A simplified simulation model of silicon photovoltaic modules for performance evaluation at different operating conditions

Journal Pre-proof A Simplified Simulation Model of Silicon Photovoltaic Modules for Performance Evaluation at Different Operating Conditions Durgesh Kumar, Pritish Mishra, Ashutosh Ranjan, Dharmendra Kumar Dheer, Lawrence Kumar

PII:

S0030-4026(20)30062-0

DOI:

https://doi.org/10.1016/j.ijleo.2020.164228

Reference:

IJLEO 164228

To appear in:

Optik

Received Date:

29 November 2019

Revised Date:

9 January 2020

Accepted Date:

13 January 2020

Please cite this article as: Kumar D, Mishra P, Ranjan A, Dheer DK, Kumar L, A Simplified Simulation Model of Silicon Photovoltaic Modules for Performance Evaluation at Different Operating Conditions, Optik (2020), doi: https://doi.org/10.1016/j.ijleo.2020.164228

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A Simplified Simulation Model of Silicon Photovoltaic Modules for Performance Evaluation at Different Operating Conditions Durgesh Kumar1, Pritish Mishra1, Ashutosh Ranjan1, Dharmendra Kumar Dheer2 and Lawrence Kumar1* 1 Department of Nanoscience and Technology, Central University of Jharkhand, Ranchi, Brambe-835205 India 2 Department of Electrical Engineering, National Institute of Technology Patna, Patna-800005 India (*Corresponding author email: [email protected]) Abstract

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We report here a simplified and improved technique for modeling and simulation for the Photovoltaic module using MATLAB/Simulink environment. Parameters of the equivalent-circuit

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model are obtained using the iterative algorithm by adjusting the output characteristics curve. The present work evaluates the current-voltage (I-V) and power-voltage (P-V) characteristics under

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different ambient conditions employing a single-diode model. The module performance is significantly affected by solar irradiance, ambient temperature and partial shading. This report

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aims to perform the detailed analysis of partial shading effect on module performance, which is considered as important real-time problem. The proposed simulation technique provides an accurate and reliable method to extract different sources of resistance, such as series and shunt

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resistance in the PV module. A MSX60 photovoltaic module is used as a reference for the present study. The characteristic curves of the simulated model are in good agreement with the available

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experimental data. The developed simulation model could also be extended for performance assessment of other photovoltaic modules and in the design of efficient power converters. Keywords: Photovoltaic module, Partial Shading, Simulink, Shunt Resistance and Series Resistance, MATLAB/Simulink 1. Introduction:

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Photovoltaic modules are the semiconductor device, which converts a portion of light energy into electrical energy. The fundamental building block of the photovoltaic module is Photovoltaic Cell, which are grouped together to form a Photovoltaic (PV) module to generate significant amount of power. To evaluate the dynamic behavior of the PV module at different environmental condition, it is imperative to establish precise equivalent model for simulation purposes. In practice, there are two major equivalent circuit models for describing the non-linear output characteristic curve of PV cell. These are classified as Single diode model (SDM) and double diode model (DDM). Generally, single diode model is extensively used in practice in

comparison to the double diode model. Although double diode model shows high level of accuracy, but at the same time, it includes too many parameters making it complex for mathematical computation and algorithm development, which makes single diode model a convenient choice for modeling of the PV cell [1, 2]. The accurate modeling of PV module requires a range of parameters that could be extracted using the mathematical analysis of the photovoltaic cell equivalent model [3-4]. In the field of the photovoltaic research, the modeling and simulation of PV cell has been reported using different simulation tools [5–14]. Among these,

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MATLAB/Simulink has been extensively used by different groups for developing the simulation models of the PV module [5, 6, 11]. In this work, a simulation model has been developed to assess the module performance at different operating conditions. An iterative algorithm has been used for

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calculation of shunt resistance and series resistance (Rsh and Rs) in the developed simulation model making the model comparable to real-time scenario, which is not reported in previous work [5, 8,

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9]. Detail analysis of partial shading effect on module performance has been presented, considering as one of the vital outdoor problems [15-17], which was missing in the study carried

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out in reference [6] and [11]. In this work, the method discussed by G. Wang et al [11] is adopted for the calculation of equivalent cell parameters making the model more accurate. The proposed

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study utilizes Solarex’s module MSX60 as a reference [18]. In order to validate the accuracy of the developed model, we have analyzed the simulated data at different environmental conditions. Both the given module data (provided by the manufacturer) and our simulated model outcomes are in

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good agreement with each other. Developed simulation model is relatively simple and easily tuneable, which can be used to simulate another solar module. This paper is arranged as follows: in section 1.2, modeling of the photovoltaic cell has been presented. Brief discussion has been made in section 1.3 for the determination of series and shunt resistance. MATLAB simulation has been reported in section 1.4. Result and conclusion has been

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made in section 1.5 and 1.6, respectively. 1.2 Modeling of Photovoltaic Cell The electrical power generated by solar cell predominantly depends upon different

conditions such as cell temperature, solar irradiance, sun’s angular position and shading condition[19]. The Ideal and practical equivalent model for solar cell has been depicted in Fig.1. The practical a solar cell can be represented by adding lumped electrical element i.e., Shunt resistance (Rsh) 𝑎𝑛𝑑 Series resistance (Rs) to the ideal equivalent circuit of solar cell. Usually, the

value of RS is very low and Rsh is very high .The Current-Voltage (I-V) characteristics of the solar cell is expressed by the following equation [20]

  V  Rs I   V  IRs   1  I  I PV  I o exp  nv Rsh t    

(1)

WhereIo is saturation current of diode,Vt =NsKT/q is the thermal voltage of module and n is the ideality factor of diode, which varies from 1 to 1.5. The output characteristics curve of the

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photovoltaic module (Fig.2) expressed by Eqn. (1) marked the important solar parameters such as open-circuit voltage; short circuit current and maximum power points. Generally, photo–generated

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(Ipv) current is approximated to short circuit current Isc (e.g. Ipv=Isc) of the module assuming the high value of Rsh and very low diode current. However, there are few reports [3, 4, 11, 21] which

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have expressed photo-generated (Ipv) current in terms of Rs and Rsh as,

(2)

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 R  Rsh   I sc I pv   s R sh  

Under real-time condition, taking account the variation in irradiance and temperature, the

G Gn

(3)

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I pv  I pv  KiT 

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photo-generated current can be expressed as:

Here 𝐼𝑝𝑣 is photo-generated current at standard testing condition (STC),Ki is the short circuit current coefficient, ∆𝑇represents the temperature difference between the operating temperature and the reference temperature. G is the irradiance at the surface of module and Gn is nominal irradiance (1000 Watt/m2) at Standard test condition (STC). The relation between temperature and

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saturation current Io is expressed as [22]  qEg  1 1   T  I 0  I rs  n  exp      nk T   Tn T    3

(4)

Where Eg is bandgap energy of Polycrystalline Silicon (Eg = 1.12 eV) at 298 K and Irs is nominal saturation current, 𝑞 is the charge of electron n is ideality factor, k is Boltzmann’s constant and 𝑇𝑛 is reference temperature. Using equation (1) at open circuit point I =0, V=Voc, Irs could be

expresses as

I rs 

I sc   VOC exp   nVt 

(5)

    1  

Here Vocis open circuit voltage of module. Several researchers [5, 6, 22] have reported some approximation to compute the value of saturation current, using equation (3). G.Wang et al. [11]

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improved the simulation model at low irradiance level by using the modified equation expressed as,

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I sc  Voc Rsh   Voc   exp  nvt   1    

(6)

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I rs 

In the proposed simulation model, the equations (1) to (6) have been used for realization of I-V

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characteristics at different operating conditions.

1.3 Calculation of Series and Shunt Resistance

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The series and shunt resistance represent the internal losses and leakage current of PV cell ,which affects the current-voltage (I–V) characteristics and efficiency of module [23]. Many different simulation studies have been reported in literature assuming very low value of Rs and large value

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of Rsh 𝑅𝑠ℎ [5]. A unique pair of Rs 𝑅𝑠 and Rsh are computed by an iterative algorithm. Iteration terminates when the Pmax(e) i.e., experimental maximum power matches with the Pmax(m) i.e. calculated maximum power. Rearranging the Eqn (1), calculated maximum power point could be expressed as,

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   q I mp    I     1   Vmp  RS mp Pmax  Vmp I ph  I 0 exp  Vmp  Rs n * N s    Rsh    k * T  

(7)

Rearranging the above equation, we get the value of Rsh at maximum power point

Rsh 

V

mp



Vmp Vmp  I mp * Rs 



* I pv  Vmp * I 0 * exp (Vmp  I mp * Rs ) N s * n * q k * T  Vmp * I o  Pmax 

The initial conditions for 𝑅𝑠 and 𝑅𝑠ℎ can be calculated as proposed in reference [4]

(8)

Rs 0  0 , Rsh0 

Vmp I SC  Vmp



Voc  Vmp

(9)

I mp

The flow chart of the developed Iterative algorithm is depicted in Fig. 3. The initial value of 𝑅𝑠 and 𝑅𝑠ℎ is estimated from eqn (9). Thereafter each iterations is followed by slight increment of 𝑅𝑠 and corresponding value of 𝑅𝑠ℎ is calculated with the help of equation (7). The maximum power of the module obtained iteratively for different value of Rs and Rsh, has been depicted in Fig 4. The calculated value of Rs and Rsh are 0.316Ω and 146 Ω, respectively for the MSX60

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module. 1.4 MATLAB Simulation of Photovoltaic Module

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Figure 5 depicts the Simulink model of the Photovoltaic module where irradiance and temperature is taken as input. The Functional block uses equation (1-6) to calculate saturation

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current(Io) photo-generated current(IPV) ( 𝐼𝑝𝑣 ), and output current(I) for different level of irradiance and temperature. The function block uses the Newton Rapson method to solve equation (1) to compute every value of I for corresponding V. A bypass diode is also considered in

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developed simulation model which limit the maximum reverse bias current across during partial shading and provides alternative path to current [24]. An array of 6 modules has been created using

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the developed simulation model to study the effect of partial shading. Here assumption has been made that the entire shaded and unshaded module operates at same temperature. The developed Simulink model is oversimplified as it uses few components though previous reported works

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employ large number of Simulink component [5]. This simulation model can be extended to simulate the behaviour of another PV module. 1.5 Result and Discussion

The solar specifications for the reference module, MSX60 module at standard test condition is tabulated in Table 1. The output from the simulated model (I-V and P-V curve) of

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reference module at standard test condition (1000Watt/m2, AM1.5G, 25°C) is shown in figures.6 (a) and (b). The calculated parameters are depicted in Table 2. The comparison of simulated model output with experimental data sheet is depicted in Table 3, which shows the good agreement between the reference model and simulated model. In real-time scenario the PV module performance is significantly affected by temperature, irradiance and partial shading condition. It is discussed below.

Effect of Temperature: Figures 7(a) and (b) depicts I-V and P-V curve of the simulated model of reference module at different temperature. It is observed that the open-circuit voltage (Voc ) decreases and short circuit current (Isc) shows slight increment with increasing temperature, eventually leading to reduced output power [25]. The observed behaviour could be elucidated on the basis of band theory of solid [26]. Similar experimental observations have been reported in literature that validates our simulated model [26]. Effect of Irradiance: Figures 8(a) and (b) depicts the I-V and P-V curve at different solar

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irradiance level (100 W/m2, 600 W/m2, 800 W/m2, 1000W/m2) with temperature 25°C. It shows that the open circuit voltage and short circuit current strongly depends upon the solar irradiance. When irradiance level increases, rate of generation of electron-hole pair increases which give

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significant rise to short –circuit current and slight increase in open circuit voltage. Similar phenomena have been observed experimentally justifying the correctness of the simulated model

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for different solar irradiance [26].

Effect of partial shading on PV module: A String of six modules connected in series has been

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selected to study the effect of partial shading. In order to facilitate the understanding, four cases have been presented. In first case, we assume that all the six modules receive uniform illumination

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of 1000W/m2 as shown in Fig 9 (a). In second case, the one module has been partial shaded receiving the irradiance level of 500 W/m2 while the other five modules operate at irradiance level of 1000W/m2 as depicted in Fig 9 (b). The third case deals with the partial shading of two module

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receiving the irradiance of 500 W/m2 and 250 W/m2 respectively and rest four modules receives full irradiance of 1000W/m2 as shown in Fig 9 (c). In the fourth case, the two modules have been partially shaded receiving the same level of irradiance of 500 W/m2 and rest four other modules receives irradiance of 1000W/m2 as depicted in Fig 9 (d). I-V and P-V characteristics of reference simulated module under the above partial shading case are illustrated in Fig 10 (a) and (b). I-V

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curves show multiple steps and P-V curve exhibits multiple maxima under partial shading condition. The appearance of multiple peaks in the P-V curve is due to the presence of bypass diodes [27, 28]. The bypass diode provides alternative path to shaded cell current resulting in no effect on the array short-circuit current (as shown in Fig 9) [16]. On the other hand, a slight drop in Voc is observed which is evident from Fig 9. In the first case where there is no shading and irradiance is 1000W/m2, only the global peak appears in the P-V curve and the maximum power is found to be 358.69 Watt. Thereafter in the second case, partial shading on one of modules receives

500W/m2 irradiance. The P-V curve shows the global peak along with one local maxima. The maximum power reduces to 298.91 Watt. On increasing the shading on the module, further drop in the maximum output power is observed which is discussed in third case. In this case two modules are receiving the irradiance of 500W/m2 and 250 W/m2 respectively and the P-V curve depicts global maxima and two local minima. The maximum power is dropped down to 239.13 Watt. In the fourth case two modules are receiving the same irradiance of 500W/m2 and P-V curve in this case depicts global maxima along with only one local maximum. The global maximum is observed

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at 239.13 Watt. It is noticeable that although the two modules in case 3 and case 4 are partially shaded with different and same irradiance level, yet there is no change in the appearance of global maxima and it gives the same maximum power. A Similar trend has been observed by other

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researchers [29]. Conclusion:

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In this paper, modeling and simulation for the PV module is presented using MATLAB/Simulink environment to assess the performance of the module at different working conditions. It shows

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good agreement with experimental data. It has been demonstrated that change in operating temperature and solar irradiance significantly affects the output current and voltage, eventually

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changes the output power. A detailed study has been performed to show the effect of partial shading conditions on the performance of the PV array. It has been observed that in case of partial shading, more than one power peaks appear in the power-voltage curve. Further, to make the

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simulation model more realistic, the value of Series and Shunt resistance has been calculated. The proposed work is expected to be helpful in order to understand the operating performance at different working conditions. It may also assist power electronics engineers in order to design the

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efficient power converter and MPPT control method.

Declaration of interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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[20]

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Fig.1. Single diode equivalent circuit of Photovoltaic cell

Fig. 2. Characteristics I-V curve of Solar cell

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Fig.3. Flow Chart for the Calculation of 𝑅𝑠 and 𝑅𝑠ℎ

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Fig.4. Pmax for different value of Rs and Rsh

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Fig.5. Simulink model of Photovolatic module

Fig.6. (a) I-V curve of reference module at Fig.6. (b) P-V curve of reference module at Standerd test condition Standerd test condition

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Fig. 7(b) P-V curve at different temperature

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Fig.7(a) I-V curve at differnt temperature

Fig.8 (a) I-V curve at different irridiance

Fig.8(b) P-V curve at different irridiance

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(a) (b) (c) (d) Fig. 9: PV array under different partial shading condition (a) All unshaded modules with irradiance of 1000 W/m2 (b) one shaded module with 500 W/m2 (c) two shaded module with 500 and 250 W/m2 (d) Two shaded module with 500W/m2.

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Fig. 10 (a) I-V curve in partial shading Fig. 10 (b) P-V curve in partial shading conditions conditions

Table 1: Parameter of Solar module MSX 60 at Standard Test Condition Maximum Power 59.85 Watt Voltage (Vmp) 17.1Volt Current (Imp) 3.5 Ampere Short-Circuit Current (Isc) 3.8Ampere Open-Circuit Voltage (Voc) 21.1Volt Temperature Coefficient of Short-Circuit Current 0.003 A/K

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Table 2: Calculated Parameters of the MSX 60 module at Standard Test Condition Shunt Resistance (Rsh) 146.081 Ω Series Resistance (Rs) 0.3160 Ω Ipv (Photo Generated Current) 3.8082 Ampere Pmax (Maximum power) 59.7831Watt

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Table 3: Comparison of simulated model result with experimental data sheet Parameters Experimental data Simulated model output 21.1 Volt

Isc

3.8 Ampere

3.7996 Ampere

Vm Im

17.1 Volt 3.5 Ampere

17.1750 Volt 3.4808 Ampere

58.85 Watt

59.7831 Watt

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Pmax

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Voc

21.10 Volt