06804647.pdf

Optimal PV Inverter Reactive Power Control and RealPower Curtailment to Improve Performance of

Unbalanced Four-Wire LV Distribution NetworksXiangjing Su, Student Member, IEEE, Mohammad A. S. Masoum, Senior Member, IEEE, and

Peter J. Wolfs, Senior Member, IEEE

Abstract—The rapid uptake of residential photovoltaic (PV)systems is causing serious power quality issues such as significantvoltage fluctuation and unbalance that are restricting the ability ofnetworks to accommodate further connections. Based on the latentreactive power capability and real power curtailment of single-phase inverters, this paper proposes a new comprehensive PVoperational optimization strategy to improve the performance ofsignificantly unbalanced three-phase four-wire low voltage (LV)distribution networks with high residential PV penetrations. Amultiobjective optimal power flow (OPF) problem that can simul-taneously improve voltage magnitude and balance profiles, whileminimizing network losses and generation costs, is defined and thenconverted into an aggregated single-objective OPF problem usingthe weighted-sum method, which can be effectively solved by theglobal Sequential Quadratic Programming (SQP) approach withmultiple starting points in MATLAB. Detailed simulations areperformed and analyzed for various operating scenarios over24 h on a real unbalanced four-wire LV distribution network inPerth Solar City trial, Australia. Finally, smart meter readings areused to justify the validity and accuracy of the proposed optimiza-tionmodel and considerations on the application of the proposedPVcontrol strategy are also presented.

Index Terms—Optimal power flow (OPF), photovoltaic (PV)power systems, power distribution, power quality, reactive powercontrol.

I. INTRODUCTION

R OOFTOP photovoltaic (PV) systems are being increas-ingly installed in low voltage (LV) distribution networks

by consumers to reduce the cost of electricity supply. However,the expanding scale of residential PV connections leads todetrimental impacts on the network operation. Two of theforemost issues are voltage regulation [1] and voltage unbalance[2]. During high PV generation periods, there is a possibility ofsignificant reverse power flow and consequent voltage rises onthe LV feeder. On the other hand, serious voltage drops mayoccur due to the intermittent loss of PV generation during cloudydays. Furthermore, the increasing installation of single-phase

rooftop PV units at random locations with various ratings isfurther worsening the already poor phase balance profile ofdistribution networks.

Traditional approaches to address voltage regulation and un-balance problems are utilizing secondary LV transformer onlinetap changer (OLTC), autotransformers, voltage regulators, andswitched capacitors, as well as increasing conductor sizes andadding energy storage devices [3]–[5]. However, tap positionscannot be changed frequently, autotransformers, voltage regula-tors, and switched capacitors introduce additional failure pointsinto the systemwhile upgrading the conductors, and adding energystorage devices are very effective but expensive approaches thatare usually not justified due to low cost benefit ratios [5].

The more recent approaches to overcome the voltage regula-tion problem in LV networks with high PV generation penetra-tion involve inverter-based reactive power control [8]–[14].Compared with the above-mentioned traditional approaches, PVinverter reactive power control is more effective, has superiortransient performance, and does not require extra investments.Generally, existing control schemes based on reactive powercapability of PV inverters are presentedmainly in two forms.Oneis the centralized control where optimal PV reactive outputs aredetermined by solving a network-wide optimal power flow(OPF) [6], [7] problem for the best operational performance.For example, the Volt/VAR control is formulated as a radial OPFproblem in [8]. Subject to voltage and PV inverter reactive powerlimit constraints, the objective is to minimize line losses, energyconsumption through Conversation Voltage Reduction (CVR),and inverter losses. Moreover, a systematic method for deter-mining both the real- and reactive-power set points of PVinverters in a residential system is proposed in [9] by solvingan OPF problem with the objective of optimizing the systemoperation and ensuring voltage regulation. Additionally, aneconomic dispatch problem for unbalanced distribution net-works is defined and solved in [10]. The objective is to minimizethe overall real power cost with constrains on the voltagemagnitudes and on the power factor at both the substation andthe nodeswith capacitors. By contrast, the other control approachis distributed control where control actions of each PV aredecided based on local measurements. For instance, in [11], asimple OPF problem is defined to minimize network losses byPV inverter reactive power control. As the cost function isseparable, a distributed online approach is then introduced foroptimality of reactive power flows in distribution systems. A

1949-3029 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

Manuscript received October 30, 2013; revised January 22, 2014; acceptedMarch 23, 2014. Date of publication April 23, 2014; date of current version June17, 2014.

X. Su and M. A. S. Masoum are with the Department of Electrical andComputer Engineering, Curtin University, Perth, Western Australia (e-mail:[email protected]; [email protected]).

P. J. Wolfs is with the Power and Energy Centre, Central QueenslandUniversity, Rockhampton, Queensland, Australia (e-mail: [email protected]).

Color versions of one ormore of the figures in this paper are available online athttp://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TSTE.2014.2313862

IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 5, NO. 3, JULY 2014 967

decentralized reactive power control is presented in [12], basedon voltage sensitivity analysis, to achieve grid voltage supportwith less total reactive power consumption by assigning alocation-dependent power factor to each PV unit. Additionally,distributed Volt/VAR controls have also been used in [13] and[14] tomaintain voltagewithin an acceptable range through localPV reactive managements.

Distributed control with a local variable requires less com-munication but is inherently locally optimal due to the lack of fullnetwork information. As for the centralized control, the majorityof the existing studies (e.g., [8]–[10]) are based on a balancednetwork model which, however, will result in incorrect predic-tions and conclusions, asmost practical distribution networks arenaturally unbalanced. Beside, some existing PV controllers areonly based on reactive power control without considering realpowermanagement (e.g., [8]), which is not an effective approachin distribution networks with high R/X ratios. Furthermore, themultiple objectives of inverter reactive power control tend to bemutually conflicting and the challenge of how to implement aPV control approach, which can balance different goals andconstraints of practical networks, still exists (e.g., [8]–[10]).

Based on both optimal reactive power control and real powercurtailment of single-phase inverters, this paper proposes a com-prehensive PV control strategy to improve the operational perfor-mance of significantly unbalanced four-wire LV distributionnetworks. The proposed multiobjective OPF problem, whichsimultaneously improves voltage magnitude and balance profilesand minimizes network losses and generation costs, is convertedinto an aggregated single-objective problem using the weightedsum method and then solved by the global SQP approach withmultiple starting points in MATLAB. Simulations are performedand analyzed for two extreme operating scenarios over 24 h on areal four-wire unbalanced LV distribution system. Smart meterreadings are used to justify the validity and accuracy of theproposed optimization model and considerations on the practicalapplication of the proposed PVcontrol strategy are also presented.

II. PV CONTROL STRATEGY

A. Reactive Power Capability of PV Inverter

Many PV inverters have a reactive power capability [15]. InFig. 1, the inverter’s capacity and real power are represented byvectors with magnitudes S and P . The semicircle with radius Sdenotes the boundary of the inverter’s operating range in PQspace. The amount of reactive power (Q) available from the

inverter is constrained by �ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiS2 � P 2

p� Q �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiS2 � P 2

p.

B. Proposed PV Inverter Control Strategy

Based on the reactive power capability and real power cur-tailment of the PV inverters [16], one of the following proposedthree control options could be selected for the desired networkperformance (Fig. 2).

Control Option 1—OPTQ1S (Optimal Q-Control With RatedInverter Capacity): This option is selected for normal operatingconditions. As the inverter real power generation is usuallybelow its rating, the inverter will have the capability to supplyreactive power, at a cost of incremental inverter losses.

Control Option 2—OPTQ1.6S (Optimal Q-Control WithIncreased Inverter Capacity): This option could be selected ifthe desired network performance is not achieved after Option 1due to limited inverter reactive power availability (e.g., in highgeneration cases). Thus the sizes of PV inverters can be increasedto allow more active reactive power control.

Control Option 3—OPTPQ1.6S (Optimal PQ-Control WithIncreased InverterCapacity):This option could be selected if thenetwork performance is still not satisfactory with Option 2. Thiscould be due to the limited effect of reactive power managementin distribution networks with high R/X ratios. Then a compre-hensive control can be implemented where real power curtail-ment is available to each inverter to allow both reactive powerand real power controls. Curtailment incurs a relatively highercost in the optimization process and partial curtailment allows allthe users to share the network resources when constraints exist.

It is known that with inverter capacity increased, theperformance-related cost will be reduced. To decide the suitableproportion by which the inverter capacity should be increased,multiobjective OPF (proposed in Section III) calculation iscarried out for the peak demand case (18:45 P.M., January 25,2012) of network in Fig. 3 with a dramatic inverter size expan-sion of 100%. As shown in Table I, out of total 34 inverters, only18 have their increased capacity partially used. To effectivelyshow the potential reactive power benefits of inverters whileconsidering the cost associated with inverter upgrade, 60% isfinally chosen in this study.

III. MULTIOBJECTIVE OPF PROBLEM AND SOLUTION

A multiobjective model is proposed to ensure reasonableoperational performance after optimization. The network isdescribed by a nonlinear load flow model with constant-powerloads. Bus 1 at the secondary side of the distribution transformeris taken as the slack bus.

Fig. 1. Inverter reactive power capability.

Fig. 2. Proposed control strategy.

968 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 5, NO. 3, JULY 2014

A. Optimization Objectives

1) Network Losses:

J1 ¼X4p¼1

Xn�1

i¼1

Xnj¼iþ1

Ipij2Rp

ij (1)

where i; j ¼ 1; 2; . . .n is the bus number and p ¼ 1; 2; 3; 4represents the phase and neutral designations (a; b; c; and n),respectively. As the network is unbalanced, both the bus number iand the phase designation p are required to identify a node ip.Accordingly, Ipijand Rp

ij are the current through and resistance ofthe branch between nodes ipand jp.

2) Voltage Magnitude Profile: To ensure voltage magnitudewithin the limits provided by utilities, a dead band-basedobjective is proposed as follows:

J2 ¼X3p¼1

Xni¼1

�V pidb

2(2)

where �V pidb

2 ¼ ðV pi � Vdb

lowerÞ2, 0 and ðV pi � V upper

db Þ2 forV pi < V lower

db , V lowerdb � V p

i � V upperdb , and V p

i > V upperdb ,

respectively.According to Australian standard AS61000 [17], which is

based on IEC61000, the preferred voltage dead band[V lower

db ; V upperdb ] should be around half of the permissible toler-

ance of nominal voltage in LV distribution networks.3) Voltage Balance Profile: Generally, network unbalance is

quantified by voltage unbalance factor (VUF). In this study, theIEC developed and IEEE recommended definition of%VUF ¼ jV�=Vþj as the ratio of the negative-sequencevoltage magnitude to positive-sequence voltage magnitude is

used [18]. A dead band-based objective is also formed to achievethe desired balance profile

J3 ¼Xi2�

�VUF2idb (3)

VUFdb and VUFi > VUFdb, respectively, while � representsthe set of three-phase buses.

4) PV Generation Cost: The proposed PV control strategy isbased on adjusting inverter real and reactive power generations.Inverter losses will rise with the generation increase, which canbe approximated as the quadratic polynomial of the apparentpower Sp

PVi with coefficients kpi1, kpi2, and kpi3 [19]

J4 ¼X3p¼1

Xi2�

kpi1SpPVi

2 þ kpi2SpPVi þ kpi3

� �(4)

where � denotes the set of buses with PV installation. Thecoefficients kpi1, k

pi2, and kpi3 can be determined by curve fitting

of each inverter’s efficiency data (provided by manufacturer).5) PV Real Power Curtailment Cost:When curtailing the PV

real power generation from initial PpPVi0 to P

pPVi, consumers will

suffer the loss of revenue from foregone energy sales

J5 ¼X3p¼1

Xi2�

ðPpPVi0 � Pp

PViÞ: (5)

B. Multiobjective Optimization by Weighted Sum Method

Optimization objectives mentioned above are mutually con-flicting. For example, more reactive power injected locally byinverters can generate a better voltage magnitude profile but alsocause a higher network loss. For multiobjective optimization(MOO) problems with multiple conflicting objectives, a solutionthat minimizes all objectives simultaneously does not exist.Consequently, the notion of Pareto optimality is used to describethe solutions of MOO problems. A solution is called Paretooptimal if none of the objectives can be improved in valuewithout detriment to any other objective [20].

In practice, the objective of solving an MOO problem is tosupport a decision maker in finding the most preferred Paretooptimal solution(s) according to his/her preferences. The mostwidely used method for solving the MOO problems is theweighted sum method [21]

F ¼Xki¼1

wiJiðXÞ: (6)

As shown above, the weighted sum method transforms multi-ple objectives into an aggregated single objective by multiplyingeach objective with a weighting factor and summing up allweighted objectives. To ensure the Pareto optimality of solu-tion(s), it is suggested that the weights be set such thatPk

i¼1 wi ¼ 1 and w � 0, which also generates a convex com-bination of objectives.

The value of a weight is significant not only relative to otherweights but also relative to its objective function magnitude,which is a critical idea but often overlooked. Thus when usingweights to represent the relative importance of the objectives,each objective function is divided by a scale factor sfi

Fig. 3. 101 Bus, 415=240 V test network diagram based on the Perth Solar City[13]. Single-phase buses are represented with both bus and phase numbers (e.g.,bus 3B is a single-phase bus connected to phase B).

TABLE IPV INVERTER CAPACITY EXPANSION

SU et al.: OPTIMAL PV INVERTER REACTIVE POWER CONTROL AND REAL POWER CURTAILMENT 969

so that they all have similar magnitudes and no objectivedominates the aggregated objective function. Common practiceis to choose the maxima of each objective as the scale factor, i.e.,sfi ¼ Jmax

i [21]. Accordingly, (9) can be improved as

F ¼Xki¼1

wiJiðXÞ=sfi: (7)

After scaling, MOO then takes place in a nondimensional,unit-less space. At the end, recover the original objective func-tion values by reverse scaling.

C. Proposed OPF Model

min F

subject to:

PpPVi � Pp

Li � Ppi ¼ 0; Qp

PVi �QpLi �Qp

i ¼ 0 (8)

PpPVi

2 þQpPVi

2 � Spi2

(9)

V pilb � V p

i � V piub (10)

where equality constraints in (8) are the power balance equations.Of these, Pp

PViðQpPViÞ, Pp

LiðQpLiÞ, and Pp

i ðQpi Þ are the PV, load,

and network real (reactive) power, respectively. Inequalityconstraints in (9) indicate the capacity limits on inverteroutputs. Beside, in line with the technical rules set by the networkoperator on nominal voltage and its permissible tolerance for LVnetworks, the boundary constraints on voltage magnitude aregiven in (10).

D. OPF Solution

MATLAB codes for the unbalanced four-wire network multi-objective OPF problem have been developed to obtain the globaloptima, using the Sequential Quadratic Programming (SQP)algorithm with multiple starting points [22], [23].

IV. SIMULATION RESULTS AND ANALYSIS

A. Test Network Based on the Perth Solar City

The selected test network for simulations and analyses of thisstudy is contained within the Perth Solar City [24]. As shown inTable II and Fig. 3, the 415/240 V network is supplied by a200 kVA 22 kV/415V distribution transformer and includes 101buses and 77 consumers. Of these, 51 consumers are single-phaseand 34 consumers have single-phase roof-top PV systemswith typical ratings of 1.59, 1.88, 2 kW, etc. Total rated PVinstallation capacity is 63.81 kW representing a network penetra-tion of 31.9%. As the consumers have a mixture of single- andthree-phase house connections, the loading is inherentlyunbalanced.

The network under study is an aerial, three-phase four-wireconstruction with four equally sized conductors on a mixture of0.9- and 1.2-m cross arms. The consumer mains are 6 mm2

copper with R ¼ 3:7�=km and X ¼ 0:369�=km, while theaerial mains are of two seven-strand, all aluminum conductortypes: 7=4:50AAC� R ¼ 0:316�=km;X ¼ 0:292�=km and7=3:75AAC� R ¼ 0:452�=km;X ¼ 0:304�=km.

B. Simulated Cases Studies

For the 101 bus network mentioned above, the following twonetwork operational extremes are simulated.

1) The first scenario is characterized by the highest powerflows (i.e., high load and low generation),which caused themost significant voltage drop in summer (January 25,2012).

2) The second scenario is related to the smallest grid powerrequirement (i.e., high generation and low load), whichcaused the most serious reverse power flow and voltage risein late spring (November 28, 2011). However, as a realnetwork, even the most serious voltage rise was still withinthe permissible tolerance. Furthermore, according to theAustralianEnergyMarketOperator (AEMO) forecasts [25],the total installed capacity of rooftop PV in Australia willincrease dramatically from1450MWat the end of February2012 to 5100MWby 2020 and 12 000MWby 2031 (basedon a moderate growth scenario). To prove the capability ofthe proposed PV control strategy on mitigating the comingmore serious voltage rise, this scenario is redefined with theoriginal PV generation doubled.

For each scenario, the proposed three-option control assess-ment strategy of Section II will be applied. A reference case issimulated based on the original network state (ORIGINAL)without any inverter control. For all the control cases (ORIGINAL,OPTQ1S, OPTQ1.6S, and OPTPQ1.6S), simulations are per-formed and analyzed over a 24-h period. Due to space limita-tion, the effects of the proposed PV control strategy and MOOmodel on the network performance are studied mainly based onphase C, which has both the most load and the most PVconnections.

C. Optimization Parameters Selection

According to the Electricity Act 1945, distribution systemsupply should function within the limits of �6% of the nomi-nated voltage [26]. Concurrently, in linewith the IEC standard, inmedium- or low-voltage network, VUF should not exceed 2%.Accordingly, voltage dead band in J2 is set as �3% of the ratedvoltage (i.e., [232.8, 247.2]) and VUF dead band in J3 is set to be1% in this study. For the second scenario, considering conser-vation voltage reduction (CVR) for higher efficiency, voltagedead band is reduced to [�3%; 2%] (i.e., [232.8, 244.8]). Addi-tionally, the relative importance of objectives is set to bedecreasing in the order of voltage magnitude profile J2, voltagebalance profile J3/real power curtailment cost J5, and networklossesJ1=PV generation costJ4withweights of 0.4, 0.2/0.2, and0.1/0.1, respectively.

TABLE IILOAD AND PV SYSTEM CONNECTIONS

aEach house has ameter installed at the connection point to its switchboard. Thereare 24 three-phase and 51 single-phase smart meters, in addition to 2 mechanicalmeters (marked as red in Fig. 3).


D. Simulation Results for High Load and Low Generation

As demonstrated in Table III and Figs. 4–8, originally thenetwork loadwasmuch higher than the PVgeneration, especiallybetween 17:00 and 23:00, causing dramatic voltage drop andserious unbalance along the feeder with the maximum objectivefunction value (Fmax) of 90.32 at 21:00. Concurrently, the poornetwork performance was not alleviated by the PV penetrations,

as the generation peak was not coincident with the load peak(Fig. 4). After applying the proposed three-option invertercontrol strategy, the network performance can be continuously

Fig. 4. Phase C real power: transformer, load, andPV=kW (HLLG). The resultsare presented based on the combination of line type and color.

Fig. 5. Phase C reactive power: transformer, load, and PV=kVar (HLLG). Theresults are presented based on the combination of line type and color.

Fig. 6. Objective function (Table III, column 2) under the proposed PV control(HLLG).

Fig. 7. Phase C voltage=V under the proposed PV control (HLLG):(a) ORIGINAL; (b) OPTQ1S; (c) OPTQ1.6S; and (d) OPTPQ1.6S.


improved with a smaller objective function value. Specifically,with capacitive reactive power injected using the latent capacityof inverters in OPTQ1S, the network performance has beensignificantly improved with Fmax at 21:00 reduced to only

0.22178 (Table III). More reactive power can be available tosupport network by increasing the inverter capacity by 60%,with the smallest Fmax of 0.177 for both OPTQ1.6S andOPTPQ1.6S (Table III). Similar results for OPTQ1.6S andOPTPQ1.6S indicate no real power is curtailed after control,which is because considerable load is connected at all timesand reverse power flow, at the whole feeder level, does notoccur.

Weighted sum method is used in this study to define therelative importance of each objective. As shown in Table IV,voltagemagnitude profileJ2 is given the highest importancewithw2 ¼ 0:4. Therefore, a continuously declining J2 can beobserved from ORIGINAL to OPTPQ1.6S at all the time pointsin Table III. Additionally, as the objectives are mutually con-flicting, therefore, as shown in Table III, objectives with lower

Fig. 8. Network VUF=% under the proposed PV control (HLLG):(a) ORIGINAL; (b) OPTQ1S; (c) OPTQ1.6S; and (d) OPTPQ1.6S.

TABLE IIINETWORK OPTIMIZATION RESULTS OVER 24 H (HLLG)

Background colors green and red represent decrease and increase comparingwiththe corresponding value of last case.


importance (e.g., network losses w1 ¼ 0:1 and voltage balanceprofilew3 ¼ 0:2) may be sacrificed at some time points to ensurethe improvement of voltage magnitude profile and the reductionof the total objective function value.

Dead band is introduced to constrain voltage magnitude andVUFwithin the given limits in Table IV.As seen in Figs. 7 and 8,after inverter control, both voltage magnitude and VUF aresignificantly improved with the lowest voltage increased and thepeak VUF decreased from 217.3 V and 1.28% for ORIGINAL to218.9 V and 1% for OPTQ1S and to 222.8 V and 1% for bothOPTQ1.6S and OPTPQ1.6S, respectively.

E. Simulation Results for High Generation and Low Load

As shown in Figs. 9–13, by doubling the generation, ascenario with seriously high PV penetrations is formed tosimulate the projected increased PV connections. Originally,as the generation is much higher than the load, especiallyduring peak generation between 12:00 and 14:00 (Fig. 9), poornetwork performance, characterized by a significant reversepower flow, dramatic voltage rise and unbalance, is causedwith the maximum objective function value (Fmax) of 0.261 at14:00 (Table V). To mitigate the voltage rise and improve theoverall network quality, inductive reactive power is injectedoptimally by the PV inverters in OPTQ1S and OPTQ1.6S. Asshown in Table V, comparing with the results of ORIGINAL,the objective function values show an obvious downward trendover 24 h with Fmax decreased significantly to 0.04259 forOPTQ1S and to 0.042 for OPTQ1.6S. However, the networkperformance has not been improved much by increasinginverter capacity, which is due to the limited effect of reactivepower control on networks with high R/X ratio. Thus, realpower curtailment is used in OPTPQ1.6S to work with reactivepower control. As seen in Figs. 9 and 10 and Table V, with realpower curtailed during the peak generation, further improvednetwork performance can be observed with lower reactivepower demand, alleviated reverse power flow and the smallestFmax of 0.04181.

As shown in Tables IV and V, voltage magnitude profile withthe highest weight w2 ¼ 0:4 is ensured to be improved first,which is supported by the continuously decreasing J2, J3, and J1with lower importance may be sacrificed to support J2 and thetotal objective function at some time points (Table V). Addition-ally, as J3 has a higher weight than J1, worse network losses aremore likely to be observed.

As shown in Figs. 12 and 13, after applying the proposedthree-option PV control, both the overvoltage and VUF arereduced to their corresponding dead band limits in Table IV.Specifically, the highest voltage and the peak VUF are decreased

from 249.3 V and 1.33% for ORIGINAL to 247.1 V and 1.02%for OPTQ1S and to 246.81 V and 1.02% for OPTQ1.6S and to246.8 V and 1.00% for OPTPQ1.6S, respectively.

Fig. 9. Phase C real power: transformer, load, andPV=kW (HGLL). The resultsare presented based on the combination of line type and color.

Fig. 10. Phase C reactive power: transformer, load, andPV=kVar (HGLL). Theresults are presented based on the combination of line type and color.

Fig. 11. Objective function (Table V, column 2) under the proposed PVcontrol (HGLL).

TABLE IVSIMULATED SCENARIOS AND OPTIMIZATION PARAMETERS SELECTION


F. Convergence Analysis and Computing Time

To ensure convergence of the proposed optimization problem,all objectives [(1)–(5)] have been carefully defined as convex

functions of the control variables. The utilization of dead bandand global MATLAB solver with multiple starting points alsocontributes to the convergence. The approach has proven robustwith all of the simulations conducted to date converging.

Fig. 12. Phase C voltage=V under the proposed PV control (HGLL):(a) ORIGINAL; (b) OPTQ1S; (c) OPTQ1.6S; and (d) OPTPQ1.6S.

Fig. 13. Network VUF=% under the proposed PV control (HGLL):(a) ORIGINAL; (b) OPTQ1S; (c) OPTQ1.6S; and (d) OPTPQ1.6S.


Based on unbalanced network model, solving the proposedOPF problem requires more time but still within an acceptablelevel. The average computing time for solving the test networkused in this study is about 5 min (308 s) on a machine with anIntel Core i5 processor at 3.2 GHz. It is much less than the 15mindata collection interval of smart meters, which enables theproposed multiobjective OPF model to be implemented inreal time.

V. MODEL VALIDATION BASED ON SMART METER READING

To further investigate the validity and accuracy of theproposed multiobjective OPF model coded in MATLABaswell as the networkmodel, unbalanced loadflow calculationsare carried out by imposing the actual loads and PV generations

boundary limits recorded by the 24 three-phase and 51 single-phase smart meters installed on the test network. Detailedcomparisons are performed between the recorded (measured)and simulation for typical days through the year (spring,summer, autumn, and winter). Due to page limitation,only one set of results (peak demand case at 18:45 P.M. onJanuary 25, 2012) is presented. As shown in Fig. 14, themaximum voltage error between the calculated values and theactual smarter meter data is 4.7 V, i.e., around 2% of the ratedvalue. Considering the following factors, the error is acceptableand both the optimization and network models are valid andaccurate.

1) Calculations are based on average values over the datacollection interval (15 min) while the smart meter data isinstantaneous.

2) Data collection by smart meters is not synchronous due todifferent time delays in communication.

3) Estimated data is used for the two buses with mechanicalmeters (marked red in Fig. 3).

TABLE VNETWORK OPTIMIZATION RESULTS OVER 24 H (HGLL)

Background colors green and red represent decrease and increase comparingwiththe corresponding value of last case.

Fig. 14. Phase voltage error analyses based on actual smart meter readings for atypical summer day (25/01/2012) in WA, Australia [13].


VI. CONCLUSION AND APPLICATION CONSIDERATION

This paper makes a comprehensive study on PV invertercontrol to improve the operational performance of unbalancedfour-wire distribution networks with high PV penetrations. APV control options assessment strategy is proposed based on thereactive power capability and real power curtailment of single-phase inverters. An OPF problem with multiple objectives ofdead band based voltage magnitude and balance profiles,network losses, PV generation and real power curtailment costsis defined and then converted into an aggregated single-objective problem using the weighted sum method, which canbe successfully solved by the SQP-based global solver inMATLAB. The performance of the proposed PV control strategyand multiobjective OPF model is demonstrated on a realdistribution network over 24 h. The validity and accuracy ofthe optimization model are also tested by comparing simulationresults against the actual smart meter readings. The resultsdemonstrate that the proposed PV control options assessmentstrategy andmultiobjective OPFmodel are feasible and effectivefor improving the voltage regulation and balance of LV four-wiredistribution networks with high residential PV penetrations,which in turn increases the capability to simultaneously supplythe increasing consumer loads and absorb higher fractions ofrenewable energy.

Despite some national standards (e.g., IEEE 1547) forbiddingthe reactive power control of low-voltage inverters for voltageregulation, reactive control is mandated for larger PV systems.Furthermore, small solar inverters with reactive power controlare already available in the European market. To implement theproposed PV control strategy in real distribution networks, thefollowing several factors should be considered.

1) PV reactive power is controlled in this study to provide gridsupport. Thus, in a way similar to the existing real powerfeed-in tariff, feed-in policies on the inverter reactivepower generation should be proposed and providefinancialbenefits for the consumers involved.

2) This study is carried out with the assumption of wide-spread two-way communication infrastructure availability.In fact, some latest advanced metering infrastructures(AMI) already have the capability of collecting datafrom and sending control signals to inverters [27].Research is currently underway to identify and standard-ize communication architecture for the next-generationPV inverters [9].

3) The control procedure: Network information (e.g., loadsand generations at each house) is collected and passed tothe centralized feeder controller, where according to thenetwork status, one of the three proposed control options(Section II) is selected and the optimal set points of eachcontrolled PV inverter are determined based on the pro-posed multiobjective OPF model. Then, the set points willbe sent to each inverter and implemented.

ACKNOWLEDGMENT

The authors acknowledge the supply of data collected underthe Perth Solar City trial, a part of the Australian Government’s

$94 million Solar Cities Program. They also acknowledge thesupport of Western Power in supplying additional network data,models, and technical reports.

REFERENCES

[1] P. M. S. Carvalho, P. F. Correia, and L. A. F. Ferreira, “Distributed reactivepower generation control for voltage rise mitigation in distribution net-works,” IEEE Trans. Power Syst., vol. 23, no. 2, pp. 766–772, May 2008.

[2] K. H. Chua, Y. S. Lim, P. Taylor, S. Morris, and J. Wong, “Energy storagesystem for mitigating voltage unbalance on low-voltage networks withphotovoltaic systems,” IEEE Trans. Power Del., vol. 27, no. 4, pp. 1783–1790, Oct. 2012.

[3] K. Tanaka, M. Oshiro, S. Toma, A. Yona, T. Senjyu, T. Funabashi, andC. H. Kim, “Decentralised control of voltage in distribution systems bydistributed generators,” IET Gener. Transmiss. Distrib., vol. 4, pp. 1251–1260, Nov. 2010.

[4] H.-G. Yeh, D. F. Gayme, and S. H. Low, “Adaptive VAR control fordistribution circuits with photovoltaic generators,” IEEE Trans. PowerSyst., vol. 27, no. 3, pp. 1656–1663, Aug. 2012.

[5] X. Liu, A. Aichhorn, L. Liu, and H. Li, “Coordinated control of distributedenergy storage system with tap changer transformers for voltage risemitigation under high photovoltaic penetration,” IEEE Trans. Smart Grid,vol. 3, no. 2, pp. 897–906, Jun. 2012.

[6] J. Yuryevich and K. P. Wong, “Evolutionary programming based optimalpower flow algorithm,” IEEE Trans. Power Syst., vol. 14, no. 4, pp. 1245–1250, Nov. 1999.

[7] D. Gan, R. J. Thomas, and R. D. Zimmerman, “Stability-constrainedoptimal power flow,” IEEE Trans. Power Syst., vol. 15, no. 2, pp. 534–540, May 2000.

[8] M. Farivar, R. Neal, C. Clarke, and S. Low, “Optimal inverter VAR controlin distribution systems with high PV penetration,” in Proc. IEEE PESGeneral Meet., 2012, pp. 1–7.

[9] E. Dall’Anese, S. V. Dhople, and G. B. Giannakis, “Optimal dispatch ofphotovoltaic inverters in residential distribution systems,” IEEE Trans.Sustain. Energy, vol. 5, no. 2, pp. 487–497, Apr. 2014.

[10] E. Dall’Anese, G. B. Giannakis, and B. F. Wollenberg, “Optimization ofunbalanced power distribution networks via semidefinite relaxation,” inProc. 44th North Amer. Power Syst. Symp., 2012, pp. 1–6.

[11] P.Šulc, S. Backhaus, andM.Chertkov. (2013). “Optimal distributed controlof reactive power via the alternating direction method of multipliers,”Computing Research Repository, [Online]. pp. 1–10, Available: http://arxiv.org/abs/1310.5748

[12] E. Demirok, P. C. Gonz´lez, K. H. B. Frederiksen, D. Sera, P. Rodriguez,and R. Teodorescu, “Local reactive power control methods for overvoltageprevention of distributed solar inverters in low-voltage grids,” IEEE J.Photovolt., vol. 1, no. 2, pp. 174–182, Oct. 2011.

[13] R. Aghatehrani and A. Golnas, “Reactive power control of photovoltaicsystems based on the voltage sensitivity analysis,” in Proc. IEEE PES Gen.Meet., 2012, pp. 1–5.

[14] P. Jahangiri and D. C. Aliprantis, “Distributed Volt/Var control by PVinverters,” IEEETrans. Power Syst., vol. 28, no. 3, pp. 3429–3439,Aug. 2013.

[15] K. Turitsyn, P. Sulc, S. Backhaus, andM. Chertkov, “Distributed control ofreactive power flow in a radial distribution circuit with high photovoltaicpenetration,” in Proc. IEEE Power and Energy Soc. Gen. Meet. (PES),2010, pp. 1–6.

[16] R. Tonkoski, L. A. C. Lopes, and T. H. M. El-Fouly, “Coordinated activepower curtailment of grid connected PV inverters for overvoltage preven-tion,” IEEE Trans. Sustain. Energy, vol. 2, no. 2, pp. 139–147, Apr. 2011.

[17] Electromagnetic Compatibility (EMC)—Limits—Steady State VoltageLimits in Public Electricity Systems, Australian Standard AS61000.3.100–2011, Dec. 2011.

[18] P. Pillay andM.Manyage, “Definitions of voltage unbalance,” IEEE PowerEng. Rev., vol. 21, no. 5, pp. 49–51, May 2001.

[19] M.Braun, “Reactive power supplied by PV inverters—Cost benefit analysis,”in Proc. 22nd Eur. Photovolt. Solar Energy Conf. Exhib., 2007, pp. 1–7.

[20] L. T. Bui and S Alam. (May 28, 2008). Multi-objective Optimization inComputational Intelligence: Theory and Practice, 1st ed. [Online].Available: http://www.igi-global.com

[21] R. Timothy Marler and J. S. Arora, “The weighted sum method for multi-objective optimization: New insights,” Struct. Multidiscipl. Optim., vol. 41,pp. 853–862, Jun. 2010.

[22] Z. Ugray, L. Lasdon, J. Plummer, F. Glover, J. Kelly, and R.Marti, “Scattersearch and local NLP solvers: A multistart Framework for global optimiza-tion,” INFORMS J. Comput., vol. 19, pp. 328–340, Jul. 2007.


[23] (2014). Matlab Global Optimization Toolbox: Global Search and Multi-start Solvers, Natick, MA, USA: MathWorks [Online]. Available: http://www.mathworks.com.au/products/globaloptimization/description3.html

[24] Perth Solar City Annual Report. (Dec. 2012). Western Power, Perth, WA,Australia [Online]. Available: http://www.westernpower.com.au/networkprojects/smartGrid/Perth_Solar_City.html

[25] Rooftop PV information paper-national electricity forecasting. AustralianEnergy Market Operator. (Jun. 2012). Australian Energy Market Operator[Online]. Available: http://www.aemo.com.au/Reports-and-Documents

[26] WesternAustralian Distribution ConnectionsManual. (Jun. 2013).WesternPower, Perth, WA, Australia [Online]. Available: http://www.westernpower.com.au/documents

[27] B. A. Robbins, C. N. Hadjicostis, and A. D. Domínguez-García, “A two-stage distributed architecture for voltage control in power distributionsystems,” IEEE Trans. Power Syst., vol. 28, no. 2, pp. 1470–1482, May2013.

Xiangjing Su (S’11) received the B.S. and M.S.degrees in electrical engineering from ZhengzhouUniversity, Henan, China, in 2008 and 2011, respec-tively. He is currently working toward the Ph.D.degree at the Department of Electrical and ComputerEngineering, Curtin University, Bentley, Australia.

Mohammad A. S. Masoum (S’88–M’91–SM’05)received theB.S.,M.S., andPh.D. degrees in electricaland computer engineering in 1983, 1985, and 1991,respectively, from the University of Colorado,Boulder, CO, USA.

Currently, he is a Professor with the Electrical andComputer Engineering Department, Curtin Universi-ty, Bentley, Australia. His research interests includeoptimization, power quality, and stability of powersystems and electric machines, as well as distributedgeneration.

Peter J. Wolfs (M’79–SM’97) received the B.Eng.and Ph.D. degrees from Central Queensland Univer-sity and the University of Queensland, Rockhampton,Australia, in 1981 and 1992, respectively.

His research interests include smart grid technol-ogy especially in regard to distributed renewableresources and energy storage impacts on systemcapacity and power quality, the impact of electricvehicles, the support of weak rural feeders and remotearea power supply.

Prof. Wolfs is a Fellow of Engineers Australia.
