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Abstract Photovoltaic power generation is growing at a rapid

rate. Most new PV installations are grid-connected small-scalesystem. The impact of these installations on the grid operationneed to be carefully studied to investigated. This paper presentsthe development of simulation tools required for suchinterconnection studies. The simulation tools were developed inthe popular electromagnetic transient simulation programPSCAD/EMTDC and include a PV array model, maximumpower point tracking controller model, and a grid connectedinverter. An example of an interconnection study using thedeveloped simulation tools is presented.

Index Terms Photovoltaic generation, PV systemssimulation, PV model, PV system grid interconnection,Distributed generation, PV grid interconnection studies,Electromagnetic transient simulation, Maximum power pointtracking, PV inverter.

I. I NTRODUCTION

ROWING attention to distributed generation (DG) andgreen energy alternatives to conventional fossil fuel-

based electricity generation has revived interest in grid-connected photovoltaic (PV) systems. The global PV systemmarket has been expanding steadily during the last few years.

As the cost of PV coming down due to economy of scaleeffects and development of new technologies, applicationssuch as building integrated PV systems are becomingincreasingly popular and cost effective [1]. When larger PVinstallations are designed, studies need to be performed at the

power system level to examine the impacts of these grid-connected PV systems. For small scale distributed generatorsconnected to medium or low voltage networks,interconnection standards such as IEEE 1547 2003 [2] andlocal utility interconnection regulations define the gridinterface response to system disturbances. The protection is

based on the philosophy that in case of grid disturbances, e.g.voltage drops or frequency deviation, distributed generatorswill be disconnected from the network immediately. Thus the

protection system at the grid interface and DG control need to be designed to meet applicable requirements.

Time domain simulation using Electromagnetic Transient(EMT) programs is a powerful method that can be used forstudies involving controller tuning, protection setting, powerquality investigations and system validations. These computer

A. D. Rajapakse is with the University of Manitoba, Winnipeg, MB,Canada (e-mail: Athula@ee.umanitoba.ca).

D. Muthumuni is with the Manitoba HVDC Research Centre, Winnipeg,MB, Canada (e-mail: dharshana@hvdc.ca).

programs offer the advantage of ability to model powerelectronic systems and associated control systems in detail [3].Several approaches to incorporate PV array models in onlinesimulation have been investigated. In [4] a fuzzy regressionmodel is proposed to simplify calculations and minimize datarequirements. An incremental model of solar cell based on thetruncated Taylor series expansion of PV cell voltage has beenused in [5] to avoid numerical iterations during thesimulations. It is not uncommon to find that the PV arraymodels used in simulation studies are oversimplified. While

these approximations may be sufficient for some studies, theoutput of a PV array is highly non-linear, and to simplify thearray to a constant voltage source or a current controlledvoltage source is often not appropriate. Specially, when thePV system is equipped with MPP tracking controls, use ofvery simple models could lead to inaccuracies. In order toovercome this deficiency, this paper develops a customcomponent of a PV array for the well-known EMT programPSCAD/EMTDC. The developed PV array model is used in aPV grid integration simulation study.

II. PV ARRAY SIMULATION

A. PV Array ModelA solar cell can be modeled using an electrical equivalent

circuit that contains a current source anti-parallel with a diode,a shunt resistance and a series resistance as shown in Fig. 1.

I sc

I d I sh

R sh

R sr +

V

_

I

+

V d

_

Fig. 1 PV cell equivalent circuit

The DC current, I g , generated when the cell is exposed tolight, varies linearly with solar irradiance. The current I d through the anti-parallel diode is largely responsible for

producing the nonlinear I-V characteristics of the PV cellshown in Fig. 2. The PV cell model can be further refined byincluding a second diode [2] as shown connected by thedashed lines. The second diode provides an even moreaccurate I-V curve that accounts for the difference in current

Simulation Tools for Photovoltaic System GridIntegration Studies

Athula D. Rajapakse, Senior Member, IEEE , and Dharshana Muthumuni

G

2009 IEEE Electrical Power & Energy Conference978-1-4244-4509-7/09/$25.00 2009 IEEE

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flow at low current values due to charge recombination in thesemiconductor's depletion region. However, for most studies aPV model with a single diode is sufficient and with two diodesmodel, determination of model parameters becomes slightlycomplicated.

I

V

Isc

V o c

MPP

Fig. 2 Typical I-V characteristics of a PV cell

The basic equation that characterizes the solar cell I-V relationship can be derived considering the equivalent circuitshown in Fig. 1. The Kirchoffs current law gives

. (1)Substitution of relevant expressions for the diode current Id

and the shunt branch current Ish yields

. (2)

In (2) I sc is the photo current and it is a function of the solarradiation on the plane of the solar cell G and the celltemperature T c:

(3)

where I scR is the short circuit current at the reference solarradiation G R and the reference cell temperature T cR. The

parameter T is the temperature coefficient of photo current.The current I o in (2) is called the dark current, a function ofcell temperature only, and given by

(4)

where I oR is the dark current at the reference temperature.The other parameters appearing in (2)-(4) are the electroncharge q, the Boltzmann constant k , the band-gap energy ofthe solar cell material e g , and the diode ideality factor n whichis between 1-2 (1.3 is typical for silicon solar cells). All of theconstants in the above equations can be determined byexamining the manufacturers specifications of the PV

modules and the published or measured I-V curves of thearray. Since a PV module is composed primarily of series-connected cells, and a PV array is composed of series- and

parallel-connected modules, the single cell circuit can bescaled up to represent any series/parallel combination.

B. Simulation of PV ArrayThe above PV cell model was implemented as a custom

component in PSCAD (see Fig. 3). The PV array wasinterfaced as a nonlinear current source. Implementation ofequation (2) which is highly nonlinear in a fixed time-step

simulation program is challenging. In fact accurateimplementation on the above equation requires iterativesolution of (2) simultaneously with the network equations.However, considering the small time steps used in typical emtsimulations, voltage calculated from the last time step can beused to determine the new current injections. In order toensure the simulation stability under rapidly changing outputvoltages, feedback of the voltage at previous time step was

provided through a first order filter. Although this numericaltechnique improves the simulation stability around the knee

point, it introduces a slight inaccuracy near the knee pointwhen simulation is run at larger time-steps.

III. M AXIMUM POWER POINT TRACKING

The amount of power that can be drawn by a solar celldepends on the operating point on the I-V curve and themaximum power output occurs around the knee point of thecurve. A maximum power point tracker (MPPT) is a powerelectronic DC-DC converter inserted between the PV arrayand its load to achieve optimum matching. By using anintelligent algorithm, it ensures the PV module alwaysoperates at its maximum power point as the temperature, solarradiation and the load vary. A number of tracking algorithmshave been proven and used and a number of DC-DC convertertopologies are possible [7-9]. A commonly used simpletechnique is the Perturb and Observe (P&O) algorithm but ithas many limitations. Another popular but slightly advancedMPPT algorithm [7, 9] is the Incremental Conductancemethod shown in Fig. 4. This algorithm was implemented inPSCAD (see Fig. 3).

IV. T EMPERATURE EFFECTS

The open circuit voltage and the maximum power point

voltage are sensitive to the cell temperature. At highertemperatures the efficiency of solar cells drops. Thesetemperature dependencies are included in the PV cell modeland it requires cell temperature as an input. Calculation of Tcrequires a thermal model which takes various inputs such assolar radiation, wind velocity, ambient temperature, etc. and

parameters such as tilt angle of the array, surface emissivity,etc (see Fig. 3). Since the thermal time constants are muchlarger than electrical time constants, in most emt simulationsuse of constant cell temperature should be sufficient.

V+

G

Tcell

V-

TskyGt

Tamb

Wvel Tpv

Tgnd Ppv

Tilt

MPPTcontrol

Vpv

IpvVmpp

Fig. 3 PV system simulat ion components library developed for PSCAD

V. G RID CONNECTED PV I NVERTER SYSTEM

A simple example of using these components for a systemstudy is shown in Fig. 5. For the simplicity of presentation, the

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grid system is represented only as an equivalent source behindthe system impedance. The inverter is connected to the 11 kVgrid through a step-up transformer. Except for the transformerwinding inductance and the smoothing inductor, no additionalharmonic filtering is provided. The output voltage of the 200kWp PV array is controlled at the maximum power point(around 1500 V) by the MPPT system. The controller used formaximum power tracing dc-dc converter is shown in Fig. 6.

Vpv T1I

P

D +

F

- A

B Compar-ator

Vpv_ref

MPPTcontrol

Vpv

IpvVmppVpv

Ipv

G1 + sT

G1 + sT

Vmppt A

BCtrl

Ctr l = 1

Mppt_ON/OFF

Fig. 6 Dc-dc converter control with MPP tracking

VI. S IMULATION R ESULTS

A. I-V Characteristics MPPT PerformanceThe I-V curve of the simulated PV array at a constant

radiation level and a constant temperature is shown in Fig. 7.The thick green line superimposed on the I-V characteristicscurve shows the variation of the operating point of the PVarray, when the maximum power point tracking is enabled.Even at constant radiation level, the operating point oscillatesdue to tracking action.

Maximum power point tracking performance undervariable solar radiation and temperature conditions is shown inFig. 8. The solar radiation and the cell temperature werevaried during the simulation resulting in a series of I-V curves.The I-V curves shown in Fig. 8 were obtained by simulating a

second PV array model with the same parameters under thesame solar radiation and cell temperature conditions as the PVarray in the system. The thick green line indicates the variationof PV array operating point during the variations of the solarradiation and the cell temperature. It is evident that the MPPTcontroller tracks the knee point fairly accurately.

gt1

gt2

gt3

gt4

gt5

gt6

1

Eab

Ebc

Idc

35

2 6 4

135

2 6 4

Ia_grid

dcVltg

#1 #2

P = 0.2036Q = -0.01998

V = 11

V A

2e-4

8 0 0 0 0

5

1 0 0 0 0

5

T1

Vpv

Icon

0.01 [H]

V+

G

Tcell

V-

SolRad

CellTemp

Ipv

Fig. 5 Example of simulating a grid connected PV system simulation (for the simplicity, the ac system is shown as an equivalent source).

Start

MeasureV(t) and I(t) , Compute V = V(t)- V(t-1), I = I(t)- I(t-1)

V =0

IncreaseV ref Decrease V ref IncreaseV ref Decrease V ref

Yes

No

No

NoNo

Yes

Yes

I =0

I >0 Yes

Yes

No

Stop?Yes

Stop

No

Fig. 4 Incremental Conductance based MPPT algorithm [7]

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-0.25 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

0.000

0.020

0.040

0.060

0.080

0.100

0.120

0.140

0.160 +y

-y

-x +x

I - V curveOperating Point

Fig. 7 I-V characteristics of the simulated PV array and MPPT tracking performance (x- axis PV array voltage (kV) and y-axis PV array current (kA).

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.000.000

0.025

0.050

0.075

0.100

0.125

0.150

0.175

0.200 +y

-y-x +x

I - V curveOperating Point

Fig. 8 MPP tracking under variable solar radiation and temperature conditions.

B. PV System Interconnection StudiesThe performance of the grid connected PV system under

variable solar radiation conditions is shown in Figs. 9-11. Thearray voltage and current response to varying solar radiationlevel is shown in Fig. 9. The PV array voltage closely followsthe reference voltage determined by the MPPT algorithm.

The point of common coupling (PCC) rms voltage and thereal and reactive power flow of the PV inverter during this

period are shown in Fig. 10. The PCC rms voltage remainsfairly constant while the output real power changes proportional to the changes in the solar radiation level. Theinverter is set to operate at unity power factor, but during thetransients, the reactive power output of the inverter changes.This is a result of the simple inverter controller used in this

paper. Fluctuations in reactive power can be minimized byimproving the inverter control, for example by usingdecoupled control based in d-q currents.

PV Array

5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0

1.00

1.10

1.20

1.30

1.40

1.50

V o l

t a g e

Vmppt Vpv

0.000

0.050

0.100

0.150

0.200

0.250

C u r r e n t ,

P o w e r

( k A

, M W )

Ipv Ppv

Fig. 9 PV array output under variable radiation conditions. (note that the Dc-Dc converter very closely tracks the operating voltage commanded by MPPT)

Inverter - Grid Interface

5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0

-0.050

0.000

0.050

0.100

0.150

0.200

0.250

R e a

l a n d

R e a c t

i v e

P o w e r

P Q

0.0

2.0

4.0

6.0

8.0

10.0

12.0

V o l

t a g e a t

P C C

Vrms

Fig. 10 Real and reactive power at the grid interface

Harmonic injection by the grid connected PV inverters is a

concern [10] and standards such the IEC standard 61727 Photovoltaic (PV) systems-----Characteristics of the utilityinterface and the IEEE standard 929-2000 Recommended

practice for utility interface of photovoltaic systems provideguidelines on harmonic limits at the PCC. The three-phasecurrent and voltage at the PCC are shown in Fig. 11. Thevoltage waveforms are not much distorted but the distortionsin the current waveforms are quite visible. These waveformscan be processed to determine the THD and TDD values tocheck whether the system complies with the standards or theregulation set by the local utility.

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Inverter

4.900 4.910 4.920 4.930 4.940 4.950 4.960 4.970 4.980 4.990 5.000

-8.0

-4.0

0.0

4.0

8.0

V o l

t a g e

( k V )

Vac

-0.0150

-0.0100

-0.0050

0.0000

0.0050

0.0100

0.0150

C u r r e n t

( k A )

Iac

Fig. 11 Inverter currents and voltages

VII. C ONCLUSIONS

A simulation model of a PV array was implemented in anelectromagnetic transient simulation program. Numericalmodel interfacing issues due to nonlinear characteristics of thePV array was briefly discussed. A model to simulate theincremental conductance based maximum power pointtracking algorithm was also implemented. Application of thesesimulation tools was demonstrated through an example of gridconnected PV system simulation.

VIII. R EFERENCES [1] P. Maycock and T. Bradford, PV Technology, Performance, and Cost:

2007 update, Prometheus Institute for Sustainable Development and PVEnergy Systems, Cambridge, MA, USA, 2007.

[2] IEEE Standard for Interconnecting Distributed Resources with Electric Power Systems , IEEE Standard 1547, 2003.

[3] A. D. Rajapakse, D. Muthumuni, N. Perera, and K. Strunz,Electromagnetic Transients Simulation for Renewable EnergyIntegration Studies, in Proc. of IEEE PES Annual Meeting , Tampa, FL,USA, 24-28 June 2007.

[4] V. Quaschning and R. Hanitsch, Numerical simulation of photovoltaicgenerators with shaded cells, in Proc. of the 30th Universities Power

Engineering Conference , Greenwich, Sept. 5-7, 1995, pp. 583-586.[5] M.T. Elhagry, A.A.T. Elkousy, M.B. Saleh, T.F. Elshatter, and E.M.

Abou-Elzahab, Fuzzy modeling of photovoltaic panel equivalentcircuit, in Proc. of the 40th Midwest Symposium on Circuits andSystems , 3-6 Aug. 1997, pp. 60 - 63 Vol.1.

[6] A. D. Theocharis, A. Menti, J. Milias-Argitis and Th. Zacharias,Modeling and simulation of a single-phase residential photovoltaicsystem, Proc. of IEEE Russia Power Tech, 27-30 June 2005, pp. 1-7.

[7] Hussein K.H., Muta I., Hoshino T., Osakada, M.: Maximum photovoltaic power tracking: an algorithm for rapidly changingatmospheric conditions, IEE Proc. Generation, Transmission and

Distribution , Vol. 142 No. 1, Jan. 1995, pp. 59 64.

[8] M. Veerachary, Power tracking for nonlinear PV sources with coupledinductor SEPIC converter, IEEE Trans. Aerospace and ElectronicSystems , Vol. 41, No. 3, July 2005, pp. 1019-1029.

[9] G. M. S. Azevedo, M. C. Cavalcanti, K. C. Oliveira, F. A. S. Neves andZ. D. Lins, Evaluation of maximum power point tracking methods forgrid connected photovoltaic systems, in Proc. of IEEE Power

Electronics Specialists Conference (PESC 2008), 15-19 June 2008, pp.1456 1462.

[10] M. Aiello, A. Cataliotti, S. Favuzza, and G.Graditi, Theoretical andexperimental comparison of total harmonic distortion factors for theevaluation of harmonic and interharmonic pollution of grid-connected

photovoltaic systems, IEEE Trans. Power Delivery , Vol. 21, No. 3, pp.1390-1397.

IX. B IOGRAPHIES

Athula D. Rajapakse (M99) received the B.Sc. (Eng.) degree from theUniversity of Moratuwa, Sri Lanka, in 1990, the M.Eng. degree from theAsian Institute of Technology, Thailand, in 1993, and the Ph.D. degree fromthe University of Tokyo, Japan, in 1998. Currently, he is an AssistantProfessor at the University of Manitoba, Winnipeg, MB, Canada. His researchinterests include power system protection, transient simulation of power and

power-electronic systems, distributed and renewable energy systems. He is aProfessional Engineer in the province of Manitoba, Canada.

Dharshana Mutumuni obtained his B.Sc. (Eng) degree from the Universityof Moratuwa, Sri Lanka in 1993 and Ph.D. degree from the University ofManitoba, Canada. He is with the Manitoba HVDC Research Centre since2000. He has extensive experience in transient simulation and providingsimulation training and currently the Technical Sales manager of ManitobaHVDC Research Centre. He is also a registered Professional Engineer in theProvince of Manitoba.