Δ P dt, Expected demand deviation at time t ( kw ) , Actual wind power generated at time t ( kw )

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1 Robust Microgrid Opertion Considering Renewble Power Uncertinties R. A. Gupt Deprtment of Electricl Engineering Mlviy tionl Institute of Technology Jipur, Indi ndishor Gupt Deprtment of Electricl Engineering Mlviy tionl Institute of Technology Jipur, Indi Abstrct Micro Grids (MGs) re clusters of the Distributed Energy Resource (DER) units nd lods. MGs re selfsustinble nd generlly operted in two modes: ) grid connected 2) grid isolted. This pper focuses on optiml MG opertion for these modes in deregulted environment considering wind uncertinty. Wind uncertinty cn be modeled by intervl forecsting using time series bsed Autoregressive Integrted Moving Averge (ARIMA) model. Other uncertinties lie Photo-Voltic (PV) genertion demnd nd grid prices re modeled in deterministic mnner. Considering the vrious uncertinties this pper proposes robust optimiztion bsed pproch for optiml scheduling of MG in deregulted environment. Proposed pproch is illustrted by prcticl cse study considering different test cses. Comprtive nlysis between obtined results nd existing pproches shows strength of proposed pproch. Keywords-Microgrid Opertion, Genertion Scheduling, Uncertinties, Robust Optimiztion. OMECLATURE The min nottions tht re used throughout in this pper re listed below nd others re defended s required. A. Sets or Indices Index of conventionl disptchble units running from to. t Index of time period running from to t w Index of wind power units running from to w Index of robustness running from to B. Vribles P t, Power generted by disptchble unit t time t ( W ) P grid, t Power imported/exported from/to the grid t time Shed dt, t ( W ) P Demnd shedding t time t ( W ) r u t, Scheduled upwrd reserve of unit t time t ( W ) d r Scheduled downwrd reserve of unit t time t, t ( W ) Δ P wt, Expected wind power devition t time t ( W ) Δ PV vt, Expected PV power devition t time t ( W ) Δ P dt, Expected demnd devition t time t ( W ) Pwt, Actul wind power generted t time t ( W ) PVvt, Actul PV power generted t time t ( W ) P Actul demnd of MG t time t ( W ) dt, C. Prmeters umber of disptchble units t umber of time periods λ grid, t Grid power price t time t ( $/Wh ) λd shed Lod shedding price ( $/Wh ) P dt, Forecsted system s demnd t time t ( W ) f P wt, Forecsted wind power genertion t time t ( W ) PV t Forecsted solr power genertion t time t ( W ) P w Totl Instlled cpcity of wind units ( W ) P Minimum output power of unit ( W ) min P Mximum output power of unit ( W ) P grid, R u, R d Cpcity of the line lining the upstrem grid nd W the MG ( ) Mximum upwrd reserve cpcity of conventionl generting units Mximum downwrd reserve cpcity of conventionl generting units I. ITRODUCTIO A microgrid is smll-scle power supply networ tht is designed to provide power for smll community. MG cn be operted into two modes: grid connected nd grid isolted. In grid-connected mode, MG cn export its excess power to the grid nd cn import its deficit power from grid. On other hnd, MG cn mnge its demnd independently in grid-isolted mode. Due to uncontrollble nture of demnd nd genertors technicl limittions, efficient nd economic mngement of these genertors is highly desirble. With incresing penetrtion of renewble sources lie wind nd solr in the distribution power system MG mngement system my become complex. The complexity of MGs energy /4/$ IEEE

2 mngement is further enhnced by the deregultion of power systems becuse of voltility of grid prices []-[2]. Severl pproches hs been proposed in the recent litertures for MG s energy mngement considering renewble resources. A simple optimiztion bsed pproch hs been used for MG opertion considering different mret policies [3]. However, renewble power nd mret price uncertinties re modelled deterministiclly. A Lgrngin Relxtion long with genetic lgorithm pproch cn optimlly schedule genertors of isolted MG [4]. However, uncertinty in renewble genertion still modelled deterministiclly. Stochstic progrmming bsed pproch suggested for optiml MG opertion considering wind nd solr power uncertinties [5]. In [5] the impct of networ losses nd networ constrints lso investigted. Renewble power uncertinties hve been modelled through different scenrios. An rtificil intelligence bsed methodology hs been proposed for optiml MG opertion with n obective of minimiztion of opertion nd emission cost considering renewble power nd demnd uncertinties [6]. These uncertinties re modelled using rtificil neurl networ. Recent studies re focused on optimizing the genertors cost in MG, however scheduling in both modes i.e. grid connected nd grid isolted is not considered nd complexity of optimiztion problem in both deterministic nd stochstic pproch is not ustified. The two min difficulties with such n pproch re: (i) nowing the exct distribution for dt, nd thus enumerting scenrios tht cpture this distribution is rrely stisfied in prctice, nd (ii) the size of the resulting optimiztion model increses drsticlly s function of the number of scenrios, which poses substntil computtionl chllenges [3]. Therefore, there is need to develop n pproch tht will ble to overcome these issues. This pper ims to develop new pproch for optiml MG opertion in both grid-connected nd grid-isolted modes considering renewble power uncertinties. Considering the vrious uncertinties this pper proposes new pproch for optiml MG opertion in deregulted environment. Proposed pproch cn model MG genertion scheduling problem in robust optimiztion frmewor. Wind uncertinty cn be modeled by intervl forecsting using time series bsed Autoregressive Integrted Moving Averge (ARIMA) model. Other uncertinties lie PV genertion demnd nd grid prices re modeled using deterministic or point forecsting. Proposed pproch is illustrted by prcticl cse study considering different test cses. Comprtive nlysis between obtined results nd existing pproches shows strength of proposed pproch. The rest of pper is orgnized s follows: Section II, describe the nture of problem nd bsic problem formultion microgrid energy scheduling model. Section III, proposes the formultion of the robust microgrid energy-scheduling model considering renewble power genertion uncertinties. Section IV, introduces the test pltform nd provides detiled cse study of proposed lgorithm nd compres the simultion results with those obtined using trditionl deterministic pproch under vrious opertionl conditions. Section V concludes the pper. II. PROBLEM DISCRUPTIO Mircogird energy controller mnges MGs with n obective of opertion cost minimiztion subect to different constrints. Prmeters in both grid-connected nd isolted mode re slightly different. The detiled formultion of MG energy mngement formultion is described below: A. Grid connected mode In grid connected mode, the upstrem grid is connected to the microgrid nd power exchnge is llowed. The upstrem grid cn prticipte in providing power nd spinning reserve to the microgrid [3]. The dy-hed unit commitment problem should minimize the totl expenses of operting the microgrid in grid-connected mode for scheduling horizon of 24 hours. The totl expenses consist of the locl genertors operting cost, the cost of the power imported from the upstrem grid. In grid-connected mode, the bsic obective function is formulted in deterministic pproch s: min ( ( ) ) * t C P, t + r, t r, t + Pgrid, t λgrid, t t= () = Subect to w f f f t, wt, vt, t = w= v= P + P + PV = Pd, t (2) w ( rt, rt, ) + ( ΔPwt, ) = w= + Δ PVvt, + Pgridt, Δ Pdt v= = 0, t wt wt f wt vt vt f vt dt f dt dt Δ P, = P, P,, w, t (4) Δ PV, = PV, PV,, v, t (5) Δ P, = P, P,, d, t (6) min t P P, P,, t (7) u u, t rt, R,,, t (8) d d, t rt, R,,, t (9) t t t P, + r, r, 0,, t (0) t t t t P, + r, r, P,,, t () grid, t grid, t, P P t (2) Obective function () sttes tht operting cost of conventionl generting units power, reserves nd cost of power imported/exported from/to grid should be minimized. Constrint (2) sttes tht sum of scheduled power of conventionl generting units, wind power units nd PV genertion must be equl to dy-hed forecsted demnd. Constrint (3) shows tht t ctul time sum of wind, PV nd demnd devition must be blnced by scheduling (3)

3 conventionl generting units upwrd/downwrd reserves nd grid imported/exported power. Constrint (4)-(6) defines devition of wind, PV genertion nd demnd. Actul vlue of wind, PV power nd demnd is ssumed to rndom vrible tht cn be obtined by multiplying error coefficient to forecsted vlues. Constrint (7) mintins scheduled conventionl genertion unit power within predefined limits. Constrint (8) nd (9) defines scheduled upwrd nd downwrd reserve of conventionl generting units must be lower thn their imum upwrd nd downwrd reserve cpcity respectively. Constrint (0) nd () sttes tht sum of conventionl units scheduled power, upwrd nd downwrd reserves must be greter thn zero nd less thn equl to their instlled cpcity. Constrint (2) ensure tht grid power t rel-time must be less thn predefined grid cpcity. B. Grid isolted mode: In the isolted mode, it is lso required to minimize the expenses of the MG; however, more ttention is given to meeting the demnd with stble opertion. The obective function in the isolted mode is stted s t min ( C( P, t) + r, t r, t) t= = (3) shed shed + Pdt, * λ d Subect to w ( rt, rt, ) + ( ΔPwt, ) = w= Shed vt, dt, t v= shed dt, dt, + Δ PV + P Δ Pd = 0, t (4) P P t (5) The remining constrints nd equtions re the sme s mentioned lredy by equtions (2), (4)-(). Obective function (3) sttes tht operting cost of conventionl generting units power, reserves, nd cost of demnd shedding should be minimized. Constrint (4) sttes tht t ctul time totl system devition must be blnced by scheduling conventionl generting units upwrd/downwrd reserves nd demnd shedding power. Other constrints re sme s in grid connected mode; however one more constrint (6) sttes tht shedding demnd power is lwys less thn the demnd. III. PROPOSED FORMULATIO A robust pproch to solving n optimiztion problem with uncertin dt hs been proposed in the erly 970s nd hs recently been extensively studied nd extended. Robust optimiztion refers to the modeling of optimiztion problem with dt uncertinty to obtin solution tht is gurnteed to be good for ll or most possible reliztion of the uncertin prmeter. There re three types of robustness in optimiztion problem (i) constrint robustness (ii) obective robustness (iii) combintionl robustness [2], [3]. If uncertinty is present in only constrint prmeter thn problem is of constrined robustness nd if uncertinty is present in only obective function prmeter thn problem is of obective robustness, nd if uncertinty is present in both constrint prmeter nd obective function prmeter thn problem is of combintionl robustness. In proposed wor, wind is considered s uncertin prmeter nd for modeling uncertinties in wind power here scenrios re not generted. Here first wind power is forecsted on the bsis of historicl dt thn its lower nd upper limits re generted t 95% confidence intervl [4]. Thn robust optimiztion formultion is used s follows: A. Grid Connected Mode: t t= =, t +, t, t + grid, t grid, t u D ( ( ) ) min C P r r P * λ (6) Subect to w P + W + z Γ + q t, t, = w= = = f f + PVvt, = Pdt, t v= u D ( rt, rt, ) + Δ PVvt, + Pgridt, Δ Pdt = 0, t = v= (7) (8) z + q Wˆ y, 0, (9) t, q 0,, (20) y 0, (2) z 0, (22) The remining constrints nd equtions re the sme s mentioned lredy by equtions (2), (4)-(). Where, Γ is the degree of robustness which controls the robustness of problem, while vrible z nd q re dul vribles used to te into ccount the nown bounds of wind power while y is n uxiliry vrible used to obtin the corresponding liner expressions. Obective function (6) similr to () however power blnce constrint (7) consists scheduled wind power in robust optimiztion frmewor. Constrint (8) shows tht t ctul time system devition must be blnced by scheduling conventionl generting units upwrd/downwrd reserves nd grid imported/exported power. Constrint (9) sttes tht dul vribles used in robust wind power scheduling must blnce the difference of lower nd upper bounds of wind power. Constrint (20), (2) nd (22) show tht dul vribles used in robust pproch must be positive. Other constrints re sme s in grid connected mode in bsic formultion of MG genertion scheduling problem. B. Grid Isolted Mode: In the isolted mode, it is lso required to minimize the expenses of the MG; however, more ttention is given to meeting the demnd with stble opertion. The obective

4 function in the isolted mode is stted s t Shed Shed min ( C ( P, t) + r, t r, t) + Pd, t * λd (23) t= = u D Shed ( rt, rt, ) + Δ PVvt, + Pdt, Δ Pdt, = 0, t = v= (24) The remining constrints nd equtions re the sme s mentioned lredy by equtions (2), (4)-(), (7), (9) - (22) Obective function (23) sttes tht operting cost of conventionl generting units power, reserves nd cost of demnd shedding should be minimized with robust optimiztion wy wind power scheduling. Constrint (24) sttes tht t rel time wind spillge must be blnced by scheduling conventionl generting units upwrd/downwrd reserves nd demnd shedding power. Other constrints re sme s in grid-connected mode in proposed pproch. C. Proposed Algorithm The following lgorithm is used to build the hourly wind power offering: Step : Prmeter Initiliztion. Set initil output of wind unit is Wt = Wt, degree of robustness is Γ = t nd incrementl fctor G tht tes incresing vlues in the intervl [0, ]. Step 2: Itertion Counter Initiliztion. Define totl number of itertion. Counter strt with =. Step 3: Wind Uncertinty Chrcteriztion. Get upper nd lower limits of wind power using ARIMA model. Then set wind power in the itertion s ˆ min Wt, = G ( Wt Wt ). Vlue of wind power is limited in the intervl [ W, W Wˆ ]. t t t, Step 4: Problem Solution. Formulted MG scheduling problem for both modes is solved considering wind uncertinty. Step 5: Chec Itertion Counter. If itertion, updte rnge of incrementl fctor G by step δ nd repet Step 3 nd 4. Otherwise, go to next step. Step 6: Published results. Show obtined optiml cost of MG long with optiml vlue of scheduled dispctble unit genertion nd reserves. Step 7: End. IV. CASE STUDY A. Dt In this study, instlled cpcity of PV unit nd wind units is considered s 200 W nd.34 MW respectively. Wind units consists EERCO turbines model which prmeters re detiled in mnufcturer dtbse [5]. The historicl wind speed dt used in this study ten form publiclly vilble dtbse t Illinois Institute of Rurl Affir, USA. [6]. Along with renewble units, 0 disptchble units re considered, there prmeters re shown in Tble I. Hourly grid price, demnd profile nd PV genertion profile is shown in Tble II. The cpcity of line lining grid nd MG is considered to 5000 W. Historicl grid price obtined for PJM electricity mret. Tble I Disptchble Unit Prmeters Disptchble unit Instlled cpcity (W) Upwrd reserve (W) Downwrd reserve (W) Mrginl cost ($/Wh) Tble II Dily Mret Prices, lod nd PV profiles Time (h) Price ($/w) Demnd (pu) PV (pu) B. Simultion Results Power Output (W) Upper limit Forecsted Lower limit Time (h) Fig. : Hourly wind power Using bove discussed dt, proposed pproch is

5 illustrted by considering two cses. In Cse I, grid connected opertion simulted while in Cse II, grid isolted opertion of MG is simulted. Both test cses re coded in GAMS pltform using CPLEX solver [7]. Fig. shows the forecsted wind power with upper nd lower level using ARIMA model. pproch re shown in Fig. 2, 3 nd 4 respectively. Fig. 5 shows power imported/exported to/from grid in Cse I. From these figures, it is observed tht when grid price is higher MG cn export their reserve cpcity to grid nd vice-vers to reduce its operting cost Grid inport/export power (W) Fig.2 : Scheduled power of disptchble units in Cse I Time (h) Fig. 5: Power imported/exported to/from grid in Cse I Similr to previous Cse, Fig 6, 7, nd 8 shows scheduled disptchble unit power, upwrd nd downwrd reserve using proposed pproch for Cse II, respectively. Fig. 3: Scheduled upwrd reserve in Cse I Fig. 6: Disptchble unit scheduled power in Cse II Fig. 4: Scheduled downwrd reserve in Cse I For Cse I, obtined scheduled power, upwrd nd downwrd reserve of disptchble units using proposed Fig. 7: Scheduled upwrd reserve in Cse II

6 V. COCLUSIO A robust optimiztion bsed pproch hs been proposed in this pper for optiml genertion scheduling of MG in both grid-connected nd -isolted modes. Wind power uncertinty hs been modeled through intervl forecsting using ARIMA model. A comprtive study on dily MG opertion cost using proposed pproch with deterministic nd stochstic pproch hs been done. A significnt reduction in opertion cost clerly shows strength of proposed pproch in MG genertion scheduling. Proposed pproch cn be enhnced by incorporting vrious uncertinties nd technicl constrints in future. Sheded demend (W) Fig. 8: Scheduled downwrd reserve in Cse II Time (h) Fig. 9: Demnd shedding in Cse II Demnd shedding in Cse II is shown in Fig. 9. Form these figures, it is visulized tht MG cn utilized its upwrd reserve cpcity during pe demnd to reduce demnd shedding events. The cost of W demnd shedding is $000. C. Discussion A comprtive nlysis is performed to illustrte proposed pproch on dily MG opertion. Obtined dily MG opertion cost using proposed robust optimiztion pproch is compred with deterministic nd stochstic pproch s shown in Tble III. From the tble it is observed tht reduction in dily cost using proposed pproch in Cse II is higher s compre to Cse I. Becuse in Cse II, smll reduction in demnd shedding event results lrge reduction is opertion cost. Tble III Compritive Anlysis of MG Dily Opertion Cost Approches Opertion Cost ($) Cse I Cse II Deterministic Stochstic (-3.07 %) (-0.67 %) Proposed (-5.02%) (-7.32 %) ACKOWLEDGEMET The second uthor cnowledges Ministry of Humn Resource nd Development, Indi for providing finncil support to do this reserch wor. REFERECES [] W. Su nd J. Wng, Energy mngement systems in micrgrid opertions, Electricity J., vol. 25, no. 8, pp , Oct [2] F. Ktirei, R. Irvni,. Htzirgyriou, nd A. Dimes, Microgrids mngement, IEEE Power Energy Mg., vol.6, no.3, pp.54 65, My- Jun [3] A. G. Tsilis, nd. D. Htzirgyriou, "Centrlized control for optimizing microgrids opertion." IEEE Trns. Energy Convers. vol. 23, no., pp , Mr [4] T. Logenthirn, nd D. Srinivsn, Short term genertion scheduling of Microgrid, in Proc. TECO IEEE Region 0 Conference Singpore, pp.-6, Jn [5] W. Su, W. Jinhui, nd R. Jehyung, "Stochstic energy scheduling in microgrids with intermittent renewble energy resources," IEEE Trns. Smrt Grid, vol. 5, no. 4, pp , 204. [6] A. Chouchi, R.M. Kmel, R. Andoulsi, nd K. gs, Multiobective intelligent energy mngement for microgrid, IEEE Trns.Ind. Electron., vol. 60, no. 4, pp , Apr [7] C. Chen, S. Dun, T. Ci, B. Liu, nd G. Hu, Smrt energy mngement system for optiml microgrid economic opertion, IET Renewble Power Genertion, vol. 5, no. 3, pp , My 20. [8] R. Jing, J. Wng, nd Y. Gun, Robust unit commitment with windpower nd pumped storge hydro, IEEE Trns. Power Syst., vol. 27,no. 2, pp , My 202. [9] Bertsims, Dimitris, Dessislv Pchmnov, nd Melvyn Sim, "Robust liner optimiztion under generl norms," Opertions Reserch Letters, vol. 32, no. 6, pp , [0] E. Kuznetsov, Y. F. Li, C. Ruiz nd E. Zio, An integrted frmewor of gent bsed modelling nd robust optimiztion for microgrid energy mngement, Appl. Energy, vol. 29, pp , 204. [] A. Y. Sber nd G. K. Venygmoorthy, Resource Scheduling Under Uncertinty in Smrt Grid With Renewbles nd Plug-in Vehicles, IEEE Syst. J., vol.6, no., pp.03 09, Mr [2] D. Bertsims nd M. Sim, The price of robustness," Oper. Res., vol. 52, no., pp , [3] D. Bertsims nd M. Sim. "Robust discrete optimiztion nd networ flows," Mth. Progrm. Ser. B, vol. 98. pp. 49 7, [4] Morles, Jun M., Roberto Minguez, nd Antonio J. Coneo. "A methodology to generte sttisticlly dependent wind speed scenrios." Appl. Energy, vol. 87, no. 3, pp , 200. [5] EERCO Wind Turbines, Wellesweiler, Germny. [Online]. Avilble: [6] Illinois Institute of Rurl Affir, USA. [Online]. Avilble: [7] Generl Algebric Modeling System, GAMS, 203. [Online]. Avilble: