible, and at the same time
meet the needs of a small family.
The lighting is the second most important of the three loads referred above. In remote locations, the
most frequently used light is the incandescent lamp, once it is cheaper than the other types. These
lamps are no longer produced in EU since 2012, due to the large energy spent and in 2016 it will be
extinct almost all over the world. Incandescent bulbs convert less than 3% of the energy they use into
visible light.13 In Angola, as referred before in chapter 2.3.5, they are still widely used but there are more
and more initiatives such as the "Green Wave" in 2014. to make the replacement for fluorescent lights
[37] [38].
The TV is the less priority load once it is for entertainment purposes but its use may be substituted by
other important loads as an iron or other devices.
3.1.1 Refrigerator
The refrigerator is constituted by an induction motor which requires a high starting torque to overcome
mechanical friction having a high starting current that may be more than 5 times the rated current.
Manufacturers consume estimation procedures
Refrigerators testing procedures are diversified globally. There are standards to regulate this market to
ensure that the devices comply with certain quality standards. In order to complement the information
from manufacturers, energy efficiency labels describe product’s energy efficiency, energy consumption,
fridge and refrigerator capacity and noise level (for refrigeration products). The energy rating calculation
differs across different products (washing machines, fridges, dishwashers, light bulbs, etc).
Since 1 July 2012 all new models must have a rating of A+, A++ or A+++. In Europe the tests are
regulated by the ISO 15502 standard. It specifies an environmental temperature of 25°C and a relative
humidity between 45% and 75%. The test lasts at least 24 hours, and the freezer and refrigerator space
has to be filled partially. During the course of testing, the doors are kept closed [39].
13 Keefe, T.J (2007). “The Nature of Light”. Archived from the original on 2012-07-24. Retrieved 2007-11-05
27
Figure 3.2 - EU energy efficiency labels (source: which.co.uk website)
This test conditions are obviously far from real conditions particularly with respect to the opening of the
door. The room temperature may be considered a good average for a house in Europe and in Angola
the average temperature does not differ too much from that as seen in 2.3.4.
The market offers various solutions at various prices, but the most common and cheaper refrigerator
power goes up to 100W.
3.1.2 Lighting
The most used lights in Angola are incandescent light bulbs, which are purely resistive loads and
electrically represented by a resistance. It is constituted by a filament that becomes incandescent when
crossed by electric current.
Figure 3.3 - Fluorescent Lamp Lighting block diagram (source: next electronics website)
The second more common lamps are compact fluorescent lamps (CFL) or compact fluorescent lights
using three to five times less energy and lasting eight to fifteen times more than incandescent light bulbs
(Figure 3.3). They also produce harmonics, if possible CFLs with low THD (below 30 percent) and power
factors greater than 0.9 should be selected.
28
Traditional (iron-core ballast and starter) fluorescent lamps also draw a higher current during the switch-
on cycle. During the start-up process, there are filaments at each end of the tube that are heated, and
this draws more current than normal operation. This surge current is typically between 1.25 and 1.5
times the normal current. Power Factor Correction (PFC) capacitors are used in parallel with many
fluorescent lamp ballasts, especially those designed for industrial use. These are necessary to minimise
the excess current drawn by a relatively linear but reactive load. When power is turned on, the surge
current may be very high - typically up to 30 Amps or more depending on the exact point in the main
cycle when power is applied. This is many times the rated current of the PFC capacitor (as determined
by the capacitance, voltage and frequency). The ballast is basically an inductor that is in series with the
gas tube to limit the current through it, which would otherwise rise to destructive levels, due to the tube's
negative resistance characteristic.
3.1.3 CRT TV
Comparing with Plasma, LCD (Liquid-Crystal Display), LED LCD and other recent TV technologies, CRT
TV’s are the least energy-efficient but also the cheaper and most common in Angola.
CRT TVs have also a high surge current when heating the metal plate at the back of the electron gun.
They are non-linear loads – a switchmode power supply. Next Figure 3.4 shows the typical operating
current waveform (blue curve) of a CRT TV experimentally obtained for the Sony TV (appendix 8.12)
with high harmonic content. The orange curve is the voltage at the terminals of the TV.
Figure 3.4 - Sony TV operating current
Most of the electronic equipment has a single-phase rectifier with a capacitive filter producing currents
with impulsive character and high THD, approximately centered in the voltage wave peak (orange). The
power factor does not apply in this case, once the current wave is not sinusoidal; however, we might
say that non-linear circuits have a poor power factor because the current waveform is distorted.
3.2 PV Panels
There are several types of active (conversion of sunlight into other forms of thermic or electric energy)
and passive (heating buildings through constructive strategies) solar systems. PV panels are active
29
solar systems constituted by solar cells associated in series and parallel to create a PV module with
appreciate power. The first generation technology is the crystalline silicon with a market share of 87%
in three mainly types: monocrystalline, polycrystalline and silicon tapes. The polycrystalline cells are
less efficiency but represent 49% of the market against 35% of monocrystalline cells. They have also a
lower manufacturing cost (about 20%) being the right choice to project the cheapest system possible
[4].
3.2.1 Working Principle
The working principle of solar cells is the photovoltaic effect discovered by Alexandre Edmond Becquerel
in 1839. In photovoltaic effect the electrons-hole pairs generated are transferred between different bands
(valence bands to conduction bands) within the material itself, resulting in the development of electrical
voltage between two electrodes. Solar cells are made of the same kinds of semiconductor materials,
such as silicon, used in the microelectronics industry. For solar cells, a thin semiconductor wafer is
specially treated to form an electric field, positive on one side and negative on the other. When photons
strike the solar cell, electrons are knocked loose from the atoms in the semiconductor material. If
electrical loads are attached to the positive and negative sides, forming an electrical circuit, the electrons
can be captured in the form of an electric current.
Figure 3.5 - Multi-junction cell (source: solar cell central)
The use of several layers revealed higher efficiencies in the conversion process with less thermal energy
lost. Since sunlight will only react strongly with band gaps roughly the same width as their wavelength,
the top layers are made very thin so they are almost transparent to longer wavelengths. This allows the
junctions to be stacked, with the layers capturing the shortest wavelengths on top, and the longer
wavelength photons passing through them to the lower layers. The example of a multi-junction cell in
Figure 3.5 has a top cell of gallium indium phosphide, then a "tunnel diode junction", and a bottom cell
of gallium arsenide. The tunnel junction allows the electrons to flow between the cells and keeps the
electric fields of the two cells separate.
A number of solar cells electrically connected to each other and mounted in a support structure or frame
is called a photovoltaic module. Modules are designed to supply electricity at a certain voltage, such as
30
a common 12 volts system. The current produced is directly dependent on how much light strikes the
module.
3.2.2 Electrical parameters
To uniform the measurements of the characteristic parameters the manufactures accepted to use the
Standard Test Conditions (STC) represent by the index r [4]:
Cell temperature, 𝜃𝑟 = 25°𝐶 ≡ 𝑇𝑟 = 298.16 𝐾;
Incident radiation, 𝐺𝑟 = 1000 𝑊/𝑚2;
Spectral Distribution of Solar Radiation AM1.514.
The thermal potential at the reference conditions:
𝑉𝑇𝑟 =
𝐾𝐵𝑇𝑟
𝑞= 0.0257 V (3.1)
The maximum output power at STC is the peak-power:
𝑃𝑃 = 𝑃𝐷𝐶𝑟 = 𝑉𝑀𝑃
𝑟 𝐼𝑀𝑃𝑟 (3.2)
The efficiency at STC:
𝜂𝑟 =𝑃𝐷𝐶
𝑟
𝐴𝐺𝑟=𝑃𝑝𝐴𝐺𝑟
(3.3)
where 𝐴 is the area of the cell/panels. With other working conditions:
𝜂 =𝑃𝐷𝐶𝐴𝐺
(3.4)
where 𝐺 is the total (beam and diffuse) radiance incident on the PV surface. The fill factor (FF) is:
𝐹𝐹 =𝑃𝐷𝐶
𝑟
𝑉𝑐𝑎𝑟 ∙ 𝐼𝑐𝑐
𝑟 (3.5)
It should as high has possible to take the most of the panel power.
A simplified model to estimate the temperature of the module uses a relation proportional to the incident
irradiance. Manufacturers provide the Normal Operation Cell temperature (NOCT15)
𝑇𝑐 = 𝑇𝑎 +𝐺(𝑁𝑂𝐶𝑇 − 20)
800 (3.6)
The efficiency of the panel may be estimated knowing the temperature of the cells, decreasing with
increasing temperature due to the higher dark current [40]. It will produce better results with experimental
data using the following expression [14]:
14 Total solar spectral irradiance distribution (direct and diffuse) at sea level, clear sky day, at an inclined plane at
37° tilt toward equator facing the sun, an absolute air mass (AM) of 1.5 (solar zenith angle 48.19°S) 15 NOCT conditions: ambient temperature of 20°C, G=800W/m². The typical value is 45°C
31
𝜂(𝑇) = 𝜂𝑆𝑇𝐶[1 + 𝛾(𝑇𝑐 − 𝑇𝑆𝑇𝐶)] (3.7)
where 𝑇𝑐 is the temperature of the cells, 𝑇𝑆𝑇𝐶 = 25°C is the temperature of the cells at STC
conditions, 𝜂𝑆𝑇𝐶 is the efficiency of the module at STC conditions and γ is the empirically estimated
relative efficiency temperature coefficient, approximately equal to -0.004/K for polycrystalline silicon
cells [41].
The voltage level is also very important as it determines the currents flowing in the circuit given a certain
power load. The higher the voltage, the lower the currents, and therefore less losses, which leads to a
cheaper system (lower regulator, fuses, cables cross section).
PV nominal voltage is used to make sure the module is compatible with a given system and refers to
the voltage of the battery that the module is expected to charge. The real PV output voltage changes
with environmental conditions, so there is never one specific voltage at which the module operates, but
a voltage rang, instead.
3.3 Energy Storage - LiFePO4 Batteries
An electric battery is a device that converts stored chemical energy into electrical energy in accordance
to the chemical reactions – redox equations. Rechargeable batteries have largely replaced primary cells,
as they save resource and reduce pollution. The most commonly used batteries for storing applications
are lead-acid batteries [7] type, but they are being substituted by Lithium-ion batteries over time due to
several advantages. Li-ion batteries have high capacity, high electrochemical potential, superior energy
density, durability, as well as the flexibility in design. All the above outstanding properties accelerate the
substitution of conventional secondary batteries.
The batteries used in autonomous PV systems must have the following characteristics:
Reduced maintenance requirements;
Long service time;
Reduced self-discharge and high energy efficiency;
High storage capacity and power density;
Good performance/price relation;
Protection against the occurrence of hazards to the environment and health.
The four most promising cell chemistries considered for energy storage applications are
LiMn2O4/graphite cell chemistry, which uses low-cost materials that are naturally abundant; LiNi1-X-
Y2CoXAlYO2/graphite cell has high specific energy and long life; Li4Ti5O12 is used as the negative
electrode material in Li-ion batteries with long life and good safety features and LiFePO4/graphite (or
carbon) cell chemistry is a type of Lithium that has a very good thermal and chemical stability, leading
to safety characteristics and very low risk of fire.
32
Table 3.1 represents a lithium ion cathode chemistry comparison (using carbon anodes). Lithium-ion
batteries advantages are evident. Less weight, more life cycles and less cycle discharge.
Table 3.1 - Battery technologies comparison [42, 43, 44]
Lithium-Ion Batteries
Specifications Lead-Acid NiCd NiMH Cobalt Manganese Phosphate
Specific energy
density (Wh/kg) 30-50 45-80 60-120 150-225 100-135 90-120
Specific power density
(W/kg) 180 150 250-1000 1000 1500 - 2400
Cycle Life (80%
discharge) 200-300 1000 300-500
500-
1000 500-1000 2000-3000
Self-discharge/month
(room temp.) 5-15% 20% 30% <5% <5% <5%
Cell Voltage 2.0 1.2 1.7 3.7 4 3.3
Thermal Stability Poor Good Very Good
Price (€/kWh) ~1500 - 250 - 390
Nowadays, the largely manufactured cathode is LiCoO₂ which offers high specific energy, but safety
risks especially when exposed to high temperatures. LiFePO4 cells have the best number of cycles
performance and thermal stability, which may be seen by the differential scanning calorimetry (DSC)
comparison in Figure 3.6. Charged cells were disassembled in an argon box. The positive electrodes
were washed in a liquid electrolyte (DMC), dried overnight, and sealed in punctured aluminium cans, for
simultaneous thermal analysis. The thermal scans were performed with a heating rate of 10 K/min up
to a temperature of 400°C in an argon stream.
Figure 3.6 - Exothermic reaction evolution with temperature [45]
The delithiated lithium nickel oxide (blue) shows the most vehement exothermic reaction at a
temperature beneath 250°C, followed by a large weight loss, due to oxygen evolution. The charged
33
lithium cobalt oxide electrode (red) also reacts at such low temperatures, but with less reaction enthalpy
and oxygen evolution. The exothermic reaction of the delithiated lithium manganese (green) spinel starts
at a much higher temperature and there is no weight loss up to 400°C. The delithiated lithium iron
phosphate (purple) however, shows no exothermic reaction and no weight loss up to 400°C, at all.
Next figure shows a simplified representation of a LifePO4 cell’s cross section:
Figure 3.7 - LiFePO4 simplified cross section cell [46]
On the top of the cell, two external electric terminals are accessible to connect to an external circuit and
a safety valve provides air circulation. The cathode (+) material is LiFePO4, a polyanion oxide,
possessing olivine-type crystal structure making its structure stability very good.
On one hand, LFP batteries present a lower capacity than other lithium-ion batteries (LiCoO2, etc), which
leads to more weight for the same amount of energy. On the other hand, LFP batteries have a much
better thermal stability, a longer cycle life. LFP batteries are extremely stable working for a wide range
of temperatures being so a safer technology. For this reasons they are ideal for off-grid PV systems
[47].
3.3.1 Cell Operation
LiFePO4 batteries have a very constant discharge voltage. Voltage stays close to 3.3V during discharge
until the battery is exhausted. This allows the battery to deliver virtually full power until it is discharged.
The characteristic of the cell defines the important relation between the cell’s voltage and correspondent
SOC. The typical cell charging curve versus its state of charge (SOC) at an 80% DOD (2.6V – 3.6V) is
represented in Figure 3.8. Note that the discharging curve has a slightly negative offset relatively to the
charging curve. This happens due to the internal resistance voltage drop of the batteries. Regarding the
charging/discharging characteristic the following conditions should be verified [48]:
The voltage of the cell must not exceed 3.65V when charging;
The voltage of the cell must not go under 2.5V when discharging;
The lifetime of the cells will be drastically reduced if charged outside the range 0°C ~ 40°C;
The lifetime of the cells will be drastically reduced if discharged outside the range -20°C ~ 60°C;
Cell’s lifetime will be reduced if charge/discharged at current rate higher than 30% of the
capacity (0.3C);
34
Cells may be damaged if operated at high pulse currents for more than a few seconds.
Figure 3.8 - LiFePO4 typical cell charging curve16 [49]
These limits vary to a certain extend with the manufacturer and for that reasons the datasheet of the
battery should be always considered. Besides, working on the “flat” part of the characteristic is more
beneficial in terms of control once the voltage variation is lower requiring a less complex control. The
less deep the discharge more cycles the battery does but less energy is extracted. It is preferable to
make deeper discharges once the battery components suffer less stress over time.
It is important to take into account the effect of temperature on the batteries. The capacity increases as
the temperature rises and vice versa. On the one hand, if the installation local has temperatures near
0ºC a higher capacity battery should be used in comparison to the capacity calculated to 25ºC.
3.3.2 State of Charge (SOC) and Depth of Discharge (DOD)
The SOC of a battery is a measure of the amount of its stored electrical energy. The DOD is exactly the
complement of SOC: when one increases, the other decreases. The prediction of the state of charge
can be performed by invasive methods and non-invasive methods. Invasive methods are based on the
chemical oxidation state of the active materials and are performed in laboratories. This method requires
the batteries to be offline.
Nowadays, the existence of mobile systems with batteries such as electric vehicles, battery operated
power tools, or temporary storage systems for renewable energy sources requires the
prediction/estimation of the state of charge with non-invasive methods. Thus, the research for non-
invasive and instantaneous methods for SOC determination is becoming dominant. That will be [47]:
coulomb counting (current based);
voltage or current pulse response;
voltage based;
battery internal impedance measure.
16 OCV - Open Circuit Voltage
35
The coulomb counting technique simply indicates the remaining capacity of the battery by using electric
current integration according to the coulomb counting equation [50]:
𝑆𝑂𝐶𝑡 = 𝑆𝑂𝐶0 −∫𝜂 ∙ 𝑖(𝑡)
𝐶𝑛𝑑𝑡
𝑡
0
(3.8)
where 𝑆𝑂𝐶0 is the initial SOC, 𝜂 the coulomb efficiency, 𝐶𝑛 the battery estimated capacity and 𝑖(𝑡) the
current. This method have some disadvantages like lack of precision due to the low accuracy of the
coulomb counting technique itself, the noise from the sensors for the acquisition of the respective
magnitudes and the increase over time of the error in the SOC estimation.
For this reason coulomb counting is usually additionally combined with others sensors such as
voltmeters to measure the battery voltage to calibrate the SOC when the actual charge approaches
either ends. After all, it is simple and has been used in many BMS’s products on the market, 123BMS™
corrects the value of the state of charge in each iteration [48].
In general, the cells voltage increases with SOC level. At 100% SOC voltage, it is not yet possible to
know what capacity really is. A 100 AH cell maybe as little as 100 AH or as much as 120 AH. However
in a battery bank, the weakest cell dictates the capacity of the whole battery system.
3.3.3 Battery pack initial balancing
New LFP batteries are usually partly charged from factory. However, due to transport, climate and
environment conditions cells’ SOC is different at the pack assembly moment. Before assembly the cells
in series to make a battery pack it is absolutely necessary to balance the cells so that they have a similar
voltage and consequent SOC when charging/discharging.
The power supply should be connected to both ends of the parallel row as in the following diagram
considering ideal batteries and the real power supply representation:
Cell 1 Cell 2 Cell 3 Cell 4
Rs
VS
Is
Power Supply Thévenin Equivalent Circuit
Figure 3.9 - Parallel cell charging with power supply
36
The starting point is to have all the cells at the same reference voltage point. It is easier to build a battery
pack with balanced cells, than to balance it after it is built. BMS balance can take weeks as it might have
a low balancing by-pass current for example, and even damage the cells if the voltage levels are not
correctly set. This balancing is done charging the cells individually or in parallel with a CC/CV power
supply (Constant current/Constant voltage). The charging/discharging current should be done at
maximum current of 1C, however to optimize durability the recommended current should be lower than
0.3C. Regarding this, before the parallel assembly it is important to ensure that all cell’s SOC is nearly
80% and consequent voltages are similar.
In order to reach 100% SOC, the power supply current should be set to 0.2C maximum and the voltage
equal to cell’s highest operating voltage specified by the manufacturer – 3.6V. The charging has two
stages:
1) The power supply starts working as a constant current source (CC), reducing the current when
the voltage gets close to 3.6V;
2) At a voltage close to 3.6V, the power supply switches to constant voltage source mode (CV)
while the current reduces approximately to zero.
The charging time taken from [48] is given by:
𝐶ℎ𝑎𝑟𝑔𝑖𝑛𝑔 𝑡𝑖𝑚𝑒 [ℎ] =(1 −
𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑆𝑂𝐶 [%]100 %
) ∙ 𝑁º 𝐶𝑒𝑙𝑙𝑠 ∙ 𝐶 [𝐴ℎ]
𝐼𝑆 [𝐴]
(3.9)
The balancing time depends on:
SOC level;
Cell’s internal series resistance;
Slope of the voltage vs. SOC curve at that SOC;
Initial SOC unbalance;
Desired final match of SOC.
The cells' unbalance, the balancing current, and the cells' OCV all decrease with a time constant that is
[48]:
𝜏[ℎ] = 𝑅𝑐𝑒𝑙𝑙 𝛥𝑉𝑆𝑂𝐶⁄ (3.10)
where 𝑅𝑐𝑒𝑙𝑙 is the relative resistance of the cell [Ω – Ah] and ∆𝑉𝑆𝑂𝐶 is the voltage drop in the SOC curve
[V]. The balance time is then [48]:
𝐵𝑎𝑙𝑎𝑛𝑐𝑒 𝑡𝑖𝑚𝑒 [ℎ] = 𝜏 ∙ 𝑒𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝑢𝑛𝑏𝑎𝑙𝑎𝑛𝑐𝑒 [%]𝐹𝑖𝑛𝑎𝑙 𝑢𝑛𝑏𝑎𝑙𝑎𝑛𝑐𝑒 [%] (3.11)
37
Figure 3.10 shows an example of LiFePO4 cells (A123 M1 type) balancing time at about 50% SOC,
balanced from 10% SOC unbalance (difference between SOCs) to 0.1% match. Its time constant τ, is
about 7.5 minutes and the balance time is about 34 minutes.
Figure 3.10 - LiFePO4 balancing time [48]
3.4 Batteries Management System
A Battery Management System (BMS) is an electronic monitor device which controls the status of
individual rechargeable cells batteries and battery pack. In order protect and maximize battery pack's
life, cell's temperature, voltage and current are monitored at a certain rate via several integrated control
modules and actuators. To provide a better performance, the SOC and eventually the SOH are
estimated and different balancing strategies can be used depending on the system application. The
general functionalities block diagram of a BMS is represented in Figure 3.11.
Power In
Control SignalControl Signal
CAN BUS (Communications)
ChargeRelay
PV
LoadRelay
Load
Battery Pack
On Board Sensors
(Voltmeter &
Thermistor)
CAN BUS Battery
SOC Model
Software Interface
Comparator / Decision Logic
By-Pass Circuit
Battery Control Unit
Battery Monitor
Unit
BMSCurrent Sensor
Figure 3.11 - BMS block diagram (adapted from “The Electropaedia” website)
38
The mains power circuit is represented outside the green box all at the voltage of the batteries (no MPPT
and no inverter for simplification). The Charge and Load relays may connect/disconnect the load and
production between electrical parameters given in the software interface. The BMS block inside the
green box is powered by the battery itself and is constituted by:
On Board Sensors – measure the electrical parameters to monitor the batteries state (cell
voltage and temperature);
Current sensor (current shunt, hall effect transducers, GMR magneto resistive sensors) – to
measure the current flowing in and out the battery pack for SOC estimation;
By-pass Circuit – constituted by a resistor in series with a controllable transistor in parallel with
each cell;
Software interface – human-machine interface to define the system desires behaviour;
CAN BUS (communication)– communication connection BUS between the BMS components;
CAN BUS – CAN BUS of the battery monitor unit;
Battery SOC Model – Estimated SOC based on expression (3.8) using the sensors’ inputs on
the boards ;
Comparator/Decision Logic – electronic circuit that compares the sensors values with the values
defined by the user in the software (this values are loaded to the microcontroller after input);
Battery monitor unit - microprocessor based unit incorporating the functions inside the grey box;
Battery control Unit – sends the control signals to the charge/load relays and to the by-pass
circuit transistor’s gate.
3.4.1 Safety Functions
The most important feature in any application is to ensure no damaging. The BMS protects each cell
from overcharge, over-discharge and external fault situations acting like an AC breaker, reading and
comparing the cell's voltage and temperature with specified data and controlling the switch of the source
and load circuits.
Monitoring cell temperature is essential for the proper working of the system. In case of overheat under
operation, protection measures like current limiting (usually loads), current interruption or cooling system
regulation can be adopted. A cooling system can be used in more complex systems, however this
traduces in a more expensive and complex solution. The monitoring is done using a thermistor on the
cell electronic board. This is a type of resistor with a characteristic that changes the resistance almost
linearly with temperature, over a limited range. In an overheating situation, its electrical signal may be
used to end the charge, stop the charge when the cell’s maximum operational temperature is reached,
or it could be used to turn on cooling fans.
3.4.2 Cell Balancing
Battery balancing is an energy transfer process where individual cells’ capacity is managed so all the
cells that constitute the battery pack have a similar SOC, ensuring a longer lifetime in service and
39
maximizing cells’ capacity. Without balancing, the battery with the lowest capacity in the pack is likely
to be a weak point during discharging, decreasing the ability of the pack to store energy over time as
the process need to be stopped. The cells must therefore be balanced. The balancing is usually
categorized in two types - active or passive. Figure 3.12 shows the some topologies which differ in the
type of passive elements connected in parallel with the cells, being used to adjust cell’s voltage and
SOC levels during charge, discharge or idle. Note that not all the existing topologies are discriminated.
Figure 3.12 - Types of balancing [51]
Figure 3.13 illustrates the simplified behaviour of the two types. Active type uses inductors or capacitors
to charge or discharge single cells transferring energy between them. There is almost no energy lost
during the balancing, so it is more efficient but it requires components of higher cost comparatively to
passive type. Passive type is a dissipative method - it balances the cell with the higher voltage (by-
passing it) in the battery pack discharging its energy to produce heat in a resistor. It is the simplest and
most commonly used due to its performance vs simplicity and cost benefit. [52]
Figure 3.13 - Passive vs active Cell Balancing (Source: Texas Instruments)
Table 3.2 shows a comparison between the two topologies of passive balancing and the some active
balancing topologies in a scale of satisfactory (±), good (+), very good (++) and excellent (+++). It is
then obvious that the passive type topologies are the best size, complexity and consequently price due
to its smaller and cheaper electronic elements.
Balancing
Passive
Fixed Shunting Resistor
Switched Shunting Resistor
Active
Capacitor Based
Single Switched Capacitor
Inductor & Transformer
Based
Single / Multi Inductor
Single Windings
Transformer
Converter Based
Buck / Boost Converter
40
Table 3.2 - Balancing topologies comparison [51]
Topology Equalization
speed Control
Complexity Implementation
simplicity Size Cost
Charge discharge
Application
Fixed Resistor ± Very Simple +++ +++ +++ Fixed Low Power
Switched Resistor
+ Simple +++ +++ +++ Charge Low Power
Single Switched Capacitor
+ Complex ++ ++ ++ Bidirectional Medium /
High
Single Inductor ++ Complex ++ + + Bidirectional Medium /
High
Single Windings
Transformer + Complex + + ± Charge Medium
Buck-Boost Converter
+++ Complex +++ + + Bidirectional Medium /
High
This facts goes in line with the objectives of this work, the choice of the passive type is justified by the
need of an economic system with the ability to control the parameters accordingly with system behaviour
over time. Therefore BMS123™ by 123electri.nl meets the requirements and is studied in more detail.
Passive or Active balancing is sub-categorized in three types – top, middle and bottom balancing. Middle
balancing is a type of balancing used in power packs [48], designed to deliver energy in a short period
of time which is not the purpose of this work. The balancing can be done during or at the end of charging
or discharging. Bottom balancing can be done making controlled discharge (connecting a known fixed
dummy load), however this is a waste of battery capacity for balancing activity (increasing wear) and
has no advantage vs top balancing where mains power is used as the energy source instead of the
battery power. Although balancing during entire charging and discharging is more accurate top
balancing is simpler and consequently less expensive.
3.4.2.1 Passive balance
The primary balance process algorithms are based on cell voltage equalizing. As explained before, the
excess energy is removed from highest voltage cells, by-passing it, until the lower voltage cell is in the
same level. The SOC is managed indirectly as it is associated to a specific voltage accordingly to cells'
characteristics. Voltage differences between cells is minimized through by-passing cells with higher
voltage. This algorithms may lead to cells overbalancing or under-balancing due to different impedance
between cells. This means that the voltage deviation can be caused by a different cell capacity or
impedance - a variation of its internal resistance due to higher temperature for example. Consequently,
this type of balancing does not guarantee a 100% SOC at the end of charge. [52]
In order to minimize the effect of impedance differences between cells some balancing techniques act
near the end of charge – top balancing, where the current starts decreasing at a higher SOC. This type
of balancing is used in 123electric BMS® used in this work as it is explained further on.
41
Cell 1
R1
Ibp1
Cell 2
R2
Ibp2
Cell N
RN
IbpN
Control
V V V
Ipack
Figure 3.14 - Passive switched shunting resistor balancing (based on [51])
The switched shunt resistor (SR), performs the voltage equalization controlling switches/transistors. It
could work in two modes. First, the continuous mode, where all switches are controlled by the same
on/off signal. Second, the detecting mode shown in Figure 3.14, where the cells voltages are monitored
and when cell’s imbalance is detected, it decides which resistor should be shunted. The current 𝐼𝑝𝑎𝑐𝑘
that circulates through the battery pack is the same in every cell, however dissimilar impedance,
temperature and capacity make cell’s voltage evolve differently. The by-pass currents 𝐼𝑏𝑝1, 𝐼𝑏𝑝2, . . , 𝐼𝑏𝑝𝑁
are 10 to 100 times smaller than 𝐼𝑝𝑎𝑐𝑘 so the balancing is smooth. The voltmeter has to be in parallel
with the cell once the switch has a drop voltage associated. The main drawback in these methods is the
excess energy from the higher cell(s) is dissipated as heat, there is a need for thermal management and
has to be applied during charging, otherwise it will shorten the battery’s run time. [51]
Figure 3.15 - Example of a passive cell balancing circuit TI BQ77PL900 [52]
Figure 3.15 shows the circuit that performs the passive balancing. In parallel with the cell, a MOSFET
transistor is controlled by the main microcontroller. When in conduction the microcontroller transistor
creates a differential voltage at the external transistor (on-board) gate, activating it, which on the other
hand closes the path that connects a resistor in parallel with the cell - 𝑅𝐵𝑎𝑙 The external transistor
resistance 𝑅𝐷𝑆𝑂𝑁 is negligible in comparison with 𝑅𝐵𝑎𝑙. The balancing current 𝐼𝐵𝑎𝑙 is low, typically under
1A and therefore may require multiple cycles to correct a typical imbalance.
42
3.4.2.2 Bottom Balancing
Batteries have a slightly different capacity at the exit of the manufacturing line which requires special
care when using a battery pack for long periods of time so the cells don’t get damaged. In bottom
balancing process, all the cells have the same reference point at the low end voltage, about 2.5V. If the
pack goes under the minimum critical voltage, all the cells get there together and there is not just one
cell going above the critical voltage what does not happen with top balancing.
a) b)
Figure 3.16 - a) Bottom balancing and respective b) after charging
To perform bottom balancing, the batteries should be discharged one by one to the 2.5V voltage, left
resting for 24 hours and discharged again to 2.5V (Figure 3.16 a). The resting voltage after discharging
is about 2.7V. After this they should be connected in series and be charged as a pack until one cell
reaches 3.6V (Figure 3.16 b). Bottom balancing makes the monitoring less exigent and simpler so it
may be used in applications that do not have a BMS to protect cells from undercharging, but it requires
protection from overcharging. [48]
3.4.2.3 Top balancing
In top balancing, the reference point is the maximum cell voltage of 3.65 V or other near that. When one
cell goes under the minimum critical voltage the remaining cells may have a higher voltage.
a) b)
Figure 3.17 - a) Top balancing and b) after discharging
Top balancing process starts by charging all the cells individually to 3.65 V to reach the 100% SOC
through a CC/CV power supply (Figure 3.17). After the individual charge they may be connected in
series and when discharging as a battery pack, the “weakest cell” will be the first to reach the minimum
voltage of 2.5V. This is the cell with less energy storage in the battery pack. As the cells are top
balanced, all the others will be above 2.5V and consequently higher SOC. This method is particularly
less risky, once if one cell is over discharged all the other may be in good conditions.
Cap
acit
y
Cap
acit
y
Vmin Vmin
Cell 1 Cell 2 Cell 3 Cell 4 Cell 1 Cell 2 Cell 3 Cell 4
Cap
acit
y
Cap
acit
y
Vmin Vmin
Cell 1 Cell 2 Cell 3 Cell 4 Cell 1 Cell 2 Cell 3 Cell 4
43
Table 3.3 - Comparison of Balancing Algorithms [48]
Voltage Based Final Voltage Based SOC History Based
Principle
of
operation
Balances whenever charging,
regardless of SOC. Strives to match
cell voltages.
Balances at high SOC. Strives to match cell voltages
Balances all the time. Strives to match cell DOD,
based on previous history of cells
Pros Very simple method
At high SOC the cell voltage changes rapidly, it gives
better data on the true SOC. Charging current can be reduced so errors due to
internal resistance variations are minimized
The BMS balancing current can be lower, and balancing can be
done in fewer cycles, as balancing can occur all the time. Cell resistance has little effect.
Cons
Cell voltage as an indications of SOC
is not effective. OCV vs SOC curve is quite flat at mid
SOC levels. Strongly affected by
cell’s resistance.
Balancing only at the top means there is less time to balance with high currents
Requires more computing power and more memory to store the history of each cell
Table 3.3 resumes the balancing typologies most frequent. Once each method has its pros and cons,
the choice depends on the application. Voltage based method produces poor results so the best choice
is to combine the final voltage based method with computing and memory capabilities. Although 123
electric BMS™ (appendix 8.9) uses the final voltage based method only, this results in the best
performance vs. price. Figure 3.18 is an example of voltage evolution in two different cells when
charging.
Figure 3.18 - Passive cell balancing based on voltage [52]
The charging process ends properly by reaching the by-pass voltage. In each cycle, the BMS shortens
the balancing time once the voltages get closer each cycle. The bigger the cells the higher the needed
time to balance.
44
3.4.3 SOC estimation
As seen before in 3.3.2, the usual method for estimating the SOC is the coulomb counting method done
with a “fuel gauge” that consists of a DC current meter. The basic calibration in this type of BMS consists
in the following steps:
1. At the beginning the algorithm considers the SOC given by the user.
2. If the first cycle is a discharging cycle, then Amperes are deducted until 2.5/V per cell is reached.
At the moment when 2.5V (or different number in Vmin value) is reached, 0% is shown at SOC
gauge.
3. After charging starts and once the voltage reaches 3.6V (or different Vmax value), the gauge is
set to 100%. Anytime when Vmin or Vmax value is reached by any cell
4. The 𝑆𝑂𝐶0 is recalibrated for the newer calculated value.
3.5 Autonomous or Off-Grid Inverters
For any photovoltaic (PV) system, the off-grid inverter is the essential electronic device that converts
low voltage DC electricity from a battery or other power source to 100V-120V or 220V-240V AC signal.
Off-grid Inverters produce a voltage wave, with an independent frequency from the grid. This is the point
where the off-grid inverters differ from grid-tied once the last need the grid voltage wave to “couple” and
inject power. Not only does the inverter convert DC to AC power but it may also regulates the PV system
if correctly dimensioned according to the battery voltage levels.
Some requirements are indispensable for an off-grid inverter [7]:
Auto starting and adequate protection warning signs;
Peak power capacity – it should support more than two times its nominal power;
Low THD;
Low stand-by power;
High efficiency;
Voltage stability – between the range of 230V±10%;
Possibility to connect other inverters in parallel.
The waveform should be selected accordingly to the type of application. They are classified in three
classes:
1. Square wave – The simplest and cheapest DC-AC converter. Usually constituted by thyristors
controlled by the grid clock, not appropriated if the loads are not purely resistive (not suitable
for off grid systems) and high THD (≈45%);
2. Modified Sine or semi-sine wave – Provide rectangular pulses with an approximate 42% THD;
3. Sine Wave – The inverter with the lowest THD (<3%). Appropriate for motor loads such as
medical equipment, refrigerators, laser printers, etc. It is also used in grid-tied applications. It is
the most expensive inverter of the three types.
45
Pure sine wave inverters are the best choice to the correct working of motor or compressor loads once
it is the inverter with less harmonics which is seen in more detail.
Pure sine wave inverters
These inverters are controlled by a Pulse Width Modulation which allows a wide amplitude of the output
sine wave and reduce the amplitude of the low order harmonics. The general block diagram of a sine
wave inverter is represented in Figure 3.19.
Bridge
Isolation Transformer
L1
N
V
V -
+
DSP Control
Filter Switch
Figure 3.19 - Block diagram of a sine wave inverter (adapted from Texas Instruments)
The battery bank DC voltage (12, 24 or 28V) is the input of the bridge which may be full bridge or half
bridge depending on the requirement. The power transformer is generally used to isolate the battery
from the load and to step up the input voltage in grid-tied inverters or just isolate the output in grid-tied
inverters. The IGBT or MOSFET transistors are modulated by a square wave switching frequency in the
range of 20 kHz (PWM – class D circuit) to create an AC voltage. A sine wave is compared with a
triangular wave to generate a PWM output which drives the transistors bridge – triangulation scheme.
This square wave is controlled by the digital signal processor (DSP Control) which also controls the
output switch accordingly to certain alarms (low input voltage, overload, short circuit, over temperature
protection, etc). The output of the insulation transformer is filtered (low pass filter) to obtain a correct
sine wave. The typical waveform of this type of transformers it shown in advance (the inverter was
chosen and test in chapter 4) in Figure 3.20:
a)
b)
Figure 3.20 - Inverter output waveform and corresponding harmonics
0 20 40 60 80 100-400
-300
-200
-100
0
100
200
300
400
Time [ms]
Vo
lta
ge
[V
]
0 100 200 300 400 500
0
50
100
150
200
Frequency [Hz]
Vo
lta
ge
[V
]
46
The experimental output voltage of the Livre Inverter (Appendix 8.10) with a RMS=200,9V confirmed a
good quality waveform due to its low harmonic content in Figure 3.20 a). The mainly harmonic is the 1st
at 50Hz with 195.68V (45.83 dB). The 3rd, 5th, 7th and 9th harmonics (odd) have a much lower amplitude
than the 1st. The THD is 1.19% (2nd to 9th harmonics) THD lower than 3% for this inverters (Figure 3.20
b).
The use of an insulation transformer means protection against indirect contacts (no need of TN-C
differential protection) and also reduces the electromagnetic interferences. However, these inverter may
not have it and transformerless inverters are gaining popularity in solar systems. The idea behind
transformer-less switching has existed long before the PV market was even developed. A pair of field-
effect transistors operates most efficiently in a complete ON or OFF state, when no current flows through
them, and they dissipate no power. Thus, amplifying an ideal square wave would theoretically be 100%
efficient. For this this reason, transformer-less inverters have a lower stand-by consume.
Efficiency
The efficiency rating indicates what percentage of DC power is converted to usable AC power. This will
never be 100% once the inverter uses some of the input DC power itself, generally around 10-30 W. In
general, off-grid inverters have an extremely flat efficiency curve for higher than 30% of the nominal
power so less battery power is wasted. This means that the drive must be sized to operate as near as
possible of inverter’s rated power.
The efficiency of the inverter is given by [4]:
𝜂𝑖𝑛𝑣 =𝑃𝑂𝑈𝑇𝑃𝐼𝑁
=𝑃𝐴𝐶𝑃𝐷𝐶
(3.12)
An inverter's efficiency is shown in Figure 3.21 efficiency curve. The inverter's efficiency increase sharply
until it reaches its peak efficiency point. It will then remain close to level, decreasing slightly as it
approaches its rated power output. Ideally, the power used should be at or above inverter's peak
efficiency point.
The manufacturer efficiency curve of the Xantrex Prosine inverter may be seen in Figure 3.21 a) for the
model of 1000W and 1800W showing the peak after 30% of the nominal power. Figure 3.21 b) shows
in advance17 the experimental characteristic of the 1500W Livre Inverter chosen to the off-grid system.
The procedure of the test is described in more detail in Appendix 8.10 plotted with 10 points until the
maximum power supply was reached (the dashed part of the curve should does not have enough points)
. The efficiency ranged from 84-90% between 200-300W with the highest value at 800W (50% of the
nominal power like in Xantrex Inverter).
17 the inverter was selected and tested after the project in chapter 4
47
a)
b)
Figure 3.21 - Inverter efficiency characteristic a) Xantrex Prosine off-grid inverter efficiency curve for 1000 and 1800W 24V system (source: Xantrex18) and b) 1500W Livre Inverter
The actual inverters available on the market (mostly PWM regulators) are designed for lead-acid, NiCd
or NiMH batteries typically ranging in the following voltage levels:
Table 3.4 - Typical actuation voltage levels of off-grid pure sine wave inverters and PWM regulators
Nominal Voltage Minimum voltage cut-off Maximum voltage cut-off
12 V 10.5V±5% 15V±5%
24 V 20 V±5% 31±5%
48 V 41V±5% 60±5%
For example, to have a 24V nominal voltage, 8 LiFePO4 cells are necessary. The minimum voltage of
this cells is 2.5V. The inverter minimum voltage of 20V divided by 8 cells will make each cell have 2.5V
which is too close to the limit and will damage the cells. For this reason the minimum and maximum
voltage levels are not in the correct range for LiFePO4 batteries requiring the use of a BMS or an inverter
with controllable voltage levels.
18 Xantrex prosine 1000/1800 Owner’s Manual
0 200 400 600 8000
20
40
60
80
100
Power [W]
Eff
icie
ncy [
%]
48
3.6 Cables
Figure 3.22 represents the losses on the DC cables, the voltage drops and power losses associated to
it. The losses on the cables connecting the batteries to the loads are not represented for simplification19.
The length of these cables is small when compared with the length of the PV cables and might be
neglected.
PV
R
R
I
PPV BatteryPinjected
ΔV
Figure 3.22 - Cable losses
where 𝑅 is the resistance on the cable PV-battery in Ohms, 𝑃𝑃𝑉 is the power at the panel’s terminals,
𝑃𝑖𝑛𝑗𝑒𝑐𝑡𝑒𝑑 is the power at the battery's terminals and ∆𝑉 is the voltage drop on the cables. R is generally
calculated according to the manufacturer resistance and length of the cable. As an example, the
specifications of the TUV cable may be consulted in Appendix 8.8.
Joule losses on the cables:
𝑃𝐽𝑜𝑢𝑙𝑒 = 𝜌𝑙
𝑆∙ 𝐼2 = 𝑅 ∙ 𝐼2 (3.13)
The power produced by the panel 𝑃𝑃𝑉, knowing the power at the end of the cables terminals 𝑃𝑖𝑛𝑗𝑒𝑐𝑡𝑒𝑑, is
given by:
𝑃𝑃𝑉 = 𝑃𝑖𝑛𝑗𝑒𝑐𝑡𝑒𝑑 + 2𝑃𝐽𝑜𝑢𝑙𝑒 (3.14)
Voltage drop, for both DC and AC cases, is given by the following formula:
∆𝑈 = 𝐾𝑐 (𝜌1𝑆cos𝜑 + 𝜆 sin𝜑) × 𝐿 × 𝐼𝐵 (3.15)
where 𝐾𝑐 is a coefficient equal to 1 for three phase and equal to 2 for single-phase circuits; 𝜌1 is the
resistivity of the conductors at the usual working temperature (1.25 times the resistivity at 20ºC – 0.0225
Ω.mm²/m for copper and 0.036 Ω.mm²/m for aluminium); S is the section of the conductors in square
millimetres; cos𝜑 is the power factor (cos𝜑 = 1 for pure resistive loads making sin𝜑 = 0); λ is the linear
reactance per length unit of the conductors (default value 0.08 mΩ/m); L is the length of the cable (m)
and 𝐼𝐵 is the current (A).
19 accordingly to the experiment made in chapter 5
49
The voltage drop in percentage is given by:
∆𝑈 [%] =∆𝑈
𝑈0× 100 (3.16)
where 𝑈0 is the voltage between the phase and the neutral.
3.7 PV System Efficiency
PVAC
Consumers
PAC
Battery Pack
BMS
PDCPDC, injectedInverter
ƞinv
ƞPV
ƞBAT
ƞBMS
Figure 3.23 - Off-grid PV system connection diagram
The total efficiency of the module interface system with the loads accordingly to the diagram of Figure
3.23 may be obtained by:
𝜂𝑠𝑦𝑠𝑡,𝑎𝑢𝑡 = 𝜂𝐵𝑀𝑆 ∙ 𝜂𝐵𝐴𝑇 ∙ 𝜂𝑖𝑛𝑣 ∙ 𝜂𝑙𝑜𝑠𝑠𝑒𝑠 (3.17)
where 𝜂𝑙𝑜𝑠𝑠𝑒𝑠 = 1 − 𝑃𝑙𝑜𝑠𝑠𝑒𝑠𝑐𝑎𝑏𝑙𝑒𝑠[%] is a factor that considers the losses on the cables.
In case the energy “injected” in the battery pack and the energy consumed by the loads is known, the
respective efficiency may be calculated by:
𝜂𝐵𝑀𝑆+𝐵𝐴𝑇+𝐼𝑛𝑣 =𝐸𝑂𝑈𝑇𝐸𝐼𝑁
=𝐸𝐿𝑜𝑎𝑑𝑠𝐸𝑃𝑉
(3.18)
However, as the batteries store energy, this efficiency needs to be estimated during a time period where
the batteries start at a certain SOC return to that same SOC point. This may be more accurately done
by a battery voltage reference point. In other words, the battery should start the test charged with a
voltage 𝑈𝑜, discharge during a certain time and charge again until 𝑈𝑜. Knowing the energy in and out
during this period, the efficiency may be calculated.
50
3.8 Conclusions
The purpose of this chapter is to introduce the basic principles of operation of all the system components
– consume, photovoltaic production, storage, control and energy conversion.
To supply the loads of the system, polycrystalline panels were chosen, once the price is more
competitive consequence of the highest presence in market. Besides, this was the highest power panel
gently provided by Resul – Energy Equipments, S.A on 2014.
Comparing weight versus available energy storage, LFP batteries are about one-third the weight and
about half the volume of a lead-acid (LA) battery with equivalent energy storage. Additionally, the
storage capacity of LAs drops by 50% at -20°C, compared to 8% with LFP. Keeping lead-acid batteries
warm so that they maintain reasonable capacity in cold climates can be challenging, giving advantage
to LFPs. LiFePO4 have the best thermal stability of all seen lithium ion types being then appropriate to
photovoltaic applications.
The characteristic curve of these batteries requires special care and project of the controllers. A battery
management system (BMS) to manage the “health” of the batteries is the best option to ensure reduced
maintenance and long service time. Some solar regulators, like PWM regulators, are not yet design for
this type of batteries. This process is done better with top balancing, once the batteries are expected to
be at full status as much as possible. This way the balancing will be done more often. At high SOC, the
cell voltage changes rapidly, which also gives better data on the true SOC.
To convert DC to AC power, pure sine wave inverters are the best inverters type to feed motor loads
and have less than 40% THD voltage compared with modified sine and square wave. Inverters should
have no screen, as this always increases stand-by power. Besides, its standby consume may be
reduced with no insulation transformer on the AC side (requires differential circuit breaker).
51
4 Autonomous PV System – Project
This chapter aims to project the photovoltaic system for Luena zone in Angola. The project is carried
out in accordance with the equipment kindly provided by Resul – Energy Equipments, S.A.20, constituted
by two 190W STP190S monocrystalline and two 225W STP225 Suntech PV Panels. The LiFePO4
batteries were also previously obtained by Electrical Department (DEEC) with the objective of studying
its performance in this type of systems.
There are several possible processes to project an autonomous PV system. Processes differ in the
initial condition that will affect the design of the remaining components [7]:
Maximum daily energy calculation;
Maximum power consumption calculation;
Number of PV modules calculation;
Battery capacity calculation.
To scale a PV system is necessary to know the average radiation values at the installation site. To
determine these values radiation PVGIS software was used [26]. This software allows to estimate online
the photovoltaic solar energy for isolated or grid-tied systems within the European and African continent
and uses Google maps ® to choose the location. This is a reliable and free software that justified the
choice for the project.
The maximum daily energy calculation process considers the following steps which will be seen in detail
[7]:
1) Determine the dairy energy consumed by the loads;
2) Calculate the energy production of the PV modules at a given tilt, β, and azimuth angle, γ;
3) Project the peak power of the PV modules;
4) Calculation of the batteries parameters;
5) Project of the solar regulator;
6) Project of the autonomous or off-grid inverter.
4.1 Loads
The more accurate the consumption data the better the project, for this reason the loads consumptions
and peak currents were analyzed and are presented next. In this chapter some assumptions were made
to match the loads profile with the average consumption of a small family house in Angola.
20 Resul website may be consulted at http://www.resul.pt/
52
4.1.1.1 Refrigerator Load Diagram
The refrigerator is the load with the load diagram more complex. The refrigerator used in the experiments
is the Kentt 201E which technical data can be seen in Appendix 8.11. This refrigerator has 7 refrigeration
levels consuming more energy for higher levels. The load diagram was obtain experimentally for a more
precise project. For a reasonable temperature vs energy use, level 3 is the appropriate one. However,
once it was not possible to simulate a diary use of the refrigerator, the level 4 was the chosen one to
compensate the extra consume caused by the opening of the door on level 3. Figure 4.1 represents the
refrigerator active power diagram for one hour at level 4 with no opening of the door measured using
Fluke 1735 power logger (Appendix 8.3). The refrigerator compressor is on for periods of approximately
4 min at an average power of 127W four times per hour.
Figure 4.1 - KENT 201E refrigerator load diagram (1h)
4.1.1.2 Lights and TV Load Diagram
For lighting purposes is estimated a power of 60W during 5 hours per day, from 18:30 to 22:30 and from
6:00 to 7:00 according to the working hours in Angola. This power may be achieved with a single lamp
or several with less power. This is the second more important load of a family’s house.
For a regular house entertaining purposes is estimated a 40W TV which is on for 2 hours per day from
20:00 to 22:00 or it can be substituted by a more important electronic device if consuming the same
equivalent energy.
4.1.1.3 Total Load Diagram
The total load diagram is the sum of the three previous loads’ consume profile represented in Figure 4.2
logged with Fluke 1735 (Appendix 8.3).
00:10 00:20 00:30 00:40 00:50 01:000
50
100
150
200
250
300
350
Time [h:min]
Po
we
r [W
]
53
Figure 4.2 - Total daily load diagram
The refrigerator switches on and off in regular periods along the day and the lights and TV working
periods are those in 4.1.1.2. Unlike the peaks of the inductive loads (refrigerator and TV) are not visible
once the integration period of the logging is higher. The maximum power of the system is 250W between
19:00 and 22:00.
4.1.2 Experimental loads power
Table 4.1 shows the experimental electrical parameters of Kentt 201E refrigerator (Appendix 8.11),
Philips 60W incandescent light and Sony KV-14LT1E 13’’ TV (appendix 8.12) measured with Fluke 1735
power logger (Appendix 8.3). The energy values represent the refrigerator daily consumption at level 4.
Table 4.1 - Loads electrical experimental parameters
Power Energy
Device Active [W] Reactive
[Var] Apparent
[VA] Factor
Active [Wh/day]
Reactive [Var/day]
Refrigerator 127 169 211 0,6 879,407 1148,471
Lights 69,6 0 0 1
TV 41 45,16 61 0.674
4.1.3 Daily consumed energy
The time of usage of each load defines the diary energy needed for the autonomous system. Table 4.2
shows the hours of use considered for this work based on the daily needs.
Table 4.2 - Experimental dairy loads energy
Equipment Power [W] Utilization [h/day] Daily Energy [Wh/day]
Refrigerator (level 4) 127 6.93 880 TV 41 2 84 Lamps 69.6 5 348
Total 237.6 5.52 1312
The total daily consume is approximately 1300Wh which should be taken in consideration for the project.
The use of individual loads independently is equivalent to a power of 238W for 5.5 hours.
0 2 4 6 8 10 12 14 16 18 20 22 240
50
100
150
200
250
300
Time [h]
Pow
er
[W]
54
4.2 PV Panels Production Capacity
The PV panels are the only source of energy once in this project it is not considered a hybrid system.
Thus, it is necessary to estimate the necessary power to feeds the loads, 𝑊𝑑 = 1300 Wh/day, having in
mind the losses that may occur on the cables, regulator and inverter as seen before in expression (3.17).
The respective efficiencies are calculated below:
𝜂𝑙𝑜𝑠𝑠𝑒𝑠 = 𝜂𝑐𝑎𝑏𝑙𝑒𝑠 = 1 − 𝑃𝑐𝑎𝑏𝑙𝑒 𝑙𝑜𝑠𝑠𝑒𝑠 ≈ 1 − 0.03 = 0.97 (4.1)
The losses on the cables may reach 3% of the total power in isolated systems [7].
𝜂𝐵𝑀𝑆 = 0.98 (4.2)
The losses on the regulator or BMS system are considered be less than 2%.
𝜂𝑖𝑛𝑣 = 0.85 (4.3)
The losses of the inverter are equal to the inverter efficiency which is usually 85% for an operating power
of 20% of the nominal inverter power according to Figure 3.21.
The efficiency factor, considering the battery efficiency equal to 1 (currents lower than 10% of the total
capacity) and all the applicable losses:
𝜂𝑠𝑦𝑠𝑡,𝑎𝑢𝑡 = 𝜂𝐵𝑀𝑆 ∙ 𝜂𝐵𝐴𝑇 ∙ 𝜂𝑖𝑛𝑣 ∙ 𝜂𝑙𝑜𝑠𝑠𝑒𝑠 = 0.98 ∙ 1 ∙ 0.85 ∙ 0.97 = 0.81 (4.4)
The radiation varies along the year and to project the system is necessary to choose which irradiance
to consider. Assessing the available energy in Luena area from PVGIS, the following values are obtained
for an optimal inclination of 19º with annual irradiation deficit due to shadowing (horizontal) equal to 0%:
Table 4.3 - Irradiation on Luena, Angola [26]
Month Irradiation
[Wh/m²/day]
Jan 4890
Fev 5070
Mar 5540
Apr 6290
May 6980
Jun 7040
Jul 7170
Aug 7330
Sept 6850
Oct 6150
Nov 5070
Dec 4730
Annual 6093
55
The best procedure is to project the system by the worst case scenario for permanent use houses, for
sporadic use houses the months of September or October should be used [7]. The worst month occurs
in the months of less radiation, this way the feed of the loads all the year is guarantee being the system
oversized. This is the most commonly used method. The 𝜏𝑑(𝛽, 𝛾) factor makes the equivalent hours of
the irradiance at 1000 W/m² (mean irradiance value for calculation purposes). The worst month
irradiance occurs on December with 4730 Wh/m²/day:
𝜏𝑑(𝛽, 𝛾) =
𝑀𝑜𝑛𝑡ℎ𝑙𝑦 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐼𝑟𝑟𝑎𝑑𝑖𝑎𝑛𝑐𝑒 [𝑊ℎ/𝑚2/𝑑𝑎𝑦]
1000 [𝑊/𝑚2]=4730
1000
= 4.73 h/day
(4.5)
4.3 PV array sizing
To better predict and deal with eventual non-ideal/standard working conditions, the efficiency of the
autonomous system must be taken in consideration. The amount of Peak Solar Hours per day, 𝜏𝑑(𝛽, 𝛾),
already considers the mean energy produced by the PV panels, consequently it is not necessary to
consider the total efficiency of the PV, 𝜂𝑃𝑉 in the calculation as used in [53]. The required PV array
power is then given by:
𝑃𝑃𝑉 =𝑊𝑑
𝜂𝑠𝑦𝑠𝑡,𝑎𝑢𝑡
× 𝜏𝑑(𝛽, 𝛾)=
1300
0.81 × 4.73= 339.31 Wp (4.6)
However, the off-grid system is not expected to have MPPT’s to make the system cheaper and with less
stand by consumption. Thus, to choose the power of the panels it is more realistic to use the maximum
power on NOCT conditions. The polycrystalline Suntech STP225 - 20/Wd (Appendix 8.7) provided by
Resul was the chosen PV one because its power is higher than the STP190. This panels produce 165W
on NOCT conditions. The number of PV modules needed to produce the required power is given by
equation (4.7):
𝑁𝑃𝑉_𝑚𝑜𝑑𝑢𝑙𝑒𝑠 =𝑃𝑃𝑉
𝑃𝑃𝑉_𝑁𝑂𝐶𝑇=339.31
165≈ 2 (4.7)
Two panels produce 330W to be connected in series or parallel regarding the chosen working voltage
of the batteries. In this case, the nominal voltage of the batteries is 24V so the panels must be connected
in parallel once is 𝑉𝑀𝑃 = 29.6 𝑉.
4.4 Batteries
The batteries should be project the more accurate way possible once to many batteries easily make the
system much more expensive. Usually, the nominal operational voltage of the PV system can choose
between 12V, 24V or 48V. When knowing the voltage, the next step is to express the daily energy
requirements of loads in terms of current and average operational time expressed in Ampere-hours. The
working voltage chosen was 24V instead of 12V to decrease the current on the cable and consequently
the losses. This way the panels have to be connected in parallel to perform a nominal voltage of 24V.
56
The daily consume in Ah is given by:
𝑊𝐴ℎ =𝑊𝐷𝑈𝐷𝐶
=1300
24= 54.17 Ah (4.8)
The battery sizing comes as [53]:
𝐶𝐵𝐴𝑇,𝑇𝑜𝑡 =𝑊𝐴ℎ × 𝑁𝐷𝐷𝑂𝐷𝑚𝑎𝑥
=54.17 × 2.5
0.8= 169.28 Ah (4.9)
where 𝑁𝐷 is the number of reserve days (working days with energy from the sun). 𝐷𝑂𝐷𝑚𝑎𝑥 is the
maximum deep of discharge of the battery which should be less than 80% allowing the batteries to
perform more than 2000 cycles (Appendix 8.6). The battery capacity is added when the batteries are
installed in parallel keeping the voltage and remains the same when they are installed in series, adding
to the voltage. It may be found batteries with different capacities ranging from 1 to 200 Ah. The number
of batteries to perform the capacity needed is calculated as:
𝑁𝐵𝐴𝑇 =𝐶𝐵𝐴𝑇,𝑇𝑜𝑡𝐶𝐵𝐴𝑇
=169.28
180= 0.94 ≈ 1 (4.10)
where 𝐶𝐵𝐴𝑇 is the capacity of a single battery. It is far cheaper to choose a single battery with a high
capacity than to associate several batteries in parallel with a smaller capacity. Besides, parallel
association makes the battery bank more unstable once the cell with the smallest internal resistance will
be overstressed over the time.
Additionally, the voltage has to be also taken in consideration. Each LiFePO4 battery has a nominal
voltage of 3.3V being the real number of batteries:
𝑁𝐵𝐴𝑇 =𝑈𝐵𝐴𝑇,𝑇𝑜𝑡𝑈𝐵𝐴𝑇
=24
3.3= 7.27 ≈ 8 (4.11)
To build a battery bank with 24V and 169 Ah, eight batteries with 180Ah and 3.3V are needed.
4.5 Autonomous or Off-Grid Inverter
Off-grid inverters having two inductive loads and the fridge an induction machine, special attention is
required when dimensioning the inverter. It shall be capable to support not only the normal operating
power of the system but also the electronic devices starting peak power. Furthermore, the inverter must
not be overloaded to operate without overheating while allowing the possible connection of extra loads
in the future. Also, the nominal power of the inverter should be chosen accordingly to its efficiency curve.
It was found in 3.5 that this efficiency is usually higher for powers higher than 40% of the rated power
of the inverter. Choosing a slightly larger inverter could allow it to operate in a more efficient power
range. In the long term, this could offer better value - the loads will take less energy out of your system
57
and the inverter will run cooler, subsequently lasting longer. These inverters support usually twice its
rated power, the best inverters support three times its rated power during periods up to 10 seconds.
The power of the inverter is usually calculated as the sum of the nominal powers of the loads plus a 25-
30% reserve power. In case of appliances with motors or compressors, the inverter size should be done
accordingly to the surge starting current/power. Generally the inverter nominal power should be 3 times
the capacity of those appliances plus the power of the purely resistive which is our study case and seen
in more detail next.
To understand what is the peak power of the loads involved it was measured the transitory current of
the inductive loads. In Figure 4.3 is represented the starting and the operating current of the Kent
refrigerator. In Figure 4.3 a) the amplitude of the sinusoidal wave is not correctly represented due to the
high time step used, this is the reason why the current signal is not symmetric to the xx axes. However
this was the only way to observe for how long lasts the peak current.
a)
b)
Figure 4.3 - Refrigerator a) starting and b) operating current
Figure 4.3 b) is the sinusoidal operating current of the refrigerator with an amplitude of approximately
0.9A. The peak amplitude current in Figure 4.3 a) is Ip=9.2A which means an AC power of:
𝑆𝑙𝑜𝑎𝑑𝑠,𝑝𝑒𝑎𝑘 = 𝐼𝑅𝑀𝑆𝑈𝑅𝑀𝑆 =𝐼𝑝
√2𝑈𝑅𝑀𝑆 =
9.2
√2× 230 = 1496.24 𝑉𝐴 (4.12)
This power peak is the first requirement of the inverter. This type of inverter usually support only one
third of its nominal power:
𝑃𝑙𝑜𝑎𝑑𝑠,𝑝𝑒𝑎𝑘 =3
4𝑆𝑖𝑛𝑣 ≈ 1122 W (4.13)
It was also observed that the compressor may request this power for periods up to 10 seconds which is
the second requirement of the inverter. The inverter should be projected by the worst case scenario
which is the starting of all the loads at the same time. However, starting of all the loads at the same time
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-10
-5
0
5
10
Time [s]
Curr
ent
[A]
-100 -80 -60 -40 -20 0 20 40 60 80 100-1.5
-1
-0.5
0
0.5
1
1.5
Time [ms]
Curr
ent
[A]
58
revealed21 no higher peak current and power than calculated in (4.12) due to the same inductive
character of the loads. Considering the general fact the inverter may support twice its nominal power
and a 20% heat security factor should be considered, the minimum inverter power is then:
𝑃𝑖𝑛𝑣_𝑚𝑖𝑛 =𝑃𝑙𝑜𝑎𝑑𝑠,𝑝𝑒𝑎𝑘
2=1122
2+ 0.2 ∙ 𝑃𝑙𝑜𝑎𝑑𝑠,𝑝𝑒𝑎𝑘 = 785.4 𝑊
(4.14)
4.6 Regulator
For the dimensioning of the regulator or BMS the maximum operating current in the circuit should be
taken into account. The currents to consider are the currents produced by the PV panels and from the
battery to the loads. The panels are connected in parallel once each panel maximum current is summed:
2 × 𝐼𝑀𝑃 = 2 × 7.61 = 15.22 A. However the current to feed the AC loads is higher than the PV total
current. This load current depends on the peak power. Accordingly to the previous analysis in section
4.5 and knowing the voltage of the battery, on the loads side the regulator nominal current should the
higher than the DC peak current (simultaneity factor of 100% - all the loads connected at the same time)
which is given by:
4.7 DC Cables
The main DC cable connected to the PV panels should be projected to support 1.25 times more than
the maximum short circuit current of the PV panels at STC conditions accordingly to IEC 60364-7-712:
𝐼𝑧 ≥ 1.25 × 𝐼𝑃𝑉𝐶𝐶𝑡𝑜𝑡𝑎𝑙= 1.25 × (8.15 + 8.15) = 1.25 × 16.3 ≥ 20.4 A (4.16)
This means that admissible current, 𝐼𝑧 ≥ 25 A, which is the current supported by the cable without the
risk of melting/fire. Considering the 52-C1 Table of the permissible currents for PVC isolated conductors
and the method B of the RTIEBT for the installation22, a permissible current of 25A means a minimum
cross section of 2.5mm² for copper conductors and 4mm² for aluminium conductors. In this work the
aluminium conductor was the chosen conductor due to its lower price.
4.8 Protection – DC Switch and DC Fuses
Accordingly to the European standard IEC 60364-7-712 it should be installed a DC circuit breaker
between the PV panels and the inverter. Its nominal current is given by [7]:
𝐼𝑛 𝐷𝐶 𝑆𝑤𝑖𝑡𝑐ℎ ≥ 1.25 × 𝐼𝑃𝑉𝐶𝐶𝑡𝑜𝑡𝑎𝑙= 1.25 × 16.13 ≥ 20.4 (4.17)
21 observed with experimental measurements 22 plumbing with insulated conductors mounted in circular pipes installed at sight
𝐼𝑟𝑒𝑔_𝑚𝑎𝑥 =𝑃𝑙𝑜𝑎𝑑𝑠,𝑝𝑒𝑎𝑘𝑈𝐷𝐶
=1500
24= 62.5 A (4.15)
59
It was chose the Hager SB432PV DC Switch with 𝐼𝑛 = 32 A.
The cabling, DC switch, BMS, batteries and the inverter should be protected by a DC Fuse. In DC current
the fuses used are gL-gG slow fusion type. A single fuse on the positive pole is enough to ensure the
protection. The nominal current, 𝐼𝑛 𝐷𝐶 𝑓𝑢𝑠𝑒, on the PV panels side should verify the condition:
𝐼𝑛 𝐷𝐶 𝑓𝑢𝑠𝑒 ≤ 𝐼𝑍 = 25 A (4.18)
Thus, to protect the cable and the DC Switch the chosen nominal current was 𝐼𝑛 𝐷𝐶 𝑓𝑢𝑠𝑒 = 25 A.
When the distance between the loads and the inverter is higher than 4m it should be installed a
differential circuit breaker with In=25A and 30 mA of sensibility. Siemens type B 5SU1356-0KK25 or
Hager LFPV meet this requirements.
4.9 Prototype costs
The solutions to this system have been chosen based on equipment assigned for research purposes by
the power company Resul S.A. (solar panels and DC cables), other acquired by the Department of
Energy, based on a search in the Portuguese market and some suppliers abroad (LiFePO4 batteries
and Inverter).
The chosen BMS was the 123BMS designed by 123electric which features software that allows the user
to change the controller parameters. Usually this type of controllers are configured for pre-set values or
have some kind of built-in display LCD that allows to change some parameters. There are currently very
few solutions on the market that do the programmable control cell by cell at such a competitive price as
the chosen 123BMS. The BMS also allows the control of the critical zone where the loads should be
turned off, solving this way the fact that the 24V inverters have a cut-off voltage of 20V (20/8= 2.5V/cell)
which is a very low voltage that will damage the cells.
According to the foreseen and in line with the objectives of this work, the chosen battery was a 3.3V
LiFePO4 battery. Although the design capacity of the battery is approximately 180Ah according to
expression (4.9), at the time of purchase, the highest capacity battery available at the supplier’s store
was 130Ah. Thus the 130Ah batteries were used for testing, reducing also the system costs that way.
The 25A DC fuse was kindly offered by Hager, S.A. ® since these fuses are sold only in large quantities.
To perform better with engine loads, the inverter must support the peak power easily. Also it should be
given margin power for future expansion of the system. As such an inverter was chosen with the capacity
to double the peak power required by the loads, i.e., an inverter with nominal power of 1500W (peak
power 3000W).
60
Within these requirements a survey of autonomous inverters was made in the market in January 2015.
These inverters have a DC working voltage of 24V, output voltage of 230V and 50Hz frequency. In
general, they have always polarity inversion, overheating, short circuit protection and efficiency higher
than 85%. Some competitive prices were found in foreign stores, however one of the factors taken into
consideration to the choice was the availability and the flexibility to exchange. The most important factor
to the decision was the stand-by consume, staying on 24/day, the stand-by power reduces the energy
of the batteries available to deliver to the loads. The inverter with the lowest stand-by consume and
lowest price was the Victron ® equivalent at a lower price: Livre Inverter (Appendix 8.10).
Table 4.4 - Pure sine wave inverter price and specifications
Photo Equipment Characteristics Price [€]
Inverter Livre 1500W
Pmax=2xPn=3000W; η > 90%; THD <3%; Pstand-by=7W
528.9€
Next, the costs of all the equipment of the system under study are presented:
Table 4.5 - Total system cost23
Item Quantity Price with VAT Total Percentage of Budget
225W polycrystalline PV Panels 2 303 € 606 € 20.0 %
DC Aluminium Cable 4mm2 50x2 m 0.86 €/m 86 € 2.8 %
LiFePO4 Batteries 3.3V 130Ah 8 127.48 € 995.84 € 32.9 %
BMS + DC Controllable Relay 1 490.58 € 490.58€ 16.2 %
BMS Board Cell Module 8 11.06 € 88.48 € 2.9 %
DC Current Sensor 100A 1 55.62€ 55.62 € 1.8 %
1500W Off-grid Inverter 1 528.9 € 528.9 17.5 %
DC Switch 1 101 € 101 € 3.3%
Dead Front Fuse Holders 1 6.22€ 6.22 € 0.2 %
Differential circuit breaker
breaker In=25A, 𝑰∆𝒏 = 𝟑 𝐦𝐀 1 68.2 € 68.2 € 2.3 %
Total 3026.8 € 100 %
The price of the PV modules is the price in Portugal corresponding to 1.35 USD/W which is in the usual
range values in Europe as described in section 2. The total 450 Wp system cost corresponds to a price
of 6.3 USD/W24. The most expensive items are the batteries (storing) and then the PV panels
(production) making more than 50% of the total cost of the system, then is the inverter (conversion) and
the BMS (control). In the future, the final cost may be eventually reduced more than 15% with a hardware
based BMS and an inverter with less margin power - Pn=750 to 1000W - (but consequently more
losses). It is somehow an expensive system for such a poor country, however the costs of constructing
the grid infrastructure in remote places will be thousand times higher and with high installation time.
23 Based on GWL website prices http://www.ev-power.eu/ and energy manufactures and suppliers in Portugal:
Hager, Siemens and Resul S.A. 24 Using a conversion ratio of 1€=1USD
61
4.10 Economic analysis of the off-grid PV system
In economic terms it makes no sense to use the usual economic indicators (NPV, IRR and payback
period) for isolated systems, as they are very simplistic. This is due to the fact that there is no direct sale
of electricity to consumers and consequently an annual gross revenue. This is the reason why this
systems should not be considered investments. However, they may be economically viable, if during its
lifetime it is possible to save in an investment as the creation of a power transmission line to a remote
location.
It may be analysed the cost of buying the energy consumed by the loads during the useful life of the
autonomous system. For that it is necessary to estimate the lifetime in years and the annually energy
consumed. Considering that the battery makes a cycle of charging and discharging daily, a total of 2500
cycles during its lifetime and according to Table 5.10, the energy consumed by the load during this
period is:
𝐸𝑡𝑜𝑡𝑎𝑙 =2500
365× 1.3
kWh
day× 365 ≈ 7years × 474.5
kWh
year≈ 3 321.5 kWh (4.19)
The equivalent cost of the energy (considering for the real cost of energy, a factor of 5) during the lifetime of the system may be calculated as:
𝐸𝑛𝑒𝑟𝑔𝑦 𝑐𝑜𝑠𝑡𝑡𝑜𝑡𝑎𝑙 = 𝐸𝑡𝑜𝑡𝑎𝑙[kWh] × 5 × 𝑡𝑎𝑟𝑖𝑓𝑓 [
€
kWh]
= 3 321.5 × 5 × 0.0265 = 440.10 €
(4.20)
The price of energy in Angola is very low and therefore to spend on energy the corresponding amount
of the total cost of the system (3000€) it would take many years. However Angola electrical tariff covers
only 20% of system costs and will increase in the future [36]. It is worth noticing that there are additional
costs associated with the construction of the non-existent power grid in rural zones. The cost of energy
is much higher than € 440 over 7 years in service. Informally, the price by kilometre for a high voltage
line is approximately one million euros, cost avoided with an autonomous systems.
To conclude, we should keep in mind that systems of this type are indicated to meet critical local needs
and their costs should be subsidized by local governments to offer the people better living conditions.
62
4.11 Conclusions
This chapter exposes the several possible calculation procedures to project the photovoltaic system for
Luena zone in Angola. In this case the maximum daily energy calculation is used to project correctly the
needed PV production power, batteries and inverter. The best way to correctly project this type of
systems is to measure the average load consume once the nominal power of the equipment is typically
under the real power. Then, the estimation of the average daily radiation is very important. Some tools
may be used to this, like PVGIS web application, which is based on several years of data. Making
measurements on site is a more accurate and reliable estimation method, which should be done
whenever as possible, to improve the project process. The project should always be done by the worst
case scenario using the lowest monthly irradiance.
All the equipment was chosen according to the project and, at the same time, the available equipment
gently provided by Resul – Energy Equipments, S.A. (solar panels and DC cables), Hager, S.A (DC
fuse) and acquired by the Department of Energy.
In economic terms, it makes no sense to use the usual economic indicators (NPV, IRR and payback
period) for isolated systems, due to the fact that there is no direct sale of electricity to consumers and
consequently an annual gross revenue. This type of systems may not be considered investments with
a return period, but rather providers of better living conditions of the populations in rural areas. The cost
of energy is very low, due to the hydric generation. It is therefore much cheaper to buy the same amount
of energy to the energy supplier. It would be necessary to study more deeply the grid
network/infrastructures costs to effectively evaluate the economic potential of such a system.
63
5 Experimental Results
This chapter shows a comparison of experimental results in balanced and unbalanced conditions,
various irradiance values, and also the power transit and battery bank energy measured during the
operation of the autonomous photovoltaic system connected to the loads.
To analyse the viability of the autonomous system, it is necessary to check some system details as:
1) Determine the amount of energy needs in a daily basis to feed the loads;
2) Verify the effective energy available in the battery pack;
3) Check the energy supplied daily by the solar energy conversion system (PV panels).
5.1 Electrical parameters measurement
To study the PV system behaviour over time, it was necessary to store its main electrical variables.
These consisted of voltage, current, and power that was generated and also consumed.
Voltage data logging was performed by a low cost NI USB-6008/6009 DAQ® and is described in more
detail in Appendix 8.5.1. The sampling rate 𝑓𝑠, used in this study was 1𝑠𝑎𝑚𝑝𝑙𝑒 𝑚𝑖𝑛⁄ ≈ 16.7 mHz. The NI
USB-6008 has 14 bits to perform the analog to digital conversion in differential mode and the USB-6009
has 16 bits corresponding to a system noise of 1.47mV and 0.37mV respectively (Appendix 8.1). In this
test the numbering of the cells, from 1 to 8 is in concordance with the convention of the BMS manual.
Thus, the cell 1 refers to the cell that connects the negative pole of the battery pack to the inverter and
cell 8 the positive pole.
The electric current logging was done using a LEM LA-25-NP transducer (Appendix 8.2) to reduce the
losses of the measurement. The procedure is described in detail in Appendix 8.5.2. The logging of the
temperature of the cells was performed using a ©Tiny Tag bound to the PV surface (Appendix 8.14).
The logging data consists of:
Voltage of the panels after the 50m cables (the parallel of the panels is done after the 50m to
reduce the current in each circuit);
Output current of the panels;
Individual cell’s voltage (8 cells);
Battery pack voltage;
AC voltage at the load terminals;
AC current at the load terminal.
5.2 The Autonomous PV Experimental Set-up
Figure 5.1 shows the major components of the PV experimental arrangement installed according to the
diagram of Figure 2.3 with AC loads only. The battery pack is installed at the bottom of the experimental
64
bench (bottom in Figure 5.1 a) and is connected to a relay (number 5 on Figure 5.1 b) which is controlled
by the BMS controller (number 6). The relay is connected to the PV panels and the inverter (number 4).
The BMS uses a current sensor (7) to measure the current going in and out of the battery pack. The PV
panel’s circuit is protected by a 25A DC fuse (2) and may be manually switched on/off by a DC switch
(3). Also visible in Figure 5.1(b) are the DAQ's that perform data logging of the voltages of the system
(1).
a)
b)
Figure 5.1 - a) Autonomous PV system testing bench and b) system components
Figure 5.2 shows a closer look at the 8 cells forming the battery pack and its BMS boards on the top of
each one. The mains are the black (- pole) and green (+ pole) cables on the bottom of the image. Each
cell is connected to a DAQ differential channel and the BMS boards are connected to each other in a
separate circuit from the battery pack.
Figure 5.2 - Battery pack and BMS monitoring boards
65
5.3 Initial Charging of the Cells
Without the initial individual charging, as described in section 3.3.3, an unbalanced situation may occur
between the batteries cells. Figure 5.3 illustrates a partial discharge test comparison between the battery
pack voltage without (Figure 5.3 a) and with initial charge balancing (Figure 5.3 b) on a constant resistive
load of 6Ω (25.5 V 6 Ω⁄ = 4.25 A = 0.06C average current). The battery voltage in both figures starts at
26.15V, the cell’s temperature was 15ºC and the test was done until the BMS detected a voltage of 2.7V
in one cell, opening the load relay and protecting the “weakest” cell. The initial individual charging or top
balancing was done using the procedure described in section 3.3.3.
a) b)
Figure 5.3 - Battery pack voltage during discharge on a constant resistive load of 6Ω a) without and b) with initial balancing
The dissipated energy should be calculated from the dissipated power in a resistor multiplied by the time
interval between samples (one minute), ∆𝑇𝑠, in which the power is considered constant:
𝐸 = 𝑃𝑅 × ∆𝑇𝑠 = 𝑉 × 𝐼 × ∆𝑇𝑠 =𝑉2𝑅⁄ × ∆𝑇𝑠 (5.1)
Figure 5.3 b) shows that with the initial balancing the battery pack voltage is more "flat" being more
constant compared with figure a), for the same resistance value and a higher voltage the power is higher.
There is also a clear gain in the discharge time which allows more energy to be delivered as it can be
seen in the following table:
Table 5.1 - Energy of the discharge tests in Figure 5.3(a) - unbalanced and Figure 5.3(b) - balanced cells
Unbalanced cells energy [Wh] Balanced cells energy [Wh]
1351 1539
Figure 5.4 shows a close up of the cell’s voltage for the same previous test in Figure 5.3. After the twelve
discharging hours until till the end of the test - fast decay period - the maximum gap voltage was 0.213V
(𝑉1𝑠𝑡 𝑐𝑒𝑙𝑙 = 2.9184, 𝑉2𝑛𝑑 𝑐𝑒𝑙𝑙 = 2.7054) with a duration of 14h20m.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
22.5
23
23.5
24
24.5
25
25.5
26
26.5
Time [hours]
Voltage [
Volts]
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
22.5
23
23.5
24
24.5
25
25.5
26
26.5
Time [hours]
Vo
lta
ge [
Vo
lts]
66
a)
b)
Figure 5.4 - Cell’s voltage during discharge on a resistive load of 6Ω a) without and b) with initial individual charging
It is clear that the cells’ voltages are much closer to each other after the initial individual charging in
Figure 5.4(b). Such a high deviation between cell’s voltages in Figure 5.4(a) is a consequence of
different cells’ SOC. The previous tests evidence the importance of the initial balancing for the proper
work of the cells as a battery pack. As it seen in section 3.3.1, LiFePO4 batteries have a very constant
discharge voltage staying close to its nominal value. A balanced pack has a maximum voltage drift of
7mV what is a good indicator for accurate monitoring systems and this influences the available energy
and duration of the discharge as seen in Table 5.1. Another key fact is that the fast voltage changing
edges of the charge and discharge curve don't have much energy. In this particular example, in Figure
5.3(b) the pack goes from 25.3 to 22.45V (when the 2nd cell almost reached the minimum voltage) in
2.5h, which corresponds to an approximate energy of 235Wh. This is less than 1/15 of the total energy
of the battery pack which is calculated below. Additionally, with high charging/discharging currents the
batteries’ voltage variation happens very fast at which makes more secure and accurate to actuate the
control circuits on the flat part of the charge/discharge curve as seen in section 3.3.1.
To check the real available energy of the battery pack 𝑊𝐵𝑎𝑡,𝑇𝑜𝑡 ,with its cells top balanced, a discharge
on a 3.3 Ω resistor was performed in order to obtain an approximately average current of 8A
(26.4 V 3.3 Ω⁄ = 8 A = 0.06𝐶) that is a value near to the current that will enter and exit the battery bank
while running as a standalone system. Figure 5.5 shows the battery’s voltage for the test that proceeded
continuously for 17h until one of the cells reached a critical voltage of 2.57V (2nd cell) with a cell
temperature of 12ºC. The total energy stored in the battery pack was calculated in approximately
3600Wh accordingly to expression (5.1) at 80% DOD (Appendix 8.6), which is higher than the nominal
theoretical value of 3328 Wh. The minimum pack voltage with top balancing was 21.5V. Note that the
Figure 5.5 axes start at 21V.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 152.7
2.8
2.9
3
3.1
3.2
3.3
Time [hours]
Vo
lta
ge [
Vo
lts]
Cell 1
Cell 8
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 152.7
2.8
2.9
3
3.1
3.2
3.3
Time [hours]
Voltage [
Volts]
Cell 1
Cell 2
67
Figure 5.5 - Discharge at approximate 0.06C current rate or 8A (3.3Ω resistor)
5.4 Bottom vs Top Balancing
The bottom balancing was performed accordingly to the procedure described in 3.4.2.2. The first
discharge was done using a resistor connected to each cell and the second using the cell boards
(Vbypass=2.56V). The top balancing as seen before, is a complete individual charge of the cells detailed
in 3.4.2.3.
a)
b)
Figure 5.6 - Discharge on a resistive load of 6Ω a) bottom and b) top balancing
As seen in section 3.4.2 which describes both balancing processes, bottom balancing exhibits more
close cell’s voltages at the final stage of the discharging. Figure 5.6 shows this differences schematized
in Figure 3.16(a) and Figure 3.17(b). Both tests took the same time to discharge the batteries
emphasizing the fact that both balancing procedures ensure a good balance of the cells.
To complete the comparison between both methods it is important to access the behaviour of both
balancing types during charging. The battery pack was then charged with the same current source after
bottom and top balancing. Figure 5.7 a) and b) represents the lowest and highest cell voltage of the
battery pack during charging. The use of the same current is important to compare the time of charging
and consequently conclude about the energy storage.
0 2 4 6 8 10 12 14 16 1821
22
23
24
25
26
27
28
Time [hours]
Voltage [
Volts]
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 152.7
2.8
2.9
3
3.1
3.2
3.3
Time [hours]
Vo
lta
ge [
Vo
lts]
Cell 8
Cell 2
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 152.7
2.8
2.9
3
3.1
3.2
3.3
Time [hours]
Vo
lta
ge [
Vo
lts]
Cell 1
Cell 2
68
a)
b)
Figure 5.7 - Charge at constant current I=6A with a) bottom and b) top balancing
Once again and contrary to what some authors’ reference [48], the charging time is the same (23h)
resulting in no energy gains obtained between the two balancing methods. The gap voltage between
the cells is higher in top balancing however is very small and reduced by the BMS across the charging
cycles, also the curves’ shape is the same what proves that both are accurate methods. The most critical
difference is the cells’ voltage at the beginning and end of charge as seen before in the discharging test
of Figure 5.6. In the bottom balancing (a), the voltage of the cells is closer and at the end of the charging
cycle the gap is higher than on top balancing (b). This makes the choice of the balancing algorithm
depend on the application for what the battery pack is destined and the type of control. It is important to
notice that in bottom balancing in Figure 5.6(a) and Figure 5.7(a) when one cell reaches the minimum
voltage all the cells follow and in top balancing in Figure 5.6(b) and Figure 5.7(b) just the cell with the
lowest capacity is damaged. With monitoring boards the system may not operate until the minimum
voltage since the monitoring boards power consume will undercharge the batteries in short time
damaging the cells to a point of no return.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 242.8
2.9
3
3.1
3.2
3.3
3.4
3.5
3.6
Time [hours]
Vo
lta
ge
[V
olts]
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 242.8
2.9
3
3.1
3.2
3.3
3.4
3.5
3.6
Time [hours]
Voltage [
Volts]
69
5.5 The Autonomous PV Run – Lisbon, Portugal
The autonomous PV system essays were performed in March 2015 with two 225W panels (Appendix
8.7) installed on top of the third floor of North tower building at IST (38º44’15.9’’N and 9º08’17.6’’W).
The approximate sun's trajectory is shown in Figure 5.8. The solar maximum angle is 48°at 13:00.25 The
panels are oriented to the geographical south (7° deviation from south to the west) with an inclination
angle of 𝛽 = 35° (optimal angle generally used in Portugal)26 [7]. For the calculations, it was used the
convention of Figure 2.7 (𝐴𝑧𝑠 = −173°). Due to its location, the PV panels are shaded between 7:00
and 8:30 caused by the building height and after 14:30 caused by the north tower building (located right
on the image) which reduces the solar radiation at least 3 hours/day resulting in a test constraint.
Figure 5.8 - PV installation site and sun trajectory in March 2015
This test was done for a load constituted by the refrigerator, TV and lights projected in 4.1 having a daily
consume of 1300 Wh and aims to prove the viability of the system.
Figure 5.9 shows in red, the measured solar radiation on a horizontal surface for an almost clear sky
working day on 14th March 2015 at the IST meteorological station which is installed on the top of the
South Tower where the shading effect after 14:30 does not happen (Appendix 8.13). It also shows in
black, the radiation incident on the PV tilted plane (35°) calculated accordingly to the expression (2.11)
in section 2.2.3. To simplify the calculations the direct irradiance on the horizontal plane 𝐺𝑏_ℎ𝑜𝑟𝑖𝑧 was
substituted by the total horizontal irradiance measured at the IST meteorological station once the diffuse
radiation represents less than 10% of the total radiation as seen in 2.2.3. The irradiance is available
from 7:00 until 18:30 at the meteorological station. At the PV location the irradiance is similar but is not
available from 7:00 to 8:30 and after 14:30 due to the location limitation described before - represented
by a grey shadow area on the graph in Figure 5.9. This day particularly had some clouds in the morning
which is visible the irradiance from 9:00 to 12:00 and clear sky from 12:00 until the end of the day. The
25 According to the webtool: http://www.sunearthtools.com/dp/tools/pos_sun.php 26 Accordingly to a report by Morse & Czarnecki (1958) the optimally fixed tilt angle is a value 0.9 times the
latitude. In Lisbon that is 38º*0.9=34.2º [25]
70
maximum irradiance on the module was 1056 W/m2 at 13:00, an average wind speed of 3.33 m/s, an
average ambient temperature of 12ºC and a cells’ temperature of 15ºC [54].
Figure 5.9 - Total solar irradiance incident on a horizontal (red) and 35º tilted plane (black) on 14th March 2015 with clouds
The solar power is only injected in the batteries when the irradiance is available and voltage of the
panels is higher than the voltage of the batteries. The figure below shows the evolution of both voltages
during the day. The voltage of the panels depends on the total irradiance incident on the module on 14th
March plotted in Figure 5.9. The PV voltage (blue curve) is approximately one volt higher than the battery
pack voltage from 8:30 until 14:00 when the sun is hitting the panels. Between 9:00 and 11:00 is visible
a decay of the voltage caused by the clouds in this period which consequently reduces the power
injected as seen further in Figure 5.12. The peaks seen on the graph after 14:00 o’clock represent the
opening of the charging relay when the charging is done and one of the cells voltage is above 3.5 V,
remaining open for approximately 10 minutes. Then, the relay closes again connecting the panels when
the voltage of the cells goes under 3.35 V. Therefore, the voltage observed is the PV open circuit voltage
(𝑉𝑂𝐶) of 34V for an approximate 1000W/m² irradiance. After 14:30 the PV voltage is lower than the
07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:000
200
400
600
800
1000
1200
Time
Irra
dia
nce [W
/m2]
Horiz. Irradiance
Module Irradiance
71
battery’s voltage once the panels are shaded producing no power. The diode of the panels ensure there
is no power flowing from the batteries to the PV.
Figure 5.10 - PV (blue) and battery pack voltage (black) on 14th March 2015
The profile of the loads influences the voltage of the batteries represented in Figure 5.11 which is a
closer look to the battery pack voltage curve of Figure 5.10. The variations in the battery’s voltage are
caused by the refrigerator. The refrigerator turns on approximately every 15 minutes causing the
batteries voltage to drop in order to provide the higher current to start the refrigerator. Meanwhile, the
power injected from the panels starts charging the batteries at 8:30 elevating the voltage gradually until
one cell reach the maximum voltage and the controller open the circuit at 14:00 for a maximum pack
voltage of 27.71V. In this period the panels feed the loads and the exceeding power is used to charge
the batteries. After 14:30 the panels inject power no more being the loads feed only by the batteries.
Figure 5.11 - Battery pack voltage on 14th March 2015
The output power and consequently the efficiency of a PV module depends mainly on the total incident
irradiance, incidence angle, PV cell temperature (which is a function of the ambient temperature and the
07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:0026
27
28
29
30
31
32
33
34
35
Time
Voltage [V
]
Battery pack
PV
07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:0026
26.5
27
27.5
28
Time
Voltage [V
]
72
wind) and cell’s age. For this reasons the output power was measured to calculate the efficiency and
see how it is affected during the day. Beside these factors the output power also depends on the Joule
losses in wirings of PV modules that is intrinsic in the injected power in Figure 5.12. The autonomous
system efficiency depends additionally on the inverter DC-AC conversion losses (BMS losses are very
low and may be neglected) relating the power consumed by the loads over the injected power in the
batteries.
In Figure 5.12 is represented the output power of one PV panel on 14th March 2015. This power was
calculated using the measured injected power at the battery terminals and the cable losses estimated
by expression (3.14). The total power going into the battery is twice this value once there are two PV
panels connected in parallel at the testing bench. The sun rises at 7:00 but only after 8:00 the sun’s
radiation hits the panels directly. The power decreases with decreasing of the irradiance caused by the
shadows of clouds from 9:00 to 10:30. It stabilizes around 10:30 and remains approximately constant
until the shadow effect at 14:30 with a maximum of 171 W per panel. Although the irradiance is
increasing after 10:30 the power reaches its maximum with a slight decrease over time which happens
due to the increase of the temperature of the cells. The same happens with the efficiency as shown
below. At 14:00 is the time when the relay actuates after the charging is achieved.
Table 5.2 - Energy and mean daily efficiency of the different components
Energy [Wh/day] Efficiency [%]
PV production
Injected in battery
Cable losses
Load consume
Bat. + BMS + Inverter losses
Bat. + Inverter +
BMS
System (Cables + Bat. + BMS + Inv.)
1693 1600 93 1270 331 79 75
With the batteries full charged at 14:15 the day before (13th March), the system functioned all day and
night for the load projected having a daily consume of approximately 1300 Wh as seen in section 0. The
charging of the battery pack was achieved in about 6 hours at 14:00. This SOC state was used as the
reference point for the estimation of the efficiency. Table 5.2 resumes the energy and mean daily
efficiency of the main components of the system. The two panels produced 1693 Wh of 1800 Wh
possible in this period (area below the graph of twice the power of the Figure 5.12 until 14:00 plus the
energy of the day before from 14:15 to 18:30). The energy produced by the panels was 1693 Wh with
95Wh of losses on the 50 meters cables (5.3%) thus “injecting” 1600 Wh in the batteries. Also 331 Wh
were lost on the DC/AC inverter conversion process and stand-by, battery and BMS controller with a
mean efficiency of 79.3% (1270 Wh delivered to the load). The mean system efficiency (DC Cables +
BMS + Batteries + Inverter) is 75% calculated in terms of energy accordingly to the expression (3.18)
considering the energy produced by the panels and the energy consumed by the loads. The typical
performance factor used to calculate the output energy for solar systems from the PV module output is
usually 85% [14]. This factor does not consider the losses on the cables, batteries, BMS and the stand
by consumption of the off-grid inverter once it is used for grid-tied systems not off-grid. This is the reason
for the 75% system efficiency obtained. The efficiency may be improved by installing the PV panels
closer to the batteries, avoiding the 5% of losses, which was not possible in this experiment. It is
73
estimated that if there were no shading effect the panels could produce more 1000 Wh/day totalizing
2700 Wh available per day.
Figure 5.12 - PV panel output power on 14th March 2015
It is visible that the current starts to be considerably high just after 8:20 when the sun hits the panels on
a favourable angle. The PV panel efficiency further represented in Figure 5.13, is calculated accordingly
to expression (3.4) using the power injected plotted in Figure 5.12. The area of incidence is constant
and the irradiance parameter 𝐺 of the equation is the black curve in Figure 5.9 which changes during
the day.27 The system has no MPPT so the panels may work in a point where the power is lower than
𝑃𝑝.
Before analysing the module efficiency it is important to notice that the manufacturer efficiency of 13.6%
is calculated at STC28 accordingly to equation (3.3). The objective of the next figure is to show the
influence of the ambient and the photovoltaic cell‘s temperature in the efficiency of the PV panels during
the 14th March 2015 day. At the beginning of the day the panels work mainly with diffuse and reflected
radiation once the sun rays hit the panels close to 8:30 as seen in Figure 5.12. For this reason the
efficiency is not under the assumed conditions of direct radiation making the calculation not valid and is
represented by a grey zone on the graph. At this time of the day the cell’s temperature is lower than the
ambient temperature increasing gradually when the ambient temperature increases and the panels start
producing electrical energy. At the time that the radiation focuses the panels with a considerable power
(600 W/m²) its temperature increases considerably to 25ºC being the efficiency 14.7% at 9:00.
Between 9:00 and 10:00 the clouds block a considerable part of the direct irradiance making the
temperature of the panels decrease (note that the decrease of the temperature of the cells may not
result in a higher efficiency once with diffuse radiation the panels have a low efficiency – the radiation is
not concentrated). The increase of the efficiency verified at this time of the day is slightly higher than the
efficiency of the manufacturer once the clouds make the diffuse radiation component increase
27 Accordingly to PV Panels specifications in 8.7 : 0.991 × 1.665 = 1.65 𝑚2 28 G=1000 W/m2, module temperature 25ºC, AM=1.5.
07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:000
25
50
75
100
125
150
175
200
Time
Pow
er
[W]
74
considerably. This confirms that the calculation process used and described in section 2.2.3 does not
work properly for more than 10% diffuse radiation conditions. The diffuse component is summed to the
direct component increasing the total incident radiation for a cloudy test conditions study.
After 11:00 the system works with clear sky, the temperature of the cells increases to 40ºC,
consequence of the increase of the radiation and ambient temperature. This was the maximum
temperature of the cell on this day for a 17ºC maximum ambient temperature. It is visible the influence
of the wind on the temperature of the cells. After 12:00 de radiation changes gradually being maximum
at 13:00 (Figure 5.9), however the temperature of the cells has big fluctuations reflecting the wind cooling
effect. This cooling leads to contrary oscillations in the injected power (Figure 5.12) and also efficiency.
The average efficiency of the PV panels is 10.8%.
Figure 5.13 - PV module temperature and efficiency on 14th March 2015
5.6 Reserve Days
With the load profile projected in section 4.1 (1300 𝑊ℎ/𝑑𝑎𝑦), the batteries charged, and no energy from
the sun the number of reserve days at a 80% DOD may be calculated according to the battery pack
energy 𝑊𝐵𝑎𝑡,𝑇𝑜𝑡, obtained in section 5.3 as:
𝑁𝐷 =𝑊𝐵𝑎𝑡,𝑇𝑜𝑡𝑊𝐷
=3600
1300= 2.77 𝑑𝑎𝑦𝑠 = 2𝑑 18ℎ 28 𝑚𝑖𝑛 (5.2)
5.7 Comparison Methods
Although it was not possible to test the system in Lisbon over one year due to the temporal limitation of
this work, a mean term analyses may be done. For that it is necessary to call upon the diary and monthly
irradiance in the remaining months of the year. The PVGIS provides an estimate of radiation for a clear
sky day, for each month of the year at a given slope of the panels. To validate those values, a statistical
comparison is made using two statistical tests: the mean bias error (MBE) and the root mean bias error
(RMSE).
The mean bias error is defined as [13]:
07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:000
5
10
15
Time
Effic
iency [%
]
0
5
10
15
20
25
30
35
40
45
50
Tem
pera
ture
[ºC
]
Ambient Temperature
PV Cell Temperature
Efficiency
75
𝑀𝐵𝐸 =1
𝑛∑𝐶𝑖 −𝑀𝑖
𝑛
𝑖=1
(5.3)
where n is the number of data pairs in a specific time period, 𝐶𝑖 and 𝑀𝑖 are the ith calculated/predicted
and measured values. This test provides information on the long-term performance. The lower the MBE
the better. A positive MBE indicates an overestimation of the predicted values while a negative MBE
indicates an underestimation. A drawback of this test is that over-irradiance of an individual observation
will cancel under-irradiance in a separate observation.
The root mean square error is defined as [13]:
𝑅𝑀𝑆𝐸 = [1
𝑛∑(𝐶𝑖 −𝑀𝑖)
2
𝑛
𝑖=1
]
1/2
(5.4)
This test provides information on the short-term performance of the correlations by allowing a term-by-
term comparison of the actual deviation between the predicted and the measured value; the lower the
RMSE the better the accuracy of the predicted values. However, a few large errors in the sum can
produce a significant increase in RMSE.
The comparison in Figure 5.14 and Figure 5.15 demonstrates the correlation between the experimental
(red) and PVGIS (black) horizontal and tilted irradiance on a clear sky day. The experimental data is the
measured GHI on 7th March 2015 at the IST meteorological station (Appendix 8.13). PVGIS irradiance
is the average daily global clear-sky irradiance in March, on a horizontal (Figure 5.14) and 35º inclination
plane (Figure 5.15) also at IST meteorological station site [26]. The data from PVGIS had to be shifted
approximately 50 minutes once it is a monthly mean and the experimental data is particular for 7th March.
Figure 5.14 - Global horizontal irradiance measured at IST meteorological station (red) and PVGIS global clear-sky irradiance (black)
07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:000
200
400
600
800
1000
Time
Irra
dia
nce
[W
/m2]
Experimental GHI
PVGIS GHI
76
Figure 5.15 - Global irradiance incident on the PV panel plane calculated from experimental GHI (red) and PVGIS database (black)
Table 5.3 summarizes the errors obtained for the GHI data in Figure 5.14 and Figure 5.15 respectively.
Table 5.3 - Statistical test results
MBE [W/m²] MBE [%] RMSE [W/m²] RMSE [%]
Horizontal Irradiance 24.76 5.22 26.71 5.63
Tilted Irradiance -28.62 -4.35 30.61 4.65
The errors values are within an acceptable range. Positive MBE for the horizontal radiation shows that
the values predicted by the PVGIS are higher than the experimentally obtained which is confirmed by
the position of the two curves in Figure 5.14. Notes that the PVGIS estimative is an average values for
a data base over several years opposite to the daily radiation of the experimental data (red). For this
reason the radiance values may vary fairly, however the maximum differential between the irradiances
of Figure 5.14 is 35 W/m² excluding the "jump" in the data at 17:00h.
The MBE negative value for the tilted plane shows that the average differential irradiance is 28 W/m²
and the PVGIS value is lower than the value calculated from the horizontal radiation contrary to Figure
5.14. This is due to the fact that PVGIS calculation method considers the diffuse radiation which lowers
the estimation, not being however a significant difference as seen in Figure 5.15. The horizontal radiation
has a slightly lower MBE and RMSE compared to the inclined plane since the calculation of the radiation
in the inclined plane has more variables introducing a progressive error in the data. Although the PVGIS
estimate is more accurate for horizontal radiation the irradiance differential on the tilted plane is not
significant so this radiation may be consider as a source for further analysis.
07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:000
200
400
600
800
1000
1200
Time
Irra
dia
nce
[W
/m2]
Calculated from GHI
PVGIS
77
5.8 Operation in the remaining months of the year
To ensure the supplying of the loads it is necessary to ensure that the daily photovoltaic production
exceeds the consumption throughout the year. This estimation is made considering the area and the
average efficiency in the following table according to the values previously obtained in 5.5Error!
eference source not found. and the monthly average PVGIS irradiation. The efficiency of the panels
takes into account the real effective temperature of the panels, and the system efficiency the
inverter+BMS daily standby consumption.
Table 5.4 - Autonomous PV system average technical data
Panel area [m²] Panels total area [m²] PV panels efficiency System efficiency
1,65 3,30 10,80% 80%
According to these values, the minimum daily PV production to ensure the loads consumption is given
by:
𝐸𝑚𝑖𝑛 =𝐸𝑙𝑜𝑎𝑑𝑠𝜂
=1300 𝑊ℎ
0.8= 1625 𝑊ℎ/𝑑𝑎𝑦 (5.5)
Figure 5.16 - Monthly global irradiation average and temperature on a 35º tilted plane [26]
The average irradiation on the panel’s plane in March is 5760 Wh/m²/day. It is noticeable in Figure 5.16
that between April and late September the irradiation is greater than this value. In March, once the
system reached full charge for several days in a row almost in the limit of the available radiation, at the
test site in the months with less radiation and length of day than March the daily charging of the batteries
is compromised. However, with the installation in a place without shading, even in the winter sunny days
the charging is achieved, once almost more 1000 Wh/day is available. The monthly average temperature
follows the tendency of the radiation except between October and January when the operation is more
critical. The annual average temperature is 16.3º.
The PV production may be calculated knowing the efficiency of the PV panels multiplied by the
irradiation available at the total area of the panels. Examining Table 5.5 it is obvious that for a clear sky
day like 14th March 2013 the PV production of 2700wh/day is higher than the PVGIS monthly average
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
Month
Irra
dia
tio
n [
kW
h/m
2/d
ay]
5
10
15
20
25
30
Te
mp
era
ture
[ºC
]
Irradiation
Temperature
78
of 2053 Wh/day which is 31.5% more. This happens due to the 30 days PVGIS irradiation average that
considers the sunny and the cloudy days in the respective month, not just one shinny day. It is also
visible that the PV production estimation using the irradiation data is close to the energy experimental
value of approximately 2700 Wh/day, which corresponds to a deviation of 2.7%.
Table 5.5 - Monthly average vs 14th March irradiation
PVGIS Estimated from IST meteo
(14th March) Autonomous PV (14th March)
Irradiation [Wh/m²/day]
PV production [Wh/day]
Irradiation [Wh/m²/day]
PV production [Wh/day]
With shadow effect [Wh/day]
No shadow effect [Wh/day]
5760 2052,88 7372,60 2627,617926 1700 2700
Accordingly to the PVGIS monthly irradiation available per square meter [26], Table 5.6 shows the
estimation of the energy delivered to the loads regarding the experimental efficiencies in Table 5.4. The
photovoltaic production and the energy available to the loads is calculated using expression (3.4) and,
(3.18) respectively.
Table 5.6 - Estimated energy available to the loads
Month Irradiation
[Wh/m²/day]
Energy on PV panels area
[Wh/day]
PV production [Wh/day]
Energy delivered to the loads [Wh/day]
Jan 3550 11715 1265 1012
Fev 4700 15510 1675 1340
Mar 5760 19008 2053 1642
Apr 6030 19899 2149 1719
May 6430 21219 2292 1833
Jun 6760 22308 2409 1927
Jul 7060 23298 2516 2013
Aug 7100 23430 2530 2024
Sept 6470 21351 2306 1845
Oct 5260 17358 1875 1500
Nov 4020 13266 1433 1146
Dec 3370 11121 1201 961
Annual 5543 18290 1975 1580
The most critical months in average terms are the lowest irradiation months identified in bold in Table
5.5 once the values are lower than the 1300 Wh/day consume. Note that in this table it is not visible in
detail how many days the batteries are at a low load percentage since to do so would it would be
necessary a daily analysis or the number of clear sky days. However, this may be estimated in PVGIS
for a stand-alone system using the following parameters: PV power 450Wp; battery voltage 24V;
capacity 130Ah; discharge cut-off limit 35%; daily consumption 1300 Wh; module inclination 35º and
orientation south (0º). The results are shown in Table 5.7.
The result goes in line with the previous conclusions taken to Table 5.6 which showed that the most
critical months go from November until February with 50% of the days with the batteries in a lower than
35% SOC state.
79
Table 5.7 - Percentage of days of full and empty battery [26]
Month Average energy
production per day [Wh/day]
Days with battery full [%]
Days with battery empty
[%]
Jan 1046 29 48
Fev 1255 54 15
Mar 1292 79 5
Apr 1296 84 0
May 1303 90 0
Jun 1301 97 0
Jul 1298 99 0
Aug 1300 96 0
Sept 1296 95 0
Oct 1276 79 3
Nov 1193 31 25
Dec 1039 17 51
Annual 1241
In these months the load profile should be adjusted to the minimum possible (the use of the lights and
TV may be reduced) being the refrigerator operation guaranteed during the whole year (Table 4.2).
Another possible measure is to manually adjust the angle of the solar panels between November and
February to a higher value. In the middle of December the maximum solar angle is 28º29. Thus, the
module inclination angle should be perpendicular to the sun rays and adjusted to:
𝛽𝑜𝑝𝑡_𝑤𝑖𝑛𝑡𝑒𝑟 = 90 − 28 ≈ 60° (5.6)
reducing to 40, the days of empty battery according to PVGIS.
The temperature of the panels varies approximately in proportion to the ambient temperature in a day
with low wind as seen in Figure 5.15. Thus, a 10ºC ambient temperature variation produces about the
same variation in temperature of the panels, which results in a change of 0.5% efficiency according to
expression (3.7). In Portugal, the temperature range can go beyond 30°C (10º C higher than the
temperature on March 14th) what constitutes a minor variation in the experimental efficiency shown in
Table 5.4.
5.9 Autonomous PV Run – Luena, Angola
Since it is not possible to make experimental tests in Angola, it is important to compare its radiation with
the radiation in Portugal where the system was tested to assess its viability and efficiency. This way, is
possible to make an extrapolation of the energy produced in Angola by correcting the real efficiency of
the panels to the average ambient temperature in Angola. This adjust method is further used accordingly
to expression (3.7). It is necessary to evaluate the photovoltaic solar resource and the ambient
temperature conditions of the installation site. Table 5.8 evidences the radiation and mean annual
29 According to the webtool: http://www.sunearthtools.com/dp/tools/pos_sun.php
80
sunshine hours between the two countries. The minimum radiation values correspond to the north and
the maximum to the south in both countries. The annual values are based on the map of Figure 5.17
and the daily values on PVGIS database. [26] [55] [56]
Table 5.8 - Radiation comparison between Angola and Portugal (source: PVGIS climate-SAF Europe and Africa
maps database 2001-2010) [10, 57, 26]
Countries 𝐺𝐻𝐼 [𝑘𝑊ℎ 𝑚2 𝑦𝑒𝑎𝑟⁄⁄ ] 𝐺𝐻𝐼 [𝑘𝑊ℎ 𝑚2 𝑑𝑎𝑦⁄⁄ ] 𝐺𝑇𝐼𝑜𝑝𝑡[𝑘𝑊ℎ 𝑚2 𝑑𝑎𝑦⁄⁄ ] Sunshine
hours
Angola 1800-2400 4.7 - 6.4 4.7 - 6.8 2000 - 2500
Portugal 1700-2000 4 - 5.3 3.3 - 7 2200 - 300030
The available annual energy on the horizontal plane is higher in Angola besides the lower number of
sunshine hours having a slightly higher solar potential. Accordingly to solarGIS maps, the annual energy
in Lisbon area is higher than 1700 kWh/m² per year. On the other way, Angola has an annual energy
higher than 1800 kWh/m² per year almost in all the country except in the zone north to Luanda (note
that the scales in the figures is different). Thus, on average, a system that works all the year in Portugal
is expected to work in Angola once the available solar energy per square meter is higher.
c)
d)
Figure 5.17 - Global horizontal irradiation in a) Angola and b) Portugal [10]
More particularly in Luena city, the values of the irradiation are shown in Table 5.9. Although the higher
number of sunshine hours in Lisbon the irradiation in Luena is higher balancing this effect.
30 Collares Pereira, Manuel, Energias renováveis, a opção inadiável, Sociedade Portuguesa de Energia Solar , SPES, 1998
81
Table 5.9 - Global irradiation in Luena, Angola and Lisbon, Portugal on the horizontal and optimal inclined plane
[10, 26, 30]
Location 𝐺𝐻𝐼 [𝑘𝑊ℎ 𝑚2 𝑦𝑒𝑎𝑟⁄⁄ ] 𝐺𝑇𝐼𝑜𝑝𝑡[𝑘𝑊ℎ 𝑚2 𝑑𝑎𝑦⁄⁄ ] 𝐺𝑇𝐼𝑜𝑝𝑡[𝑘𝑊ℎ 𝑚
2 𝑦𝑒𝑎𝑟⁄⁄ ] Sunshine hours
Luena 2150 4.7 – 7.3 (β=19°) 2226 (β=19°) 2400
Lisbon 1800 3.3 – 7.1 (β=35°) 2024 (β=35°) 3000
Figure 5.18 represents the monthly average irradiation on both sites evidencing the fact that Luena has
a higher solar potential which goes in accordance with the solarGIS map and information on the previous
table. The irradiation gap plays a more relevant role between October and January which is favorable
to the energy production. The irradiation values are obtained for an optimal inclination angle of 19º in
Luena [26].
Figure 5.18 - Monthly average global irradiation on a β=35º plane in Lisbon, Portugal (blue) and β=19º in Luena, Angola (black) [26]
The ambient temperature is higher in Luena almost during all the year accordingly which constitutes a
downside to the energy production. Figure 5.19 shows the average temperatures in both locations. The
maximum difference between the lowest and highest temperature is 12ºC and as seen in section 3.2.2,
a 10ºC temperature gap makes the efficiency decrease by 0.5%. The annual average temperature in
Luena is 21.2º opposed to 16.3º in Lisbon (ΔT=5ºC). [26, 30]
Figure 5.19 - Monthly average temperatures in Lisbon, Portugal (blue) and Luena, Angola (black) [26, 30]
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
Month
Irra
dia
tio
n [
kW
h/m
2/d
ay]
Lisbon
Luena
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec5
10
15
20
25
30
Month
Te
mp
era
ture
[ºC
]
Lisbon
Luena
82
The efficiency variation with ΔT=5ºC is approximately 0.3% accordingly to expression (3.7).
Consequently, for the energy production estimation in Table 5.10 the same method and values of Table
5.4 are used except for the efficiency, where 10.5% is considered. Once again, the monthly irradiation
values were taken from PVGIS database for Luena location at the optimal angle of 19 degrees. The PV
production is calculated multiplying the energy available on the PV panel’s area (3.3 m²) by the panel’s
efficiency (10.5%), and the energy delivered to the loads multiplying the PV production by the system
efficiency (80%).
Table 5.10 - Estimated energy available to the loads in Luena, Angola
Month Irradiation
[Wh/m²/day] Energy on PV panels
area [Wh/day] PV production
[Wh/day] Energy delivered to the loads [Wh/day]
Jan 4890 16137 1694 1356
Fev 5070 16731 1757 1405
Mar 5540 18282 1920 1536
Apr 6290 20757 2180 1744
May 6980 23034 2419 1935
Jun 7040 23232 2439 1952
Jul 7170 23661 2484 1988
Aug 7330 24189 2540 2032
Sept 6850 22605 2374 1899
Oct 6150 20295 2131 1705
Nov 5070 16731 1757 1405
Dec 4730 15609 1639 1311
Annual 6093 20105 2111 1689
On an average basis, even with higher temperatures and a consequent lower efficiency the higher solar
potential in Angola leads to better energy production results. Analysing Table 5.10 we might conclude
that only January and December are critical with an energy delivered to the loads close to the 1300Wh
daily consume, in opposition to the period between November and February in Portugal which leads to
a better behaviour. The next table shows the results obtained from PVGIS for a stand-alone system in
Luena using the following parameters: PV power 450Wp; battery voltage 24V; capacity 130Ah;
discharge cut-off limit 35%; daily consumption 1300 Wh; module inclination 19º and orientation north
(180º).
The percentage of days with fully discharged batteries is less than 5% validating (Table 5.11). The
highest percentage occurs in December but is far from the 50% Portugal percentage which will produce
better results.
83
Table 5.11 - Percentage of days of full and empty battery [26]
Month Average energy
production per day [Wh/day]
Days with battery full [%]
Days with empty battery [%]
Jan 1290 68 2
Fev 1301 68 1
Mar 1299 63 3
Apr 1298 91 1
May 1299 97 0
Jun 1300 100 0
Jul 1300 100 0
Aug 1301 99 0
Sept 1294 96 1
Oct 1300 90 1
Nov 1297 65 0
Dec 1291 49 4
Annual 1298
84
5.10 Conclusions
In this chapter the projected system was tested to study the real behavior, efficiency and parameters of
each component. Additionally two types of balancing were analyzed – bottom and top – to understand
which is more advantageous to LiFePO4 batteries. The simplification beam radiation method revealed
good results for clear sky conditions. Less accuracy is found when the weather conditions are far from
clear sky which was already expected. Additionally, the reflected radiation component may be significant
at some hours of the day due to the installation constraints, in this case reflected on the building.
The type of balancing should be chose accordingly to the application once both showed the same
discharging time. If the system may have periodical maintenance and the user may check the monitor
state of the batteries by any means (Ex.: EV’s), bottom balancing is the best option. Bottom balancing
requires cheaper electronic systems that only monitor the batteries state instead of balancing (BMS) as
the balancing may be yearly performed by a maintenance intervention. On the other hand, if the system
is expected to work without maintenance and technical intervention for long periods, a top balancing
BMS is the best option. When the battery get fully charged very often which is the case of off-grid
systems, top balancing works better once the cells are balanced nearly the high SOC. The disadvantage
of BMS systems is the higher probability of reducing batteries’ lifetime due to the regular stand-by energy
consumption. The consequences of this effect go beyond the ambit of this work. An autonomous PV
system in Angola should have the less maintenance possible and may not be accessible to the user.
This requirements make the BMS the only viable option. It provides the balance in every charging cycle
with less expended energy in the process over time.
With monitoring boards the system may not operate until the minimum voltage since the monitoring
boards power consume will undercharge the batteries in short time damaging the cells to a point of no
return. For this reason, a bottom balancing BMS must be projected with a considerable safety voltage
margin. The cells should operate in the flat zone of the charging/discharging curve to a minimum voltage
of 3.1V (Figure 5.6), this ensures that even with a low battery SOC the control system may be connected
enough time until the next solar charging is made.
The experimental tests performed revealed good results for the projected system, the correct charging
of the batteries and feed of the loads every day making the PV system works for the consumer daily
needs, even with the shadow constrain at the installation site. The consumer’s energy consume requires
a minimum PV production of 1625 Wh/day, the excess produced energy charges the batteries. The
panels showed an efficiency of 10.8% and the system battery+BMS+inverter an efficiency of 75%. The
cable losses seen in section 4.2 revealed to be 5.5% of the energy produced by the panels. This losses
obviously depend on the length of the cables and represent a little more than the 3% usually considered
for the project in [7]. The number of reserve days of the system is up to two days what gives a good
chance to the batteries charge again in a place with good sunshine index. The batteries should be
installed in a place as cold as possible to achieve the best batteries’ capacity performance. Portugal has
more constrains in the winter than Angola during the rainy season due to Angola’s higher solar potencial.
85
Both sites require the panels inclination angle adjust during the less favourable months reducing the risk
of the system shutdown.
86
87
6 Conclusions and Future Prospects
6.1 Conclusions
This paper approached the autonomous energy supply to a typical rural house in Angola. The projected
and tested system during the month of March proved to be able to feed the previous specified load with
an average consumption of 1300Wh/day. Although March is not the month of the year with the lowest
monthly average irradiation in Portugal the measured system efficiency is considered the same all the
year. The efficiency of the PV panels obtained experimentally in Portugal was adjusted to the average
temperature in Angola, this way, it was made an extrapolation to the monthly irradiation values in Angola.
The results showed a good production energy during almost all the year, except in January and
December which revealed critical production values of 1356Wh and 1311Wh, respectively. This values
are too close to the daily consumed energy and suggests the addition to the system of a 2nd alternative
source of energy (wind generator, diesel generator, etc.). Another possible solution to improve
performance in the critical months is a manual change of the tilt angle of the panels in order to align
them with the sun. Using a β=0º tilt angle the irradiation may be 10% higher according to PVGIS data.
The estimation method of solar direct radiation incident on the plane of the panels (Gb_module) calculated
from experimental measurements of radiation in the horizontal plane on site (Gb_horiz), revealed a
deviation of about 2.7% from the experimental value. This value shows that the procedure used for the
calculation (section 2.2) is suitable for clear sky days. However, this method has the limitation of not
working properly when the solar angle is close to zero.
With respect to the batteries, the initial charging revealed to be essential to ensure a long life of the
batteries and with a balanced pack (close SOC) it is possible to achieve more energy. In order to keep
the balance at levels of millivolts without maintenance over the life of the battery, it is necessary to use
a Battery management System (BMS) which should balance the cells near the end of the charging
curve. Thus, the balancing is done close to the high charge states in which the batteries should remain
as long as possible. Also the control systems are closely related to the performance of the batteries.
These systems should consume the lowest power possible, as their use "drains" battery power
continuously to supply the installed sensors. This fact will unbalance the batteries faster compared with
a system without a battery management system. The Deep of Discharge (DOD) must not exceed 80%
(Vmin> 3.0 V), since if the system is discharged for an extended period, BMS stand-by consumption,
although very small, can cause the cells to be exceed the minimum voltage. However, the implications
of this idle power have not been verified experimentally once it would be necessary to measure the cells
capacity after some years of operation. The stand-by power of ©BMS123 is less than 0.3W (idle current
<10mA). The control system had some limitations in reading the output currents of the batteries. Since
the inverter voltage input signal is a square wave the current is not a constant DC value. This introduces
small errors on the real SOC Coulomb counting estimation method which may lead the controller to
open the circuit before the batteries are actually discharged. This may be fixed by calibrating the current
sensor offset or ignoring the estimation of SOC that could make the system simpler and cheaper to
88
implement. Nevertheless, the cells’ protection is ensured once the relays open the circuit based on
voltage signals which work properly.
On site, the polycrystalline solar panels used showed a daily average efficiency of 10.8% and the total
system a 75% efficiency which may be improved about 5%, if the panels are installed at a distance lower
than 10m of the battery pack.
Actually, PV modules present a relatively high cost, however its cost have been reducing across the
years. In the future, it is expected to observe a growing investment in these systems by developing
countries such as Angola. This work was an approach to autonomous PV isolated systems with the
objective of clarify and deepen some aspects in the management and control of LiFePO4 battery storage.
It is expected to open new opportunities for further investigations which may improve with more detail
methods of operation of these systems.
89
6.2 Future Work
Due to the need for access to energy, environmental concerns and the growing demand for renewable
energy, isolated photovoltaic systems should also feel an increase in demand. It is expected that "plug
and play" (easy installation) solutions emerge. The controller used in this system has very favorable
characteristics to its comprehension and modification that may in the future be improved and compacted
in order to integrate and manufacture a system ready easy to install.
For end users, this BMS has features that are not of the most importance to isolated systems. This
happens since this BMS was firstly designed to electric vehicles and then integrated in isolated systems.
Among this features is the SOC estimation. For isolated systems in rural places, the consumer will not
have a computer access the sensors’ readings, so he will not have information on the batteries’ SOC.
Thus, a controller of this type may be based only on voltage levels, both switch on/off as well as
reconnection voltage. This way, it may be set that the relays are to be reconnected when the
predetermined voltage is reach, not the predetermined SOC as it happens actually. The system will be
more economical if the electronic boards are pre-programmed to the voltage levels, in LiFePO4 this
levels are between 3 to 3.6V.
It would be also interesting to study the batteries’ manufacturing energy cost versus the energy delivered
during its lifetime in a more environmental approach. The temperature management is also an important
aspect to improve, however this is more relevant with high current applications.
As concluded before, to improve significantly its autonomous capacity, these systems should be
integrated with alternative energy sources that allow the supply of the loads not only during the hours of
sun but during all day. Wind sources are the ideal solution, this will increase the cost of the installation
but decrease the effort of batteries as the loads can be supplied almost exclusively by generation. It
would be interesting to analyse the cost benefit of implementing a wind generator, in opposition to
increase the solar power production and storage capacity.
The development and continuous improvement of energy sources shows a promising future for these
systems making possible to provide electric energy for all.
90
91
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8 Appendix
8.1 National Instruments NI-USB6008/9 Data Acquisition Device
96
97
8.2 Current Transducer LA-25-NP Datasheet
98
99
Figure 8.1 - LA 25-NP current transducer characteristic
8.3 Power Logger Fluke 1735
8.4 Tektronix TDS 2001/2012C Oscilloscope
y = 5,6026x - 0,0833
0
1
2
3
4
5
6
7
8
9
0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6
Prim
ary
cu
rre
nt [A
]
Secondary voltage [V]
Model Fluke 1735 Three-Phase Power Logger
Memory 3.5MB for measuring data
Sample Rate 10.24 kHz
V-RMS wye resolution 0.1V
Operating Error ±0.5% of measured value +10 digit
A-RMS resolution 0.01A
Operating Error ±1% of measured value +10 digit
Brand Tektronix
Model TDS 2001/2012C
Analog Bandwidth 100MHz
Sample Rate 2GS/s
Record Length 2.5k Point
Analog Channels 2
100
8.5 Data logging
Data logging is the process of using a computer to collect data through sensors, analyse, save and
output the results. Data logging also implies the control of how the computer collects and analyses the
data. Data logging is commonly used in scientific experiments and in monitoring systems where there
is the need to collect information faster than a human can and in cases where accuracy is essential.
8.5.1 Voltage log
The voltage logging in this work was done using the four National Instruments NI USB-6009 DAQ® input
channels and LabVIEW Signal Express software for data acquisition.
The maximum input voltage of the DAQ is 20V (Appendix 8.1). All the signals lower than 20V like the
cell’s voltage may be directly connected to the DAQ. The voltage higher than 20V as the PV voltage or
the battery bank voltage are read through a voltage divider to decrease the voltage by a 2 times factor.
Figure 8.2 - Connecting a Differential Voltage Signal [NI USB-6008/6009 User Guide]
After the DAQ have been connected the LabVIEW Signal Express or LabVIEW software may be used
to log the data. LabView software offers the capabilities of LabView Signal Express but in at a lower and
more complex level of interface. For logging purposes Signal Express is more intuitive and has an easy
to use interface.
Figure 8.3 - LabVIEW Signal Express Monitor / Record interface
101
The range of the input, type of acquisition, number of samples and frequency of acquisition is defined
here. It was used a continuous sample acquisition mode, with a frequency of 1sample/min and a 1440
number of samples. Every time the number of samples is reached after starting the log is saved to a file
and it may be used a routine to start a new saving after the previous has finished to save loggings every
day for several days in a row.
Figure 8.4 - LabVIEW Signal Express Playback interface
The playback window is where the signals are analysed and exported to Excel or to a text file to be the
plotted.
8.5.2 Current log
In order to log the current in high power circuits directly with NI® DAQ an extra resistance is necessary
and therefore its voltage can be read. However, with this assembly a considerable energy will be
dissipated in the resistor. A better solution is to use a transducer as LEM LA25-NP® to measure the
current.
This transducer consists of a u-shaped magnetic core with a primary winding (power circuit) and
secondary winding (measure circuit). The magnetic field created by the power circuit circulating in the
core changes the position of a moving part and consequently the output of an Op Amp powered by +15/-
15V. This way the sensor provide isolated measurements from the power stage.
According to the law of Conservation of Energy, the relationship between the voltage on the primary and
secondary in an ideal transformer is given by:
𝑈1𝐼1 = 𝑈2𝐼2 (8.1)
102
For a primary nominal current, 𝐼𝑃𝑁 = 25 𝐴 and primary maximum current, 𝐼𝑃 = 36 𝐴, the turns ratio is
(according to datasheet 8.2):
𝐾𝑁 = 𝑚 =𝑈1𝑈2⁄ = 1/1000 (8.2)
Substituting (8.2) in (8.1):
𝐼2 = 𝑚 × 𝐼1 (8.3)
With a peak current no higher than 36𝐴, the sensor works in the linear zone which means that the
current and the voltage have a linear relation.
This secondary voltage 𝑈2 = 𝑈𝑆, is the voltage at the terminals of the resistor 𝑅𝑀 and can be theoretically
calculated using expression (8.4) knowing the secondary current.
𝑈𝑆 = 𝑅𝑀 × 𝐼2 (8.4)
The secondary voltage 𝑈𝑆 is logged using the NI-6009 and the primary current may be obtained by the
following voltage/current relation substituting (8.3) in (8.4) :
𝐼1 =𝑈𝑆
𝑅𝑀 ×𝑚 (8.5)
Figure 8.5 - LEM LA25-NP equivalent circuit according to datasheet parameters [58]
To achieve the best relation, the sensor’s experimental characteristic may was obtained measuring
several points with a current source connected to the primary of LA-25 NP starting from 0A and reading
the secondary’s voltage using the following circuit:
103
DCV
1 A
0 V
M
OUT
IN
UpUs
Figure 8.6 - Experimental setup to obtain LA-25 NP characteristic
This leads to the relation between voltage and current:
𝐼 [𝐴] =𝑉𝑠
0.1785− 0.0833 (8.6)
Figure 8.7 - Experimental characteristic test of the LEM LA25-NP
The voltage measured is 0.927 𝑉 which corresponds to a current of 5.224 A according to the expression
(8.1). The current read by the current probe is 5.157 A, giving a 47 mA or a 0.9% current error.
104
8.6 CALB SE130AHA Battery Cell Datasheet
Model name SE130AHA Alternative product marking CSE130AH Nominal voltage 3,3 V Operating voltage under load is 3,0 V Capacity 130 Ah +/- 5% Internal impenetrableness <1 mOhm 1kHz AC Operating voltage min 2.6V - max 3,6 V At 80% DOD Discharging cut-off voltage 2.5 V The cells is damaged if voltage drops
below this level Charging cut-off voltage 3,65 V The cells is damaged if voltage exceeds this level Recommended charging -
discharging Current 39 A 0,3C
Maximum short-time discharging current 1000 A 10C period = 10s
Life cycles 2000 0,3C 80% DDC Operating thermal ambient - charging 0°C ~ 45°C
High risk of damaged cells if out of these ranges Operating thermal ambient -
discharging -20°C ~ 55°C
Storage thermal Ambient -20°C ~ 45°C Shell Material Plastic Flame retardants Dimensions 182 x 56 x 278 mm Millimetres (tolerance +/- 1 mm) Weight 4,4 kg Kilograms (tolerance +/- 100 g)
105
8.7 Suntech polycrystalline STP225 – 20/Wd PV panels Specifications
106
Solar Cell Electrical Model
The simplified electrical model of a solar cell (Figure 8.8 a) is the 3 parameters model (1M3P), which
are: 𝐼𝑃𝑉 the illumination current associated to the photoelectric effect, 𝐼0 the reverse bias saturation
current for the diode and 𝑚 the diode ideality factor. The p-n junction is represented by a diode in parallel
with the current source which depends on the voltage at the terminals of the cell. A more accurate and
realistic model would take into account the influence of contacts - a series resistor Rs - and leakage
currents -shunt resistor Rsh (Figure 8.8 b) [4, 59].
ID
pvI
D
I
V
a)
ID
pvI
D
I
V shR
sR
b)
Figure 8.8 - Equivalent electrical model of a solar cell a) three parameters and b) five parameters [59]
This is known as the single mechani Regarding the three parameter (ideal) model:
𝐼 = 𝐼𝑃𝑉 − 𝐼𝐷 (8.7)
𝐼𝐷 = 𝐼0 (𝑒𝑞𝑉
𝑚𝐾𝐵𝑇 − 1) (8.8)
𝐼𝑃𝑉 ∝ 𝐴𝐺 (8.9)
where 𝐼0 is the reverse bias saturation current for the diode, 𝑞 = 1.6 × 10−19C is the modulus of the
electron charge, 𝑚 is the diode ideality factor, 𝐾𝐵 = 1.38 × 10−23J/K is the Boltzmann constant, 𝑇 is the
absolute temperature of the cell and 𝑉 the voltage at the terminals of the cell, 𝐴 is the area of the cell
and 𝐺 the solar irradiance. This model tells that the power is proportional to the area of the panels and
to the irradiance on the cells.
The I(V) characteristic (Figure 8.9) of a photovoltaic cell exposed to solar light varies accordingly to
different solar irradiances, the shaded area is the PV working region.
107
Ipv
V
G
G
G
I
Figure 8.9 - Stationary characteristic I(V,G) of a photo-diode exposed to solar light [59]
To better understand the real behaviour of the panels (voltage gaps and shading effects), the five
parameters model (1M5P) should be used cell (Figure 8.8 b). This is a more accurate and realistic model
which take into account two more parameters: the influence of contacts, using a series resistor Rs, and
leakage currents, using a shunt resistor Rsh. For that model:
𝐼 = 𝐼𝑃𝑉 − 𝐼𝐷 − 𝐼𝑠ℎ = 𝐼𝑃𝑉 − 𝐼0 (𝑒𝑞(𝑉+𝑅𝑠𝐼)𝑚𝐾𝐵𝑇 − 1) −
𝑉 + 𝑅𝑠𝐼
𝑅𝑠ℎ (8.10)
Using the short circuit and open circuit (𝑉 = 0) and after some manipulation of the expressions the
relation between the current and the voltage is given by:
𝐼𝑐𝑐 = 𝐼𝑃𝑉 − 𝐼0 (𝑒𝑞𝑅𝑠𝐼𝑐𝑐𝑚𝐾𝐵𝑇 − 1) −
𝑅𝑠𝐼𝑐𝑐𝑅𝑠ℎ
≈ 𝐼𝑃𝑉 − 𝐼0 (𝑒𝑞𝑅𝑠𝐼𝑐𝑐𝑚𝐾𝐵𝑇 − 1) (8.11)
where 𝐼𝑐𝑐 is the current value when the cell is short circuited (𝑉 = 0) and the simplification is made
knowing that in general 𝑅𝑠ℎ ≫ 𝑅𝑠.
The open circuit voltage 𝑉𝑜𝑐 is the voltage across the diode with 𝐼 = 0. For simplicity, the cell open circuit
voltage Voc is calculated assuming the ideal characteristics of the solar cell; the accuracy is not much
affected by this assumption. Thus using (8.7) and (8.8):
𝑉𝑜𝑐 =𝑚𝐾𝐵𝑇
𝑞ln (1 +
𝐼𝑃𝑉𝐼0) (8.12)
According to the power convention, the power related with the diode is P= - V I. In the PV quadrant of
the stationary current-voltage characteristic this value is negative, meaning that in this zone the device
is active or, equivalently, the power is delivered by the solar cell and given by:
𝑃 = 𝑉𝐼 = 𝑉 (𝐼𝑃𝑉 − 𝐼0 (𝑒𝑞𝑅𝑠𝐼𝑐𝑐𝑚𝐾𝐵𝑇 − 1) −
𝑉 + 𝑅𝑠𝐼
𝑅𝑠ℎ) (8.13)
108
The temperature influence and the solar irradiance may be included in the single model assuming that
𝑚 is constant, the temperature variation is included in 𝐼0 and the variation of the incident irradiance in
the parameter 𝐼𝑐𝑐:
𝐼𝑐𝑐(𝐺) = 𝐼𝑐𝑐𝑟𝐺
𝐺𝑟 (8.14)
109
8.8 TUV Solar Cable
8.9 BMS Off-Grid 123 Electric31
123electric Battery Management System is primarily intended for prismatic LiFePO4-cells, but can also
be adapted by the end-user for other cells like Li-Ion and LiPo in the range of 2V to 5V. It measures
each cell voltage and temperature (thermal management) and computes this parameters to calculate
the SOC of the battery pack. Balancing is done during charging only.
123electric BMS is designed for battery-packs that have many cells in series, to form a high voltage
battery-pack. Each cell is equipped with a small BMS-board that monitors cell parameters like current,
voltage and bypass-current and communicates over a one-wire interface with the BMS-controller. Once
the software values are loaded to the microcontroller it is not required a permanent connection to the
computer to operate the system. This BMS-controller collects this data, and displays that via a USB-
interface on a Windows Computer.
Supply-voltage of BMS-controller 8-60 Volt
Idle current of the BMS-controller (including the current sensor)
< 10 mA
Number of cells 2 - 255
Balancing current 1 Amp.
Idle-current BMS-board < 100 uA
Current-sensor 100 Amp.
A/D-resolution 1024 steps ( 10 bit )
Cell-voltage in steps of 0,01 Volt ( 2,00 – 5,00 V )
Cell-temperature in steps of 1 degree ( -40 to 99 Celsius )
Scan-time per cell 0,015 Seconds
System structure
Consumer relay (Max. 60 Ampere DC)
Charge relay (Max. 60 Ampere DC)
Voltmeter
31 http://www.123electric.nl/uploads/file/BMS_EV_Manual_v1_3.pdf
Current Sensor used (100A)
Cell Capacity (10 - 999 Ah)
Real Time Clock (24 h)
Section 6mm2
Insulation Thickness 0.90 / 1.10
Overall Diameter 6.8 mm
Max Electric resistance at 20ºC
3.39 Ω/km
Reactance (at 50 Hz) 0.135 Ω/km
110
Consumers start time
Consumers stop time
Minimum Cell Voltage (error-level)
Maximum Cell Voltage (error-level)
Bypass Voltage (balancing voltage)
Recharge Voltage
Minimum Cell Temperature (error-level)
Maximum Cell Temperature (error-level)
Gauge linearization (for current- and
capacity- gauge)
Current-scale selection
Control Conditions
Charge Relay - The incoming charge current will be blocked through the relay when the battery pack
capacity is 100% SOC, and switches on again if the capacity is below the programmable “Charge
restart”.
Consumers Relay - The consumers will be switch off if the battery pack capacity is 0% or one of the
cells goes below the programmable minimum cell voltage, and switches on again if the capacity is
above the programmable “Discharge restart”.
SOC estimation
The system sets the coulomb counter to 100% when either all cells get to V-bypass or one cell reaches
V-max (values may be changed on the software) using the couloumb counting method which updates
the capacity of the cell in each iteration.
BMS software – parameters settings
a)
b)
Figure 8.10 – BMS 123 a) dashboard and b) system settings
On the BMS software, the readings of the sensors may be observed (battery pack current of 0A, SOC
of 91%, battery pack voltage of 26.7V, minimum and maximum cell voltage, 3.33V and 3.34V
respectively and temperature, both 21ºC. In this case both relays are connected (green symbols in
Figure a). The voltage and temperature levels, the charge/discharge capacity and stop and start time
that actuate the controllable relays may be set in the software window of system settings (Figure 8.10
b). The voltage levels will define what will be the DOD of the discharge which should not be higher than
80% (approximately 3.1 to 3.55V).
111
8.10 Livre Pure Sine wave Inverter 1500W
Experimental Efficiency Characteristic Procedure
To measure the real characteristic of the inverter it was set an experiment with a 1000W DC power
supply (Figure 8.11 a) and a resistive load (Figure 8.11 b). This power supply was used to test the high
and low voltage alarms and switch off voltage which were in accordance to the datasheet. The
resistance was changed from 517 Ohm to 62.2 Ohms and the DC and AC powered were measured to
plot the real efficiency curve.
a) b)
Figure 8.11 - Inverter characteristic with a resistive load
Nominal Power Pn=1500W
Peak Power 2xPn=3000 W
Pstand-by 7W (tested)
DC input voltage 12V, 24V or 48V
Vmin (cut-off) 10.5V± 0.5V, 21V±1V, 42V±2V
Vmax (cut-off) 15V± 0.5V, 30V±1V, 60V±2V
Output voltage 220V
Output frequency 50Hz
THD <3%
USB Output DC 5V +/-5% 500mA
Notes External fuse
Protection Overheat, Low-High voltage, Short-Circuit,
Polarity
Certificates CE, ISO9001, RoHS
112
8.11 KENTT 201E Refrigerator Datasheet
Kentt 201E uses a SOKO HEKOM AE 1336A compressor made in Yugoslavia.
The refrigerator is constituted by a start-up winding to create a flux 90º in space relatively to the main
winding and supplied by a current with a 90º offset in time, Îaux (Figure 8.12 b). This phase offset
difference is obtain through a resistor, an inductance or a condenser in series with the starting winding
which is disconnected after the motor has started (Figure 8.12 a).
a)
b)
Figure 8.12 - Capacitor-start motor a) connections and b) phasor diagram at starting [60]
The single phase induction motor may be seen as one stator winding and two imaginary rotor windings.
One rotor is rotating in forward direction (direction of rotating magnetic field) with slip s, while other is
rotating in backward direction (direction of oppositely rotating magnetic field), with slip 2 - s. The
oppositely rotating mmfs have the same magnitude. The equivalent circuit of a single-phase induction
motor is the circuit in next figure:
Type 200
Model 201 E
Gross Capacity 200 l
Available Capacity 179 l
Freezer Capacity 14 l
Voltage (frequency) 230V (50Hz)
Suction/Pressure 10/30 bar
Power 90 W
113
Figure 8.13 - Single-phase equivalent circuit with core losses [61]
The upper part of the circuit represents the forward-moving and the lower part the backward mmf.
𝐸𝐹 – voltage associated with the forward mmf
𝐸𝐵 – voltage associated with the forward mmf
𝐸 = 𝐸𝐹 + 𝐸𝐵 – voltage applied to the stator
𝑟1 𝑎𝑛𝑑 𝑗𝑥1 – stator resistance and stator leakage reactance
𝑟2 𝑎𝑛𝑑 𝑗𝑥2 – rotor resistance and rotor leakage reactance referred to the stator
2𝑅𝑚 – total resistance of the winding, friction and iron losses
2𝑗𝑋𝑚 – total magnetizing reactance
𝑠 – slip
𝑍1 = 2𝑟1 + 2𝑗𝑥1 – total stator impedance
114
8.12 Sony KV-14LT1E 13’’ Color TV Datasheet
TV System B/G/H
Colour System PAL; SECAM, NTSC 3.58, 4.43
(only video in)
Channels
VHF E2-E12
UHF E21-E69
CATV S1-S20
HYPER S21-S41
Sound 1 x 6W (musical)
1 x 3W (RMS mono)
Weight 11.5 Kg
Energy consumption 42 W
Standby consumption ≤0.55 W
Dimensions 393 x 358 x 415 mm
115
8.13 IST Meteorological station
The IST meteorological station is located at Latitude 38.736º, Longitude -9.138º, Altitude 90m (+49m)
on the top of south tower and is equipped with a CR10X data logger from Campbell Scientific, Inc. The
station records in 5 min time period the data is constituted by32:
1. Air temperature [ºC];
2. Real fell temperature [ºC];
3. Relative humidity [%];
4. Wind velocity [km/h];
5. Wind direction;
6. Precipitation [mm];
7. Air pressure [hPa];
8. Total solar irradiance on a horizontal plane [W/m²].
8.14 Temperature Logger Tiny Tag Talk 2 – TK-4014
©Tinytag Talk 2s is a compact, lightweight, economical logger housed in a 35mm film canister. With
©Tinytag Explorer Software all the data may be analysed, stored and exported.
8.15 Economic Evaluation Indicators
To understand if an investment is worth it is important to study its economic viability. Some of the
indicators regularly used are presented below. It is more correct to refer this indicators as previsions
once the future is always unknown. The solar panels and batteries are expensive compared to diesel
generators however PV panels require less maintenance and have a long lifetime. A system initially
more expensive may prove to be more economical at the end of its lifetime requiring a study more
detailed.
8.15.1 Net Present Value (NPV)
Net present value is a calculation used to determine the present value of an investment by the
discounted sum of all cash flows (monetary flux) received from the project. In other words, the amount
32 IST Institutional meteorological station website: http://meteo.ist.utl.pt/odata-now
Reading range -40ºC to +85ºC
Sensor type 10K NTC Thermistor (internally mounted)
Total Reading
Capacity
16 000 readings
Reading resolution 0.05ºC or better
Logging interval 1sec to 10 days
Stop options When full
After n readings
Never (overwrite oldest data)
116
invested is compared to the future cash amounts after they are discounted by a specified rate of return
where the period of time corresponds to the life time of the system in study.
In the simplified model assumptions: all the investment at t=0, the annual utilization of the installed
capacity is constant and equal to ℎ𝑎, the operation and maintenance expenses during the lifetime are
constant and equal to 𝑂&𝑀, there are no expenses with fuel and others or they are included in 𝑂&𝑀
expenses [4].
𝑁𝑃𝑉 = −𝐼𝑜 +∑𝑅𝐿𝑗
(1 + 𝑎)𝑡
𝑛
𝑡=1
(8.15)
where 𝐼𝑜 is the initial investment, 𝑛 is the lifetime of the project, 𝑅𝐿𝑗 is the total income for each year
which is given by the income subtracted to the 𝑂&𝑀 expenses and 𝑎 is the rate of return.
The decision based on the NPV is done according to the following conditions:
NPV<0 – the investment is not returned, once the project should be rejected;
NPV=0 – the investment is returned exactly at a rate of return 𝑎 that allows the investor to pay
its initial investment, however there is no profits;
NPV>0 – the investment is returned at a given rate of return 𝑎 and generates profits equal to
the NPV making the project attractive.
8.15.2 Internal Rate of Return (IRR)
The internal rate of return is the rate of return that makes the NPV equal to zero, in other words the
project allows to return the investment [4].
∑𝐸𝑥𝑝𝑙𝑜𝑟𝑎𝑡𝑖𝑜𝑛 𝑐𝑎𝑠ℎ𝑓𝑙𝑜𝑤
(1 + 𝐼𝐼𝑅)𝑗
𝑛
𝑗=1
−∑𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 𝑐𝑎𝑠ℎ𝑓𝑙𝑜𝑤
(1 + 𝐼𝐼𝑅)𝑗
𝑛−1
𝑗=0
= 0⇔
∑𝑅𝐿𝑗
(1 + 𝐼𝐼𝑅)𝑗
𝑛
𝑗=1
−∑𝐼𝑗
(1 + 𝐼𝐼𝑅)𝑗
𝑛−1
𝑗=0
= 0
(8.16)
The IRR measures the interest of the project on the financial market evaluation scale what does not
happen with the previous indicators. If the IRR is higher than the rate of return considered in the NPV
calculation means that the project generates a profitability higher than the opportunity capital cost. In
this situation the project should be economically viable.
8.15.3 Payback Period
The payback period is the time (years) necessary to return the investment during the exploration of the
project. It more elaborated than the payback calculation. An approximate way to calculate the payback
period is to consider the annual mean income during the lifetime of the project. In this case the formula
is given by [4]:
117
𝑃𝑎𝑦𝑏𝑎𝑐𝑘 𝑃𝑒𝑟𝑖𝑜𝑑 = 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 𝑐𝑎𝑠ℎ𝑓𝑙𝑜𝑤
∑𝐸𝑥𝑝𝑙𝑜𝑟𝑎𝑡𝑖𝑜𝑛 𝑐𝑎𝑠ℎ𝑓𝑙𝑜𝑤
(1 + 𝑎)𝑗𝑛𝑗=1
𝑛
=
∑𝐼𝑗
(1 + 𝑎)𝑗𝑛−1𝑗=0
(
∑
𝑅𝐿𝑗(1 + 𝑎)𝑗
𝑛𝑗=1
𝑛
)
≅𝐼𝑡
(
∑
𝑅𝐿𝑗(1 + 𝑎)𝑗
𝑛𝑗=1
𝑛
)
(8.17)
The project is accepted when the payback period is shorter than its lifetime. In a photovoltaic project
connected to the grid, the payback period is usually between the 6 to 8 years of exploration.