GESEP – Gerência de Especialistas em Sistemas Elétricos de Potência

Título:

Modeling and control of a flexible photovoltaic array simulator

Autores:

CUPERTINO, ALLAN F. ; SANTOS, GUILHERME V. ; PEREIRA, HEVERTON A. ; SILVA, SELENIO R. ; MENDES,

VICTOR F.

Publicado em:

2015 IEEE 24th International Symposium on Industrial Electronics (ISIE)

Data da publicação:

2015

Citação para a versão publicada:

CUPERTINO, ALLAN F. ; SANTOS, GUILHERME V. ; PEREIRA, HEVERTON A. ; SILVA, SELENIO R. ; MENDES,

VICTOR F. . Modeling and control of a flexible photovoltaic array simulator. In: 2015 IEEE 24th

International Symposium on Industrial Electronics (ISIE), 2015, Buzios. 2015 IEEE 24th International

Symposium on Industrial Electronics (ISIE), 2015. p. 318.

Modeling and Control of a Flexible Photovoltaic

Array Simulator

Allan F. Cupertino∗†, Guilherme V. Santos†, Heverton A. Pereira∗‡, Selenio R. Silva∗,Victor F. Mendes∗,∗ Graduate Program in Electrical Engineering, Federal University of Minas Gerais

Av. Antonio Carlos 6627, 31270-901, Belo Horizonte, MG, Brazil

Emails: guilherme.vianna.santos@gmail.com, selenios@cpdee.ufmg.br, victormendes@cpdee.ufmg.br† Department of Materials Engineering, Federal Center for Technological Education of Minas Gerais

Av. Amazonas 5253, 30421-169, Belo Horizonte, MG, Brazil

Email: allan.cupertino@yahoo.com.br‡ Departamento de Engenharia Eletrica, Universidade Federal de Vicosa

Av. P.H. Rolfs s/n, 36570-900, Vicosa, MG, Brazil

Email: hevertonaugusto@yahoo.com.br

Abstract—Photovoltaic (PV) systems have gained prominencein the current context of distributed generation systems. Thefundamental element of a PV grid-connected systems is the powerconverter. Power converters must be tested and certified accord-ing to the international standards, before being commercialized.Therefore, a flexible equipment to test the converters is necessary.This paper presents the modeling and control structure of a solararray simulator (SAS) of 10 kW for testing power converters.The limitations of conventional structures are pointed out and animproved structure based on two converter stages is proposed.The feasibility of the proposed SAS is shown through simulationsusing the Matlab/Simulink. The simulator is tested for the systemconnected to resistive loads and to a photovoltaic converter model.The dynamical behavior is evaluated through solar irradiancevariations and partial shadowing tests. The results of the proposedstructure show flexibility and good levels of power quality.

I. INTRODUCTION

The fundamental element of grid-connected photovoltaicsystem is the power converter which injects generated powerinto the electrical grid. Power converters must be tested andcertified according to the present standards, before beingcommercialized [1].

Nowadays, some documents standardize the tests to certifypower converters for photovoltaic applications. The oldestdocument is the standard of International ElectrotechnicalCommission (IEC) [2]. IEC 61683 describes different method-ologies to test the efficiency of inverters and minimum require-ments of the data acquisition equipments.

The documents elaborated by International Energy Agency[3] and Sandia National Laboratories [4] define methodologiesto test maximum power tracker accuracy, safety criteria, anti-islanding protection, etc. The Brazilian certification criteriais based on information of these documents. However, fewBrazilian laboratories certify devices for PV systems.

In a first approach, test of power converters for PV appli-cations consists in the connection of the device to a PV arrayexposed to solar irradiance. However, this method is unprac-tical due to dependence of weather conditions. Furthermore,the size of the solar array has to be adapt in order to test

converters of different rated power. Therefore, this approachresults in low flexibility.

In this situation, IEC 61683 suggests the use of a deviceknown as solar array simulator (SAS). This device is a powersource which reproduces I-V characteristics similar to a PVarray [2]. SAS can emulate the solar array behavior for a setof weather conditions (irradiance and temperature variations)and partial shadowing. Furthermore, this device can operatewith different power levels and it can be used to test inverterswith different rated power.

Most of commercial converters for photovoltaic applica-tions control the solar array output voltage in order to trackthe maximum power point. Since the purpose of the SAS isto reproduce the I-V characteristic of a solar array, the outputcurrent must be controlled. The current reference is calculatedaccording to the output voltage which is controlled by theconverter under test. The calculation of the current referencemay be complex due to the nonlinear behavior of solarpanels. In the literature, several methodologies are proposedto perform this calculation, as analogical based method, look-up table based method, analytical method, hybrid method andneural networks based method [5]–[10].

Generally, the SAS topologies present two stages: a rectifierstage based on diodes and a dc/dc converter. Dc/dc Buckconverter is the most employed in the literature [5]–[10]. Morecomplex topologies of dc/dc converters are presented by [11],[12]. Rectifiers based on diodes has harmonic distortion in gridcurrent and its output voltage is not controllable. Furthermore,the traditional dc/dc buck converter is not controllable withoutload. Therefore, open circuit point of solar panel is notemulated if this converter is employed [11], [12]. These areimportant limitations of traditional SAS structure.

Based on the mentioned limitations, an improved structureof the SAS is proposed in this work. The proposed structurehas two stages: first one is based on PWM voltage sourcerectifier, which controls the first dc bus voltage and guaranteeshigh power factor with low harmonic distortion, and the secondone consists in a bidirectional converter, permitting a stableoperation at point of open circuit.

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II. MODELING AND CONTROL STRUCTURES

The proposed SAS structure is presented in Fig. 1. Thelook-up table based method is used in order to obtain the cur-rent reference [6]. In the following subsections are presentedthe SAS stages and the control strategy.

Vga Vgb Vgc

igb igciga

i r ic

vdc

vs

iL i s

PV inverterunder test

PV arraySimulator

Lb

Cb

Cdc

Lf Lf Lf

Fig. 1. Proposed structure for SAS (Devices in red color represent changesin traditional structure presented in literature).

A. Ac/dc stage

The rectifier stage of the SAS is based on a three phasePWM converter. A inductive filter is used in order to reducethe harmonic content generated by the IGBTs switching. Thedesign of this filter is presented in [13]. The classical controlstructure based on synchronous reference frame (dq) was em-ployed to control the PWM rectifier. For the system modeling,grid voltages are considered balanced and without harmoniccomponents. In this situation, the differential equations in thesynchronous reference frame dq are written as:

vd = −Rf id − Lf

diddt

+ ωnLf iq + Vd

vq = −Rf iq − Lf

diqdt

− ωnLf id + Vq

(1)

where Vd e Vq are the direct and quadrature components ofgrid voltage, vd and vq are the components of the fundamentalvoltage generated by the rectifier, id and iq are the componentsof the grid currents, Lf is the filter inductance and Rf is thefilter resistance.

Synchronization of the converter with grid voltage is basedon a Dual second order generalized integrator phase-lockedloop (DSOGI-PLL), proposed by [14]. This PLL has goodresponses for voltage unbalances and voltage harmonics.

The modulation strategy implemented is the space vectorPWM (SVPWM) technique. The control structure consistsin two cascade loops: internal loops control the direct andquadrature components of grid currents and external loopsregulate the dc bus voltage and the reactive power injectedinto the grid [15]. The control structure of PWM rectifier ispresented in Fig. 2.

The control digital implementation uses a sample timeequal to the switching frequency. Parameters of the PWMrectifier are presented in Appendix A.

+

-

+

+

+

r

SVPWMid

id*

Vd

wn qLi

DSOGI-PLL

VABC

VABC*

PI

-

+Vdc*

Vdc

ABC

dq

PI

+

-

+

-

iq

iq*

wn dLi

PI

-

+Q*

Q

PI

Fig. 2. Complete Control structure of PWM rectifier.

B. Dc/dc stage

The dc/dc stage control presents two modes:

• First one is the open-circuit control mode. It is re-sponsible to start the converter switching operationand to control the output voltage when the simulatoris unloaded (the tested converter is not operating). Inthis operation mode, voltage output reference is thesolar array open circuit voltage;

• Second one is the solar array simulator control mode.Based on the voltage imposed by the converter undertest, the current reference is obtained based on I x Vcharacteristic.

The control strategy of the dc/dc stage is shown in Fig. 3. Inthis block diagram is possible to see both operation modes: theopen-circuit control mode is based on a proportional-integral(PI) compensator. The SAS control mode is based on a look-up table of I x V curve. This method consists in the followingsteps: for given values of solar irradiance G and temperatureTc, a table with values of I-V curve is chosen. The value ofthe output voltage is interpolated in this table and the result isthe reference value of the inductor current. This interpolationis dynamic permitting the SAS to emulate [6].

PI

vs

G Tc

+-

*

PI+-

iL

PWMVoc

DDS1

S2

iL

Fig. 3. Complete control structure of dc/dc converter.

In the dc/dc converter modeling, the following points wereconsidered:

• The converter switches are driven in complementary;

• The dc bus voltage of the rectifier is constant;

• The power consumption of the inverter under test ismodeled as a resistance in parallel with a currentsource connected to the output of the solar arraysimulator.

ＳＱＹ

Based on these considerations, simplified model of thedc/dc stage is presented in Fig. 4. The transfer function whichrelates inductor current and converter duty cycle is given by[16]:

ic

vdc

vs

iL i s

Lb

Cb

*

Rs

i s

i load

Fig. 4. Simplified model of dc/dc converter.

Gid(s) =(RsCb + 1)Vdc

RsLbCbs2 + (Lb +RLbRsCb)s+ (Rs +RLb).

(2)

The transfer function that relates the inductor current andthe dc bus voltage, considering solar array simulator unloaded,is given by:

Gvi(s) =1

Cbs. (3)

The current control loop is used in both control modesof the PV array simulator using PI compensator. A PI com-pensator is also used in the voltage control loop. Thesecompensators are designed by poles placement based method.Parameters of the converter are presented in Appendix. Thedigital implementation of the control uses a sample time equalto the switching frequency.

III. SIMULATION RESULTS

In this section the simulations results of the proposed PVarray simulator structure are presented and their analysis iscarried out. The parameters of simulation model are presentedin the Appendix.

The voltage control performance during the system start-up, i.e., the SAS operating unloaded is presented. After, the SAScontrol response is analyzed during variations of irradianceand partial shadowing, considering a resistive load. Finally, thesimulation results for the simulator supplying a photovoltaicconverter are discussed.

A. Proposed Start-up and open circuit voltage control

The first step to start-up the SAS is to pre-charge the firstdc-link (Cdc) using resistors to limit the inrush currents. After,the PWM rectifier control is turned-on and the voltage (vdc)is increased following a ramp until the rated value. The nextstep is to turn-on the control of the dc-dc stage and to increase

the voltage of the second dc-link (Cb) slowly. The reference ofthis voltage is set to the open circuit voltage of the simulatedsolar array, condition generally used by the solar converters tostart the MPPT. This process is presented in Fig. 5.

0 0.5 1 1.5 2

350

400

450

(a)

vd

c [V

]

→ Start of DC/DC stage operation

vdc

*

vdc

0 0.5 1 1.5 20

200

400

(b)Time [s]

vs [

V]

vs

*

vs

Fig. 5. Start-up process of proposed structure of SAS.

Now, two key points of the proposed SAS can be discussed.First one is based on the fact that several papers in literature donot implement a voltage control strategy for the open circuitvoltage stabilization (Fig. 3). In order to show the impact ofnot using this external loop control for the system start-up,two control strategies are simulated: S1, which the dc-linkvoltage is controlled all the time and S2, which this control isdisabled after the voltage reaches the reference value (open-circuit voltage). In S2, after the start-up, the current reference isobtained from the I x V curve. Fig. 6 (a) shows the simulationresults. One can see without the dc-link voltage control, theSAS output voltage cannot remain constant if the control of thesolar converter is not operating. This is strategy is necessaryfor safety reasons during the system start-up and also if theconverter under test fails.

The second point is related to the converter topology. Anunidirectional buck converter (one switch) is cheaper for theSAS and therefore several works employ this topology. Thiswork proposes the use of two switches (Fig. 1). For sake ofcomparison the two topologies were simulated: S3 is the SASproposed in this work and S4 employs the unidirectional buckconverter. Simulation results during variations in the secondDC-link reference are presented in Fig. 6 (b). As can be seen,the unidirectional topology cannot decrease the output voltagefast, because it cannot synthesize zero or negative averagecurrent. In the proposed structure the output voltage can bechanged fast, responding for example to a irradiance variationduring the system start-up.

B. SAS dynamic behavior with resistive load

In this subsection, in order to analyze variations of theinput and output powers of the SAS, the solar irradianceand the load are changed according to Fig. 7. The load isconsidered a variable resistance, which objective is shown the

ＳＲＰ

0 1 2 3 40

50

100

150

200

250

300

350

400

(a)

vs [

V]

1 2 3 4390

395

400

405

410

415Detail

S1

S2

1 1.2 1.4 1.6 1.8 2 2.20

50

100

150

200

250

300

350

400

450

(b)Time [s]

vs [

V]

1 1.5 2350

400

450

Detail

S3

S4

Fig. 6. Simulation results comparing control strategies S1 and S2.

SAS operation in various points on the I-V characteristic curveemulated. At time 7 seconds, a partial shadowing is considered.

0 1 2 3 4 5 6 7 8 90

400

700

1000

Irra

dia

nce

[W

/m2]

Time [s]0 1 2 3 4 5 6 7 8 9

0

50

100

Load

Res

ista

nce

[Ω

]

Fig. 7. Simulated solar irradiance and load resistance profiles.

Fig. 8 presents the behavior of the PWM rectifier. Onecan see load variations generate disturbances in the rectifierdc-link voltage, but the voltage variations are smaller than2 % of the rated value, proving the dc-link voltage controlis adequate. Fig. 8 (b) presents the grid active and reactivepowers. The reactive power is controlled in zero, resulting ina unitary power factor.

1.5 2 2.5 3 3.5 4445

450

455

460

(a)

vd

c [V

]

vdc

*

vdc

2 3 4 5 6 7 8 9−5

0

5

10

(b)Time [s]

Pg [

kW

] an

d Q

g[k

VA

]

Pg

Qg

Fig. 8. Dynamic behavior of PWM rectifier during SAS operation withresistive load: (a) Dc bus voltage; (b) Active and reactive power supplied byelectrical grid.

Fig. 9 (a) and (b) present the behavior of dc/dc converter,showing the output current is follows the reference i∗L. Loadchanges results in change of operation point. The inductorcurrent iL presents a larger ripple which is filters by meansof output capacitor. Therefore, SAS output current presentssmaller ripple, but its dynamic behavior changes in terms ofovershoot. When non-uniform shadow starts, an overshoot isobserved in the current response.

Fig. 10 presents paths of SAS in I x V plane. Thesepaths illustrates inductor current variation which follows I x Vreference curves. System starts at point A (open circuit voltage)changes to point B (load variation with constant irradiance),C (irradiance variation with constant load), D(load variationwith constant irradiance) and finish at point E (constant irradi-ance with load variation). Transient in current response whenpartial shadowing starts results in a larger error when SASoperation point changes from D to E. However, this transientis fast and probably will not influence the MPPT algorithm ofphotovoltaic inverter.

ＳＲＱ

2 3 4 5 6 7 8 90

100

200

300

400

(a)

vs [

V]

2 3 4 5 6 7 8 9−10

0

10

20

30

40

(b)Time [s]

i L [

A]

iL

iL

*

is

Fig. 9. Dynamic behavior of dc/dc converter during SAS operation withresistive load: (a) Output voltage; (b) Inductor and output currents.

0 50 100 150 200 250 300 350 4000

5

10

15

20

25

30

35

A

E

B

C

DR = 100 Ω

R = 5 ΩG = 1000 W/m2

G = 700 W/m2

G = 400 W/m2, non−uniform

Cu

rren

t [A

]

Voltage [V]

Emulator

Reference

Fig. 10. Paths of SAS in I x V plane with resistive load.

C. SAS dynamic behavior testing a photovoltaic converter

In order to evaluate the dynamic behavior of the proposedSAS during the test of a photovoltaic converter, a boostconverter is simulated. This converter was chosen since severaltopologies of commercial photovoltaic inverters present a dc/dcboost input stage. Fig. 11 shows the boost converter and thecontrol strategy. A classical MPPT algorithm based on perturband observe is employed [17].

The irradiance profile presented in Fig. 7 is used in this

PI

Vs

IL

+-

*

PI+-

iL

PWMDD S1

Lb

Cb

iL

Vinv

Is

Vs

MPPTVs

Is

Fig. 11. Control strategy of MPPT boost converter.

simulation. The SAS output voltage (now imposed by theMPPT converter) and the output current are presented in Fig.12. These values change in terms of solar irradiance due toconverter MPPT operation. The resulting output power andP x V reference curves are presented in Fig. 13. MPPTof the converter reach point of maximum power point anddo not changes significantly the SAS dynamic behavior. Ahigher power ripple is observed for 400W/m2, because theinfluence of inductor current ripple increases when the outputcurrent reduces. Nevertheless, one can see that the SAS canemulate the array I-V curve and the tested converter reachesthe maximum power point as expected.

2 4 6 8 10 12300

320

340

360

380

400

(a)

vs [

V]

2 4 6 8 10 12 14

0

10

20

30

(b)Time [s]

i L [

A]

iL

is

iL

*

Fig. 12. SAS output voltage and current during the test of the MPPTconverter.

ＳＲＲ

0 100 200 300 4000

2

4

6

8

10

G = 1000 W/m2, T

c = 25 ºC

G = 700 W/m2, T

c = 25 ºC

G = 400 W/m2, T

c = 35 ºC

Po

wer

[k

W]

Voltage [V]

Simulator

Reference

MPP

Fig. 13. Paths of SAS in P x V plane during the operation of the MPPTconverter.

IV. CONCLUSION

This work presented a topology of solar array simulatorbased on a PWM rectifier and a bidirectional dc/dc converter.The proposed control strategy stabilizes the SAS output whenit is unloaded, permitting a correct system start-up. Limitationsof unidirectional buck converter topology, used in severalworks, are pointed out.

Simulation results show that the SAS can emulate the Ix V curves of solar arrays during irradiance variations andpartial shadowing. The simulations were carried out first usinga resistive load and after testing a MPPT converter, bothdemonstrating good results.

The next step in the development is to implement theproposed strategies in a test bench in order to validate thework with experimental results.

ACKNOWLEDGMENT

The authors would like to thank CNPQ, FAPEMIG andCAPES for their assistance and financial support.

APPENDIX

Simulation parameters of dc/dc converter are presented inTable IV. Parameters of PWM rectifier are presented in TableIV.

TABLE I. DC/DC CONVERTER PARAMETERS.

Parameter Value

Pmax 10 kW

fs 10 kHz

L 5 mH

C 1 mF

RL 62.5 mΩ

TABLE II. PWM RECTIFIER PARAMETERS.

Parameter Value

Pmax 10 kW

Vg 220 V

fn 60 Hz

fs 6 kHz

Lf 4 mH

Rf 5mΩ

Cdc 3.06 mF

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