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Physics Journal

Vol. 2, No. 1, 2016, pp. 23-34

http://www.aiscience.org/journal/pj

* Corresponding author

E-mail address: mhshahrokh@ieee.org (M. H. S. Abadi), toghyani.rizi@gmail.com (M. T. Rizi)

A New Approach for Modeling of Photovoltaic

Cell/Module/Array Based-on Matlab

M. Toghyani Rizi, M. H. Shahrokh Abadi

*

Faculty of Electrical and Computer Engineering, Hakim Sabzevari University, Sabzevar, Iran

Abstract

A step-by-step mathematical modeling of one-diode equivalent circuit of photovoltaic cell/module, implemented in

matlab/simulink was developed. The model was designed to take different inputs in terms of voltage, insolation, temperature,

series and parallel resistances to simulate the electrical behaviour of the module and to produce V-I and P-V curves. The

novelty of this work is consideration the effects of series and parallel resistances of the model as the independent inputs.

Furthermore, hot spot heating and bypass diode operation of the module were investigated. Finally, using the proposed model,

a photovoltaic array in parallel mode was developed and simulated.

Keywords

Photovoltaic Cell, Module, MATLAB, Simulink, Series Resistance, Parallel Resistance, I-V Curve, P-V Curve

Received: September 14, 2015 / Accepted: December 13, 2015 / Published online: December 29, 2015

@ 2016 The Authors. Published by American Institute of Science. This Open Access article is under the CC BY-NC license.

http://creativecommons.org/licenses/by-nc/4.0/

1. Introduction

Solar energy has the advantage of being environmentally

friendly, pollution free, cost-efficient, and generally is

unlimited in availability [1-4]. All these factors and

dimensions of solar energy have attracted the attention of

many researchers toward the photovoltaic (PV) systems and

devices. The market for PV systems is growing worldwide

[5]. Today’s solar PVs provide nearly 4800 GW. Between

2004 and 2009, grid connected PV capacity reached 21 GW

with an increasing rate of 60% annually [5]. However,

studies on the characteristics of a PV system are frequently

analyzed through the use of a CAD model, which is always

going to be a big challenge for solar cell systems and has

been concerned by many researchers [6-8].

There are common and simple models of solar panel that

have been developed and integrated to software, e.g. Matlab.

Extensive works exist in literature about modeling solar

power generation by photovoltaic cell [9-11]. In 2011, a 36

W PV module for simulation purposes, called Solkar, has

been developed by Pandiarajan and Muthu [12], in which, the

effects of series and parallel resistances of PV module, as

independent inputs, have not been considered in the model.

In this paper, a step-by-step procedure for simulating PV

module using subsystem blocks, with user-friendly icons of

Matlab/ Simulink block libraries is developed in six steps. In

section 2, the mathematical relationships between PV cell

parameters, the modeling procedure, and simulation

scenarios have been presented. Simulation results respect to

the inputs alteration have been given in section 3. In section

4, the PV array has been presented and simulated followed by

conclusion in section 5. It will be shown that a major

improvement to realize the PV characteristics has been done

by implementation of a new equation for output current, I

pv

.

Also inserting a delay block to resolve an algebraic loop error

due to the simulation is the other superior of the current

work. Another novelty of the presented model is building a

PV array based-on the improved PV module in parallel

mode. Hot spot heating effect and bypass diode operation is

also added to accomplish the work.

24 M. Toghyani Rizi and M. H. Shahrokh Abadi: A New Approach for Modeling of

Photovoltaic Cell/Module/Array Based-on Matlab

2. Model for the PV Module

2.1. Analytical Model

A one-diode equivalent circuit of solar cell (Fig. 1) has been

considered as the basis model through this work. In this

model, I

ph

represents the current generated by the photons

and does not change when temperature and incident radiation

of light are constant. Losses have been introduced by adding

a series and a parallel resistance, R

s

and R

p

, respectively, with

regard to the internal cell resistances, contact resistances, and

the effect of leakage currents. Also, I

D

, I

pv

, and V

pv

correspond to the diode current, the output current, and the

terminal voltage, respectively [13]. A solar panel has been

formed by using N

s

and N

p

number of the solar cell put in

series and parallel to fulfill the required power. For the

simulation the SOLKAR 36 W PV module has been

considered as the reference module. The electrical parameter

of this module has been given in Table 1 [14-15].

Fig. 1. One-diode equivalent circuit of solar cell.

(a)

(b)

Fig. 2. (a) A typical module with 36 series cell, (b) Model of solar panel

consists of N

s

and N

p

number of series and parallel cells.

Table 1. Electrical parameters of SOLKAR 36w PV module* [15].

Parameter Value

Rated Power, W 37.08

Voltage at Maximum Power (V

MP

), V 16.56

Current at Maximum Power (I

MP

), A 2.25

Open Circuit Voltage (V

OC

), V 21.24

Short Circuit Current (I

SCR

), A 2.55

Total Number of Cells Connected in Series (N

S

) 36

Number of Cells Connected In Parallel (N

P

) 1

* The electrical specifications have been given at irradiance of 1 kW/m

2

and

cell temperature of 25°C.

Considering the following parameters and definitions, the

photovoltaic array can be described through the equations 1

to 5 as it follows [16-17]:

pv

V

is output voltage of a PV module (V)

pv

I

is output current of a PV module (A)

ref

T

is the reference temperature = 300 °K

Tak is the module operating temperature in Kelvin

ph

I

is the light generated current in a PV module (A)

0

I

is the PV module saturation current (A)

A

is an ideality factor = 1.6

k

is the Boltzmann constant =

23

1.3805 10 j

k

−

×

q

is Electron charge =

19

1.6 10 C

−

×

s

R

is the series resistance of a PV module

p

R

is the parallel resistance of a PV module

SCr

I

is the PV module short-circuit current at 27 °C and

2

1kW m

= 2.55A

i

k

is the short-circuit current temperature co-efficient at

0.0017

SCr

IC

=

λ

is the PV module illumination

2

( )

kW m

0

g

E

is the band gap for silicon =

1.1eV

s

N

is the number of cells connected in series

p

N

is the number of cells connected in parallel

The module photo current:

[ ( )].

PH SCr I ak ref

I I K T T

λ

= + −

(1)

The module reverse saturation current, –I

rs

:

Physics Journal Vol. 2, No. 1, 2016, pp. 23-34 25

exp 1

SCr

rs

oc

ak

I

IqV

NskAT

= −

(2)

Module saturation current variations due to the temperature

fluctuations is calculated from:

3

0

1 1

( ) . exp[

G

rs

ref ref ak

qE

T

I I T kA T T

= −

(3)

The output current of PV cell can be determined by KCL at

the input node, given as:

0

exp 1

pv pv s

pv PH pv pv s

ak p

(V I R )

q

I = I I ( (V I R ) )

kT A R

+

− + − −

(4)

Therefore, the equation for the current and voltage terminal

of the array becomes:

0

exp 1− + −

+

−

pv pv s

pv P PH P S P

ak

P pv

pv s

S

p

q V I R

I = N I N I ( ( ) )

N N

kT A

N V

( I R )

N

R

(5)

where

, 1

pv oc P

V V N= =

and

36

s

N=

.

2.2. Simulink Modeling

Using the Matlab/Simulink simulation tool, the model of

photovoltaic cell implemented as it has been presented in Fig.

3. The model consists of a direct implementation of the

analytical expressions described above as six subsystems. A

step by step procedure of model illustration to create these

subsystems has been given in detail.

Fig. 3. Implemented model of PV module.

Step1:In this step a subsystem to convert Celsius degrees to

Kelvin has been implemented and given in Fig. 4. The basic

equations for the conversion are:

Operating Temperature:

273

k ak

T Temp T Temp+ = = +

(6)

Reference Temperature:

273 27 300

k ref rk

T T T+ = = + =

(7)

Step2: Using equation (1), in this step, I

ph

has been carried

out based on the inputs given in Fig. 5. The parameters used

in this step are:

Insolation

λ

–

2

( )

kW m

Module operating temperature, T

ak

= 30 to 70°C

Module reference temperature, T

rk

= 27°C

Short circuit current (I

SC

) at reference temp = 2.55A

(a)

(b)

Fig. 4.(a) Block diagram of °C to °K subsystem1, (b) Internal circuit of

subsystem1.

26 M. Toghyani Rizi and M. H. Shahrokh Abadi: A New Approach for Modeling of

Photovoltaic Cell/Module/Array Based-on Matlab

(a)

(b)

Fig. 5.(a) Block diagram ofsubsystem2, (b) Internal circuit of subsystem2.

(a)

(b)

Fig. 6. (a) Block diagram ofsubsystem3, (b) Internal circuit of subsystem3.

Physics Journal Vol. 2, No. 1, 2016, pp. 23-34 27

Step3: This block uses short circuit current of I

SC

= 2.55A as

the input at reference temperature and module reference

temperature of T

rk

= 27°C and then calculates the I

rs

based-on

the Equation (2). The subsystem has been described in Fig. 6.

Step 4: In this step, saturation current, I

S

, has been calculated

using the reverse saturation current, I

rs

, the module reference

temperature, T

rk

= 27°C, and the module operating

temperature, T

ak

, with respect to the Equation (3). The detail

of this subsystem has been given in Fig. 7.

(a)

(b)

Fig. 7. (a) Block diagram of I

S

subsystem4, (b) Internal circuit of subsystem 4.

28 M. Toghyani Rizi and M. H. Shahrokh Abadi: A New Approach for Modeling of

Photovoltaic Cell/Module/Array Based-on Matlab

(a)

(b)

Fig. 8. (a) Block diagram of subsystem5, kAT

ak

, (b) Internal circuit for the block.

(a)

(b)

Fig. 9. (a) Block diagram for the subsystem6 to calculate I

pv

, (b) Internal circuit for this block.

Physics Journal Vol. 2, No. 1, 2016, pp. 23-34 29

Step5:In this subsystem, operating temperature in Kelvin, T

ak

,

is taken to calculate kAT

ak

, a parameter used in the Equations

(4) and (5).

Step6: This block executes an internal function, Fcn, to carry

out the I

pv

. The function has been given based-on previously

defined I

pv

in the Equation (5):

( )

(2)

(3) exp (1) (6) 1 (4)

36

(1) (6) (5)

36

= − + −

− +

u

Fcn u u u u

uu u

(8)

where each unit block of u(1) through u(6) have been

illustrated in Fig (7). It is important to mention that in this

block the effect of both series and parallel resistances have

been considered. Also, through this work 36 cells in series

(N

s

= 36) has been considered in one row (N

p

= 1) as a

module. While performing the Fcn in the Matlab, an

algebraic loop warning is appeared in the command window,

which was solved by inserting a delay block in the feedback

loop coming from the output I

pv

before entering the

exponential block so that the current value can be calculated

based on its previous values.

Step7: The final step is interconnection of all the six

previously defined subsystems to implement the whole PV

module, given in Fig. 3. The block diagram of the module

has been given in Fig. 10.

Fig. 10. Block diagram of the PV module.

2.3. Simulation Scenarios

Examining the outputs of a PV system include the

instantaneous power and current characteristics. These

parameters are altered by the input parameters of: solar

insolation, temperature, voltage, series and parallel

resistances as shown in the Fig. 11. All these inputs, except

for the V

in

(repeating sequence), are created by signal builder

blocks. A multiplexer is used to collect the results produced

by simulation into a variable “V

out

” that is used later to plot

the different curves under Matlab command mode.

Fig. 11. Simulink model of the PV module.

30 M. Toghyani Rizi and M. H. Shahrokh Abadi: A New Approach for Modeling of

Photovoltaic Cell/Module/Array Based-on Matlab

3. Results and Discussions

3.1. Effect of Alteration of Sunlight

Irradiation

I-V and P-V characteristics of the module have been obtained

and shown in Fig. 12 under different irradiation of λ = 0.2,

0.6, and 1 kW/m

2

, at 27°C, using series and parallel

resistances of 0.1 Ω and 100 Ω, respectively.

It can be seen from Fig. 12(a) that an increment in the

insolation from 0.2 to 1, causes a significant increasing in the

maximum available power, P

m

, from 7 to 40 watts,

respectively. Correspondingly, graph in Fig. 12(b) shows a

proportional relationship between the short-circuit current

and the incident sunlight by a ratio of 5, at any voltage less

than 15 V, which enunciates that the PV-cell behaves more

like a current source than a voltage source [17].

(a)

(b)

Fig. 12. (a) P-V vs. (b) I-V curves of the module under different values of

incident sunlight.

3.2. Effect of Temperature Variation

Fig. 13 shows the current versus voltage and the power

versus voltage characteristics of the module at temperatures

of 25°C, 50°C, and 75°C, where the sunlight irradiation has

been fixed at 1 kW/m

2

and fixed series and parallel

resistances of 0.1 Ω and 100 Ω, respectively. The figure

shows that any increase in the temperature causes a

decrement in the maximum power, P

m

. This is due to an

increment in the saturation current, I

0

, given in Equation (3),

when the temperature is increased. Furthermore, the short

circuit current remains almost constant when the temperature

is changed at voltages up to 13 volts.

3.3. Effect of Series Resistance, R

s

The simulation was run at different values of R

s

= 0, 0.4,

and 1 Ω, and the related graphs of V-I and P-V

characteristics have been obtained as shown in Fig. 14.

The results show a great impact of series resistance of the

module on the slope of the I-V curve at the voltages

almost near the open-circuit voltage, V

oc

. Degradation in

the cell current due to greater values of R

s

indicates more

power dissipation.

(a)

(b)

Fig.13. (a) P-V vs. (b) I-V curves of the module at temperatures of 25°C,

50°C, and 75°C.

Physics Journal Vol. 2, No. 1, 2016, pp. 23-34 31

(a)

(b)

Fig. 14. (a) P-V vs. (b) I-V curves at different R

s

An important parameter of PV cells is called fill factor (FF),

which in conjunction with V

oc

and I

sc

determines the

maximum power from a solar cell, and can be calculated

from:

max

oc sc

P

FF V I

=

(9)

Fig. 14(a) also demonstrates that the output power of cell is

reduced at higher values of R

s

, resulted in lower FF.

3.4. Variation in Shunt Resistance, R

sh

An alternate current path, rather than the output current, is

produced when the PV cell is distracted from the ideal

condition. This digression is due to the shunt resistance. Such

a diversion reduces the amount of current flowing through

the solar cell junction and considerably reduces the voltage

from the solar cell. A simulation is produced at different

values of shunt resistance, R

sh

= 1, 10, and 1000 Ω and V-I

and P-V characteristics of the cell were obtained as shown in

Fig. 15. It is clear that when the R

sh

is lowered the output

current of PV cell is diminished steeply, indicates more

power dissipation which can be translated into Fill Factor

lowering. To achieve higher output power and Fill Factor, for

any applicable PV cell, R

sh

must be increased while the R

s

must be decreased, simultaneously.

(a)

(b)

Fig. 15. (a) P-V vs. (b) I-V cell characteristics at different shunt resistance.

3.5. Hot Spot Heating Effect and Bypass

Diode Operation

Hot-spot heating occurs when there is one low current solar

cell in a string of at least several high short-circuit current

solar cells, as shown in the Fig. 16 [13, 18, 19].

Fig. 16. Hot-spot heating effect.

One shaded cell in a string reduces the current through the

“good” cells, causing the good cells to produce higher

voltages that can often reverse bias the bad cell. Hot-spot

heating occurs when a large number of series connected cells

cause a large reverse bias across the shaded cell, leading to

large dissipation of power in the poor cell. Essentially the

entire generating capacity of all the good cells is dissipated in

the poor cell. The enormous power dissipation occurring in a

32 M. Toghyani Rizi and M. H. Shahrokh Abadi: A New Approach for Modeling of

Photovoltaic Cell/Module/Array Based-on Matlab

small area results in local overheating, or “hot-spots”, which

in turn leads to destructive effects, such as cell or glass

cracking, melting of solder or degradation of the solar cell.

The destructive effects of hot-spot heating may be

circumvented through the use of a bypass diode. A bypass

diode is connected in parallel, but with opposite polarity, to a

solar cell as shown below [20-22].

Fig. 17. One-diode equivalent circuit of solar cell by considering the bypass

diode.

The operation of the bypass diode has been considered by

implementing a Simulink model, given in Fig 18(a), using

the Equation (10):

0

ln ( 1)

bypass

Dbypass t

I

V V I

= − +

(10)

Where

0

25 , 1

t

V mV I A

µ

= =

The decision for being a diode in circuit or not is taken by

Switch1. The Diode = 0 is referred to as no bypass diode,

then the output voltage of PV is switched for the simulation,

which means the PV operates normally. If Diode signal is “1”

and V

pv

<V

Dbypass

, then the diode is forward biased and

I

Dbypass

versus V

Dbypass

curve can be obtained (Fig. 18(b)). The

function of saturation block is to rectify the crossing current

because bypass diode current cannot be negative. For the

modeling, it has been assumed that the hot spot heating has

been occurred and V

pv

= –1 V. A scope observation of internal

signals of the model has been given in Fig. 18(c).

(a)

(b)

Physics Journal Vol. 2, No. 1, 2016, pp. 23-34 33

(c)

Fig. 18. (a) Simulink behavioral model of bypass diode operation (b) Bypass current vs. bypass voltage curve, (c) Scope signals

4. PV Array

In order to realize a PV array, four modules have been

connected together in parallel as shown in Fig. 19 (a), and then

the whole array was simulated. The results of current and

power of array versus voltage are shown in Fig. 19 (b) and (c),

respectively. An output power of about 160 W can be obtained

from the array when the terminal voltage is about 17 volts.

(a)

(b) (c)

Fig. 19. (a) PV array model, (b) I-V curve, and (c) P-Vcurve of PV array.

34 M. Toghyani Rizi and M. H. Shahrokh Abadi: A New Approach for Modeling of

Photovoltaic Cell/Module/Array Based-on Matlab

5. Conclusion

A step by step mathematical modeling of solar energy

conversion through photovoltaic effect was demonstrated

using Matlab/Simulink. The model was simulated respect to

the variation effects of voltage, insolation, temperature, series

and parallel resistance. In this model, the simulation error

due to an algebraic loop has been modified by insertion of

delay block. The presented model can be considered as a

basis model for PV systems/arrays in the framework of the

Sim-Power-System Matlab/SIMULINK toolbox in the field

of solar PV power conversion systems to predict the behavior

of solar PV cells/module/ array under different

circumstances.

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