A Photovoltaic System Model For Matlab/Simulink Simulations

Cemal Keles, B. Baykant Alagoz, Murat Akcin, Asim Kaygusuz, Abdulkerim Karabiber Electrical Electronics Engineering Department

Inonu University Malatya, Turkey

cemal.keles@inonu.edu.tr

Abstract— Solar energy maintains life on the earth and it is an infinite source of clean energy. There is an increasing trend for the use of solar cells in industry and domestic appliances because solar energy is expected to play significant role in future smart grids as a distributed renewable source. Optimal and large-scale integration of renewable sources into smart grid is possible by the aid of computer simulations and hence there is a growing demand for computer modeling and simulation of renewable sources. This study presents a generalized photovoltaic (PV) system simulation model for Matlab/Simulink simulation environment. The proposed model is based on a behavioral cell model for modeling solar radiance to electricity conversion and an electrical driver interface for implementing electrical characteristic of power limited systems in power simulations. The model is efficient in computational complexity and it is easy to configure for representing wide-range of PV installations.

Keywords-solar energy; photovoltaic cell; photovoltaic module; simulink; smart grid

I. INTRODUCTION Among several renewable energy resources, energy

harvesting from the photovoltaic (PV) effect is the most essential and sustainable way because of abundance and easy-accessibility of solar radiant energy around the earth. In spite of the intermittency of sunlight, solar energy is widely available during daylight and it is free to use. Recently, photovoltaic system is recognized to be in the forefront in renewable electric power generation because it can generate direct current electricity without heavy environmental impacts and contamination [1].

PV modules are the fundamental power conversion unit of a PV generator system. The output characteristics of PV modules depend on the solar insolation, the cell temperature and the output voltage of the PV module [2]. Since PV modules exhibit nonlinear electrical characteristics, designing and simulation of this system require reliable PV modeling. Moreover, mathematical modeling of PV module is continuously updated to enable researcher to have a better understanding of its working [3].

Many researchers have been proposed several models for Matlab/Simulink in the literature. Tsai et al. proposed a model taking sunlight irradiance and cell temperature as input parameters [1]. Salmi et al. proposed a model of PV cell based on the fundamental circuit for a solar PV cell considering the effects of physical and environmental parameters [2]. Tsai

developed a novel model of PV module using Matlab/Simulink and this model was verified for an experiment structure. Author also underlined the effect of solar irradiation on cell temperature, which made the output characteristics more practical [4]. Altas et al. developed Matlab/Simulink PV model using basic circuit equations of the PV solar cells including the effects of solar irradiation and temperature changes. They tested the model response in a DC load and an inverter simulation [5].

There is an increasing trend for domestic use of hybrid renewable sources, preferably wind and solar combination. Hence there is need for simulation models of the wind turbine and PV modules to efficiently design and integrate these sources to power systems. Nowadays, smart grid researchers demand wind turbines and PV panel models to deploy in their power system simulations as distributed generators and explore impacts of distributed generation on power distribution. These models should also represent the transient responses of renewable energy sources for stability and reliability analyses.

Matlab/Simulink provides a user-friendly, modular and visual simulation environment for the transient analysis of power electronics. This environment facilitates design and simulation of the power systems and it is very convenient to perform transient analyses for the academic and industrial proposes. Although there are wind turbine models in SimPowerSystems library of Simulink, a general purpose PV module component working in conjunction with power electronic circuit are still needed [1]. The PV modules used for transient simulations of large-scale renewable source integration should not only be reconfigurable for wide-range of panel models but also present low-computational complexity in grid simulations due to the memory and calculation time limitation of computers. Recent PV models have low computational complexity [5] or electrical characteristics well suiting for PV modules [1].

This study aims to developed a general propose Simulink PV module. This module can be easily reconfigurable for the electrical response of PV panels in a wide spectrum. For this propose, a modified sigmoid function was used to approximate electrical characteristics of PV panels, empirically. This gains the module considerable degree of freedom to represent diverse PV systems. The proposed PV model is composed of a behavioral PV block, based on electro-physics of the PV cell, and a power-limited electrical driver module, characterized by the modified sigmoid function. The behavioral PV block

calculates voltage and current of PV module for a given solar radiance and panel temperature. Then, the power-limited electrical driver block receives the voltage and current values from the behavioral PV block and it injects an electrical power to electrical load appropriate to I-V characteristics of PV cells.

II. METHODOLOGY

Fig. 1 shows the top-level block diagram of the proposed PV module. The first block, reffered as to behavioural PV model, performs theoritical calculations based on physics of the PV cell and it yields nominal values of voltage and current generated by the panel. The second block electrically drives to the electrical load according to the limited power I-V characteristics. Depending on the load value, the voltage drop over load (VL) and the load current (IL) are adjusted according to maximum power provided by PV panel. The maximum power point (MPP), namely the peak power, is limited by approximately Pm ≅ VmIm.

Figure 1. Block diagram of PV simulation model.

A. Behavioral PV Modeling The physics of the PV cell is very similar to that of the

classical diode with a pn junction [6]. When the junction absorbs light, the energy of absorbed photons is transferred to the electron-proton system of the material, creating charge carriers that are separated at the junction [7]. An ideal PV cell is assumed to have no series loss and no leakage to ground. However, due to its non-ideal structure in nature, there are some losses occurred in real PV cells. Therefore, these losses are expressed by using resistances in equivalent circuits. Fig. 2 shows an equivalent electrical circuit modeling the complex physics of the PV cells [8-10]. The behavioral model of the proposed PV model is based on this equivalent electrical circuit model. Current source, Iph, which is a current produced by the photons, is constant at a fixed value of radiation and temperature. The shunt resistance, Rsh, is used to represent the shunt-leakage current, Ish. The series resistance, Rs, is used to represent the voltage drop at the output. PV power conversion efficiency (PPCE) is sensitive to small changes at Rs, but the PPCE is not sensitive to changes at Rsh. The small increase in Rs significantly reduces the output of the PV module [8]. In the equivalent circuit, the current, Icell, delivered to the external load equals the current IL and voltage over the load equals the voltage of PV cell, Vcell [2,9]. Current and voltage of PV panel depends on load value and presents nonlinear, power limited electrical characteristics.

Figure 2. Equivalent electrical circuit model of PV cells.

The Equation (1) describing output current of the non-ideal PV cell was derived using Kirchhoff’s current law as follows [11]:

shdphcell IIII −−= (1)

The overall current, which the PV cell can provide, was formulated by Equation (2), where G and Gr are active and the reference radiation, Tc and Tcr are module temperature and reference temperature of the module, respectively [11]. Producers usually provide electrical specifications of the PV module at standard conditions, namely solar radiation of 1000 W/m2 and cell temperature of 25oC. These values correspond to Gr and Tcr, respectively [11].

( )⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−+−⎟⎟

⎠

⎞⎜⎜⎝

⎛+= sc

rcrc

rrcell I

GGTT

GGII 1α (2)

The parameter Isc represents short circuit current of the module and α is the temperature coefficient of short circuit current. The voltage of PV cell was formulated by Equation (3) and Equation (4) [11], where ß are temperature coefficient of open circuit voltage.

( ) rscrccell VIRTTV +Δ−−−= β (3)

( )⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−+−⎟⎟

⎠

⎞⎜⎜⎝

⎛=Δ sc

rcrc

rI

GGTT

GGI 1α (4)

Herein, Rs is used to represent the voltage drop at the output of the PV cell. The parameters Ir and Vr are reference values taken from I-V curve [12, 13].

PV module is formed by connecting PV cell in series and parallel to each other. In this case, the output current and voltage of PV module is expressed in Equation (5) and Equation (6), respectively.

cellscm VNV = (5)

cellpcm INI = (6)

Herein, Vm is the output voltage, and Im is the output current. Nsc and Npc are expressed numbers of series and parallel connected PV cells, respectively [11]. Simulink schema of behavioral PV model, using the Equation (2) and Equation (3), is demonstrated in Fig. 3.

Iph

Id Ish

Rs

Icell

Vcell

PV cell

IL

RL Rsh

PV Simulation Model

Load

VL

IL

Vm,Im Behavioural PV Model

Power-limited Electrical Driver

Figure 3. Behavioral PV model simulink schema.

B. Power-limited Electrical Driver Modeling In order to implement PV panel power limits, calculated by

the current and voltages values of behavioral model, in the power system, there is need for an electrical driver component that exhibits an I-V characteristic complying with the response of PV panels.

Power-limited electrical driving of the electrical loads is implemented in the form of modified sigmoid function given by Equation (7). This function can approximate to limited power I-V characteristic of PV panels as illustrated in Fig. 4(a) and Fig. 4(b). Maximum power point of the Equation (7) approximates to value of Pm ≅ VmIm, where Im and Vm are calculated by the behavioral model. Voltage drop between surface of PV silicon layers (Vg) is adjusted according to the load current IL. When IL current exceeds the theoretical PV current Im, Vg voltage exhibits sharp decreases and thus limits the power injection to the load as in Fig. 4.

( )mL IIm

g eV

V −+= ϕ1

(7)

Figure 4. I-V characteristic in (a) and P-V characteristic in (b) by Equation (7) for Im=0.5, Vm=1.5, and φ=20. Maximum power point is indicated by

MMP.

Peak point (MMP) of power-limited I-V characteristic is apparent in Fig. 4(b). The parameter φ is used to adjust decline of panel voltage Vg against the increase of load current IL.

Fig. 5 shows simulink model of the power limited electrical driver. Equation (7) governs the voltage controlled voltage source that is connect to load via an internal resistor, Ri. Here, the internal resistor Ri resistance between metal contacts of silicon layers and panel output ports. Ci represents internal capacitance caused from capasitive structures in the panel and it is used to configure transient responce of PV module. Internal resistor and capacitor defines a time constant for the modeling transient regime of PV panel, which can be expressed as τ =(Ri //RL)Ci. The load current is measured from the output of panel and provides a feedback for Equation (7).

2V-

1V+

20

Ri

temperature

radiation

Vm

Im

PVModul

i+ -

IL

eu

s

-+

1

Ci

2radiation

1temperature

Figure 5. The simulink model of electrical driver.

III. PV MODULE SIMULATION EXAMPLES This section illustrates PV module simulation examples.

The module parameters were largely configured according to Solarex MSX60 specifications for solar radiation of 1000 W/m2 and cell temperature of 25oC. Parameter settings are listed in Table 1.

TABLE I. PARAMETER SETTINGS USED PV MODULE IN SIMULATIONS

Module Parameters ValuesReference Voltage (Vr) 17.1 V Reference Current (Ir ) 3.5 A Short circuit current temperature coefficient (α) 3.10-3 mA/oC Open circuit voltage temperature coefficient (ß) -73.10-3 mW/oC Short circuit current (Isc) 3.8 Serial resistance (Rs) 0.47 Ohm Internal resistor (Ri) 1 Ohm Internal capacitance (Ci) 1.10-2 F

A. Tests for Constant Resistive Load Fig. 6 shows a Simulink simulation of the proposed PV

module connected to a DC resistive load. The load resistor RL was set to 4.5 Ohm for working nearby MPP. A reference radiation (G) of 1000 W/m2 and module temperature (Tc) of 25oC were used in the simulation. The internal resistor Ri and capacitor Ci were set to 1 Ohm and 10-2 F, respectively. Transient response of PV module, when connected to the resistive load, is illustrated in Fig. 7 (a), (b), and (c). Voltage and current of the load are settled to its steady state value after roughly 0.05 second transient regime. Settling time can be

0.5 1 1.5

0

0.2

0.4

0.6

V

I

Power-limited Working Region of Electrical Driver

(a)

0.5 1 1.5

0.2

0.4

0.6

0.8

V

P

MMP Pm ≅ VmIm

(b)

Deltai2

Im

1Vm

u[1]*Nsc

u[1]*beta

beta*(Tc -Tcr)

u[1]*alfa

alfa*G/Gr

Vr

Rs25

Ref. temperature

Isc

Iru[1]/1000

G/Gr

1

u[1]*Npc

2radiation

1temperature

adjusted by Ci and Ri. Adjustment of transient response of PV module is, particularly, useful for voltage and power stability analyses of power systems supplied by PV panels. Power injected the load by PV module was reached to its steady state operating conditions after development of transient regime. This allows more realistic analysis of PV panels in power system simulation.

Discrete,Ts = 5e-005 s.

pow ergui

v+-

Voltage

temperature

radiation

V+

V-

Simulink PV Model

Load

i+ -

Current

2radiation

1temperature

Figure 6. Simulink simulation of PV module for a DC load.

Figure 7. Current [A] in (a), Voltage [V] in (b) and Power [W] in (c) of PV module for a load resistance of 4.5 Ohm.

Fig. 8 (a) and (b) demostrates power injection of PV module for various values of load and load voltages. MMP points indicates power limits of PV modules. This is very useful for testing MPP tracking methods in Matlab/Simulink.

Figure 8. (a) Power injection versus load resistance characteristics. Maxsimum power point is tracked at 4.5 Ohm load resistance. (b) Power

injection versus of load voltage characteristics. Maxsimum power point is tracked at 14 Volt load voltage.

B. Solar Power For Three Phase AC Power Distribution Simulation Simulink simulation of a PV array supplying three phase

AC distribution system is shown in Fig. 9. The DC/AC converter with pulse wide modulated three arms IGBT inverter causes DC instability due to periodical switching of PV module current. In order to reduce negative impacts of possible reverse current of DC/AC converter on PV module, a diode is used. Output of PV module is connected to DC/AC converter to supply 1000 Watt resistive loads per phase. In order to draw adequate power from PV module, 10 numbers of series and 5 numbers of parallel cells structure (Nsc =10 and Npc =5) were configured for the PV module.

Figure 9. Simulink simulation of a PV array supplying three phase AC distribution.

Fig. 10 (a) and (b) show DC voltage (VP) supplied from PV module and average magnitude of the power (PL) drawn

(a)

0 0.1 0.2 0.30

1

2

3

I L

Second

0 0.1 0.2 0.3

2

4

6

8

10

12

14

VL

Second

(b)

(c)

0 0.1 0.2 0.30

10

20

30

40

50

PL

Second

2 4 6 8 10 12 140

10

20

30

40

RL

PL

MMP

(a)

5 10 15

10

20

30

40

VL

PL

(b)

MMP

powergui

Discrete,Ts = 5e-005 s.

T

25

Rc

Rb

Ra

PV Model

T

G

V+

V-

Measurement

Cur V+

V-

Va+

Va-

G

1000Diod

DC/AC Converter

DC V +

DC V -

A

B

C

Current

i+ -

from PV module. Fig. 10(c) shows line to neutral AC voltages measured from resistive loads. After a transient regime continuing 0.1 second, average power drawn from PV module goes into steady regime and settles roughly at 3000 Watt.

Figure 10. (a) output voltage of PV module (VP ), (b) average magnitude of power injected from PV module to DC/AC converter ( PL), (c) Three phase

line to neutral voltage (Va -Vb -Vc ).

IV. CONCLUSION In summary, this study presents a general purposes PV

simulation module and its application examples in Matlab/Simulink simulation environment. This PV model is easy to configure for a desired PV response characteristics and it directly connects to SimPowerSystems electrical circuit for transient response analyses. The PV module has two main parts: A behavioral model of PV cells and a power–limited electrical driver for circuit connection. The behavioral model

estimates voltage and current potential of PV panel for a given solar radiation (G) and module temperature (Tc) conditions. The power–limited electrical driver implements a relevant electrical response on the load. The proposed PV module can be employed in transient analysis of power system supplied with PV panels. It is also useful for testing MPP tracking methods.

Nowadays, solar energy integration in microgrids [14, 15] is becoming primary concern of power system industry. Modeling renewable energy sources for a large-scale power system integration simulation is more important today, because these simulation tools will be a part of optimal design and intelligent management process.

REFERENCES [1] H.L. Tsai, C.S. Tu, and Y.J. Su, “Development of generalized

photovoltaic model using Matlab/Simulink,” Proceedings of the World Congress on Engineering and Computer Science 2008, WCECS’08, San Francisco, USA.

[2] T. Salmi, M. Bouzguenda,A. Gastli, and A. Masmoudi, “Matlab/Simulink based modelling of solar photovoltaic cell,” Int J of Renewable Energy Research 2012, vol. 2, no. 2, pp. 213–218.

[3] N. Pandiarajan, and R. Muthu, “Mathematical modeling of photovoltaic module with simulink,” 1st International Conference on Electrical Energy Systems ICEES’11, 2011; pp. 258–263.

[4] H.L. Tsai, “Insolation-oriented model of photovoltaic module using Matlab/Simulink,” Solar Energy 2010, vol. 84, pp. 1318–1326.

[5] I.H. Altas, and A.M. Sharaf, “A photovoltaic array simulation model for Matlab-Simulink GUI environment,” International Conference on Clean Electrical Power 2007, ICCEP’07, Capri, pp. 341–345.

[6] H. Patel, and V. Agarwal. Matlab-based modeling to study the effects of partial shading on PV array characteristics. IEEE Trans on Energy Conversion 2008, vol. 23, no. 1, pp. 302–310.

[7] M.R. Patel, Wind and Solar Power Systems 1998, CRC Press, USA, 351p.

[8] M.R. Patel, Wind and Solar Power Systems: Design, Analysis, and Operation 2005, CRC Press, Second Edition, USA, 472p.

[9] P. Maffezzoni, L. Codecasa, and D. D’Amore, “Modeling and simulation of a hybrid photovoltaic module equipped with a heat-recovery system,” IEEE Trans on Industrial Electronics 2009, vol. 56, no. 11, pp. 4311–4318.

[10] R. Ramaprabha, B. Mathur, K. Santhosh, and S. Sathyanarayanan, “Matlab based modelling of SPVA characterization under reverse bias condition,” Third International Conference on Emerging Trends in Engineering and Technology 2012, IETET’12, Kurukshetra, Haryana, India, pp. 334–339.

[11] R.P. Vengatesh, and S.E. Rajan, “Investigation of cloudless solar radiation with PV module employing Matlab-Simulink,” International Conference on Emerging Trends in Electrical and Computer Technology 2011, ICETECT’11, pp. 141–147.

[12] S. Nema, R.K. Nema RK, and G. Agnihotri, “Matlab/simulink based study of photovoltaic cells/modules/array and their experimental verification,” International Journal of Energy and Environment 2010, vol. 1, no. 3, pp. 487–500.

[13] S. Kim , and M.J. Youn, “Variable-structure observer for solar array current estimation in a photovoltaic power-generation system,” IEE Proceedings-Electric Power Applications 2005, vol. 152, no. 4, pp. 953–959.

[14] A, Karabiber, C. Keles, A. Kaygusuz, and B.B. Alagoz, “An approach for the integration of renewable distributed generation in hybrid DC/AC microgrids,” Renewable Energy 2013, vol. 52, pp. 251–259.

[15] J. Paska, P. Biczel, and M. K1os, “Hybrid power systems – An effective way of utilising primary energy sources,” Renewable Energy 2009, vol. 34, pp. 2414–2421.

(a)

0 0.2 0.4 0.6 0.8 10

50

100

150

Vp

Second

(b)

(c)

0.306 0.308 0.31 0.312 0.314-500

0

500

Va-V

b-Vc

Second

0 0.2 0.4 0.6 0.8 10

1000

2000

3000

4000

PL

Second

Steady State Regime Transient Regime