1

Abstract-- This paper proposes a MATLAB Simulink

simulator for photovoltaic (PV) system. The main contribution of this work is the utilization of the two-diode model to represent the PV cell. This model is known to have better accuracy at low irradiance level which allows for a more accurate prediction of PV system performance. To reduce computational time, the input parameters are reduced to four and the values of Rp and Rs are estimated by an efficient iteration method. Furthermore, all the inputs to the simulator are information available on standard PV module datasheet. The simulator supports large array simulation that can be interfaced with MPPT algorithms and power electronic converters. The accurateness of the simulator is verified by applying the model to two PV modules. It is envisaged that the proposed work can be very useful for PV professionals who require simple, fast and accurate PV simulator to design their systems.

Index Terms-- PV module; Multi-crystalline; STC; MATLAB Simulink.

I. INTRODUCTION arge and small scale PV power systems have been commercialized due to its potential long term benefits.

Their growth rates have been accelerated by the generous fed-in tariff schemes and other initiatives provided by various governments to promote sustainable green energy. In PV power generation, due to the high cost of PV modules, optimal utilization of the available solar energy has to be ensured. This requires an accurate, reliable and comprehensive simulation of the designed system prior to installation.

The most important component that affects the accuracy of the simulation is the PV cell modeling, which primarily involves the estimation of the non-linear I-V and P-V characteristics curves. By far, the simplest is the single diode model i.e. a current source in parallel to a diode. It only requires three parameters, namely short-circuit current (Isc), open circuit voltage (Voc) and diode ideality factor (a). This model is improved by the inclusion of one series resistance, Rs [1]−[5]. Despite its simplicity, it exhibits serious deficiencies when subjected to temperature variations. An extension of the model which includes an additional shunt resistance Rp

This work was supported in part by the Pusat Tenaga Malaysia (PTM)

under Grant 68704. Z. Salam is with the Universiti Teknologi Malaysia, Johor Bahru 81310

(e-mail: zainals@fke.utm.my). K. Ishaque is with the Universiti Teknologi Malaysia, Johor Bahru 81310

(e-mail: kashif@fkegradutae.utm.my). Hamed Taheri is with the Universiti Teknologi Malaysia, Johor Bahru

81310. 978-1-4244-7781-4/10/$26.00 ©2010 IEEE

[6]−[10]. Although significant improvement is achieved, this approach demands significant computing effort. Furthermore its accuracy deteriorates at low irradiance, especially in the vicinity of Voc.

For improved accuracy, the two-diode model (with Rp and Rs) is proposed [11]. The inclusion of the additional diode increases the parameters; the main challenge now is to estimate the values of all the model parameters while maintaining a reasonable simulation time. Several computational methods are proposed [12]−[15] but in all these techniques, new additional coefficients are introduced into the equations, increasing their computational burdens. Furthermore difficulty arises in determining the initial values of the parameters; in some cases heuristic solutions need to be sought. Another approach to describe the two-diode model is by investigating its physical characteristics such as the electron diffusion coefficient, minority carrier’s lifetime, intrinsic carrier density and other semiconductor parameters [16]−[19]. While these models are useful to understand the physical behavior of the cell, information about the semiconductor are not always available in commercial PV datasheets. Hence a useful PV simulator using such model is not feasible because in majority of the cases the PV designers are not equipped with the detail knowledge of semiconductor processes.

In this paper, an improved modeling technique for the two-diode model is proposed. The main contribution of this work is the simplification of the current equation, in which only four parameters are required. To compute the values of the series and parallel resistances, a simple and fast iterative method is used. The accurateness of the model is verified by manufacturer’s data. The performances of the model are compared against the single diode RS [2] and RP [10] models. It is envisaged that the proposed work can be very useful for PV power converter designer and circuit simulator developers who requires simple, fast and accurate model for the PV module.

II. MODELING A. PV Cell Modeling

A more accurate two diode model is depicted in Fig. 1 [11]. Equation (1) describes the output current of the cell:

1 2 ( )s

PV d dp

V IRI I I IR+= − − − (3)

where

1 011 1

[exp( ) 1]dT

V IRsI Ia V+= − (4)

and

Zainal Salam, Kashif Ishaque, and Hamed Taheri

An Improved Two-Diode Photovoltaic (PV) Model for PV System

L

2

2 022 2

[exp( ) 1]sd

T

V IRI Ia V+= − (5)

Where Io1 and Io2 are the reverse saturation currents of

diode 1 and diode 2, VT1 and VT2 are the thermal voltages of respective diodes. a1 and a2 represent the diode ideality constants. The Io2 term in (5), compensate the recombination loss in the depletion region as described in [20].

Figure 1. Two diode model of PV cell.

Although greater accuracy can be achieved using this

model, it requires the computation of seven parameters, namely IPV, Io1, Io2, Rp, Rs, a1 and a2. To simplify, several researchers assumed a1=1 and a2=2. The values are approximations of the Schokley-Read-Hall recombination in the space charge layer in the photodiode [39]. Although this assumption is widely used but not always true [21]. As discussed in the introduction section, many attempts have been made to reduce the computational time of this model. However they appear to be unsatisfactory. B. Improved Computational Method

1) Simplification of Saturation Current Equation: The equation for PV current as a function of temperature and irradiance can be written as:

_( )PV PV STC I

STC

GI I K TG

= + Δ (6)

Where

_PV STCI (in Ampere) is the light generated current at

STC, STCT T TΔ = − (in Kelvin, TSTC =25oC), G is the

surface irradiance of the cell and STCG (1000W/m2) is the

irradiance at STC. The constant Ki is the short circuit current coefficient, normally provided by the manufacturer. The well known diode saturation current equation is given as:

30 0,

1 1( ) exp[ ( )]gSTCSTC

STC

qETI IT ak T T

= − (7)

Where Eg is the band gap energy of the semiconductor and

0,STCI is the nominal saturation current. An improved equation to describe the saturation current which considers the temperature variation is given by [x]:

_0

,

( )exp[( ) / ] 1

sc STC I

oc STC V T

I K TI

V K T aV+ Δ

=+ Δ −

(8)

The constant Kv is the open circuit voltage coefficient. This

value is available from the datasheet. To further simplify the model, in this work, both reverse saturation currents Io1, Io2 are set be to equal in magnitude.

_01 02

, 1 2

( )(9)

exp[( ) /( ) / ] 1sc STC I

oc STC V T

I K TI I

V K T a a p V

+ Δ= =

+ Δ + − Equation (9) can be solved analytically. This is an

advantage over other methods which requires Io1, Io2 to be computed using numerical iteration. Detailed analyses of (9) have shown that if 1 2( ) /a a p+ = 1, the following expression for Io1, Io2 results:

_01 02

,

( )exp[( ) / ] 1

sc STC I

oc n V T

I K TI I

V K T V+ Δ

= =+ Δ −

(10)

This generalization can eliminate the ambiguity in

selecting the values of a1 and a2. Using (4) and (7), five parameters of this model can be readily determined, i.e. IPV, Io1, Io2, a1 and a2. Furthermore, iteration process to compute I01 and I02 is avoided, resulting in reduced computing time.

2) Determination of Rp and Rs Values: The remaining two parameters, i.e. Rp and Rs are obtained through iteration. Several researchers have estimated these two parameters independently, but the results are unsatisfactory. In this work, Rp and Rs are calculated simultaneously, similar to the procedure proposed in [10]. This approach has not been applied for two-diode model. The idea is maximum power point (Pmp) matching; i.e. to match the calculated peak power (Pmp,C) and the experimental (from manufacturer’s datasheet) peak power (Pmp,E) by iteratively increasing the value of Rs while simultaneously calculating the Rp value. From (1) at maximum power point condition, the expression for Rp can be rearranged and rewritten as

1 2 max,

( )[ ]

mp mp m sp

mp PV d d E

V V I RR

V I I I P+

=− − −

(11)

Fig. 2 depicts the mechanism of the iteration to obtain the

correct Rs value. Two types of PV modules, Kyocera KC200GT [22] and Solarex MSX-60 [23] are chosen for illustration. In every case, Rs is increased until Pmax,C becomes exactly equal to Pmax,E . Meanwhile, for every iteration, the value of Rp is calculated simultaneously using (11). With the availability of all the seven parameters, the output current of the cell can now be determined using the standard Newton-Raphson method. The flowchart that describes the Pmp matching algorithm is given in Fig. 3.

3

0 5 10 15 20 25 30 350

20

40

60

80

100

120

140

160

180

200

V (V)

P (

W)

Mpp

Mpp

MSX-60

KC200GT

Figure 2. Matching P-V curves methodology for two PV modules

III. RESULTS AND DISCUSSION A. Verification of Two Diode Model

The two diode model described in this paper is validated by measured parameters of selected PV modules. The specifications of the modules are summarized in Table I. Table II shows the parameters for the proposed two-diode model. Although it has more variables, the actual number of parameters computed is only four because Io1=Io1 while a1 and a2 can be chosen arbitrarily from (9).

TABLE I. MODULE SPECIFICATION

Parameter MSX-60 KG200GT Isc 3.8 A 8.21 A Voc 21.1 V 32.9 V Imp 3.5 A 7.61 A Vmp 17.1V 26.3 V Kv −80 mV/oC −123 mV/oC Ki 3 mA/oC 318 mA/oC

Ns 36 54

TABLE II. PROPOSED TWO-DIODE MODEL PARAMETERS

Parameter MSX-60 KG200GT Isc 3.8 A 8.21 A Voc 21.1 V 32.9 V Imp 3.5 A 7.61 A Vmp 17.1V 26.3 V Io1= Io2 4.704 × 10-10 A 4.218 × 10-10 A IPV 3.808 A 8.23 A Rp Rs

152.6 Ω 0.34 Ω

145 Ω 0.32 Ω

Fig. 4 shows the I-V curves for KC200GT module, for

different levels of irradiation (per unit quantity: Sun=1 equivalent to 1000W/m2). The calculated values from the proposed two-diode and Rp- models are evaluated against measured data from the manufacturer’s datasheet.

The proposed two-diode model and the Rp-model exhibit similar results at STC. This is to be expected because both models use the similar maximum power matching algorithm to evaluate the model parameters at STC. However, as irradiance goes lower, more accurate results are obtained from the two-diode model, especially in the vicinity of the open circuit

voltage. At Voc, the Rp-model shows departure from the experimental data, suggesting that Rp-model is inadequate when dealing with low irradiance level. This is envisaged to have significant implication during partial shading.

Figure 3. Matching Algorithm

The performance of the models when subjected to

temperature variation is considered next. All measurements are conducted at STC irradiance of 1000W/m2. The proposed model is compared to the Rs-model. The comparison specifically is chosen to highlight the significant problems with the Rs-model when subjected to temperature variations. Two modules are tested, namely the KC200GT and MSX-60. As can be seen in Fig. 5, the curves I-V computed by the two-diode model fit accurately to the experimental data for all temperature conditions. In contrast, at higher temperature, results from the Rs-model deviates from the measured values quite significantly. B. Simulation with Converter and Controller

The capability of the proposed two-diode model to interface with power electronics converters is illustrate in Fig. 6, in which a simulation of a grid connected PV system involving a boost-type dc-dc converter (with MPPT controller) and an inverter is carried out. The PV modules are KC2000GT configured in a 50x10 array. The MPPT controller utilizes the conventional Perturbation and Observe (P&O) algorithm. The control variable of the inverter is the RMS current reference, IRMSref . The inverter output current iac, is controlled such that it is in phase with the grid voltage. The results are shown in Fig. 7. It can be seen in Fig. 7 (a)−(b), MPPT controller calculates the correct Vmp (26.3×50 ≅ 1310) voltage and Imp (7.6×10 ≅ 76.2) current. Moreover, AC output power is almost

4

equals to the input power. This exercise has proven the accurateness of the simulator.

0 10 20 300

2

4

6

8

V (V)

I (A

)

KC200GT Multi-Crystalline PV Module

Sun=1

Sun=0.8

Sun=0.6

Sun=0.4

Sun=0.2

Proposed Two-diode Model Rp-Model Experimental Data

Figure 4. I-V curves of Rp-Model and proposed two-diode model of the

KC200GT PV module for several Irradiation levels.

0 5 10 15 200

1

2

3

4

V (V)

I (A

)

MSX-60 Multi-crystalline PV Module

Proposed Two-Diode ModelRp-Model Experimental Data

0oC

25oC

50oC

75oC

Figure 5. I-V curves of Rs and proposed two-diode model of the KC200GT

PV module for several temperature levels.

~

Figure 6. Grid connected system interfacing with PV simulator

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.11300131013201330

PV

arr

ayV

olt

age

(V)

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.175

76

77

PV

arr

ayC

urr

ent

(A)

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.19

9.5

10x 10

4

Po

wer

(W

)

Pout Pref

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

2000

4000

AC

Po

wer

(W

)

Time(s)

Pin Pout

(a)

(b)

(c)

(d)

Figure 7. (a)−(c) Output voltage, current, and output power from the PV

array. (d) AC power output of inverter

IV. CONCLUSION In this paper, an improved two-diode model is proposed.

To reduce computational time, the input parameters are reduced to four and the values of Rp and Rs are estimated by an efficient iteration method. The accurateness of the proposed two-diode model is verified by the actual data from the manufacturers. It is observed that the two-diode model is superior to the Rp and Rs models. Furthermore a complete grid connected PV system, together with the power converters and controllers are simulated. The results are found to be to be in close agreement with theoretical prediction.

V. ACKNOWLEDGMENT The authors would like to thank Universiti Teknologi Malaysia for providing the facilities and research grant to conduct this research.

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Zainal Salam obtained his B.Sc., M.E.E. and Ph.D. from the University of California, Universiti Teknologi Malaysia (UTM) and University of Birmingham, UK, in 1985, 1989 and 1997, respectively.

He has been a lecturer at UTM for 24 years and is now a Professor in Power Electronics at the Faculty of Electrical Engineering. He has been working in several researches and consulting works on battery powered converters. Currently he is the Director of the Inverter Quality Control Center

(IQCC) UTM which is responsible to test PV inverters that are to be connected to the local utility grid. His research interests include all areas of power electronics, renewable energy, power electronics and machine control.

Kashif Ishaque received the B.E. degree in Industrial Electronics engineering from, Karachi, Pakistan, in 2007, and the M.E. degree in Mechatronics and Automatic Control in 2009 from the Universiti Teknologi Malaysia (UTM), Malaysia, where he is currently working toward the Ph.D. degree in electrical engineering.

His research interests include photovoltaic modeling and control, intelligent control, nonlinear systems control and optimization techniques such as

Genetic Algrithm (GA), particle swarm optimization (PSO) and differential evolution (DE).

Hamed Taheri was born in Babol, Iran in 1985. He received his B.Sc. degree in Electrical Engineering from University of Mazandaran, Iran, in 2009. Currently he is working toward the M.Eng degree in Electrical Engineering in Universiti Teknologi Malaysia (UTM), Malaysia. He is an assistant of the Inverter Quality Control Center (IQCC) UTM which is responsible to test PV inverters that are to be connected to the local utility grid.

His research interests include maximum power point tracking control of photovoltaic system, power

systems, power quality, transformer and power electronics.