Multi-Stage Power Distribution Planning to Accommodate High Wind Generation Capacity

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1 Mult-Stge ower Dstrbuton lnnng to Accommodte Hgh Wnd Generton Cpcty Nkolos C. Koutsouks, vlos S. Georglks, Senor Member, IEEE, nd Nkos D. Htzrgyrou, Fellow, IEEE School of Electrcl nd Computer Engneerng, Ntonl Techncl Unversty of Athens (NTUA), Athens, Greece E-ml: {koutsouks, pgeorg, Abstrct The ncresng ntegrton of wnd power nd other dstrbuted energy resources nto modern power dstrbuton systems hs mde the power dstrbuton plnnng (D) very nterestng nd chllengng optmzton problem. Ths pper proposes long-term, mult-stge D method for the optml reconductorng of feeders n order to effcently meet the lod growth demnd nd optmlly ccommodte hgh wnd generton cpcty. The proposed D method consders vrous ctve network mngement (ANM) schemes nd t s formulted s mxed-nteger qudrtclly constrned progrmmng problem. Results on n 18-bus test system ndcte tht the proposed D method cn effcently ccommodte hgh wnd generton cpcty wth smultneous reducton of the network nvestment nd opertonl costs, hghlghtng the mportnce of ANM. Index Terms Mult-stge plnnng, network renforcement, power dstrbuton plnnng, MIQC, wnd power. Sets N T rmeters b, C C L I. NOMENCLATURE set of buses plnnng perod susceptnce of type feeder between buses nd, Ω -1 nstllton cost of conductor, $/km upgrde cost of substton, $/MWh g conductnce of type feeder between buses, nd, Ω -1 mx I mxmum current mgntude of conductor, A L length of feeder between busses nd, km D, ctve power demnd of bus, MW Q D, rectve power demnd of bus, MVr nterest rte r S wdg, rted wnd pprent power t bus, MVA mn /U mx U mn/mx voltge mgntude squred, V mn /φ mx φ mn/mx ngle of the DG unt s power fctor Vrbles CF curtlment fctor of the wnd generton t bus E Losses nnul energy losses, MWh I current mgntude between buses nd, A G, ctve power generton of bus, MW wdg, ctve wnd power generton of bus, MW Q G, rectve power generton of bus, MVr Q wdg, rectve wnd power generton of bus, MVr U voltge mgntude squred of bus, V V voltge mgntude of bus, V z t bnry vrble for the plcement of type feeder (,) between buses nd t yer t. θ Angle of bus, degrees φ Angle of the DG unt s power fctor t bus, rd II. INTRODUCTION The mn obectve of the power dstrbuton plnnng (D) s to desgn the dstrbuton network n order to effcently meet the lod growth demnd. The D problem determnes the optml locton nd sze (cpcty) of future substtons nd/or feeders n the most economc nd relble wy. In the lst yers, the hgh penetrton of dstrbuted generton (DG) technologes, energy storge nd the ctve demnd response hve trnsformed the D nto more complcted nd chllengng problem. The D consttutes mxed-nteger non lner progrmmng problem (MINL). A comprehensve revew of D models nd methods cn be found n [1] [3]. The D cn be modeled ether s sttc or s mult-stge problem. In the sttc (or sngle-stge) D, the soluton s determned n only one stge of the plnnng perod, whle n the mult-stge D, the plnnng requrements re determned n successve stges long the

2 plnnng perod. In [4] nd [5], the D problem s smplfed to mxed-nteger lner progrmmng (MIL) problem nd mult-stge plnnng scheme nvestgtes the mpct of dsptchble dstrbuted generton (DDG) for vrous lod levels. The mult-stge D wth the ntegrton of DDG s lso solved by the dscrete prtcle swrm optmzton (DSO) method [6] nd by bck propgton pproch bsed on cost-beneft nlyss [7]. Furthermore, the hgh penetrton of renewble energy sources (RES) hs exposed the D n further chllenges. In [8], the trde-offs between the optml DG plcement nd the conventonl grd renforcement re evluted through mult-obectve optmzton scheme nd the mportnce of trff schemes s hghlghted. In [9], the proposed D method bsed on genetc lgorthm (GA) suggests tht the ont ntegrton of RES nd demnd response leds to plnnng solutons wth smller nvestment cost on network components nd wth hgher envronmentl benefts thn ntegrtng RES lone. The pssve operton of the dstrbuton systems nd the uncertn generton output of the RES my led to further nvestment costs on new or exstng feeders n order to vod overlods due to strong generton. The nstllton of energy storge systems (ESSs) could llevte the negtve effects of ntense generton, but ther nstllton cost s hgh nd certn ncentves should be gven n order to be proftble. On the other hnd, the dopton of ctve network mngement (ANM) schemes, such s Volt/VAR control, generton curtlment, rel-tme reconfgurton, etc., could reduce the nvestments on new network components. Ths pper dels wth the mult-stge dstrbuton system plnnng n the presence of hgh wnd generton cpcty consderng ANM, such s DG rectve control nd generton curtlment. The plnnng horzon s dvded nto successve stges nd the proposed model defnes the optml conductor sze of the network s feeders n order to effcently meet the lod growth demnd nd optmlly ccommodte hgh wnd generton cpcty. To decrese the computtonl burden the D problem s formulted s mxed-nteger qudrtclly constrned progrmmng (MIQC) problem, pproprtely doptng the generl methodology of [10]. An 18-bus test system [11] s used to demonstrte the effcency of the proposed method. III. ROBLEM FORMULATION For the D problem, the followng ssumptons re tken nto ccount: The plnnng perod s dvded nto stges wth fxed durton. The plnnng decson on feeders reconductorng cn be tken n ech stge. The dstrbuton network topology s fxed nd no ddtonl buses re consdered to be dded durng the plnnng perod. All DG unts re prvte nvestment, whch mens tht the locton nd sze of these unts re known nd they re decded by the prvte nvestor n ccordnce wth the techncl rules set by the Dstrbuton System Opertor (DSO). The profle of typcl dy wth n hourly tme frme s ssumed to represent the lod demnd nd ts correspondng uncertntes re modeled wth the norml probblty dstrbuton functon (pdf). Webull pdf s used to cpture the uncertntes of the wnd velocty nd, thus the uncertntes of the wnd generton. The selecton of the feeders conductor sze s determned for the mxmum stress condtons. As mxmum stress condtons the mxmum lod wth no generton nd the mnmum lod wth mxmum generton re consdered. The determnton of the energy losses s obtned through probblstc power flow nlyss. The Actve mngement s lmted: ) to the coordnted ctve nd rectve dsptch of the DG unts nd b) to the generton curtlment of the DG. The proposed method dels wth the mnmzton of the nvestment cost n feeders reconductorng nd the mnmzton of the opertonl costs durng long term plnnng perod. The D problem s modeled s MIQC wth the obectve functon (1) subect to the constrnts (5) (1). 1 t mn f = C L z + CL E t Losses + (1) (,) t T ( 1 r), N The frst prt of the obectve functon (1) represents the nvestment cost of the feeders reconductorng nd the second prt represents the cost of the energy losses. The N nonlner power flow equtons re replced wth N lner equtons (5), (6) nd N qudrtc constrnts (7), s, N : follows ( ) W H U = V () = V V cos( θ θ ) (3) = V V sn( θ θ ) (4) ( g + ), U g, W b H G, + wdg, D, =, (5), N ( b + ), U b, W g H Q G, + Qwdg, QD, =, (6), N U U W H = 0 (7) The remnng nequlty constrnts of the optmzton procedure re s follows: I,, = ( g + b ) ( U + U W ), N I mn mx t ( I ) z N, (,) mx U U U N (8) (9) (10)

3 t T, N z t (,) t (,) 1, N (11) { 0,1} z (1) The ctve nd rectve power blnce of the system s gven n (5) nd (6), respectvely. The squre of the current mgntude s clculted ccordng to (8). The lmt of the current flow of the brnch wth conductor type tht connects bus to s represented by (9). Constrnt (10) represents the lmts of the voltge mgntude for ll system s buses. In order to ensure tht there wll be t most one chnge on every feeder s conductor type durng the whole plnnng perod, constrnt (11) s ppled. Constrnt (1) depcts the bnry nture of the decson vrble z t. A conductor type s (,) selected (not selected) for the brnch tht connects bus to durng the yer t f the correspondng vlue of (1) equls to one (zero). The D problem descrbed by (1) nd (5) (1) refers to the pssve mngement of the dstrbuton system, n whch no ctve mngement of the wnd generton unts s ppled. In ths pper, dfferent ANM schemes re ncorported for the soluton of D problem. A. Rectve ower Control of the Wnd Generton The coordnted ctve nd rectve power dsptch of the wnd generton unts cn be benefcl for the dstrbuton systems by preventng some constrnt volton nd by possbly deferrng nvestments on new network components. Consderng the smll ngle pproxmton for the power fctor of the DG unts, the ANM scheme cn be mplemented n the optmzton procedure by modfyng (5) nd (6): G, + S = sn φ φ (13) φ cosφ 1 (14) wdg, wdg, Qwdg, S = + (15) φ = 1 wdg, Swdg, wdg, = (16) Qwdg, = Swdg, φ (17) ( g + ), U g, W b, H, N QG, + Swdg, φ QD, 1 φ D, (18) ( b + ), U b, W g, H, N (19) φ mn mx φ φ (0) For smll vlues of the ngle φ n rdns, ts sne nd cosne cn be pproxmted wth (13) nd (14), respectvely, wth reltvely smll error. Therefore, the pprent, ctve nd rectve power of the wnd genertors re gven by (15), (16) nd (17), respectvely. Equtons (5) nd (6) tht represent the ctve nd rectve power blnce cn be modfed to (18) nd (19), respectvely. The rnge of the wnd genertor s power fctor s represented by (0). For exmple, f the power fctor of wnd genertor vres from 0.9 nductve to cpctve, the vlue of φ vres from 5.84 to Thus, the D problem wth the control of the power fctor of the DG unts s modeled s MIQC problem wth the obectve functon (1) subect to (7) (1), (15) (0). B. Generton Curtlment of the Wnd Generton The dopton of the generton curtlment of the wnd generton s n ANM scheme cn lmt the overlods cused by hgh generton. Ths strtegy cn decrese the wnd generton output ccordng to () n order to vod ny constrnt volton nd t could led to zero ddtonl nvestment costs. However, hgh mounts of curtled wnd generton should be compensted to the DG nvestors dependng on the regulton. Thus, only moderte generton curtlment could ctully beneft the DSOs. The generton curtlment could esly be dopted n the optmzton procedure by ddng contnuous vrble s curtlment fctor to the ctve power blnce (5) of the system, s follows: G, + wdg, = ( g + ), U g, W b, H, N CF D, (1) 0 CF 1 () The D problem consderng generton curtlment s ctve mngement s formulted by (1) subect to (6) (1), (1) (). IV. RESULTS AND DISCUSSION The proposed model for the long-term dynmc dstrbuton system plnnng s tested n n 18-bus test system [11], shown n Fg. 1, n order to nvestgte ts performnce. The conductor type of the lnes, the length of the lnes nd the lod demnd of every bus n the reference yer re shown n Tble I. The vlble conductors durng the plnnng perod re presented n Tble II. The exmned plnnng perod s 10 yers nd the lod growth rte s consdered 3% per yer. The nterest rte s equl to 7.5% nd the cost of energy losses s 50 $/MWh. Durng the plnnng perod, t s plnned to be nstlled wnd frm wth rted cpcty 4MVA t bus 8 durng the second yer of the plnnng perod nd nother wnd frm wth rted cpcty 4 MVA t bus 6 durng the sxth yer of the plnnng perod.

4 Fgure bus test system. TABLE I. 18-BUS TEST SYSTEM DATA FOR THE REFERENCE YEAR Bus Conductor Length From To Type (km) (MW) (MVr) TABLE II. TECHNICAL CHARACTERISTICS OF AVAILABLE CONDUCTORS Type R (Ω/km) X (Ω/km) Therml Investment cost lmt (MVA) (10 3 $/km) The lod profle of ech bus s conssted of dfferent lod levels, s shown n Fg., nd ech lod level represents the men vlue of the lod demnd for certn durton wth stndrd devton ssumed to be 10% of the men vlue. The techncl chrcterstcs of the vlble wnd turbnes re Vc = 4 m/s, Vn = 15 m/s nd Vco = 5 m/s nd the shpe nd scle fctor of the Webull pdf re consdered 1.93 nd 7.94, respectvely. Three scenros hve been exmned for the soluton of the D. In Scenro I, the D s solved wthout consderng ny control on the wnd generton output (pssve mngement) nd the results re shown n Tble III. In Scenro II, the D s solved consderng the control of the rectve output power of the wnd generton unts nd the results re gven n Tble IV. In Scenro III, the dopton of the wnd generton curtlment s consdered for the soluton of the D nd the results re shown n Tble V. Q Fgure. Lod profle. Scenro I yelds the soluton wth the hgher nvestment cost nd wth the hgher energy losses compred wth the other two scenros. The lck of control of the wnd generton output cn hve negtve effects on the plnnng of the dstrbuton system. The overlods cused by hgh wnd generton nd mnmum lod demnd leds to the reconductorng of some of the exstng feeders. On the other hnd, the pplcton of ctve mngement n the D leds to solutons wth lower nvestment nd opertonl costs s shown n Tbles IV nd V. From the ANM schemes tht were exmned n ths pper, the most promsng results were gven by the dopton of the generton curtlment (Scenro III). The pplcton of generton curtlment to the wnd genertors results to plnnng soluton wth 35.5% lower nvestment cost nd 14.6% lower operton cost compred wth the plnnng soluton of Scenro I (pssve mngement) of the dstrbuton system. Furthermore, the rectve output power control of the wnd genertors lso benefts the plnnng of the dstrbuton system s shown n Tble IV, snce t results to plnnng soluton wth reduced nvestment cost on network components nd wth lower nnul energy TABLE III. LANNING SOLUTION OF SCENARIO I (ASSIVE MANAGEMENT) Bus Yer for lne Conductor Type From To reconductorng Investment Cost ($) Cost of Energy Losses ($) Totl Cost ($)

5 TABLE IV. LANNING SOLUTION OF SCENARIO II (REACTIVE OWER CONTROL OF WIND GENERATION) Bus Yer for lne Conductor Type From To reconductorng Investment Cost ($) Cost of Energy Losses ($) Totl Cost ($) TABLE V. LANNING SOLUTION OF SCENARIO III (WIND GENERATION CURTAILMENT) Bus Yer for lne Conductor Type From To reconductorng Investment Cost ($) Cost of Energy Losses ($) Totl Cost ($) losses compred wth the plnnng soluton of Tble III. Fgure 3. Network nvestment cost mde by DSO to ccommodte vrous rted wnd generton cpctes for the 18-bus system for dfferent network mngement schemes. ton of the techncl constrnts of the network.. Unlke the rectve power support, mor curtlment of the wnd generton could cuse loss of proft for the owner of the DG unts nd the DSO my hve to refund the owner, dependng on the regultory frmework. Fg. 4 shows the totl wnd energy curtled s percentge of the totl wnd generton for dfferent rted cpctes of wnd genertors. As t ws expected when the nstlled rted cpcty of the wnd generton s reltvely smll (8MVA) the energy curtled s estmted to be 3.05% of the totl energy produced from the wnd generton unts n order to cheve the plnnng soluton wth the lower nvestment cost. Ths rto ncreses sgnfcntly s the nstlled cpcty of the wnd generton ncreses. If the curtled wnd energy s compensted, ths ANM my not be proftble for the DSO. Thus, only lmted Fg. 3 llustrtes the mpct of the ntegrton of dfferent wnd generton cpctes on the nvestment cost on network components mde by the DSO for the forementoned plnnng strteges. The plnnng strtegy tht preserves the pssve mngement of the dstrbuton system leds to ner lner ncrese of the network nvestment costs s the cpcty of the wnd generton ncreses. The mplementton of the rectve control of the wnd genertors lso results to lner ncrese of the network nvestment costs. However, the results of ths ANM scheme re more benefcl for the system thn the preservton of the pssve mngement. The ANM scheme tht would llow sgnfcnt deferrl of the nvestment costs, s shown n Fg. 3, s the curtlment of the ctve wnd generton. Ths strtegy llows theoretclly the cut-off of every wnd genertor up to ts totl generton (100% generton curtlment) for preservng the non vol- Fgure 4. Totl wnd energy curtled (%) s percentge of the totl wnd generton for dfferent rted cpctes durng the plnnng perod.

6 generton curtlment n extreme nd rre condtons could be benefcl n prctce for the DSO. V. CONCLUSION A mxed nteger qudrtclly constrned progrmmng model ws presented n ths pper for the soluton of the mult-stge D problem consderng ctve mngement of the nstlled wnd generton unts. The exmned ANM schemes nclude the rectve control of the wnd genertors nd the wnd generton curtlment. The results show tht ncludng the opertonl spects of the ctve mngement n the power dstrbuton plnnng cn led to solutons wth lower network nvestment cost nd wth decresed energy losses compred wth the trdtonl pssve mngement of the dstrbuton systems. Even though the generton curtlment yelded the best results, the compenston of the curtled wnd energy my be reson for not pplyng ths plnnng strtegy. ACKNOWLEDGMENT Ths work hs been performed wthn the Europen Commsson (EC) funded SuSTAINABLE proect (contrct number F7-ENERGY ). The uthors wsh to thnk the SuSTAINABLE prtners for ther contrbutons nd the EC for fundng ths proect. REFERENCES [1] S. K. Khtor nd L. C. Leung, "ower dstrbuton plnnng: revew of models nd ssues," IEEE Trns. ower Systems, vol. 1, no. 3, pp , Aug [].S. Georglks nd N.D. Htzrgyrou, "A revew of power dstrbuton plnnng n the modern power systems er: Models, methods nd future reserch, " Electrc ower Systems Reserch, Vol. 11, pp , Aprl 015. [3] CIGRE Workng Group C6.19, "lnnng nd optmzton methods for ctve dstrbuton systems," Techncl Brochure 591, CIGRE, rs, Dec [4] S. Hffner, L. Fernndo, A. erer, L. A. erer, L. S. Brreto, S. Member, nd A. Sets, "Multstge Model for Dstrbuton Expnson lnnng Wth Dstrbuted Generton rt I: roblem Formulton," IEEE Trns. ower Delvery, vol. 3, no., pp , Apr [5] S. Hffner, L. Fernndo, A. erer, L. A. erer, L. S. Brreto, nd S. Member, "Multstge Model for Dstrbuton Expnson lnnng wth Dstrbuted Generton rt II: Numercl Results," IEEE Trns. ower Delvery, vol. 3, no., pp , Apr [6] I. Zr, G. Ledwch, S. Member, A. Ghosh, nd G. ltt, "Consderng Lod Growth, Lne Loss, nd Relblty," IEEE Trns. ower Systems, vol. 8, no., pp , My 013. [7] A. S. Bn Humyd nd K. Bhttchry, "Comprehensve mult-yer dstrbuton system plnnng usng bck-propgton pproch," IET Gener. Trnsm. Dstrb., vol. 7, no. 1, pp , Dec [8] E. Hesen, S. Member, J. Dresen, R. Belmns, G. Ault, nd S. Member, "Opportuntes for Actve DER Mngement n Deferrl of Dstrbuton System Renforcements," n ower Systems Conference nd Exposton, 009, SCE '09, pp [9] B. Zeng, S. Member, J. Zhng, nd X. Yng, "Integrted lnnng for Trnston to Low-Crbon Dstrbuton System Wth Renewble Energy," IEEE Trns. ower Systems, vol. 9, no. 3, pp , My 014. [10] E. Romero-Rmos, J. Rquelme-Sntos, nd J. Reyes, "A smpler nd exct mthemtcl model for the computton of the mnml power losses tree, " Electrc ower Systems Reserch, vol. 80, no. 5, pp , My 010. [11] W. M. Grdy, M. J. Smoty, nd A. H. Noyol, "The Applcton of Network Obectve Functons for Actvely Mnmzng the Impct of Voltge Hrmoncs n ower Systems," IEEE Trns. ower Delvery, vol. 7, no. 3, pp , July 199.