cuantificarea impactului sistemelor fotovoltaice

7/25/2019 Cuantificarea Impactului Sistemelor Fotovoltaice

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A Statistical Approach to Quantify the Impact on

Voltage Quality Caused by PV Generators

N Saadat, SS Choi and DM Vilathgamuwa

Centre for Smart Energy Systems, School of EEE

Nanyang Technological University, Singapore

[email protected], [email protected], [email protected]

Abstract A probabilistic method is proposed to evaluate voltage

quality of grid-connected photovoltaic (PV) power systems. The

random behavior of solar irradiation is described in statistical

terms and the resulting voltage fluctuation probability

distribution is then derived. Reactive power capabilities of the PV

generators are then analyzed and their operation under constant

power factor mode is examined. By utilizing the reactive power

capability of the PV-generators to the full, it is shown that

network voltage quality can be greatly enhanced.

Keywords- photovoltaic generators; statistical analysis; voltage

quality; reactive power capability.

I. INTRODUCTION

Duo to the concern on the environment and energy supplysecurity, developing viable renewable sources for electricity

production has attracted much attention in recent years. Thephotovoltaic (PV) power generation is a most promisingmethod among the various renewable sources. Thus one

witnesses a steady increase in the amount of PV powergeneration in power systems. Often a grid-connected PVgeneration system operates under the maximum power pointtracking (MPPT) mode but because of theintermittent/unsteady behaviour of the solar insolation, theoutput power of the PV varies and it can lead to degradation onnetwork voltage quality. Therefore, there is great motivation toresearch into ways to reduce the negative impacts. Forexample, one possible solution to the problem is to utilizeenergy storage systems with the PV-generation system [1].

There are three main factors influencing voltage quality:the varying solar power injection, changeable impedance of theexternal network connected to the PV generators and the

inevitable varying loads. In the present investigation onevaluating the impacts of photovoltaic generation on networkvoltage, only the first factor is considered. While often grid-connected PV generators operate under constant power factormode, the converters associated with the generators do possessreactive power capacity which one can take advantage of. Bycontrolling the reactive power flow in the manner described inthis paper, the full reactive capability of the PV-generatorconverters shall be exploited to enhance grid voltage quality.

As solar insolation is random, the approach used here inassessing voltage quality is by statistical means. The technique

is similar to that utilized in [2],[3] where attempts were madeto evaluate grid voltage quality in the presence of wind farms.Specifically, in this paper, the solar power injected to the gridis described in terms of probabilistic distributions and the

probability of the resulting voltage deviation is then calculated.

The performance of utilizing the reactive power capacity of thePV-converters versus that of constant power factor operation ofthe PV are compared in terms of enhancing voltage quality.

In Section II, a brief description of the grid-connected PVsystem and its impact on voltage quality is included. PVoperation of maximum power point (MPP) is also given.Section III describes the reactive power capacity of the PV-generator and shows how voltage quality can be enhancedthrough manipulating the reactive power flows. Section IV

presents the proposed statistical method in evaluating voltagequality due to the grid-connected PV system. In Section V, anumerical example is presented to demonstrate theeffectiveness of the proposed method.

Figure 1. Schematic diagram of a PV-generator connected to grid

II.

PRELIMINARY CONSIDERATIONS

A. Network Description

Fig. 1 shows a PV-generator connected to a grid at the pointof common coupling (PCC). The voltage phasor at the PCC is

denoted as = ii VV . As the external system connected to the

PV-generator is complex, a Thevenin equivalent model is usedto represent the grid. The voltage source Esequals to the no-load voltage at the PCC. The electrical strength of the grid can

be related to the source impedance ZS and load has beenincluded to form part of the Thevenin equivalent. The focus of

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attention is the voltage quality at the PCC when the PV-generator injects into the grid the complex powerPi+ jQi.

The PV system can operate in either constant power factoror variable power factor modes. If the PV-generator is tooperate under constant power factor, one can express Qi interms ofPi through the use of a constantKpwhere

ipi PKQ = (1)

cos

cos1 2=pK

(2)

In (2), cos is the power factor at the PV inverterterminals.

B. Impact of PV Generation on PCC Voltage

With the PV generator injecting Si=Pi+ jQi into the grid,the voltage at the PCC will deviate from Eswhen Si0. IfEsisthe reference voltage and equals to 1 pu, then the voltagedeviation Vat the PCC with respect toEscan be expressed as

Si EVV = (3)

i

iSiS

V

QXPRV

+= (4)

The derivation of (4) is well-known and it governs thesteady-state value of the voltage variation. However, it

provides only an approximate measure of V [4]. Also it isassumed over the interval of interest, any voltage controldevice in the network has not been initiated as to cause anychanges to the grid impedance (ZS) and Es. Therefore in thisderivation, Es and ZS are assumed constant. In this way, theimpact of the PV generator output power on the PCC voltagequality could be readily assessed via (4).

On the other hand, the approach used in this paper does notmake use of the approximate expression (4). Instead thevoltage deviation is calculated via basic circuit analysis of (3),as shown in the Appendix. It is shown that the PV-generatorinjected active and reactive power and the PCC voltage arerelated by equation (5).

( )

=+

=+

0

02

iSiSiS

iSiSiSi

PXQRSinVE

QXPRCosVEV

(5)

In (5), is the phase angle of iV . Equation (5) can be used

in formulating the voltage quality assessment using thefollowing approach: since ZS and Es are pre-specified, theinjected photovoltaic real powerPican be treated as a randomvariable, the distribution of which follows certain probabilisticform. This follows from the observation that solar isolation is arandom process. If constant power factor mode is assumed forthe PV-generator, Qican be obtained using (1). This allows the

PCC voltage phasor iV to be determined using (5). In this way,

the statistical approach can determine the likelihood ofoccurrence of given level of voltage deviation. This shall be theapproach used in this work and a statistical technique will be

proposed in Section IV in the analysis of the voltage quality atthe PCC.

C. PV-Generator Maximum Power Point

At a given solar insolation level, there is a unique state atwhich the maximum power can be extracted from the PVmodule. This point is called maximum power point (MPP).Typical I-V curve and power output of a PV module aredepicted in Fig. 2.

Figure 2. I V curve and power output for a PV module: MPP corresponds

to the module delivering the maximum power

Figure 3. Photovoltaic cell equivalent circuit

Maximum power point tracking methods usually are basedon iterative algorithms but in probabilistic analysis of MPP, ananalytical solution for MPP is necessary. Roudriguez et al in[5] presented an analytical solution for determining the MPP inPV systems. Fig. 3 shows the photovoltaic cell equivalentcircuit. The method is based on knowing the open circuitvoltage (VOC) and short circuit current (IL) of the PV module: itallows a point which will be inside a disc of small radius

within the MPP to be determined. This proof is based on meanvalue theorem.

The analytical maximum power point for a module can becalculated from (6)

**

pvpvMPP ivP = (6)

PMPPis the output power of the PV at MPP,v*pvand i

*pvare

the voltage and current obtained from the analytic solution ofthe MPP respectively. The effect of variation of open circuitvoltage due to temperature is negligible [5].

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III. REACTIVE POWER CAPABILTY OF PVGNERATOR

As shown in the schematic diagram of Fig. 1, the PV panelis connected to the grid by the DC-AC inverter. The voltagedeviation on the output terminal of the PV generators can beregulated by adjusting the amount of reactive power flow fromthe PV-generators. There is, however, a limit on the amount ofreactive power that can be injected/absorbed by the inverter.Let the inverter apparent power rating be Sinv whereas the

injected real power is Pi, while PMPP is the solar powerharnessed by the PV module and is the input power to theinverter. Suppose losses in the inverter are negligible and therating of the inverter matches that of the PV module. Thereforethe lower and upper limits on the inverter reactive power are

22

min, iinvinv PSQ = (7)

22

max, iinvinv PSQ += (8)

That is, the reactive power capacity of PV generator is

max,min, inviinv QQQ (9)

The above derivation is very useful in the following way.

Using the results from Section II.B and if the PV-generator-inverter system were to operate under constant power factormode, it may result in unacceptable degradation in voltage

quality in iV . Hence the proposal in this paper is to relax theconstant power factor operating mode by taking advantage ofthe available apparent power capacity of the inverter given by(9). Using (3) and (5), one calculates the appropriate amount ofreactive power required to control Vi and in ensuring Qi iswithin the acceptable range determined by (7) (9). Vcan bemitigated by adjusting Qiwithin the reactive power capacityrange given by (9). That is, for given injected power Pi, Qiisregulated until V is minimized. A statistical approach toassess voltage quality and the reactive power required is

described next.

IV. STATISTICAL EVALUATION OF VOLTAGE DEVIATIONS

As the injected solar power is random, statistical approachshall now be used to assess voltage quality. Assuming the PVoperates under MPP mode, the statistical distribution of Pican

be determined from the statistical distribution of solarinsolation level. Then voltage deviation can be evaluated onthe basis of given insolation probability. When the PV-generators operate at MPP and with no internal losses, all ofthe output power from the PV module is converted toPi.

In the following, the probabilities of voltage deviationunder constant power factor mode and the proposed variable

power factor mode are discussed.

A. Probabilistic Model of Insolation and Injected SolarPower

For statistical study of a random event, a probabilitydistribution can quantify the random behavior of the event.From the insolation data collected from the site of the PV-module, an appropriate distribution can be found to fit theisolation data. SinceILis proportional to insolation, so one canstate

( ) ( )lIKlI nsiL = (10)

In (10),Ins(l)denotes the insolation level,Kiis a coefficientfor conversion of insolation to short circuit currentILand lis anindex. Since Pi = PMPP, Pi and PMPP are continuous randomvariables and to quantify the probability distribution of acontinuous variable, one makes use of discrete probabilityfunction. In this method, random variable is divided into sub-sections and every sub-section represents a particular value of

the random variable. Thus discrete probability of a randomvariablexcan be determined using (11).

( )( ) ( )( ) ( )( )2/2/ += lxFlxFlxprob CDFCDF (11)

In (11), prob(x) denotes the probability function of x,FCDF() is the Cumulative Density Function (CDF) ofx, is thewidth of random variable range. As MPP is a strictly increasingfunction of IL for fixed open circuit voltage, therefore for anyIL(i)

( ) ( )( )( )

( )

CDF

lVFlVprobVprob ==> > 1|| || (15)

Thus (15) provides the likelihood of Vexceeding the level.From this probability level, one can then decide whether thevoltage quality at the PCC is acceptable under the constant

power factor operating condition.

C.

Statistical Voltage Analysis at PCC: PV Operates within

Reactive Power Capability Of Inverter

In this case the PV generator relaxes the constant powerfactor requirement and instead, it makes fuller use of the

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reactive power capacity of the inverter. The strategy is asfollows.

When the reactive power capacity of the PV generator issuch that described by (9), Vcan be mitigated by adjusting Qiwithin the permitted range to minimize V. Therefore for giveninjected power ofPi, Qiis adjusted until Vwill be minimized.If Si of the PV generator-inverter reaches its rated powercapacity, the PV-generator-inverter will operate at the rated

power limit.

To demonstrate the effectiveness of the reactive powercapability of PV generator to reduce voltage deviation,numerical examples are used in the next section.

V.

NUMERICAL EXAMPLES

A. Reactive Power Capability

In Section III, the reactive power capacity of the PV-generator-inverter has been discussed and (7)-(9) define thiscapacity. Suppose the PV-inverter capacity is equal to the rated

power of the PV module. The upper and lower reactive power

limits of the combined PV-inverter system is shown in Fig. 4.Feasible output power is therefore within the Pi-Qi area

bounded by the limits.

Figure 4. Reactive power capability of the PV-inverter system: expressed in

pu of PV-module capacity

TABLE I. PVMODULE PERFORMANCE DATA UNDER STANDARD TESTCONDITIONS (1KW/M2,AM1.5,25CCELL TEMPERATURE)[7]

Manufacturer KyoceraModel KC-120-1Material MulticrystalNumber of cells 36Rated power P

DC,STC

W ) 120Voltage at maximum

power V)

16.9

Current at rated power A) 7.1open-circuit voltage V

OC

V) 21.5Short-circuit current I

L

A) 7.45Length mm/in.) 1425/56.1Width mm/in.) 652/25.7Depth mm/in.) 52/2.0Weight Kg/lb) 11.9/26.3Module efficiency 12.9%

B.

Probability Distribution of Injected Power

As explained in Section II, it can be assumed thatPi=PMPP.In this research, the authors used the insolation data collected at

Nanyang Technological University (NTU) campus using aninstalled PV module. Distribution fitting toolbox (dfittool) inMATLAB software was used to examine different forms of

probability distribution to fit the empirical data. NoneParametric Distribution obtained using Kernel density estimatemethod [6] was eventually selected for this study. Fig. 5depicts the CDF of PMPP for the NTU PV module. Also, theauthors assumed the specifications shown in Table I to model

the PV module.

Figure 5. Probability distribution ofPMPPof the NTU PV module

C.

Voltage Deviation Distribution: PV at Fixed Power

Factor at PCC.

In this example, ESis constant at 1-pu to represent a largesource, with ZS=0.02+j0.12 pu. Voltage deviations at the PCCfor fixed power factor were calculated from (3) for three powerfactors of 0.96, 0.98 and 1.0. The results are as shown in Fig. 6.It can be seen that increasingPiwill cause Vto increase. Thecorresponding reactive powers from the PV generator are asshown in Fig. 7. For a given Pi,V increases as power factordecreases due to the presence of the source reactance. Hence toreduce V, the PV-inverter system should operate as close tounity power factor as possible.

Probability distributions of Vunder 0.98 and unity powerfactor condition are shown in Fig. 8 and Fig. 9. Such plots can

provide helpful information. For example in Fig. 8, probabilityof V larger than 0.5% for 0.98 operation is determined bysumming all the probability of all Vevents larger than 0.5%.It is equal to 59.40% which means that one can expect V to belarger than 0.5% for just over half the time.

Figure 6. Voltage deviation under fixed power factor condition

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Figure 7. Reactive power output of PV Generator under fixed power factor

condition.

Figure 8. Voltage deviation distribution at PCC under power factor=0.98

condition

Figure 9. Voltage deviation distribution at PCC under power factor=1.0

condition

D. Voltage Deviation Distribution with the ProposedReactive Power Compensation

According to proposed method for minimizing voltagedeviation, reactive power can be determined. The optimalreactive power output of the PV generator is shown in Fig. 10at various levels of Pi. When Qiis within the boundary of thereactive power limit curves shown in Fig. 4, the optimal Qivalue is obtained at the condition of V = 0. The resulting Qi

profile is labeled as the Optimal result in Fig. 10. AtPicloseto 1 p.u., Qistrikes the lower limit curve and Qi shall then be

set equal to the corresponding lower limit value. In which case,Vis no longer zero.

Voltage deviation probability distribution obtained underthe proposed method is shown in Fig. 11. From Fig. 11, it isseen that the PV-inverter can mitigate the voltage deviationsfurther. The proposed method could reduce V to zero with aprobability of 99.92% whereas under fixed power factorstrategy, the corresponding probability is between 13.51% and6.6% when the power factor varies from 0.98 to unity.Similarly, the probability of V larger than specific value alsodecreases significantly when the power factor is allowed tovary. For example prob(V>0.5%) ranges from 0.594 to 0.3when operating at fixed power factor between 0.98 to unity,whereas the varying power mode has lowered the probability toless than 0.001.

Figure 10. Reactive power capability of PV generator which produces voltage

deviation distribution on Fig. 11

Figure 11. Voltage deviation probability distribution with reactive power

capability of PV generator.

VI. CONCLUSIONS

The effect of random behaviour of photovoltaic power hasbeen considered and a statistical approach is proposed toquantify the impact on voltage quality caused by the PVgenerators. The probability of voltage deviation is compared inthe case of the PV-generators operating under fixed powerfactor mode against that of flexible power factor mode. Thelatter mode takes full advantage of the PV-inverter reactive

power control capability to enhance voltage quality. A

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computational approach to statistically quantify the resultingvoltage quality improvement of the grid-connected PV systemhas been given.

APPENDIX

In this Section, the derivation of (5) is explained. In Fig. 1,output power of the PV-generator is determined using

iiii jQPIV +=* (16)

Output current of PV- generator is derived as follows:

SS

Sii

jXR

EVI

+

= (17)

By substitution (17) into (16) and after some manipulations,the following equation is obtained.

( ) ( ) 02 =+ SSiiSii jXRjQPEVV (18)

Express the voltage of PCC as

siniii jVCosVV += (19)

By combining (18) and (19) and separating the resultingequation into the real and imaginary parts, (5) can be obtained.

REFERENCES

[1] Y. Cheng, "Impact of large scale integration of photovoltaic energysource and optimization in smart grid with minimal energy storage," inProc. of the Int. Sym. on Industrial Electronics, pp. 3329-3334, 2010.

[2] S. Zhang, K. J. Tseng and S. S. Choi, "Statistical voltage quality

assessment method for grids with wind power generation," IETRenewable Power Generation, vol. 4, no. 1, pp. 43, 2010.

[3] Q. Li, Y. Yuan, S. S. Choi and W. S. Wang, "Statistical voltage qualityevaluation of wind farm-connected grid network," in Proc. Int. PowerEngineering Conf., pp. 408, 2010.

[4] M. Crappe, Eds., Electric Power Systems, Wiley-ISTE, 2008.

[5] C. Rodriguez and G. A. J. Amaratunga, "Analytic Solution to thePhotovoltaic Maximum Power Point Problem," IEEE Transactions onCircuits and Systems I: Regular Papers, vol. 54, no. 9, pp. 2054-2060,2007.

[6] A. Azzalini and A. Bowman, Applied smoothing techniques for dataanalysis, Oxford University Press, 1997.

[7] G. Masters, Renewable and efficient electric power systems, Wiley-IEEE Press, 2004.

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