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Proceedings of the 1stInternational Nuclear and Renewable Energy Conference (INREC10), Amman, Jordan, March 21-24, 2010

INREC10-1

A PROPOSED DYNAMIC MODEL OF PHOTOVOLTAIC-DG SYSTEM

Magdi M. El-Saadawi Ahmed E. Hassan Khaled M. Abo-Al-Ez Mahmoud S. Kandil

Mansoura University

Department of Electrical EngineeringP.O. Box 35516, Mansoura, [email protected],[email protected],[email protected], [email protected]

ABSTRACT

Dynamic modeling is important to predict the energy productionof Photovoltaic (PV) systems. It is needed to make informedtechnical and economical decisions. The simulation models of PVsystems in literature are good enough for steady state analysis,

but they are not suitable for dynamic analysis of grid operatingand control conditions. This paper proposes a dynamic PV modelsuitable for Decentralized Generation (DG) applications. The

proposed model relates the electrical output of the PV system to

various input environmental parameters. The model is developedin Matlab-Simulink environment, and it is validated comparingthe developed PV performance characteristic curves with those ofthe manufacturer's data sheet and those developed by a

commercial software package for a Solarex-MSX 60W PV type.

Key words: Photovoltaic (PV) model, Decentralized Generation(DG), Temperature coefficients.

1. INTRODUCTIONDynamic modeling and simulation of modern Decentralized

Generation (DG) electrical systems is a challenging process because of the several modeling steps presenting the power

generation dynamics of the DG system [1]. Photovoltaic (PV)technology is offering one of the best DG power productionoptions [2]. Modeling of the PV system is needed for testingdifferent control algorithms and operation scenarios before real-

time implementation. PV simulation models have been developedfor years. literature review of some of recent work is presented in[3-6].The work in those literatures uses general and simplifiedmathematical models, which are good enough for steady state

analysis and for modeling the PV system annual performance.But those models lack the availability for dynamic analysis withreal grid conditions, and with various dynamic controlalgorithms. Other PV models are available within some

commercial software packages. These packages are used forsizing and economic studies such as (Hybrid2, SOMES,PVSYST, Solar Studio, PV F-Chart, PV-Design Proetc) [7].These types of software can perform extensive sensitivity

analysis, but they generally do not permit the user to modify theoperating algorithms that determine the behavior and interactionson individual system components. The PV model should bedynamic and flexible enough to easily present the components of

the required PV equivalent circuit. The model should also predicthow PV current and voltage will vary with ambient temperatureand solar radiation conditions.

2. PV MODELLING FRAMEWORKThere are some steps that form a proposed framework for

building accurate and flexible model of the PV system. Thosesteps are briefly presented in Figure 1. In this paper, a PV modelis developed based on the proposed framework. This model allows

the operation of a single solar cell, and hence a panel, to besimulated using available data from manufacturer data sheets, andfield tests. These data are used to provide values for the model

parameters. The model is tested and verified by comparing the

results showing the I-V and P-V characteristics to those providedby both the manufacturer, and a commercial PV software package.All the proposed modules are built using Matlab-Simulink [8],which is an open-architecture tool that has a high level of

flexibility in the interaction of the model components as will beillustrated in the sections of this paper.

Figure 1.A proposed framework for building a PV model

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2.1. PV Equivalent Electrical Circuit ModelIn the crystalline silicon PV module; The complex physics of

the PV cell can be represented by the equivalent electrical circuit

shown in Figure 2 For that equivalent circuit; a set of equationshave been derived, based on standard theory [10-12], that allowthe operation of a single solar cell, to be simulated using data from

manufacturers or field experiments.

Figure 2.Equivalent electrical circuit of PV module

The circuit parameters are as follows [10-12]:

The output-terminal current I equals to the light-generatedcurrent IL, less the diode-current Id and the shunt-leakagecurrent Ish.

The series resistance Rs represents the internal resistance tothe current flow, and depends on the p-n junction depth, theimpurities and the contact resistance.

The shunt resistance Rsh is inversely related with leakagecurrent to the ground.

In an ideal PV cell, Rs = 0 (no series loss), and Rsh = (noleakage to ground). In a typical high quality one square inchsilicon cell, Rs = 0.05 to 0.10 ohm and Rsh = 200 to 300 ohms[10]. The PV conversion efficiency is sensitive to small variations

in Rs, but is insensitive to variations in Rsh. A small increase in Rscan decrease the PV output significantly [10].

2.2. Mathematical Modeling of the PV SystemThe equivalent circuit of Figure 2, the current delivered to the

external load equals the current IL generated by the illumination,less the diode current Id and the ground-shunt current Ish. The loadcurrent is given by the expression:

(1)where:

V0 = Vsh = voltage on the diode and the shunt resistance

Id = diode Current (A).The cell could be represented by a voltage-current equation:

(2)where:

V = cell output voltage (V).I = load (cell) output current (A).IL = Photocurrent (A).I0= Reverse diode saturation current (A).

The two most important parameters widely used fordescribing the cell electrical performance are the open-circuitvoltage Voc and the short-circuit current Isc. The short-circuit

current is measured by shorting the output terminals, andmeasuring the terminal current under full illumination. The

maximum photo-voltage is produced under the open-circuitvoltage. The open circuit voltage Voc of the cell is obtained whenthe load current is zero, i.e., when I = 0.

2.3. Mathematical Modeling of Environmental FactorsIn this research paper, a model of the PV system with

increased accuracy and complexity could be developed byincluding temperature dependence of the photocurrent IL and the

saturation current of the diode I0. The series resistance Rs isincluded, but the shunt resistance is ignored. The proposed modeladopts the simplified single diode version of the two diode model

presented in [13]. In the proposed model a single diode could be

used with adjusting the diode quality factor for the best curvefitting.

The general equation describing the (I-V) characteristics of thePV cell is obtained from Eq.1 by ignoring the last term of the

shunt resistance, and using the famous formula used for the diodecurrent [10], as follows:

/ 1 (3)where:

IL = photocurrent (A).I0 = diode saturation current (A).

q = electron charge = 1.6* 10-19 Coulombs.n = ideality factor.

K = Boltzmann constant = 1.38 * 10-23 Joule/oK.Tr = rated cell temperature in Kelvin.Rs = cell series resistance (ohm).

The non-linear Eq.3 describes the PV cell (I-V)characteristics, which adopts the equivalent circuit of PV cell

presented in Figure 2 and includes an explicit solar radiationdependency of the photocurrent (IL). The diode current (Id) ismodeled as a thermally activated device to account for variationsof module performance with temperature. Eq.3 is considered as

the benchmark model for a certain level of cell operating

temperature (Tr) in Kelvin, and Solar radiation level (Gr) in(W/m2). If those two important environmental variables are takeninto consideration, the voltage and current output of the PV cell

will follow their changes which should be included in the final PVcell model. When the cell is not illuminated, the relationship

between the cells terminal voltage and current is given by theShockley equation [10]. When the cell is open circuited and

illuminated, the photo-current flows entirely in the diode. The (I-V) curve is offset from the origin by the photo generated current ILas illustrated in Eq. 3.The value of the saturation current I0 at different operating

temperatures is calculated as presented in Eq. 4 [12, 13]:

(4)

/ 1 (4.a)where:

Vg = The band gap voltageVoc(Tr) = Open Circuit voltage at rated operating conditions.Isc(Tr) = Short circuit current at rated operating conditions.

An estimate must be made of the unknown ideality factor "n",which takes a value from 1 to 2. A value of 1.3 is suggested as

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typical in normal operation [6]. The relationship of I0 in Eq. 4 iscomplex, but fortunately contains no variables that requireevaluation [14]. The photocurrent IL(A) is directly proportional to

solar radiation level G (W/m2), as presented in Eq. 5 [14]:

1 (5) ,/ (5.a)

(5.b)where:

Isc = the short circuit temperature coefficient (A/sec)

When the cell is short circuited, a negligible current flows in

the diode. Hence the proportionality constant in Eq. 5.a is set sothe rated short circuit current ISC at the rated temperature isdelivered under rated radiation (usually 1 Sun =1000W/m2).

The relationship between the photo-current and the

temperature is linear in Eq. 5, and is deduced by noting the changeof photo-current with the change of temperature with the constant

value Iscspecified in Eq.5.b.The open circuit voltage is varied with temperature as

illustrated in Eq. 6:

1 (6)where:VOC = the open circuit temperature coefficient (V/sec).

The Manufacturers usually provide data about the temperature

coefficients. Temperature coefficients provide the rate of change(derivative) with respect to temperature for the main PV

performance parameters. ASTM standards address twotemperature coefficients, one for short circuit current and one for

open circuit voltage [15, 16]. The temperature coefficient for opencircuit voltage is usually assumed to be independent of the solar

radiation level, which is a reasonable simplification. Thetemperature coefficient for short circuit current must be scaled by

the ratio of actual radiation level to the level of 1000 W/m2 used

for determining the coefficients [17, 18]. All the constants in the

above equations are provided for typical rating conditions of 25oCcell temperature, a prescribed solar radiation of 1000 W/m2

radiation level, and zero angle of incidence.

2.4. Building the PV Simulation ModelMatlab-Simulink is used for the modeling task [10]. The

Simulink block diagram presenting the PV model is the core of

the system model. The model is flexible for any number ofmodules connected in series and/or parallel branches dependingon the PV system power required. A Solarex MSX60 PV type [19]is chosen for PV array modeling. This type is well-suited for

virtually all applications where PV systems are a feasible energysource, including pumping and irrigation, remote villages and

clinics, and aids to navigation. The MSX60 module provides 60Watts of rated power, and has 36 series connected polycrystalline

silicon cells. The performance of typical MSX60 modules isdescribed by the electrical characteristics parameters shown inTable 1[18, 19]. The Matlab-Simulink model is developed for onecell of the PV module based on the manufacturer data, and themathematical equations (from Eq. 3 to Eq. 6) as shown in Figure 3

the output presents the PV cell operating current. Three sub-systems are combined to present the complete PV cell model forspecific type of PV systems such as the Solarex MSX60 type, as

shown in Figure 4:1. Manufacturer data block: it presents the key specification

parameters of the PV module type in Table 1.

2. PV cell model bock: it presents one PV cell modeldeveloped in Figure.2.

3. PV voltage block: this block is built to find the value ofthe PV cell output voltage based on Eq.2 to give the

flexibility to use the model as a current or voltage sourceduring computer simulations, and to calculate the celloutput power.

As discussed earlier in this paper the model is subjected to

environmental conditions which are presented by the inputparameters of temperature and solar radiation level. The number

of series connected modules and parallel branches are alsoincluded in the input parameters, as illustrated in the graphical

user interface (GUI) block in Figure 5.

Table 1.Key specifications of Solarex MSX 60 [18,19].

Description Value

Typical peak power (Watts) 60

Voltage at peak power (Volts) 17.1Current at peak power (Amperes) 3.5

Guaranteed minimum peak power (Watts) 58

Short circuit current Isc (Amperes) 3.8

Open circuit voltage Voc (Volts) 21.1

Temperature coefficient for Isc = I 0.00063Temperature coefficient for Voc = V 0.0042

Figure 3. The proposed PV cell Simulink model

Isc_TaC

Isc_Tac

Voc_Tac

IL-Id

Voc1=Voc_T1/Ns

Voc_T1

EQ. (6)

EQ. (5)

IL= Photocurrent

I0

I0 (T1)

Vcell

q/ nK (TaC)

EQ. (4)

1+ K0(TaC-T1)

EQ.(2)

IL_T1

EQ.(3)

Icell

1

q:Electroncharge 2

1.6e-19

q:Electroncharge1

1.6e-19

q: Electroncharge

1.6e-19

nor A: Ideality ofcurve

fittingfactor 1

1.2

nor A: Ideality ofcurve

fittingfactor

1.2

Vg: bandgapvoltage , 1.12eV forxtal Si

1.12

exp(u)

exp(u)

u(1)^(3/u(2))

Math

Function

eu

K: boltzmanconstan 1

1.38e-23

K: boltzmanconstan

1.38e-23

Constant5

1

Constant4

1

Constant3

1

-1

Constant1

1

Constant

1

BETA_Voc

10

dIsc/dT= ALPHA_Isc

9

VD_Rs

8

Ns (Number ofsereis cells )

7

Input8:

OperatingTemp (TaC)

6

Input8:

irradiation

5

Input7:

Voc_T1

4

Input5:

Isc_T1

3

T1_refrence

2

Va: operatingvolatge (V)

1

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Figure 4. The Complete PV cell Simulink block diagram

Figure 5. GUI block of Solarex MSX60 PV system

3. TESTING AND VALIDATION OF THE MODELThe proposed model is able to calculate current, voltage, and

power relationships, for different environmental conditions of

solar radiations, and ambient temperatures. The I-V and P-Vcharacteristics are produced by the proposed model for the chosenPV array type through Matlab-Simulink environment. Thevalidations of the results are done for three steps:

Validation under standard test conditions (full sun radiation(1000W/m2) and 25oC temperature).

Validation under different temperature level.

Validation under different solar radiation levels.Testing results of PV operating characteristics would be

compared to the ones produced by PV commercial software, and

the manufacturer data sheets, as will be explained in the followingsections.

3.1 Model Validation under Standard Test Conditions

The results are developed for standard test conditions of fullsun radiation (1000W/m2) and 25oC temperature, and they are

presented in Figure 6.

Figure 6.I-V and P-V characteristics of the PV model

PV-Design Pro. software package [20] is used to present theI-V and P-V characteristics for the same PV type from a large data

base built in it. This package is a detailed simulation program with

algorithms developed by King et al. [21]. These algorithms areused for the annual performance prediction of PV systems such asPV powered water pumping system. Figure 7 shows the I-V andP-V characteristics for the Solarex MSX 60 as developed by the

PV-Design Pro. at standard test conditions.

Figure 7.I-V and P-V characteristics of the Solarex MSX 60

by PV Design Pro. [20]

Table 2 shows the values of maximum power point at standardtest conditions (1000 W/m2, 25oC) as obtained from theManufacturer data sheet [10,19], the implementation of both PV-

Design Pro. software, and the proposed Simulink model.

Table 2. Maximum power points for different models(25oC and 1000 W/m2)

Model (at standard

test conditions)

Maximum

Power (Pm)

(W)

Voltage

at Pm

(V)

Current

at Pm

(A)

Manufacturer testsand data sheet

60 17.1 3.5

PV Design Pro.Software

59.85 17.1 3.5

Proposed model 60.1825 16.860 3.569

0 2 4 6 8 10 12 14 16 18 200

10

20

30

40

50

60P-V Characteristics

Output Voltage (V)0 2 4 6 8 10 12 14 16 18 20

0

0.5

1

1.5

2

2.5

3

3.5

I-V Characteristics

Output Voltage (V)

Discrete,

Ts = 2e-005 s.

powergui

Vpv

PV

To Workspace

irradiation (Suns)

Operating Temp (k)

N_Parallel

N_Series

Operating Voltage

Vpv

Ipv

Ppv

Solarex MSX60 Module(36 series cells)

1000

RADIATION

-C-Operating

Temperature (TaC=Kelvin)1

1

Nps = Number of Panels inEACH PARALLEL

STRING (I)

1

N_panels = Number of parallel

panel connection strings (I)

1000

1KW/m2

Variables

3

Ppv

2

Ipv

1

Vpv

T1

Isc_T1

Voc_T1

No_of_Series_Cells of_One_Module

TOTAL_Series_Resistance

ALPHA_Isc1

BETA_Voc1

Manufacturerdata

Va: operating volatge (V)

T1_refrence

Input5: Isc_T1

Input7: Voc_T1

Input8: irradiation

Input8: Operating Temp (TaC)

Ns (Number of sereis cells)

VD_Rs

dIsc/dT= ALPHA_Isc

BETA_Voc

Icell

IL

I0

MSX-60 PV CELL model

3.8

Icell

Icell

IL

I0

TaC

Ns

Rs

V_MODULE

Iarray

VD_Rs

I2V Transform

5

Operating Voltage

4

N_Series

3N_Parallel

2

Operating Temp (k)

1

irradiation (Suns)

RS

PV cellmodelblock

Manufacturerdata block

PVVoltageblock

OutputCurrent

(A)

OutputPower

(W)

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Comparison of the results in Table 2 shows that it is withinacceptable accuracy and that the model is well-designed tosimulate the performance characteristics of the actual MSX60 PV

system under standard test conditions.

3.2 Model Validation for Different Temperature Levels and

Constant Radiation

To assure the flexibility and the accuracy of the developed

Simulink model, the model is tested under different temperaturelevel of 50oC, and the I-V and P-V characteristics are developedin Figure 8.

Figure 8.I-V and P-V Characteristics of the proposed modelat 50oC

The PV-Design Pro. offers a comparison between the I-Vcharacteristics for both 25oC and 50oC at a radiation of 1000

W/m2, from which; it is possible to obtain the values of the I-Vcurve knee points of the voltage and the current which presentsthe maximum power points, as presented in Figure 9.

Figure 9. I-V characteristics of the Solarex MSX 60 by PV-Design Pro. at 25oC and 50oC with 1000 W/m2 [20]

Table 3 shows the values of maximum power point at standardtest conditions (1000 W/m2, 25oC) as obtained from theManufacturer data sheet [10,19], the PV-Design Pro. software,

and the proposed Simulink model.

Table 3. Maximum power points for different models (50

o

C and1000 W/m2)

Model (at 50oC

and 1000 W/m2)

Maximum

Power (Pm)

(W)

Voltage at

Pm

(V)

Current

at Pm

(A)

Manufacturer testsand data sheet

54 15 3.6

PV-Design Pro.

Software54.2 14.8 3.648

Proposed model 53.8953 15.1640 3.5542

It is noticed from the results presented in Table 3 that it isaccurate enough to use the developed Simulink model fordifferent operating temperature levels, for a constant solar

radiation level.

3.3 Model Validation for Different Radiation Levels and

Constant Temperature

To further show the capability of the developed Simulink

model to operate, not only at different temperatures, but also fordifferent solar radiation levels, the model is simulated underdifferent radiation levels and the results are compared to assurethe accuracy. The PV-Design Pro. offers the I-V characteristics

with constant temperature of 25oC and for different radiationlevels from 200 W/m2 (bottom curve) up to 1000 W/m2 (uppercurve), as shown in Figure 10. The simulations results using thedeveloped Simulink model developed for both I-V and P-V

characteristics are shown in Figures from Figure 11 To Figure 14.

Figure 10.I-V characteristics of the Solarex MSX 60 by PV-Design Pro. At 25C for radiation levels from 200 W/m2 to

1000 W/m2 [20]

Figure 11.I-V and P-V characteristics at 25oC and 200 W/m2


0 2 4 6 8 10 12 14 16 18 200

5

10

15

20

P-V Characteristics

Output Voltage (V)0 2 4 6 8 10 12 14 16 18 20

0

0.5

1

1.5

I-V Characteristics

Output Voltage (V)

0 2 4 6 8 10 12 14 16 18 200

2

4

6

8

10

P-V Characteristics

Output Voltage (V)0 2 4 6 8 10 12 14 16 18 20

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

I-V Characteristics

Output Voltage (V)

0 2 4 6 8 10 12 14 16 18 2005

10

15

20

25

30

35

40

45

50

P-V Characteristics

Output Voltage (V)0 2 4 6 8 10 12 14 16 18 20

0

0.5

1

1.5

2

2.5

3

3.5

I-V Characteristics

Output Voltage (V)

OutputCurrent

(A)

OutputCurrent

(A)

OutputCurrent

(A)

OutputPower

(W)

OutputPower

(W)

OutputPower

(W)

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Figure 13. I-V and P-V characteristics at 25oC and 600 W/m2


The comparison of the I-V characteristics at each radiationlevel verifies the accuracy of the developed Simulink model.

4. CONCLUSIONSThis paper introduces a model of PV system for computer

analysis. Based on a proposed framework, a detailed simulation

model of the PV system is developed, and demonstrated inMatlab-Simulink for a typical 60W solar panel. The I-V and P-Vcharacteristics of the model, is compared with those availablefrom the datasheets and those developed by PV-Design Pro.

software package. Results of comparison verify the accuracy ofthe developed Simulink model, and they show the model realityand flexibility with different levels of environmental conditions.The proposed model has the advantage of generalized structure so

that it can be used for performance testing of different PVcommercial types, and it could be used for simulation and study ofdifferent decentralized generation applications by establishing

proper interfacing and controllers, which will be investigated in a

future work.

5. REFERENCES[1] Kandil, M. S., El-Saadawi, M .M., Hassan, A. E., Abo-Al-Ez

K. M., "Performance Analysis of a Biomass MicroturbineDG for Rural Electrification", 3rd International Power

Engineering and Optimization Conference (PEOCO2009),Shah Alam, Malaysia, June 2009.

[2] Thompson, A.M., "Reverse-Osmosis Desalination ofSeawater Powered by Photovoltaics without Batteries",

Doctoral Thesis, Loughborough University, 2003.[3] Walker, G., "Evaluating MPPT Converter Topologies Using

a MATLAB PV Model", Journal of Electrical andElectronics Engineering, Australia, IE August, Vol.21, No.1,2000.

[4] Lopez, L.A.C, Lienhardt, A.M., "A Simplified NonlinearPower Source for Simulating PV Panels", 34th IEEEConference of Power electronics specialists PESC'03, June2003.

[5] Gow, J.A., Manning, C.D., "Development of a PhotovoltaicArray Model for Use in Power Electronics SimulationStudies", IEE Proceeding on Electric power applications,

Vol.146, March 1999.[6] Gonzalez-Longatt, F. M., "Model of Photovoltaic Module in

MATLAB", Proceeding of 2nd CIBELEC 2005 Conference,Venezuela, 2005.

[7] Colin, H., Boulanger, P., "Photovoltaic Hybrid SystemModelling with Hybrid2 Software", Journal of PVHPS,September 2000.

[8] http://www.mathworks.com.[9] Ferret, F. A., Integration of Alternative Sources of Energy,

IEEE Press & Willey Interscience, 2006.[10]Patel, M.R., Wind and Solar Power Systems, CRC Press,

1999.[11]Sorensen, B., Renewable Energy: Its Physics, Engineering,

Use, Environmental Impacts, Economy and PlanningAspects, Elsevier Academic Press, 2004.

[12]M. Buresch, Photovoltaic Energy Systems Design andInstallation, McGraw Hill. Inc., 1983.

[13]Thevenard, D., "Review and Recommendations forImproving the Modeling of Building Integrated Photovoltaic

Systems", 9th

International IBPSA Conference, Montreal,Canada, 2005

[14]Schmitt, W., Modeling and Simulation of PhotovoltaicHybrid Energy Systems Optimization of Sizing and ControlConference Record of the IEEE Photovoltaic Specialists

Conference, 2002.

[15]ASTM E 948 standard, "Electrical Performance of Non-Concentrator Terrestrial PV Cells Using Reference Cells".

[16]ASTM E 1036 standard, "Electrical Performance of Non-Concentrator Terrestrial Photovoltaic Modules and ArraysUsing Reference Cells".

[17]King, D. L., "Photovoltaic Module and Array PerformanceCharacterization Methods for All System OperatingConditions",NREL/SNL Program Review, AIP Press, 1996.

[18]King, D.L., Kratochvil, J.A., Boyson, W.E., "Temperature

Coefficients for PV Modules and Arrays: MeasurementMethods, Difficulties, and Results", Proc. 26th IEEEPhotovoltaic Specialists Conference, Anaheim, CA,1997.

[19]http:// www.solarex.com.[20] PV-Design Pro.2000, Solar design studios, V4.0, Maui Solar

Energy Software Corp., Haiku, HI.[21]King, D.L., W.E.Boyson, and J.A. Kratochvil, "Photovoltaic

Array Performance Model", Sandia Report No. SAND 2004-3535, 2004.

0 2 4 6 8 10 12 14 16 18 200

5

10

15

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35

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P-V Characteristics

Output Voltage (V)

0 2 4 6 8 10 12 14 16 18 200

0.5

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1.5

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2.5

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I-V Characteristics

Output Voltage (V)

0 2 4 6 8

10 12 14 16 18 20

0

5

10

15

20

25

30

35

P-V Characteristics

Output Voltage (V)0 2 4 6 8 10 12 14 16 18 20

0

0.5

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1.5

2

I-V Characteristics

Output Voltage (V)

OutputCurrent

(A)

OutputCurrent

(A)

OutputPower

(W)

OutputPower

(W)

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