Optimal Sizing and Allocation of Residential Photovoltaic Panels in a Distribution Network for Ancillary Services Application

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1 Optmal Szng and Allocaton of Resdental Photovoltac Panels n a Dstrbuton Networ for Ancllary Servces Applcaton Reza Ahmad Kordhel, Student Member, IEEE, S. Al Pourmousav, Student Member, IEEE, Jayarshnan R.Plla, Member, IEEE, Hany M. Hasanen, Senor Member, IEEE, Brgtte Ba-Jensen, Senor Member, IEEE, and M. Hashem Nehrr, Lfe Fellow, IEEE. Department of Energy Technology, Aalborg Unversty, Denmar. Electrcal Power and Machnes Department, Faculty of Engneerng, An Shams Unversty, Caro, Egypt. Department of Electrcal and Computer Engneerng, Montana State Unversty, USA e-mal: ra@et.aau.d, s.pourmousavan@msu.montana.edu, jrp@et.aau.d, hanyhasanen@eee.org, bbj@et.aau.d,hnehrr@msu.montana.edu Abstract- Tremendous penetraton of renewable energy n electrc networs, despte ts valuable opportuntes, such as balancng reserve and ancllary servce, has rased concerns for networ operators. Such concern stems from grd operatng condtons. Such huge penetraton can lead to volaton n the grd requrements, such as voltage and current lmts. Ths paper proposes an method for determnng the number of photovoltac (PV) panels together wth ther arrangement n the grd n order to mze ancllary servce, wthout volatng grd operaton lmts. The proposed method s based on genetc algorthm. To do so, sngle-objectve and mult-objectve have been consdered. The proposed method s mplemented on a model of a part of a Dansh dstrbuton grd to verfy ts effectveness. The smulaton results prove the vablty of the method, whle eepng the grd requrements wthn standard operatng lmts. I. INTRODUCTION Whle government polces and renewable energy ntatves are great ncentves to ncrease small PV nstallaton for the next decades [], t has rased techncal concerns regardng voltage rse and reverse power flow n dstrbuton networs. Overvoltage problem commonly has been reported n the dstrbuton networs wth hgh PV penetraton level when a consderable number of households decded to nstall PV panels []-[5]. To overcome ths problem, dfferent methods, such as reactve power control methods among feeders and mposng curtalment, are proposed to deal wth the overvoltage ssue [6]. Addtonally, as PV penetraton ncreases, more reverse power flow wll be drected toward upper grd, whch consequently leads to a new set of techncal ssues. Such reverse power flow mght exceed voltage lmtatons and power lmtatons of transformers. However, the reverse power flow can be notfed as a source of ancllary servces for the upper grd. In ths paradgm, an excess PV generaton mght be purchased by the system operators nstead of conventonal spnnng and non-spnnng reserves. Ths mght be very helpful for the system operators to reduce costs and transmsson congeston, partcularly durng pea hours. As a result, larger PV penetraton essentally provdes more ancllary servce resources for the upper grd, consderng the fact that the techncal lmtatons of the dstrbuton networ should not be volated. Dfferent methods for szng and allocaton of dstrbuted generaton n the dstrbuton networs are proposed n dfferent studes [7]-[9]. However, these studes focus on mnmzng operatonal cost and/or emsson, loss mnmzaton [8], and voltage correcton and so on. In ths paper, mum PV penetraton s formulated as an problem to mze reverse power flow to the upper grd, as a source of ancllary servce. To the best of our nowledge, ths objectve for resdental PV szng and allocaton has not been reported n any lterature. Dfferent objectves are defned and compared (as sngle and multobjectve) for PV szng and allocaton for a sample dstrbuton networ. Genetc algorthm (GA), as a heurstc technque, s employed to solve the nonlnear problem. In order to follow practcal applcaton of resdental PV panels, the PV szng problem s formulated as an nteger problem. Therefore, the number of PV panels nstalled on each bus s lmted to the number of households on the same bus. Dfferent techncal constrants, such as voltage and current lmts of lnes, buses, and the transformer nomnal power, are consdered n the problem. Fnally, the proposed method s utlzed for a sample dstrbuton networ, where sze and locaton of PV panels s calculated on each bus for dfferent objectve functons. The rest of the paper s organzed as follows. The problem s explaned n secton II. Also, dfferent objectve functons, as well as ther coeffcents, are explaned n detal n ths secton. The appled technque s presented n secton III. The proposed method s tested on a model of a Dansh dstrbuton grd. Secton IV presents the grd overall vew. Secton V dscusses results and compares the outcome of dfferent methods. The concluson of the results /4/$.00 ' 04 IEEE 68

2 s presented n secton VI. II. METHODOLOGY It s well-nown that ancllary servce s a major concern n power system operaton, where generaton and demand should always reman balanced wthn power systems. Tradtonally, spnnng and non-spnnng reserves were the only optons to provde ancllary servces. However, the large PV penetraton level n the dstrbuton systems provded a new opportunty for ancllary servces whch possbly can decrease operatonal cost and transmsson congeston [0]. Because of the paradgm shft n ancllary servces, mum PV penetraton n the dstrbuton networs s desrable for the system operators, as long as t does not volate any techncal lmtatons. To do so, a general approach s proposed to determne the mum PV sze and locatons n a dstrbuton networ for mum grd support wthout volatng any techncal constrant. In ths study, three dfferent objectves are consdered whch are structured as dfferent sngle and mult-objectve functons. The proposed objectves nclude: ) mzng power to the upper grd (reserve), ) mnmzng voltage devaton, and ) mnmzng power loss. Because grd support s the prmary goal of ths study, the man objectve s the frst objectve. Consderng dfferent grd requrements and ther correlaton, such as the correlaton between power and voltage or power and losses, the problem s complex. Due to the correlaton between objectves, optmzng one functon mght lead to unwanted effects on other objectves, whch mght not be desrable. Therefore, smultaneous of the objectve functons can lead to better results, whle grd constrants must also be met [7], []. Therefore, two methods can be defned to deal wth such problem: sngleobjectve method and mult-objectve method. Sngle and mult-objectve formulatons are explaned n the followng sub-sectons. A. Sngle-Objectve Approach In general, the sngle-objectve method can be expressed as: mn f ( x) g ( x) = 0 ; =,,...,m () subject to : h ( x) 0 ; j =,,...,n j Where m s the number of equalty constrants and n s the number of nequalty constrants. As mentoned before, dfferent functons can be defned for ths problem, wth respect to what the user expects from the. For our purpose, mzng power to the upper networ (called Pupper ( x )) s a prorty. Therefore, the problem wth a sngle objectve functon s lmted to mze power to support the upper grd. Based on the conventon used n ths study, power flow to the upper grd s negatve. As a result, the problem of mzng power flow to the upper grd wll alternatvely be changed to mnmzng power flow through transformer, as follows: ( ) P x mn (mean ( P ( x ))) () upper In (), the average power flowng through the transformer to the feeders durng the day s obtaned. Then, to mze the power to the upper grd, ths average value s mnmzed. In ths study, no equalty constrant s nvolved n the problem. Inequalty constrants are smlar to the alternatve problem where transformer nomnal capacty, standard voltage devaton for buses, and cable nomnal currents are consdered,.e.: ) Voltage of all buses, V bs,, must stay wthn a specfc lmt,.e., V V mn ;,,..., b, s V b = l. ) Power flowng through transformer must be less than transformer nomnal power. ) Current lmts of the cables. Here, V mn and V are the mnmum and mum voltage values of the grd buses, b s the number of the bus, and S s the tme nterval of the calculaton. In ths wor, 5-mnute tme ntervals are consdered for calculatons. B. Mult-Objectve Approach Although the prorty of the PV szng and allocaton s gven to the grd support objectve, t s desred to consder other techncal ssues n the smultaneously. Therefore, the mult-objectve (MO) optmal structure s proposed as []: mn F( x) () F ( x) = f ( x), f ( x),..., f ( x) trafo [ ] From (), dfferent functons (namely f ( ) x ) mght be consdered n the MO problem. Smlar constrants as n the sngle-objectve functon problem are utlzed for the MO problem as well. Here, K s the number of objectve functons. In our study, three objectve functons are consdered, as follows: = ( ) (4) f ( x) m ax P x m n (m ean ( P ( x))) upper trafo f ( ) ( )) x = ( V (5) b,s f ( ) x = P (6) loss, total Where V bs, s the voltage at bus b at tme nterval s. As can be seen, the functon defned n (4) s smlar to that n () In (5), mum voltage devaton at each grd bus s calculated durng the day. Among all these voltage devatons, the mum devaton s taen nto account for, where the procedure accordng to () tres to mnmze ths mum devaton. Also, the grd total loss durng the day s calculated and taen as the thrd objectve to be mnmzed, as mentoned n (6). Smlar nequalty constrants gven for the sngle-objectve problem n () are utlzed for the MO problem as well. As mentoned above, MO functon can be obtaned by combnng dfferent objectves. Dfferent methods have been presented so far to deal wth MO problems, among whch Pareto optmalty s a predomnant method []. A comprehensve revew of dfferent Pareto optmalty methods 68

3 s presented n []. A very common method for combnng dfferent objectve functons, whch s used n ths paper, s called weghted-sum approach. In ths method, dfferent objectve functons are added together wth a weghtng factor to form a sngle objectve functon as gven below: mn w f( x) (7) = Objectve functons are weghted based on ther sgnfcance n the. Typcally, sum of all weghtng factors are equal to one: w = (8) = Where f ( x ) s th objectve functon from exstng objectves. In ths method, smlar constrants can be employed for the problem n hand. Typcally, there are two methods to calculate weght factors: ran order centrod (ROC) method, and ran sum (RS) method []. ROC method: In ths method, a unform dstrbuton of the weghts s assumed on the smplex of ran-order weghts. Then, for w > w >... > wm, f s the ran poston of w, and s the number of objectve functons: w = l (9) RS method: Ths method s approprate when there s a prorty sequence among the objectve functons. The weghtng values can be calculated as follows: ( + ).( + ) l= w =, =,,..., (0) As mentoned earler, the hghest prorty s gven to the frst objectve. Voltage devaton and power loss are second and thrd n the lst, respectvely. Mnmzng voltage devaton has hgher prorty than power loss, snce power loss does not change sgnfcantly wth dfferent PV szes and allocaton. Ths s due to the grd sze under study and ts low power loss. Ths fact wll be shown n the secton V.B as a smulated case study. The focus of ths paper s to mze power flow to the upper grd. Optmzaton varables are the number of PV panels for each bus n the grd. To set the upper lmt for the varables, t s assumed that a typcal household nstalls a mum of 6-W ( sets of -W) PV panel. Such assumpton sounds reasonable, consderng the avalable roof area of a typcal house. III. OPTIMIZATION TECHNIQUE Wth the objectve functons and constrants n hand, t s requred to utlze an approprate technque to solve the problem. The problem n ths study ncludes nteger decson varables, namely the number of PV panels whch can be nstalled on each bus. In addton, the objectve functons (whether sngle objectve or MO problems) are nonlnear functons, and mght not converge. Therefore, heurstc methods seem to be the best opton for the problem n hand. There are several heurstc technques wth ther own weanesses and strengths. However, only a few of them are capable of solvng nteger problems. Amongst all, (GA) s chosen n ths study to solve the problem. It s avalable n a MATLAB toolbox, and s capable of solvng nteger problems. Genetc algorthm s a search heurstc that mtates the process of natural selecton by routnely provdng solutons to problems. Some man parameters of ths method are: selecton, crossover, mutaton, and populaton. The prncples of ths technque, together wth ts dfferent parameters are explaned n []-[5]. Detals of GA parameters are presented n Table I. For the MO problem, dfferent weghtng factors are calculated based on (9) and(0), and s reported n Table II. As an example, to calculate the weght factor for the frst objectve functon, f ( x ), n ROC method, we would have: = w = = ( + + ) = l = l 8 For f ( x ), the calculaton would be smlar: 5 = w = = ( + ) = l = l 8 The same calculaton can be done for the rest of the factors. TABLE I. GA PARAMETERS. No. of Stall Tolerance Name Populaton generaton generaton functon Value e-8 TABLE II. WEIGHTING FACTORS FOR DIFFERENT OBJECTIVES IN THE MO PROBLEM. Objectve Functon Method f ( ) f ( ) f ( ) ROC /8 5/8 /8 RS / / /6 IV. CASE STUDY In order to evaluate the effectveness of the proposed PV szng and allocaton method, several smulaton studes are carred out on a dstrbuton networ model. The dstrbuton networ model s chosen from Dansh dstrbuton grd, and ts sngle lne dagram s shown n Fg.. The number of households on each feeder s presented n Table III. All the grd buses are shown n ths fgure. However, to eep the fgure more obvous, only some of the households are shown n the fgure. In order to buld a practcal dstrbuton networ for smulaton studes, approprate load data and PV model are utlzed. Consderng avalable grd data, the Velander method [6] s appled to determne load demand. Ths method s created based on large emprcal data and s wdely accepted among dstrbuton system operators (DSOs) and researchers n Scandnavan countres. In ths study, the actual load demand data for a typcal summer day s used whch 68

4 orgnally was avalable as annual energy demand data. Eq () represents the Velander formula [6]. P = * E * E () In ths equaton, E s the annual energy demand of the household. To have a more realstc load model, concdent load behavor s also taen nto account [6]. Eq () presents the formula for calculatng ths factor. P () cl = n P = In ths equaton, n s the number of households on a feeder, P s the mum demand of the feeder, and P s the mum demand of household on the feeder. For resdental solar PV panels, a realstc and smplfed model s used n ths study [7], [8]. Such model gves accurate results, whle elmnatng unnecessary detals for a steady state analyss. Eq () descrbes the model. G P = * P + α ( t t ) () 0 pv 000 STC In ths equaton, P STC s the power of the array under standard test condton, P STC = 000 ( W / m), G represents rradaton, t represents ambent temperature, and t 0 stands ο for standard temperature: t 0 = 5 c. Also, α s a factor ο whch depends on panel type. Here, α = / c [6]. It should be noted that the orgnal networ encounters some voltage ssues even n normal operatng condtons. By other words, voltage at some buses (e.g., bus4 and bus5 on feeder6) s below the IEEE standard mnmum voltage,.e (p.u.) [9]. Measured voltages at these buses are shown n Fg. for normal operaton. It s evdent from the fgure that voltage n these buses drops sgnfcantly, especally durng evenng tme. However, as long as voltage devaton of a customer does not exceed 0%, t would be acceptable as operatng voltage [0]. V. SIMULATION RESULTS In ths secton, dfferent smulaton studes are carred out on the dstrbuton system shown n Fg. to optmally sze and locate PV panels. In the frst sub-secton, smulaton results for normal operaton, sngle and mult-objectve functons are presented and explaned. In the second subsecton, a smulaton study s performed to show that power loss mnmzaton s not an effectve objectve functon of a system of ths sze. A. Sngle and Mult-Objectve Optmzaton Table IV presents the optmal results of each method. It should be mentoned that n ths table, the number of -W panels for each bus n the grd s presented. Therefore, not all the households on all buses are capable of nstallng PV panels. It mght be possble for some households to nstall more than one set of -W panel, whle ths mght not be the case for other households. TABLE III. NUMBER OF HOUSEHOLDS ON EACH FEEDER. Feeder No. of household Fg.. Grd Confguraton. Fg.. Voltage of crtcal buses n normal grd operaton. The number of households on each bus of the grd s also presented n ths table. Voltage of grd crtcal buses for the sngle-objectve method s presented n Fg.. Voltage profles for the mult-objectve methods are presented n Fg.4 and Fg.5. From Fg., t s obvous that voltage profles are wthn standard lmts. On the other hand, for ROC method, shown n Fg.4, voltage n two grd buses s more than normal devaton. However, total voltage devaton of these buses s stll less than 0% devaton. Therefore, the results are vald, although t s very margnal. The least change n load profles mght mae queston these results. On the other hand, voltage profle of RS method, shown n Fg.5, demonstrates that all voltages are wthn standard lmts. As mentoned earler, a clear advantage of mult-objectve approach to sngle objectve approach s ts accurate results. The results of sngle objectve approach would vary n dfferent runs. The change s manly n the arrangement of the panels, but the number of panels would vary as well. On the other hand, runnng mult-objectve approach for several tmes has led to smlar results. Therefore, the results from mult-objectve are more promsng and relable. On the other hand, allocatng a hgher weght factor to the frst objectve n ROC method has led to 684

5 hgher number of PV panels. On the other hand, as mentoned earler, the obtaned results for ROC approach are margnal values. Therefore, t s a good practce to have the results from both methods. Ths wll help to fnd out mum grd capablty usng ROC method, whle achevng a more applcable result by RS method. Also, transformer power profle from the dfferent methods, together wth the normal transformer profle, s presented n Fg.6 to llustrate the comparson. Regardng the results, the grd behavor under hgh PV penetraton can be analyzed. From the voltage profles, the frst pont s the postve effect of PV panels on grd voltage profles. The grd has some voltage ssues n normal condton, especally n some crtcal and heavy loaded buses, presented n Fg., whle addng PV panels wth any of the proposed methods has mproved these voltage profles. Presence of PV panels, as a power source, covers part of the load demand. As a result, the power flowng from the upper grd decreases. Less power flowng through the lnes leads to smaller current n the lne cables, whch results n less voltage drop. The effect of the panels on the grd power condton s easy to realze from Fg.6. The normal profle of the grd s also presented n ths fgure. From the fgure, the grd has two pea values durng ts daly curve; a small pea durng mornng tme, and the man pea whch happens n the evenng. Addng PV to the grd has changed the profle, shavng the mornng pea and lowerng the evenng pea. Such effect s reasonable, consderng the fact that the PV power producton depends manly on the rradaton. Fg.. Voltage of buses usng sngle-objectve method. Fg. 4. Voltage of buses usng ROC mult-objectve method. TABLE IV. NUMBER OF -KW PV PANELS FOR EACH GRID BUS. Feeder Bus No. of Sngleobjectve approach ROC households RS approach Fg. 5. Voltage of buses usng RS mult-objectve method. Fg.6. Power profle of the transformer. 685

6 As the day comes to ts mdday tme, durng whch the rradaton s mum, the PV producton ncreases, whle durng evenng tme, due to small rradaton, the PV producton s not sgnfcant. Of course, the man pont n ths fgure s the negatve power flow through transformer. As the PV producton ncreases, t exceeds the grd consumpton. Therefore, the extra power of PV panels goes to the upper grd through the transformer. The mum power to the upper grd s around 05W for the sngle-objectve method, occurrng around p.m. to p.m. For the multobjectve methods, ths value s much more notceable, wth 50W for RS approach and 40W for ROC approach. Such sgnfcant value of power to the upper grd s a sgnfcant potental to be used as a reserve or balancng capacty for the upper grd. B. Power Loss as Sngle Objectve Functon As mentoned n secton II, for mult-objectve, the least weght s dedcated to total power loss, denoted as f ( x ). The reason s that the total power loss value of the grd s small, as the grd s a small dstrbuton networ. To verfy that assgnng a hgher prorty to voltage rather than to total loss s reasonable, a separate sngle objectve s done. In ths case, total power loss, f ( x ), s the objectve functon. The results are presented n Table V. From the table, t can be realzed that the networ total power loss has not changed n dfferent repeats, although the arrangement of the panels has changed a bt. Also, to have a more accurate comparson, the total power loss of the networ usng dfferent s s presented n Table VI. From the results, one can realze the nsgnfcant effect of on grd total loss, comparng to grd normal power loss. The total power loss presented n Table V s almost the same as the total power loss of other methods n Table VI. Therefore, f ( ) x doesn t have a sgnfcant effect on the results. However, ths mght not be the case for a large-scale networ wth sgnfcant power loss. So, for dfferent networs wth dfferent scales, ths fact needs to be addressed. Feeder TABLE V. Bus NUMBER OF -KW PV PANELS FOR EACH GRID BUS. st nd rd Feeder 5 6 Total Power loss (W) Bus st nd rd TABLE VI. TOTAL POWER LOSS OF DIFFERENT OPTIMIZATION METHODS. Method Sngle objectve ROC RS Total power loss n W VI. CONCLUSION An algorthm s proposed n ths paper to fnd out the mum number of PV panels n a dstrbuton grd, as well as ther arrangement. An algorthm based on GA s proposed. Two approaches were consdered to deal wth the problem: sngle-objectve approach, and mult-objectve approach. Each approach, together wth ts equatons and constrants s explaned. The proposed method s appled to a model of a Dansh dstrbuton grd to fgure out ts applcablty n dealng wth a realstc case. Grd operatng requrements are also taen nto account. Smulaton results verfy that the s capable of optmzng PV panel penetraton n the grd to mze reverse power flow and provde ancllary servce for the upper grd, wthout volatng grd constrants. Revewng the results, t can be seen that mult-objectve approach presents more promsng results comparng to sngle-objectve approach. Consderng the ponts mentoned n the paper, usng storage together wth PV panels could help usng the panels power producton n evenng pea tmes. As dscussed earler, mum power producton of panels occur n the mddle of the day, whle a sgnfcant pea of the load profle s durng evenng tme. Therefore, there s a major need for reserve power and balancng power durng these hours. Usng a storage system enable the grd to deal wth such ssue. Our next step s to utlze avalable storages n the grd, such as electrc vehcles, to cope wth such problem. REFERENCES [] Renewable Development Intatve, European Ban for Reconstructon and Development (EBRD). [Onlne]. Avalable: 686

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