1 establishment and study of a photovoltaic system with the mppt function

Establishment and Study of a Photovoltaic System with the MPPT Function


Ting-Chung Yu Yu-Cheng Lin Department of Electrical Engineering

Lunghwa University of Science and Technology

Abstract

The main purpose of this paper is to develop a photovoltaic simulation system with maximum power point tracking (MPPT) function using Matlab/Simulink software in order to simulate and evaluate the behaviors of the real photovoltaic systems. A model of the most important component in the photovoltaic system, the solar module, is the first to have been established. The characteristics of the established solar module model were simulated and compared with those of the original field test data under different weather conditions. After that, a model of a photovoltaic system with maximum power point tracker, which was developed by DC-DC buck-boost converter with two different MPPT algorithms respectively, was then established and simulated. According to the comparisons of the simulation results, the I-V curves of the established solar module model could closely match those of the original field test data, and the model of the photovoltaic system that was built in this paper can track the maximum power point of the system successfully and accurately using two different MPPT algorithms respectively under arbitrary temperature and irradiance conditions. The accuracy and practicability of the proposed photovoltaic simulation system are, therefore, validated. Keywords: Photovoltaic simulation system, solar module, maximum power point tracking

(MPPT), DC-DC buck-boost converter.

1. Introduction As reported in the literature, the

amount of traditional energy such as petroleum and coal has been gradually becoming insufficient to meet demands. The problem of a looming energy crisis has stimulated rapid development of the renewable energy to accommodate requirements worldwide as economies continue to grow and develop. In all kinds of renewable energy technologies, photovoltaic technology is one of the best renewable energy technologies because it wont produce noise, air pollution or greenhouse gases.

Most of the photovoltaic simulation systems proposed in literature [1][4] were established using hardware and software to perform and simulate the operation of

equipment in the system such as solar modules, maximum power point trackers, PWM controllers, DC-DC converters, and so on. Y. Yusof, S. Sayuti and M. Wanik [1] proposed a solar cell model that simulated the maximum power and I-V curve diagram of the proposed model using C language. However, it is hard to connect the proposed solar cell model to the other equipment in the photovoltaic system model. C. Hua, J. Lin and C. Shen [3] used DSP to implement their proposed MPPT controller, which controls the DC/DC converter in the photovoltaic system. K.H. Hussein, I. Muta, T. Hoshino and M. Osakada [4] also used hardware to implement an incremental conductance algorithm to track the maximum power. The main distinguishing feature of this

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,2011.12 paper is to establish a model for the photovoltaic system with maximum power point tracking function that solely uses software simulation. This simulation system could predict and evaluate the behaviors of a real photovoltaic system without using any hardware equipment. Two commonly used algorithms are used to implement the MPPT function of the system, and are discussed later.

This paper includes 6 sections. The rest of this paper is organized as follows. Section 2 introduces the characteristics of solar modules and shows the relationship of current and voltage for the solar modules along with the variations of irradiance and temperature. Section 3 interprets the modeling of the DC-DC buck-boost converter. Sections 4 introduces and explains two MPPT algorithms used in the paper, section 5 shows the simulation results of the proposed photovoltaic simulation system, and the last section is the conclusion of this paper.

2. Characteristics of a Solar

Module The basic structure of solar cells is to

use a p-type semiconductor with a small quantity of boron atoms as the substrate. Phosphorous atoms are then added to the substrate using high-temperature diffusion method in order to form the p-n junction. In the p-n junction, holes and electrons will be rearranged to form a potential barrier in order to prevent the motion of electrical charges.

When the p-n structure is irradiated by sunlight, the energy supplied by photons will excite the electrons in the structure to produce mobile hole-electron pairs. These electrical charges are separated by the potential barrier at the p-n junction. The electrons will move towards the n-type semiconductor and the holes will move towards the p-type semiconductor at the same time. If the n-type and p-type semiconductors of a solar cell are connected with an external circuit at this moment, the electrons in the n-type semiconductor will move to the other side

through the external circuit to recombine with the holes in the p-type semiconductor. The above phenomenon shows how currents of the external circuit generate.

Because the output voltage of a solar cell is extremely low (about 0.50.7V), solar cells have to be connected in series and in parallel in practical applications first in order to obtain a higher terminal voltage. After connection, solar cells have to be strengthened by a supported substrate and covered by tempered glass to comprise the solar module (Fig. 1). After this, solar modules can be connected in series and in parallel to create a solar array according to capacity demands. At present solar modules are combined with architecture, such as walls and rooftops, in order to achieve the broadest development.

Each solar cell can be represented as a structure consisting of a photocurrent source, diode and resistors. Therefore, the equivalent circuit of a solar module [5], [6] can be shown in Fig. 2.

From the equivalent circuit shown in Fig. 2, the relationship between output voltage and output current of the solar module is as follows [5], [6]:

PM

SMPVBPVBkTnNRIVq

oPphPVB RRIVeINII S

SMPVBPVB

)1()(

(1) with IPVB: output current of the solar module

(A). VPVB: output voltage of the solar module

(V). Iph: current source of the solar module by

solar irradiance (A). Io: reverse saturation current of a diode (A). NP: parallel connection number of the solar

module. NS: series connection number of the solar

module. n: ideality factor of the diode (n = 1~2). q: electric charge of an electron

( 19106.1 C). k: Boltzmann's constant ( J/K1038.1 23 ). T: absolute temperature of the solar cell

(K). RSM and RPM are the internal series

resistance and parallel resistance,

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respectively, of the solar module. Since the value of RSM is usually small and the value of RPM is usually very large, RSM and RPM are negligible under ideal conditions. In order to make the simulation results more realistic in this paper, RSM and RPM are considered to be included in an equivalent circuit. The equation of the photocurrent source can be expressed as

PM

SMSCMkTnNRqI

oPSCMph RRIeINII S

SMSCM

)1( (2)

With ISCM being the short-circuit current of a solar module.

Fig. 1. Diagram of a solar module

Fig. 2. The equivalent circuit of a solar module

Since the open-circuit voltage and short-circuit current of the solar module are dependent on the variation of irradiance and temperature, the equation of open-circuit voltage and short-circuit current of the solar module can be derived from the following expressions:

)(1000 refC

SCBSCM TT

ISI (3)

)( refCOCBOCM TTVV (4) with ISCM: short-circuit current of the solar

module ISCB: short-circuit current of the solar

module under the conditions of reference temperature and 1000W/m2.

VOCM: open-circuit voltage of the solar module.

VOCB: open-circuit voltage of the solar module under the conditions of reference temperature and 1000W/m2.

S: solar irradiance (W/m2). Tref: reference temperature of the solar

module (25oC). TC: temperature of the solar module. : temperature coefficient of the

short-circuit current for the solar module (mA/ oC).

: temperature coefficient of the open-circuit current for the solar module (V/ oC).

The output power of the solar module can be expressed as follows:

PM

SMPVBPVBPVBkTnNRIVq

oPVBPphPVBPVBPVBPVB RRIVVeIVNIVIVP S

SMPVBPVB )()1()(

(5) In the following section,

Matlab/Simulink is used to set up the solar module model as well as to simulate the I-V curve and the output power of the solar module according to the equations derived above. The test solar module used in this paper is HIP-200NHE1 (Heterojunction with Intrinsic Thin Layer), manufactured by Sanyo Electric Company. The electrical parameters of the test solar module were measured by Sanyo Electric Company under the reference conditions (AM1.5, irradiance of 1000W/m2 and temperature of 25oC) as shown in Table 1.

Table 1 Electrical Parameters of the Sanyo HIP-200NHE1 Solar Module

Parameter Value

Maximum power (Pmax) 200 (W)

Max. power voltage (Vmp) 40.0 (V)

Max. power current (Imp) 5.00 (A)

Open-circuit voltage (VOC) 49.6 (V)

Short-circuit current (ISC) 5.50 (A)

Temperature coefficient of ISC 1.65 (mA/oC)

Temperature coefficient of VOC -0.129 (V/ oC)

Fig. 3 shows the comparisons of I-V

curves for simulation results and original field test data of the test solar module under fixed temperature of 25oC and the

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,2011.12 variation of solar irradiances. Fig. 4 shows the comparisons of I-V curves for simulation results and original field test data of the test solar module under fixed irradiance of 1000W/m2 and a variety of temperatures. According to Fig. 3 and Fig. 4, the simulated I-V curves of the proposed solar module model in this paper match very closely the measured I-V curves of Sanyos field test data under different irradiance and temperature conditions. The proposed solar module is, therefore, validated to be accurate and practicable.

Fig. 3 Comparisons of the I-V curves of the test solar module under fixed temperature and different irradiance conditions

Fig. 4. Comparisons of the I-V curves of the test solar module under fixed irradiance and different temperature conditions

3. Modeling of the DC-DC Buck-

Boost Converter Generally speaking, the output voltage

of a typical photovoltaic system is usually

less than that of its load. Therefore, a DC-DC boost converter is used as the maximum power point tracker in most photovoltaic systems. In order to extend the applicability of the proposed photovoltaic simulation system, a DC-DC buck-boost converter is used as the maximum power point tracker in the proposed photovoltaic system model.

A DC-DC buck-boost converter is a switched-mode device that periodically cycles the operation of an electrical switch on and off. The output voltage of this converter can be greater or less than the input voltage of the converter. A DC-DC buck-boost converter with a maximum power point tracking algorithm can adjust the output voltage of the solar module in order to operate on maximum power point in the photovoltaic system.

The circuit diagram of the DC-DC buck-boost converter is shown in Fig. 5 [7], [8]. The rL and rC shown in Fig. 5 represent the parasitic resistors of inductor L and capacitor C respectively. The DC-DC buck-boost converter used in this paper is operated in continuous current mode (CCM), and the parasitic components are also included in the converter model to conform realistic circuit operation.

The power switch Q is an electronic switch, usually a field effect transistor (MOSFET) or, at higher power levels, an insulated gate bipolar transistor (IGBT). This switch is able to switch on and off at high speed, with low resistance when on and very high resistance when off. The power switch operation can be divided into two states: A. The power switch Q is turned on

When the power switch Q is turned on, the diode is cutoff due to reverse-biased voltage. The equivalent circuit of the converter is shown in Fig. 6.

The state-space equation of DC-DC buck-boost converter can be derived in the following section. According to Kirchhoff's voltage law, the voltage across the inductor L can be expressed as

LLinL riVv (6)

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SincedtdiLv LL , (2) can be modified to

LLinL riVLdtdi

1 (7)

According to Kirchhoff's current law, the current of the capacitor C can be expressed as

C

CRC rR

vii

(8)

Equation (8) can be modified to

C

CC

rRv

Cdtdv

1 (9)

The output voltage of the converter can be expressed as

CC

o vrRRV

(10)

Fig. 5. The circuit of the DC-DC buck-boost converter

Fig. 6. The equivalent circuit of the DC-DC buck-boost converter when the power switch is closed

B. The power switch Q is turned off

When the power switch Q is turned off, the diode is conducted due to forward-biased voltage. The equivalent circuit of the converter is shown in Fig. 7. According to Kirchhoff's current law, the current of the inductor L can be expressed as

R

rdt

dvCv

dtdvCiii

CC

CC

RCL

(11)

Equation (11) can be modified to

CC

LC

C vrR

irR

RCdt

dv 11 (12)

According to Kirchhoff's voltage law, the loop voltage of the inductor L and capacitor C can be expressed as

0 CCCLLL rivdtdiLri (13)

Equation (13) can be rearranged to

C

CL

C

CLCLL vrR

RirR

RrrrRrLdt

di 1 (14)

The output voltage of the converter can be expressed as

CC

LC

Co vrR

RirR

RrV

(15)

Fig. 7. The equivalent circuit of the DC-DC buck-boost converter when the power switch is opened

By mixing in switching control parameter u and rearranging (7), (9), (12) and (14), the derivative of iL and vC can be expressed as

CLLCC vuRiRi

rRCdtdv

1 (16)

]})([1{1 uRvRviRrrrRruiRrrR

uVLdt

diCCLCLCLLC

Ci

L

(17) When the DC-DC buck-boost

converter operates in steady-state, the net change of the inductor current over one period should be zero; that is,

0 offLonL ii (18) 01)( L

TDVLDTV oin (19)

The output voltage of the converter can be derived from (19) and is expressed as

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,2011.12

ino VDDV

1

(20)

withTt

tttD on

offon

on

; 10 D ; D is the

duty ratio. The Vin and Vo in (20) indicate

magnitudes of input and output voltage, respectively, of the converter. According to Figs. 5 to 7, the output voltage Vo has opposite polarity of the input voltage Vin. Output voltage magnitude of the buck-boost converter could be greater or less than the source voltage, depending on the duty ratio of the switch. If D > 0.5, Vo is greater than Vin. If D < 0.5, Vo is less than Vin.

The operation of the DC-DC buck-boost converter used in this paper is in CCM, the minimum inductance and capacitance designed to generate continuous current can be expressed as [8]

f

RDL2

1 2min

(21)

)/(min oo VVRfDC

(22)

witho

o

VV : output voltage ripple

In order to verify the correctness of the DC-DC buck-boost converter model proposed in this paper, a test case is performed in the following section. The input voltage of the test case is 40V, and the output voltages are set to be 60V and 20V respectively. The load resistance, switching frequency and output voltage ripple are set to be 50, 25Hz and 1% respectively. The minimum value of inductance and capacitance of the converter can be calculated by (21) and (22).

The appropriate parameters chosen for the DC-DC buck-boost converter in the test case are listed in Table 2. The converter simulation results for voltage step-up and voltage step-down are shown in Fig. 8. According to Fig. 8, it can be observed that the buck-boost converter can transform the source voltage to 60V (voltage step-up) and 20V (voltage step-down) successfully.

The correctness of the DC-DC buck-boost converter model is therefore validated.

Table 2 Parameters of the DC-DC Buck-Boost Converter

Parameter Value Input voltage (Vin) 40.0 (V) Load resistance (R) 50 ()

Inductance (L) 0.16 (mH) Capacitance (C) 48 (F)

Switching frequency (f) 25 (kHz)

Fig. 8. Output voltage of the DC-DC buck-boost converter

4. The Algorithms of Maximum

Power Point Tracking Perturbation and observation (P&O)

and incremental conductance (INC) algorithms are used in this paper respectively to implement the maximum power point tracking function [3], [9], [10], [11]-[15]. The advantages of these two power-feedback type MPPT algorithms include simple structure, less measured parameters and no need of measurement in advance. A. Perturbation and observation algorithm

By continuously perturbing the output power of the solar module, the P&O algorithm could find the location of maximum power point and send a control signal to the DC-DC buck-boost converter through a PWM controller to modulate the operating point of the solar modules. The basic theory of the P&O algorithm is to periodically vary the duty ratio in order to adjust the voltage across the solar module,

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and hence the module current and power. The magnitudes of output voltage and

power before and after the variations are observed and compared in order to determine that the output voltage of the solar module should be increased or decreased for the following perturbation step. By using the procedures of perturbation, observation and comparison again and again, the output power of the solar modules can then reach its maximum working point gradually. The power tracked by the P&O algorithm will oscillate and perturb up and down near the maximum power point. The magnitude of oscillations is determined by the magnitude of variations of the output voltage. The flow chart of the P&O algorithm is shown in Fig. 9.

Fig. 9. Flow chart of the P&O algorithm B. Incremental conductance algorithm

The theory of the incremental conductance method [11]-[14] is to determine the variation direction of the terminal voltage for PV modules by measuring and comparing the incremental conductance and instantaneous conductance of PV modules. If the value of incremental conductance is equal to that of instantaneous conductance, it represents that the maximum power point is found.

When the operating point of PV modules is exactly on the maximum power point, the slope of the power curve is zero (dP/dV = 0) and can be further expressed

as,

dVdIVI

dVdIV

dVdVI

dVVId

dVdP

)(

(23) By the relationship of dP/dV = 0, (23) can be rearranged as follows,

VI

dVdI

(24)

dI and dV represent the current and voltage variations before and after the increment respectively. The static conductance (Gs) and the dynamic conductance (Gd, incremental conductance) of PV modules are defined as follows,

VIGs (25)

dVdIGd (26)

The maximum power point (operating voltage is Vm) can be found when

mm VVsVVdGG (27)

When the equation in (24) comes into existence, the maximum power point is tracked by MPPT system. However, the following situations will happen while the operating point is not on the maximum power point:

)0 ,( ; dVdPGG

VI

dVdI

sd (28)

)0 ,( ; dVdPGG

VI

dVdI

sd (29)

Equations (28) and (29) are used to determine the direction of voltage perturbation when the operating point moves toward to the maximum power point. In the process of tracking, the terminal voltage of PV modules will continuously perturb until the condition of (24) comes into existence. Fig. 10 is the operating flow diagram of the incremental conductance algorithm.

In theory, INC algorithm can calculate and find the exact perturbation direction for the operating voltage of PV modules. However, the perturbation phenomenon is still happened near the maximum power point due to the less probability of meeting condition dI/dV =I/V.

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,2011.12

Fig. 10 Flow chart of the INC algorithm

5. Simulations of the Photovoltaic Systems

In order to verify and compare the effects of the two MPPT algorithms for the photovoltaic simulation system, some test cases are implemented under different irradiance, temperature and load conditions to observe whether the output power (load power) of the photovoltaic simulation system can reach the maximum power of the solar modules or not. The solar module used in the following test cases is the same as that used in Section 2. The schematic diagram of the photovoltaic simulation system is shown in Fig. 11.

Fig. 11 The schematic diagram of the photovoltaic simulation system

The weather conditions and load resistances used in the test cases are shown in Table 3. The simulation results of the test cases are shown in Fig. 12-20. Table 3 Weather conditions and load resistances of the test cases

Weather condition Case irradiance temperature Load

1 1000W/m2 25oC 10 2 700W/m2 30oC 15 3 400W/m2 20 oC 25

A. Perturbation and observation algorithm (a) Case 1

Fig. 12 Comparison of the output power with and without MPPT

Fig. 13 P-V curve of a solar module

(b) Case 2



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(c) Case 3



B. Incremental conductance algorithm (a) Case 1


(b) Case 2


(c) Case 3


Figs. 12, 14, 16 and 18-20 are comparison diagrams of output powers for the PV system with the two MPPT algorithms under different test conditions. Fig. 13, 15 and 17 are the P-V curve diagram of PV modules under each test condition, which are used to collate the tracking results simulated by the PV system. From Figs. 12, 14, 16 and 18-20, it can be observed that the output powers with MPPT algorithms are obviously greater than those without MPPT algorithms. After cross matching procedures, the output tracking powers of two MPPT algorithms can all approach the ideal maximum powers. They are very close to each other. It indirectly indicates and validates that the two MPPT algorithms used in this paper have considerable accuracy.

Figs. 21-23 illustrated the comparisons of output power of the PV system with P&O and INC algorithms under different test cases. Table 4 is the computer elapsed time when the PV simulation system is executed with the two MPPT algorithms under three different test conditions. According to the results of Figs. 21-23 and Table 4, it can be found that the tracking speed of the P&O algorithm is faster than that of the INC algorithm under all test cases. The tracking speed of the MPPT simulation systems is dependent not only on computer specifications, but also on perturbation sizes of MPPT algorithms. For P&O and INC algorithms, since both algorithms use voltage perturbations of PV modules to track the maximum power point, the tracking number will be close to each

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,2011.12 other based on the condition of the same perturbations. However, INC algorithm spends more time to track the maximum power point because of its complicated judgment procedure.

Fig. 21 Comparison of P&O and INC algorithms under case 1



Table 4 Comparison of the elapsed time for different MPPT systems

Computer elapsed time (s) Case 1 2 3

P & Q 0.0399 0.0396 0.0414 INC 0.0532 0.0528 0.0552

6. Conclusion The main purpose of this paper is to

establish a model for a photovoltaic system with maximum power point tracking function completely through the use of software techniques. A model of a solar module was first established and then combined with an MPPT algorithm, as well as models of a PWM controller and a DC-DC converter, in order to set up a complete photovoltaic simulation system. In order to extend the operation range of the photovoltaic simulation system, a DC-DC buck-boost converter with P&O and INC algorithms is used in this paper to implement the MPPT task.

The simulation results shown in the paper not only verify the accuracy of the characteristics for the established solar module model, but also prove that the photovoltaic simulation system can accurately track the maximum power point rapidly and successfully using two different MPPT algorithms respectively under different test conditions. The correctness and practicability of the pure software photovoltaic simulation system established in this paper are then validated.

By comparing the simulation results of P&O and INC algorithms, it can be found that P&O algorithm possesses faster dynamic response than INC algorithm owing to its simple judgment procedure in every perturbing period. However, INC algorithm has advantages of exact perturbing (ideal) and tracking direction, it is suitable for rapid changing weather conditions. References [1] Y. Yusof, S. Sayuti, M. Latif, and M.

Wanik, Modeling and simulation of maximum power point tracker for photovoltaic system, in Proceedings of Power and Energy Conference, pp. 8893, Nov. 2004.

[2] H.-L. Tsai, C.-S. Tu, and Y.-J. Su, Development of Generalized Photovoltaic Model Using MATLAB/SIMULINK,in Proceedings

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of the World Congress on Engineering and Computer Science, pp. 846854, Oct. 2008.

[3] C. Hua, J. Lin, and C. Shen, "Implementation of a DSP-controlled photovoltaic system with peakpower tracking," IEEE Transactions on Industrial Electronics, Vol. 45, no. 1, pp. 99107, Feb. 1998.

[4] K.H. Hussein, I. Muta, T. Hoshino, and M. Osakada, "Maximum photovoltaic power tracking: an algorithm for rapidlychanging atmospheric conditions," IEE Proceedings-Generation, Transmission and Distribution, Vol. 142, no. 1, pp. 5964, Jan. 1995.

[5] F. Lasnier, T. G. Ang, Photovoltaic Engineering Handbook, New York: IOP Publishing Ltd, 1990.

[6] L. Castaner and S. Silvestre, Modelling Photovoltaic Systems Using PSpice, West Sussex, England: John Wiley & Sons Ltd, 2002.

[7] M.H. Rashid, Power Electronics Circuits: Devices and Applications, 3rd edition, Upper Saddle River, NJ: Prentice-Hall, 2004.

[8] D.W. Hart, Introduction to Power Electronics, Upper Saddle River, NJ: Prentice-Hall, 1997.

[9] Y.-T. Hsiao and C.-H. Chen, Maximum Power Tracking for Photovoltaic Power Systems, in Proceedings of the IEEE 37th IAS Annual Meeting, vol. 2, pp. 10351040, Oct. 2002.

[10] M. El-Shibini and H. Rakha, Maximum Power Point Tracking Technique, in Proceedings of Electrotechnical Conference, pp. 2124, Apr. 1989.

[11] Jia-Chen Zhuang, Photovoltaic Engineering-Solar Cells, Chuan Hwa Book CO., LTD, Taipei, 1997.

[12] D. P. Hohm, M. E. Ropp, Comparative study of maximum power point tracking algorithms, Progress in Photovoltaics: Research and Applications, vol. 11, no. 1, pp. 4762, January 2003.

[13] T. Esram, P. L. Chapman,

Comparison of Photovoltaic Array Maximum Power Point Tracking Techniques, IEEE Transactions on Energy Conversion, vol. 22, no. 2, June 2007.

[14] Jae-Ho Lee, HyunSu Bae, Bo-Hyung Cho, Advanced incremental conductance MPPT algorithm with a variable step size, 12th International Conference on Power Electronics and Motion Control, 2006 (EPE-PEMC 2006), pp.603-607, Aug. 30-Sept. 1, 2006.

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1 establishment and study of a photovoltaic system with the mppt function

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