medsolar training course module 1 - cedro-undp.org · the objectives to be met in the sizing of a...

MEDSolar Training Course

Module 3

Power Plant Design

Herminio Martínez-García

Department of Electronics Engineering

Barcelona College of Industrial Engineering (EUETIB)

Technical University of Catalonia - BarcelonaTech (UPC)

The objectives to be met in the sizing of a photovoltaic system are:

• Operate efficiently at the lowest possible cost.

• Be able to meet the expected demand for electricity

consumption.

• Match, as far as possible, the PV system to the consumption

characteristic.

• Setting the nominal voltage of the photovoltaic system.

• Proper sizing of photovoltaic module (in Wp).

• Dimensioning suitable battery (in Ah).

• Ensure proper connections and protections of the

installation.

• Proper implementation and ensure appropriate

maintenance measures.

Introduction (I)

Introduction (II)

DC Grid

(normally

lighting)

Batteries

(they accumulate the energy to

be used at times of low or no

sunshine )

AC Grid

(used to supply

different

appliances)

PV

Modules

or Panels

Inverter

(it converts the

direct current DC

into alternating

current AC)

Regulator

(it controls the

charge of

batteries, and

converters the

DC voltage from

PV modules into

another DC

voltage)

Solar collection

area (m2)

Storage capacity

(Ah)

Total losses of the

installation

Inst. amortization

& profitability

Energy demand or

electricity

consumption

(Wh/day)

Available solar

radiation energy

(MJ/m2)

Total monthly and

annual solar

production

Efficiency of PV

solar panels

Input Data Output Data

Other Data of InterestVoltages of interest

(in panels and

installation)

Introduction (III)

Dimensioning of

DC/DC controller

(A)

Dimensioning of

the DC/AC

inverter (W)

Sections of Wiring

Consumption of Electrical Equipment and Supplies (I)

When the size of a PV facility is carried out, it’s necessary to check the

consumption of all electrical, electronic and electrical appliances to be

connected to the aforementioned PV facility.

This consumption is usually stated on the nameplate of the

equipment or manufacturer’s catalog.

If you do not have these real data, approximate tables should be used.

Due to the high involved consumption, in PV facilities, it is not

recommended to use electric heating equipment such as electric

ovens, microwave, radiators, hot water washers, dryers, electric

water heaters, etc.

They may be substituted for thermal applications, that have better energy

efficiency.

In addition, we recommend using energy-efficient appliances, since

consumption, size and investment of the PV facility is reduced.

Consumption of Electrical Equipment and Supplies (II)

Information Labeling About Energy Efficiency (I)

Energy Efficiency Label. Old Labeling

Moderate or medium

energy consumption

High energy

consumption

High energy

efficiency

More efficient

Less efficient

Between 110% and 125%

Higher than 125%



Between 75% and 90%

Between 55% and 75%

Between 42% and 55%

Between 30% and 42%

Energy consumption higher than 30% of the average

Information Labeling About Energy Efficiency (II)

Examples of Energy Efficiency Label. For refrigerators and freezers.

An improved method for sizing a solar photovoltaic installation process consists

of:

• Determination of the nominal operating voltage for the system.

• Estimation of demand or overall power consumption of the facility (in

Ah/day).

• Loss assessment of photovoltaic solar installation.

• Choosing the optimum inclination of the photovoltaic panels.

• Calculation of daily total solar radiation received by month for that

angle.

• Panel model selection and determination of the electrical parameters

(nominal power, voltage, efficiency, etc.) provided.

• Calculation of the total number of modules in parallel and in series.

• Calculation of the total capacity of the storage batteries.

• Sizing regulator (DC/DC converter).

• Sizing the inverter (DC/AC converter).

• Sizing of wiring required for installation.

• Summary table of values over the 12 months.

Improved Design Guide in the Sizing of PV Systems

Application Example (I)

Autonomous PV Systems with DC and AC Loads.

Regulator

(voltage regulation subsystem)

DC Consumption

AC Consumption

Batteries

(accumulation subsystem)

Inverter

(DC into AC

conversion subsystem)

PV Modules or Panels

(generation subsystem)

Mountain house, near the Lleida Pyrenees (Spain), where conventional

electricity available is expensive by distance.

Installation consisting of:

• PV panels.

• DC/DC regulator.

• DC/AC converter.

• Storage batteries.

In the design study, we will explain the need of including a generator or a

wind turbine support.

Application Example (II)



Ah/day).




angle.










Nominal Operating Voltage.

• As it is a domestic house, we can choose nominal voltages equal

to 12 V, 24 V, 48 V or 120 V.

• We can select 24 V, in order to obtain lower section for the

wiring that connect PV panels and DC-DC regulator.

In general, it is recommended:

• 12 V: For power lower than 1.5 kW.

• 24 V: For powers between 1.5 kW and 5 kW.

• 48 V or 120 V: For power higher than 5 kW.

• > 120 V: For high power plants.

As in our design example, the consumption is near 1.5 kW (see following

consume tables), we can select a 24-V nominal voltage, in order to

minimize wiring current.

Important: Having a higher voltage, makes that wiring that connect

PV panels and regulator may have smaller section.

Determination of the Nominal Operating Voltage for the System


• Estimation of demand or overall power consumption of the facility

(in Ah/day).




angle.










DC Energy Consumption of the Facility (in Wh/day).

Energy Consumption of DC Equipments

Equipment, Device or

Electrical Appliance

Power

(W)

Nº

of Units

Functioning

(h/day)

Consumption

(Wh/day)

Spotlights in the

Dining Room20 1 3 60

Spotlights in the

Kitchen11 1 2 22

Spotlights in the

Bathroom11 1 1 11

Spotlights in the

Bedroom11 × 3 = 33 3 2 66

Refrigerator 60 1 12 720

TOTAL 135 879

Estimating the Demand of Electricity for the Facilities (I)

AC Energy Consumption of the Facilities (in Wh/day).

Total Energy Consumption, Etotal, of the Facility (Wh/day).

Energy Consumption of AC Equipments

Equipment, Device or Electrical

Appliance

Power

(W)

Nº

of Units

Functioning (h/day) Consumption

(Wh/day)

TV 50 1 4 200

Small

Appliances

200 1 2 400

Washing Machine 500 1 4 h @ week 285.7

TOTAL 750 885.7

879 / 885.7 /

1764.7 /

total DC AC

total

E E E Wh day Wh day

E Wh day

Estimating the Demand of Electricity for the Facilities (II)

Total Net Energy Consumption Required by the Facility, Ctotal

(Ah/day).

Connection Energy Losses, Closs (Ah/day). As a first approximation,

one may choose a value between 10% and 20%, depending on the desire

safety margin. Taking 10% in our case:

Total Energy Consumption Needed or Required, Creq (Ah/day).

1764.7 /73.53 /

24

total

total

nom

E Wh dayC Ah day

V V

107.353 /

100loss totalC C Ah day

73.53 / 7.35 / 80.88 /

req total loss

req

C C C

C Ah day Ah day Ah day

Estimating the Demand of Electricity for the Facilities (III)



Ah/day).




angle.










We can carry out an estimation of total losses of the facility, KT, thanks

to:

Being:

,

1 1 A aut

T B C R X

D max

K DK K K K K

P

Loss Estimation of the Photovoltaic Solar Facility (I)

Daily losses due to battery self-discharge,given at 20 C.

Losses due to battery efficiency.

Losses due to the inverter (DC/AC converter) efficiency (if any).

Losses due to the regulator (or

A

B

C

R

K

K

K

K

,

DC/DC converter) efficiency.

Other not considered losses (Joule efect, due to voltage drops, etc.).

Days of autonomy of the installation.

Maximum deep of discarge (DoD) (in %).

X

aut

D max

K

D

P

KA: It usually comes in the datasheets provided by the battery

manufacturer. Its default value is 0.5%. However, very common values

of 0.6% and 0.7% are also very common. The range is between 0.1% and

2%.

KB: This loss is due to the battery energy dissipated as heat due to the

chemical processes in its charge and discharge cycles. It usually has a

value of 5%, but can be chosen a value of 10% for old batteries,

strong discharges or low temperatures. The margin ranges is between

0.0% and 20%.

KC: The default value typically ranges between 5% (DC/AC converter’s

efficiency of 95%) and 20% (efficiency of 80%). The margin ranges is

between 0.0% and 40%.

KR: It usually depends on the technology used, but, if it is not known, the

default value is chosen 10% (DC/DC converter’s efficiency of 90%).

KX: A default value of 10% is chosen. The margin range is between 0.0%

and 20%.

Loss Estimation of the Photovoltaic Solar Facility (II)

Estimation of the total losses of the facility, KT:

,

1 1 A aut

T B C R X

D max

K DK K K K K

P

Loss Coefficient or Loss Parameter Practical Range

KA 0.001 – 0.020 (0.1% – 2%)

KB 0.00 – 0.20 (0.0% – 20%)

KC 0.00 – 0.40 (0.0% – 40%)

KR 0.00 – 0.40 (0.0% – 40%)

KX 0.00 – 0,20 (0,0% – 20%)

PD,max 0.10 – 0.80 (10% – 80%)

Daut 3 – 20 days

Loss Estimation of the Photovoltaic Solar Facility (III)

Daut: It is the number of consecutive days, in the absence of sunlight, that

the storage system is able to meet consumption without exceeding the

maximum depth of discharge of batteries.

It depends, among other factors, on the type of facility, climatic or

weather conditions, etc.

As a general rule, the MINIMUM autonomy of PV systems with

storage is 3 days.

Loss Estimation of the Photovoltaic Solar Facility (IV)

The number of autonomy days in the system depends on its use and

application:

• Areas with regular Sun: 3 days.

• Non-critical systems (Mediterranean climate, etc.): Between

2 and 5 days.

• Systems with irregular Sun: 5 to 7 days.

• Critical systems (professional systems): 5 to 10 days.

• Critical areas, with little sunshine: 15 days.

Loss Estimation of the Photovoltaic Solar Facility (V)

Necessary days of autonomy for critical and non-critical PV systems

operation vs. minimum available peak sun hours.

Loss Estimation of the Photovoltaic Solar Facility (VI)

(PSH)

A linear approximation to the data in previous Fig. yields the following

equations for estimating necessary storage days, based on minimum

average peak sun hours over the year, PSH:

… providing that PSH>1 h.

However, we can find tables showing (for instance, according to the

Spanish provinces) the days of autonomy.

These values are, in some cases, oversized.

1.9 18.3 for critical applications.

0.48 4.58 for non-critical applications.

aut

aut

D PSH

D PSH

Loss Estimation of the Photovoltaic Solar Facility (VII)

Depth of discharge (DOD) of a battery is defined as the percentage of

its capacity that has been “removed” from it, compared to full-charge

capacity.

PD,max is the maximum DOD allowed before disconnecting the regulator

to prevent from possible problems and to lengthen its lifetime.

It depends, among other factors, on the type or battery technology:

• Nickel-cadmium batteries (Ni + Cd): 1%.

• Lead batteries (or lead-acid) (Pb): 40%.

• Lead-calcium batteries (Pb + Ca): 50%.

• Lead-antimony batteries (Pb + Sb): 70%.

You should avoid, if possible, very deep discharge (greater than 60%

or 70%).

In any case, the maximum recommended for PD,max is 80%.

Loss Estimation of the Photovoltaic Solar Facility (VIII)

PD,max is the maximum discharge allowed to the battery before

disconnecting the regulator to protect it.

The maximum depths of discharge that are usually considered for a

daily cycle (maximum daily DOD) are around 15-20%.

In the case of seasonal cycle, which is the maximum number of days

that a battery can be discharged without receiving enough solar

radiation on the modules, is around 4-15 days, and a depth of discharge

of approximately 70%.

Loss Estimation of the Photovoltaic Solar Facility (IX)

Estimation of the total losses of the facility, KT:

,

1 1 A aut

T B C R X

D max

K DK K K K K

P

Loss Coefficient or Loss Parameter Practical Range

KA 0.001 – 0.020 (0.1% – 2%)

KB 0.00 – 0.20 (0.0% – 20%)

KC 0.00 – 0.40 (0.0% – 40%)

KR 0.00 – 0.40 (0.0% – 40%)

KX 0.00 – 0,20 (0,0% – 20%)

PD,max 0.10 – 0.80 (10% – 80%)

Daut 3 – 20 days

Loss Estimation of the Photovoltaic Solar Facility (X)

Total Energy Consumption Needed or Required Considering the

losses, C’req (Ah/day). In the case at hand:

73.53 / 7.35 / 80.88 /

80.88 /' 147.44 /

0.549

req

req

req

T

C Ah day Ah day Ah day

C Ah dayC Ah day

K

,

1 1 A aut

T B C R X

D max

K DK K K K K

P

0.005 12 days

1 0.05 0.15 0.10 0.10 1 0.5490.7

TK

Loss Estimation of the Photovoltaic Solar Facility (XI)



Ah/day).




angle.










Selection of the Angle of Inclination of the PV Panels.

• We can choose to set an “empirical” inclination that guarantees

plenty of sunlight on photovoltaic panels; for example, 60º.

Other alternatives are to perform any of the methods developed.

The best known are:

• ‘Critical month criterion’. It attempts to optimize the

consumption/radiation ratio in each month, and keep the data

of the worst month.

• ‘Annual maximum energy harvesting criterion’. It aims to

optimize the consumption/radiation relationship, not in the

critical month, but over a year, taking into account the annual

average global solar radiation.

Choosing the Optimum Inclination of the Photovoltaic Panels

Inclination or tilt angle of a PV module:

Solar radiation

Inclination

(tilt angle)

PV

module

Horizontal ground

Determination of the Suitable Tilt Angle for Photovoltaic Panels (I)

Some guidelines recommend an inclination equal to the

latitude, obtaining a value of annual average global solar

radiation slightly higher.

However, it is advisable to increase this inclination 10º, since

the distribution of solar contributions in the worst months

(winter) is better.

Determination of the Suitable Tilt Angle for Photovoltaic Panels (II)

sunlight in

winter

sunlight in

summer

Moreover, the inclination is calculated taking into account the period of

use of the facility. It is recommended that:

• 10º higher than the latitude to use facilities throughout the year

(e.g., for solar collectors in domestic hot water, DHW).

• 5º below the latitude to use facilities in summertime (e.g.,

outdoor pools or season hotels).

• 15º – 20º higher than the latitude to facilities for exclusive use

in winter season (e.g., ski resorts).

Minor differences in slope do not significantly influence the total annual

energy, but can determine a higher or lower average global solar

radiation in the winter months.

Determination of the Suitable Tilt Angle for Photovoltaic Panels (III)

In this case, the calculation of the optimum inclination of the receiving

surface will be such that the energy consumption/radiation ratio is

optimized for every month.

The procedure is as follows:

• Firstly, we must have an array with the values of global solar

radiation received for each month (usually measured in

kWh/m2), and for different inclinations.

• Secondly, from previous table, daily average

consumption/global solar radiation ratio is determined; i.e.,

the daily average consumption for each month, will be divided

by the values of each cell of previous table.

Optimum PV Panel Tilt Angle According to Critical Month Criterion (I)

For instance, for a particular place, we can have the following global

solar radiation received for each month and for different inclinations:

Optimum PV Panel Tilt Angle According to Critical Month Criterion (II)

Month

If we supposed a daily average consumption Lmd=3000 Wh/day, we have

this new table:

Optimum PV Panel Tilt Angle According to Critical Month Criterion (III)

Month

Then, we have to do the following two calculations:

• Step 1: For each tilt angle, the maximum ratio will be taken

up, thereby obtaining the critical month (for each given tilt

angle).

• Step 2: From all previous maximum values, we chose the

minimum of them, so that solar energy harvesting in the

critical month is maximized…

• … That is, it is chosen the optimum inclination for the worst

month, so that the tilt angle for the worst month is optimized.

Optimum PV Panel Tilt Angle According to Critical Month Criterion (IV)

Therefore, it is example, the optimum tilt angle for the PV modules

should be 40º.

Optimum PV Panel Tilt Angle According to Critical Month Criterion (V)

Month

Optimum Inclination According to Annual Maximum Energy Harvesting Criterion (I)

In this case, the aim is to determine the optimal inclination of the

receiving surface so that the consumption/radiation ratio is optimized,

not for critical month, but over a year.

We will proceed very similarly to the previous case, except that we take

into account only the overall annual average radiation (the average of the

twelve monthly values) for each inclination, and consumption, which in

this case is the annual average consumption.

Continuing with data from the previous example, the source table in this

case is similar to the following:

Annual

Average

The consumption/radiation ratio will be:

Finally, the optimum value will be the minimum:

The optimal tilt angle (inclination) will be, using this criterion, 10º.

Optimum Inclination According to Annual Maximum Energy Harvesting Criterion (II)

Annual

Average

Annual

Average



Ah/day).



• Calculation of daily total solar radiation received by month for

that angle.










Determination of Monthly Solar Radiation for the Inclination

Obtained.

• As in the case studied for solar thermal systems (CENSOLAR

tables).

• Tables using solar radiation as a function of inclination.

• http://re.jrc.ec.europa.eu/pvgis/

Anyway, differences between these methods in order to obtain solar

radiation should be minimal.

Sources for Determination of Solar Radiation on a Geographic Point

Irradiance and Solar Radiation

The irradiance is the instantaneous power of solar radiation received per

unit area, expressed in the corresponding SI unit (W/m2).

The irradiation or solar radiation (H) is the energy incident per unit area

in a given time.

The irradiation H corresponds to the integration of the irradiance in a

given period:

If the second one is considered constant, we have:

The units most commonly used for irradiation H are the kWh/m2 or

MJ/m2.

Over one day, as shown in tables, H is expressed in kWh/m2/day, or

MJ/m2/day.

H Irradiance t

1

0

t

H Irradiance dt

Orientation: South

Units: KJ/m2/day

Place: Lleida (Spain)

Latitude: 41º 41

Calculation of Solar Radiation Monthly Available (Method A)

In the particular case considered here, and using book tables [Tobajas-

2008], for an inclination of 60º, we have the following solar radiation

values:

http://re.jrc.ec.europa.eu/pvgis/

Calculation of Solar Radiation Monthly Available (Method B) (I)

Calculation of Solar Radiation Monthly Available (Method B) (II)

Calculation of Solar Radiation Monthly Available (Method B) (III)

Calculation of Solar Radiation Monthly Available (Method B) (IV)

Calculation of Solar Radiation Monthly Available (Method B) (V)

Correction of the Incident Solar Energy on Solar Panels (I)

The resulting value of E may be corrected to take account of

the actual orientation of the panels.

If the deviation in orientation of the panels is less than 20°,

it is not necessary to make any corrections.

If the deviation is greater than 20º (but always less than

70º), the power available by the PV modules must be

reduced in value that can be estimated, approximately, with

the following expression:

0.3Orientation Losses 0.71 0.29 cos 0.95

It is the inclination angle of the PV modules (in º).

It is the deviation of the orientation of the PV panel

relative to the South direction (in º).

South

Direction

Correction of the Incident Solar Energy on Solar Panels (II)




0.3Orientation Losses 0.71 0.29 cos 0.95

For example, if the PV panels’ inclination is α=51º, and the

deviation of the orientation of the panels, relative to the

South, is β=30º, then we have:




Correction of the Incident Solar Energy on Solar Panels (III)

0.3

0.3

Orientation Losses 0.71 0.29 cos 0.95

0.71 0.29 cos 0.95 30 51

0.71 0.29 0.04724 0.6973



Ah/day).




angle.

• Panel model selection and determination of the electrical

parameters (nominal power, voltage, efficiency, etc.) provided.








Selection of the PV Module. For instance, the commercial model

ATERSA’s A-150M.

Selection of the PV Module for the Application (I)

Nominal Power (W)

Maximum Power Point Current (Imp)

Maximum Power Point Voltage (Vmp)

Short-Circuit Current (Isc)

Open-Circuit Voltage (Voc)

Energy Provided by the Group of Photovoltaic Modules (PV

Generator). The energy (in Ah/día) provided by the array of

photovoltaic modules, Emod, is given by:

Being:

( )mod mod mpE I PSH

Energy provided by the PV module (in / ).

Efficiency of the PV module. It can be chosen a typical valuen between 85% and 95%.

Current at the module's MPP (in ).

Peak solar hou( rs)

mod

mód

mp

E

I

P

Ah día

A

SH

(in ) for an inclination of the PV module.h

Selection of the PV Module for the Application (II)

The parameter ηmod represents an overall loss factor that provides

reduction in the energy provided by such factors as:

• Dirt of the photovoltaic module and opacity of the glass.

• Reflection losses at times of very oblique incidence.

• Effect losses wiring.

• Etc.

For photovoltaic panels ...

• For monocrystalline and polycrystalline Si, ηmod can be caught

between 90% and 95%.

• For amorphous Si, between 65% and 85%.

Selection of the PV Module for the Application (III)

The ‘peak solar hour’ or ‘peak sun hour’ (PSH) is a parameter that

measures the “effective” or “net” solar radiation, and is defined as the

time in hours of a hypothetical constant irradiance of 1000 W/m2.

The PSH of a locality is the number of hours that should have an

irradiance of 1000 W/m2 to meet the real daily energy incident in

that locality.

For example, a radiation energy or equal to 3500 Wh/day equals an

irradiance of 1000 W for 3.5 h; so that PSH=3.5.

The Peak Solar Hour (PSH) for Obtaining the Provided Energy (I)

If a graph is shown of incident radiation on the earth’s surface, it appears

that levels vary throughout the day.

Graphically, the PSH is interpreted as a function of constant value that

delimits the same area as aforementioned distribution.

1000 W/m2

The Peak Solar Hour (PSH) for Obtaining the Provided Energy (II)

Peak Solar Hours

Irra

dia

nc

e

Day hours

1 PSH is equal to 3.6 MJ/m2 or, what is the same, 1 kWh/m2, as shown

in the following conversion:

After obtaining the value of the PSH, we can calculate how much daily

power theoretically we can get from the PV panels multiplying the power

by the PSH, although different correction factors must also be

considered.

Moreover, we must also have into account that, depending on the angle

of the PV panels, the amount of PSH we will vary.

We can get better performance depending on it.

2 2

1000 3600 1 /1 1 3.6

1 1

W s J s MJPSH h

h Wm m

The Peak Solar Hour (PSH) for Obtaining the Provided Energy (III)

From the solar radiation, H (expressed in kJ/m2/day), we have the

equivalent PSH, at a certain inclination α, which can be obtained as:

2/( ) ( ) 0.0239 0.0116

kJ mPSH H

day

2

2

2 2

/( )

/ 1( ) ( )

3600 3600

kJ mH

daykJ m PSHPSH H

day kJ m kJ m

2

2

2 2

/( )

/ 1( ) ( )

1000 1000

W mH

dayW m PSHPSH H

day W m W m

The Peak Solar Hour (PSH) for Obtaining the Provided Energy (IV)

In the present example, the monthly PSH can be obtained from the daily

solar radiation as:

/day

The Peak Solar Hour (PSH) for Obtaining the Provided Energy (V)

Orientation: South

Units: Kj/m2/day

Place: Lleida (Spain)

Latitude: 41º 41

Month Jan. Feb. Mar. Apr. May. Jun. Jul. Aug. Sep. Oct. Nov. Dec. Avg.

H(0º)

kJ/m2

6.078 12.168 15.592 19.226 21.954 24.262 24.638 21.340 16.740 11.980 6.302 4.006

H(60º)

kJ/m2

11.148 20.092 19.136 18.106 17.258 17.496 18.406 18.694 18.516 17.234 10.652 8.314

HSP(60º)

(h/day)3,097 5,581 5,316 5,029 4,794 4,860 5,113 5,193 5,143 4,787 2,959 2,309 4,515



Ah/day).




angle.



• Calculation of the total number of modules in parallel and in

series.







Possible Interconnections of Photovoltaic Modules

If the total set voltage exceeds 75 VDC, notice that it could be dangerous

for people.

Parallel connection.

Series connection. Mixed connection.

Number of Photovoltaic Modules in Parallel, nPP. The required

number of panels in parallel will be the ratio between the energy

consumption required to meet the needs Creq (in Ah/day), divided by the

energy (also in Ah/day) from the photovoltaic panel set, Emod:

Being:

' '

( )

req req

PP

mod mod mp avg

C Cn

E I PSH

Nº of PV panels connected in parallel to meet energy needs.

Total energy consumption required to cover energy needs (in / ).

Energy provided by a single PV module (in / ).

Eff

'

PP

req

mod

mod

A

n

C h day

AE h día

iciency of the PV module. It can be select a value between 85% and 95%.

Current at the MPP of the PV module (in ).

Annual average PSH (in ) for the inclination angle o( ) f the PV module.

mp

avg

I

P

A

S hH

Determining the Number of Photovoltaic Modules in Parallel (I)

Taking the average value of PSH, PSHavg, and not the monthly value, and

considering a photovoltaic panel ηmod=90%, the required number of

panels in parallel will be:

With that, we need 9 panels in parallel.

When the number of rows in parallel is not an integer, it is

recommended to round up, except in those cases where the result

approximates closely to the nearest integer number.

' 147.44 /8.25 modules

( ) 0.9 4.40 4.515 /

8.25 modules 9 modules

req

PP

mód mp avg

PP PP

C Ah dayn

I PSH A h day

n n

Determining the Number of Photovoltaic Modules in Parallel (II)

Number of Photovoltaic Modules in Series, nPS. The required number

of panels connected in series will depend on system nominal voltage,

Vnom, and the PV module MPP (maximum power-point) voltage, Vmp:

Being:

nom

PS

mp

Vn

V

Nº of panels connected in series to meet the nominal voltage of the system.

Nominal voltage of the system (in ).

MPP voltage provided by a single PV module (in ).

PS

nom

mp

n

V

V

V

V

Determining the Number of Photovoltaic Modules in Series (I)

The number of modules in series is calculated based on the nominal

system voltage, Vnom, and the voltage at the maximum power point

(MPP), Vmp, of the selected PV module:

Thus, following with the example, we need a single panel in series.

240.71 panels 1 panel

34

nom

PS PS

mp

V Vn n

V V

Determining the Number of Photovoltaic Modules in Series (II)

Total number of PV modules, ntotal. It will be the product of the number

of panels in parallel, nPP, by the number of panels in series, nPS:

In our case:

Therefore, the connectivity scheme of the photovoltaic modules required

for the facility is designed as shown:

9 1 9 panelstotal PP PSn n n

total PP PSn n n

Determining the Total Number of Photovoltaic Modules of the Facility

To the DC-

DC

regulator

PV module

block 1

PV module

block 2

PV module

block 3

PV module

block 9

+

–



Ah/day).




angle.










Nominal Capacity and Discharge Rate of a Battery (I)

The battery capacity is the amount of electricity that can supply

(measured in Ah), and it is given under a discharge rate.

Therefore, a battery capacity is determined based on the duration of

discharge, and this value is provided by the manufacturer for a duration

of 10 h (C10). This value is often called ‘nominal capacity’.

However, according to some public European Institutions, the ‘nominal

capacity’ is the amount of charge that can be drawn from a battery in 20

h, measured at a temperature of 20 °C, until the voltage between its

terminals reaches 1.8 V/battery cell.

According to these public European Institutions, for other rates can be

used the following empirical relationships:

• C100/C20 ≈ 1.25.

• C40/C20 ≈ 1.14.

• C20/C10 ≈ 1.17.

The parameters that define the capacity of a battery are:

• Discharge time (h).

• Discharge current (A).

• Operating temperature (°C).

• Final voltage (V).

The ‘charge rate’ (or ‘discharge rate’) is the ratio Cn/I (measured in

hours).

For example, a battery with Cn=300 Ah, that provides a discharge current

of 5 A, has a discharge rate of 60 h ...,

whereas if it provides 10 A, the discharge rate is 30 h.

Therefore:

disc discC t I

Nominal Capacity and Discharge Rate of a Battery (II)

However, previous equation is completely ideal:

In the practice, we have the named Peukert equation or relation

(originally introduced by the German W. Peukert in 1897 for lead-acid

batteries, and defines one of the most important parameters to evaluate

the performance of a battery):

… where the parameter ‘k’ is the named Peukert constant or

coefficient, that depends on the battery type used.

Typically, it can be selected k=1.2, but it is important to know the

manufacturing technology of the battery.

disc discC t I

k

disc discC t I

disc k

disc

Ct

I

The larger the parameter ‘k’ and current, we

get further away from the ideal value tdisc.

Nominal Capacity and Discharge Rate of a Battery (III)

For instance:

• k = 1.05 – 1.15 for VRSLAB AGM batteries.

• k = 1,10 – 1.25 for gel batteries.

• k = 1.20 – 1.60 for flooded batteries.

AGM (VRLA): In AGM (Absorbed Glass Mat) batteries, the electrolyte

is contained in the absorbent fiberglass between the plates. This

technology based on regulated valve, has low maintenance because it

requires no water refill.

Gel (VRLA): In gel batteries (technology dryfit), the electrolyte is

contained in a gel suspension between the plates. This valve regulated

technology is low maintenance because it requires filling of water.

Liquid electrolyte or lead open: Lead-acid batteries have elements with

liquid electrolyte, and they are available in flat and tubular plate with a

wide variety of plate sizes.

Nominal Capacity and Discharge Rate of a Battery (IV)

Autonomous PV facilities are usually provided with an autonomy

between 5 and 15 days, approximately.

Therefore, in PV applications, the battery capacity is defined by its

ability to deliver a given charge in 20 h, 100 h, or 120 h, at 25 °C,

called C20, C100, and C120, respectively.

The more intense the discharge of a battery, less energy is able to

provide.

Fortunately, in PV systems, no aggressive discharges are required, but

rather progressive.

Thus, batteries are often used to discharge in 100 h (C100).

In addition, capacities are usually specified with discharge times of 100

h, because the autonomy of 5 or more days, the discharge would occur,

for example, in 24 h/day × 5 days = 120 h.

Thus, by default, 100 h is then chosen (C100).

Nominal Capacity and Discharge Rate of a Battery (V)

Notice that the capacity of a battery depends also on the temperature,

apart from the discharge rate.

The battery capacity decreases due to the temperature, especially

for T<20 °C.

The reference temperature to give the battery capacity is usually 25 ºC.

Thus, if the temperature is different, it should be corrected.

An approach to the correction factor in order to obtain a discharge

capacity for a temperature different to 25 °C is given by the following

table:

Temperature (in ºC) –20 –10 0 +10 +20 +25 +30 +40

Correction factor for a

discharge rate of 120 h0.58 0.72 0.83 0.91 0.98 1.00 1.02 1.05

Nominal Capacity and Discharge Rate of a Battery (VI)

1160

T

Tk

If the average operation

temperature is below 20 ºC, it

is recommended to correct

calculated nominal capacity,

by dividing its value by a

factor kT:

Nominal Capacity and Discharge Rate of a Battery (VII)

Temperature (in ºC) –20 –10 0 +10 +20 +25 +30 +40

Correction factor for a

discharge rate of 120 h0.58 0.72 0.83 0.91 0.98 1.00 1.02 1.05

% Capacity

Temperature (ºC)

Dependency of the capacity vs. temperature

Calculating the Total Capacity of Storage Batteries. It is determined

by the needs of the system, taking into account the days of autonomy,

according to:

Where:

,

'100

req aut

alm

D max

C DC

P

,

Nominal capacity of the accumulation system (in ).

Total energy consumption required to cover energy needs (in / ).

Days of autonomy for the PV system.

Maximum depth of disc

'

h

alm

req

aut

D max

Ah

Ah a

D

P

d y

C

C

arge (in %).

Calculation of the Required Accumulation System (I)

Nº of Batteries in Series, nBS. It is determined as a function of the

nominal voltage of the system, and the nominal voltage provided by a

single battery.

Nº de Batteries in parallel, nBP. It is determined as a function of the

total capacity of the accumulation system, and the nominal capacity

provided by a single battery:

Where:,

nom

BS

bat nom

Vn

V

,

Nº of batteries connected in series to obtain the nominal voltage of the system.

Nominal voltage of the installation (in ).

Nominal voltage of a single battery (in ).

Nº of batter

BS

nom

bat nom

BP

V

V

n

V

V

n

,

ies connected in parallel to provide the required consumption.

Nominal capacity of the accumulation system (in ).

Nominal capacity of a single battery (in ).

alm

bat nom

hC

C

A

Ah

,

alm

BP

bat nom

Cn

C

Calculation of the Required Accumulation System (II)

In the case that we have, for a DOD of 70%, we have:

Thus, we need an accumulation system with a 24-V nominal voltage, and

a total capacity around 2500 Ah (approximately).

Choosing a battery model with enough capacity, as the model 2 YS 31P

from the manufacturer Surrette/Rolls, with 2430 Ah @ 20 h, and a

nominal voltage of 2 V, we will need 1 single battery in parallel, and 12

batteries in series:

,

' 147.44 / 12100 2527.54

0.7

req aut

alm

D max

C D Ah day daysC Ah

P

,

2412 battery

2

nom

BS

bat nom

V Vn

V V

,

2527.541.04 1 battery

2430

alm

BP BP

bat nom

C Ahn n

C Ah

Calculation of the Required Accumulation System (III)

Calculation of the Required Accumulation System (IV)

To the

DC-DC

regulador

(24 V)

Battery 1

(2 V)

+

–

Battery 2

(2 V)

Battery 12

(2 V)

Battery subsystem connectivity scheme required for the designed PV

facility, consisting of 12 batteries, each of 2 V.

Calculation of the Required Accumulation System (V)

When the voltage across the battery is the same as that of a basic cell,

typically from 2 V, the battery is often called ‘element’.

When the accumulation subsystem is formed by a set of elements, these

must be connected in series and/or parallel to obtain the voltage and/or

the storage capacity required.

Batteries that are not single ‘elements’, often have a typical voltage of 12

V across its terminals, and are known as ‘monoblock’ or simply

‘batteries’.

In a similar way that elements, type ‘monoblock’ batteries must be

connected in series and/or parallel in order to obtain the voltage and/or

storage capacity required.

Calculation of the Required Accumulation System (VI)

The most recommended kind of batteries for this type of PV systems is

lead-acid stationary, with cells of 2 V each.

They are arranged in series to complete the typical voltages of 12 V, 24

V, 48 V or more, which will be adequate in each case and application.

In addition, they will be associated in parallel to obtain the total required

capacity.

These batteries can stay charged longer periods of time, and they

withstand deep discharges sporadically.

Calculation of the Required Accumulation System (VII)

Calculation of the Required Accumulation System (VIII)



Ah/day).




angle.










The regulator controls the charging of the storage subsystem (batteries)

from the PV array, and its discharge to the load.

The performance characteristics that define a regulator or DC/DC

converter are:

• The nominal DC output voltage (in V).

• The nominal input current from the generator (in A).

• The nominal output current to the load (in A).

• The efficiency at nominal power (in %).

Sizing of the Required DC-DC Regulator (I)

Sizing of the DC-DC Regulator. The regulator is determined by the

maximum current supplied by PV solar panels.

The maximum current delivered by the array of PV modules is the

controller input (considering a security increase of 20% –safety

coefficient of 1.2–):

Being:

1.2G PP mpI n I

Current at the MPP provided by a PV module (in ).

Efficiency of the PV module. It can be selected a typical value between 85% and 95%.

Maximum power provided by the PV module (in ).

Vo

mp

mod

mp

mp

I

P

V

A

W

ltage at the MPP provided by the PV module (in ).

Maximum current provided by the PV array (in ).

Nº of PV modules connected in parallel to cover the facility's needs.

G

PP

V

AI

n

mod mp

mp

mp

PI

V

Sizing of the Required DC-DC Regulator (II)

It should be taken into account the total load current from the known

powers:

Where:

If there are no efficiency data for the inverter, an acceptable estimation is

85%.

Total load power (in ).

Total DC-load power (in ).

Total AC-load power (in ).

Nominal DC voltage of the system (in ).

Total load current (in ).

Efficency of the inverter or

total

DC

AC

nom

L

inv

P

P

P

V

W

W

W

V

AI

DC/AC converter (in %).

DC AC

L

nom inv nom

P PI

V V

total DC ACP P P

Sizing of the Required DC-DC Regulator (III)

From these two currents, the maximum of both will be that the regulator

must support:

Sizing of the Required DC-DC Regulator (IV)

,reg G LI max I I

DC Energy Consumption of the Facility (in Wh/day).

Energy Consumption of DC Equipments

Equipment, Device or

Electrical Appliance

Power

(W)

Nº

of Units

Functioning

(h/day)

Consumption

(Wh/day)

Spotlights in the

Dining Room20 1 3 60

Spotlights in the

Kitchen11 1 2 22

Spotlights in the

Bathroom11 1 1 11

Spotlights in the

Bedroom11 × 3 = 33 3 2 66

Refrigerator 60 1 12 720

TOTAL 135 879

Sizing of the Required DC-DC Regulator (V)

AC Energy Consumption of the Facilities (in Wh/day).

Total Energy Consumption, Etotal, of the Facility (Wh/day).

Energy Consumption of AC Equipments

Equipment, Device or Electrical

Appliance

Power

(W)

Nº

of Units

Functioning (h/day) Consumption

(Wh/day)

TV 50 1 4 200

Small

Appliances

200 1 2 400

Washing Machine 500 1 4 h @ week 285.7

TOTAL 750 885.7

879 / 885.7 /

1764.7 /

total DC AC

total

E E E Wh day Wh day

E Wh day

Sizing of the Required DC-DC Regulator (VI)

In our example, these values give:

Or we must select a regulator that can support 47.52 A at its input

terminals and 42.39 A at its output.

If necessary, we can add different regulators, connected in groups of PV

panels (all of the same model).

1.2 1.2 9 4.40 / 47.52G PP mpI n I panels A panel A

135 7505.63 36.76 42.39

24 0.85 24

DC AC

L

nom inv nom

P P W WI A A A

V V V V

, 47.52 , 42.39 47.52reg G LI max I I max A A A

Sizing of the Required DC-DC Regulator (VII)



Ah/day).




angle.










Performance characteristics that define an inverter or DC/AC converter

are:

• Output waveform (sinusoidal, rectangular, trapezoidal, etc.).

• Nominal power (in kW).

• Nominal DC input voltage (in V).

• Nominal AC output voltage (in V).

• The operating frequency (in Hz).

• Efficiency at nominal power (in %).

The input voltage to the inverter is NOT always constant; thus it should

be able to convert different DC voltages within a certain range (about

15%).

The nominal power should be slightly higher than the maximum power

demanded by the output load.

If it is much higher than the demanded by the load, the converter

efficiency will drop significantly.

Sizing of the Required DC-AC Inverter (I)

In general, we can use the following expression for the sizing of the

inverter:

Where:

If there is no efficiency data, an acceptable estimated value is 85%.

AC

inv

inv

PP

Power required for the DC/AC converter (in ).

Total power consumed by the AC loads (in ).

Efficiency of the inverter (en %).

inv

AC

inv

W

P W

P

Sizing of the Required DC-AC Inverter (II)

Critical efficiency

region

Optimal efficiency

region

Sizing of the Required DC-AC Inverter (III)

The nominal power should be

slightly higher than the maximum

power demanded by the output load.

If it is much higher than the

demanded by the load, the converter

efficiency will drop significantly.

Sizing of the Required DC-AC Inverter (IV)

Sizing of the Required DC-AC Inverter (V)

Sizing of the Required DC-AC Inverter (VI)

In our example case, we have:

Thus, we need an inverter of 1 kW, approximately.

750882.35

0.85

AC

inv

inv

P WP W

Sizing of the Required DC-AC Inverter (VII)



Ah/day).




angle.










An improper sized wiring of the electrical circuit leads:

• A voltage drop excessive across the wiring. It will increase the losses

in the system.

• A temperature increase in the wiring. It will cause a fire hazard, and a

deterioration of insulating materials that will involve a risk of short

circuits.

In PV facilities, two different wiring must take into account:

• Wiring for DC circuitry. Because we usually have low voltages,

currents by wiring are greater than in 230 V-AC circuits. Thus, these

cables are typically thick, especially for 12-V installations.

• Wiring for AC circuitry. Although we have high voltages (230 V), the

currents through the wiring is lower than in the DC section. In addition,

it could be added cos(φ) for reactive loads (motors, pumps, etc.).

Sizing Wiring Required for the Photovoltaic Facility (I)

Conditions that the wiring sizing must meet:

• Maximum voltage drop. Limited by national regulations.

• Heating of the conductor at the maximum allowable current.

The maximum admissible temp. will be: T=70 °C for

thermoplastic insulation, and T=90 °C for thermosets.

• Short circuit current. This current should not exceed the

maximum allowable temp.

In a general case, the conductor section that simultaneously meets the

three conditions above must be installed in the calculated line.

However, in a PV facility, the 3rd condition is not applicable because the

PV panels self-limiting its maximum current value to ISC.

In addition, ISC is the maximum permissible current value to meet the 2nd

condition.

Sizing Wiring Required for the Photovoltaic Facility (II)

The resistance of an power line, Rlin, and its section, S, may be obtained

by following expressions:

Where:

2 1 2lin

U L LR

I S S

2

Total electrical resistance ("round trip") of the lines (in ).

Total voltage drop of the line (in ).

Current flowing through the line (in ).

Resistivity of the electrical material (in

lin

V

A

m

R

U

m

I

2

2

/ ).

Conductivity of the electrical material (in /( )).

Wiring lenght (only "one way") (in ).

Wiring section (in ).

L

m

m m

m

S

m

mm

2LI

SU

Sizing Wiring Required for the Photovoltaic Facility (III)

The resistivity of Cu and Al, at 20 °C, are, respectively:

• ρCu=0.0168 Ω·mm²/m ~ 0.0175 Ω·mm²/m.

• ρAl=0.0265 Ω·mm²/m.

And the conductivity of Cu and Al, also at 20 ° C, are respectively:

• σCu=59.5 m/Ω·mm² ~ 55.6 m/Ω·mm².

• σAl=37.7 m/Ω·mm².

It is recommended that the currents obtained for calculating

sections is increased by 20% ~ 25% to ensure that both the wiring

and protection elements operate below the 80% capacity.

It is necessary to specify outside cables, resistant to degradation by

sunlight.

Consider the option of conduit cables.

Consider possible correction terms due to Tª effect, if cables are

exposed to T>30 °C.

Sizing Wiring Required for the Photovoltaic Facility (IV)

Admissible voltage drop in typical conductors for general facilities.

In domestic uses (housing), in general, the voltage drop should be below

3%.

Circuit % of voltage drop admissible

Panels – Regulator 3% – 5%

Regulator – Batteries 0.5% – 1%

Regulator – Inverter 0.5% – 1%

Batteries – Inverter 0.5% – 1%

Regulator – DC Loads 3%

Inverter – AC Loads

(according to some European

regulations)

3% (housing)

5% (industries)

Sizing Wiring Required for the Photovoltaic Facility (V)

Maximum Currents Allowable According to the Section for Bipolar

Cables with Cu Conductors Insulated with Rubber or PVC. As an

approximate orientation, we have:

Sizing Wiring Required for the Photovoltaic Facility (VI)

Nominal Section

(mm2)

Current

(A)

Nominal Section

(mm2)

Current

(A)

0.75 8 10 44

1.0 10.5 16 59

1.5 13 25 78

2.5 18 35 97

4.0 25 50 115

6.0 32 70 140

The maximum current provided by the PV panel at the input terminals of

the regulator will be (considering a security increasing of 20%):

Being:

1.2G PP mpI n I

Current at the MPP provided by the PV panel (in ).

Efficiency of the PV panel. It can be chosen a typical value between 85% & 95%.

Maximum power provided by the PV panel (in ).

Voltage

mp

mód

mp

mp

A

W

I

P

V

at the MPP provided by the PV panel (in V).

Current provided by the PV generator set (in ).

Nº of panels connected in parallel to meet the energy needs.

G

PPn

AI

mód mp

mp

mp

PI

V

Sizing Wiring Required for the Photovoltaic Facility (VII)

Autonomous PV Systems with DC and AC Loads.

Imód-reg

IL,DC

Ireg-inv IL,AC

Ireg-bat

ΔUmód-reg

ΔUL,DC

ΔUL,AC

ΔUreg-bat

ΔUreg-inv

Smód-reg

Sreg-bat

SL,AC

SL,DC

Sreg-inv

Sizing Wiring Required for the Photovoltaic Facility (VIII)

Regulator

(voltage regulation

subsystem)

DC Consumption

AC Consumption

Batteries




Inverter

(DC into AC


In our case, we have the following currents, considering a security factor

of 20%, in order to avoid of arriving to the maximum current capability

and subsequent wiring heating:

1.2 1.2 9 4.40 / 47.52mod reg G PP mpI I n I panels A panel A

, 1.2 5.63 6.75L DCI A

1.2 36.76 44.12reg invI A A

,

7501.2 1.2 3.26 3.91

230L AC

WI A A

V

47.52reg bat mod reg GI I I A

Sizing Wiring Required for the Photovoltaic Facility (IX)

Wiring length that exists and permitted voltage drops in the different

existing sections between the elements of the PV system:

ΔU=5%

ΔU=3%

ΔU=3%

ΔU=0.5%

ΔU=0.5%

L=8 m

L=20 m

L=1 m

L=1 m

L=35 m

Sizing Wiring Required for the Photovoltaic Facility (X)

Regulator

(voltage regulation

subsystem)

DC Consumption

Batteries




Inverter

(DC into AC


AC Consumption

In our case:

Normalized Europe sections used for the wiring of the electrical facilities

are:

Circuit Vnom

(DC o AC)

(V)

ΔV

(%)

U

(V)

Length L

(m)

Current I

(A)

Obtained

Section

(mm2)

Normalized

Section

(mm2)

Panel – Regulator 24 V 5% 1.2 V 8 47.52 A 11.40 mm2 16 mm2

Regulator – Battery 24 V 0.5% 0.12 V 1 47.52 A 14.24 mm2 16 mm2

Battery/Regulator –

Inverter

24 V 0.5% 0.12 V 1 44.12 A 13.23 mm2 16 mm2

DC Grid 24 V 3% 0.72 V 20 6.75 A 6.74 mm2 10 mm2

AC Grid 230 V 3% 6.9 V 35 3.91 A 0.713 mm2 1.5 mm2

2 · ²2 0.0359

55.6 / · ²

LI LI mm LIS

U m mm U m U

Sizing Wiring Required for the Photovoltaic Facility (XI)

1,5 mm2 – 2,5 mm2 – 4 mm2 – 6 mm2 – 10 mm2 – 16 mm2 – 25

mm2 – 35 mm2 – 50 mm2 – 70 mm2 – 95 mm2 – 120 mm2 – 150

mm2 – 185 mm2 – 240 mm2 – 300 mm2

Sizing Wiring Required for the Photovoltaic Facility (XII)

Wiring sections obtained by previous general equation corresponds to a temp =

27 °C (300 K).

To ensure that this section is valid even if the wiring temp, at full load and at

steady state, was the maximum allowable under these conditions, the value

initially obtained by the mentioned calculations should be increased according to

the following table:

Isolation

Type

Maximum

Allowable

Temperature

Section

Increasing

Thermoplastic

Thermostable

For DC circuits, color code to be used is:

• Red. Para el positive (+) pole.

• Black. For the negative (–) pole.

And for AC circuits, the color code to be used is:

• Black, brown or gray. For the phase conductors (L).

• Blue. For the neutral conductor of the installation (N).

• Bicolor (yellow and green). For the ground conductor of the

electrical facility (GND).

Sizing Wiring Required for the Photovoltaic Facility (XIII)



Ah/day).




angle.










Resume Table of the Photovoltaic Facility Designed

Jan. Feb. Mar. Apr. May. Jun. Jul. Aug. Sep. Oct. Nov. Dec.

DC Voltage (V) 24 24 24 24 24 24 24 24 24 24 24 24

Consumption (Wh/day) 1764.7 1764.7 1764.7 1764.7 1764.7 1764.7 1764.7 1764.7 1764.7 1764.7 1764.7 1764.7

Consumption without losses

(Ah/day)73.53 73.53 73.53 73.53 73.53 73.53 73.53 73.53 73.53 73.53 73.53 73.53

Consumption with losses

(Ah/day)147.44 147.44 147.44 147.44 147.44 147.44 147.44 147.44 147.44 147.44 147.44 147.44

Rad. H(60º) (kJ/m2/day) 11,148 20,092 19,136 18,106 17,258 17,496 18,406 18,694 18,516 17,234 10,652 8,314

PSH (for 60º) 3.097 5.581 5.316 5.029 4.794 4.860 5.113 5.193 5.143 4.787 2.959 2.309

Ah/module·day 12.26 22.10 21.05 19.91 18.98 19.25 20.25 20.56 20.37 18.96 11.72 9.14

Nº required mod., nPP 12.03 6.67 7.00 7.41 7.77 7.66 7.28 7.17 7.24 7.78 12.58 16.13

Nº installed modules

(nPP·nPS)9·1 9·1 9·1 9·1 9·1 9·1 9·1 9·1 9·1 9·1 9·1 9·1

Ah provided 110.38 198.91 189.46 179.23 170.86 173.21 182.23 185.08 183.30 170.61 105.46 82.29

Deficit or surplus (Ah) -37.06 51.47 42.02 31.79 23.42 25.77 34.79 37.64 35.86 23.17 -41.98 -65.15

Autonomy days, Daut 12 12 12 12 12 12 12 12 12 12 12 12

PD,máx 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7

Battery Capacity, Calm

(Ah)2527.5 2527.5 2527.5 2527.5 2527.5 2527.5 2527.5 2527.5 2527.5 2527.5 2527.5 2527.5

MEDSolar Training Course

Module 3

Power Plant Design

Thank You for Your Attention!

Herminio Martínez-García

Department of Electronics Engineering

Barcelona College of Industrial Engineering (EUETIB)

Technical University of Catalonia - BarcelonaTech (UPC)

medsolar training course module 1 - cedro-undp.org · the objectives to be met in the sizing of a...

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