Aalborg Unvertet A Data-Drven Stochatc Reactve Power Optmzaton Conderng Uncertante n Actve Dtrbuton Networ and Decompoton Method Dng, ao; Yang, Qngrun; Yang, Yongheng; L, Cheng; Be, Zhaohong; Blaaberg, Frede Publhed n: IEEE ranacton on Smart Grd DOI (ln to publcaton from Publher): 0.09/SG.07.67748 Publcaton date: 07 Document Veron Accepted author manucrpt, peer revewed veron Ln to publcaton from Aalborg Unverty Ctaton for publhed veron (APA): Dng,., Yang, Q., Yang, Y., L, C., Be, Z., & Blaaberg, F. (07). A Data-Drven Stochatc Reactve Power Optmzaton Conderng Uncertante n Actve Dtrbuton Networ and Decompoton Method. IEEE ranacton on Smart Grd, PP(99), -. DOI: 0.09/SG.07.67748 General rght Copyrght and moral rght for the publcaton made acceble n the publc portal are retaned by the author and/or other copyrght owner and t a condton of acceng publcaton that uer recogne and abde by the legal requrement aocated wth thee rght.? Uer may download and prnt one copy of any publcaton from the publc portal for the purpoe of prvate tudy or reearch.? You may not further dtrbute the materal or ue t for any proft-mang actvty or commercal gan? You may freely dtrbute the URL dentfyng the publcaton n the publc portal? ae down polcy If you beleve that th document breache copyrght pleae contact u at vbn@aub.aau.d provdng detal, and we wll remove acce to the wor mmedately and nvetgate your clam. Downloaded from vbn.aau.d on: november 30, 07
A Data-Drven Stochatc Reactve Power Optmzaton Conderng Uncertante n Actve Dtrbuton Networ and Decompoton Method ao Dng, Member, IEEE, Qngrun Yang, Student Member, IEEE, Yongheng Yang, Member, IEEE, Cheng L, Student Member, IEEE, Zhaohong Be, Senor Member, IEEE, Frede Blaaberg, Fellow, IEEE Abtract o addre the uncertan output of dtrbuted generator (DG) for reactve power optmzaton n actve dtrbuton networ, the tochatc programg model wdely ued. he model employed to fnd an optmal control trategy wth mum expected networ lo whle atfyng all the phycal contrant. heren, the probablty dtrbuton of uncertante n the tochatc model alway pre-defned by the htorcal data. However, the emprcal dtrbuton can be baed due to a lmted amount of htorcal data and thu reult n a uboptmal control decon. herefore, n th paper, a data-drven modelng approach ntroduced to aume that the probablty dtrbuton from the htorcal data uncertan wthn a confdence et. Furthermore, a data-drven tochatc programg model formulated a a two-tage problem, where the frt-tage varable fnd the optmal control for dcrete reactve power compenaton equpment under the wort probablty dtrbuton of the econd tage recoure. he econd-tage varable are aduted to uncertan probablty dtrbuton. In partcular, th two-tage problem ha a pecal tructure o that the econd-tage problem can be drectly decompoed nto everal mall-cale ub-problem, whch can be handled n parallel wthout the nformaton of dual problem. Numercal tudy on two dtrbuton ytem ha been performed. Comparon wth the two-tage tochatc and robut approache demontrate the effectvene of the propoal. Index erm Stochatc optmzaton; reactve power optmzaton; column-and-contrant generaton algorthm; actve dtrbuton networ; dtrbuted generaton NOMENCLAURE Indce and Set,, Index for bue t Index for tme perod B Set of bue E Set of branche h wor wa upported n part by Natonal Key Reearch and Development Program of Chna (06YFB090904), n part by Natonal Natural Scence Foundaton of Chna (Grant 560737), n part by Chna Potdoctoral Scence Foundaton (05M580847), n part by Natural Scence Ba Reearch Plan n Shaanx Provnce of Chna (06JQ505), the proect of State Key Laboratory of Electrcal Inulaton and n part by Power Equpment n X an Jaotong Unverty (EIPE630).. Dng (e-mal: tdng5@mal.xtu.edu.cn), Q. Yang, C. L and Z. Be are wth the State Key Laboratory of Electrcal Inulaton and Power Equpment, Department of Electrcal Engneerng, X an Jaotong Unverty, X an, Shaanx, 70049, Chna; Y. Yang and F. Blaaberg are wth the Department of Energy echnology, Aalborg Unverty, Aalborg DK-90, Denmar (e-mal: yoy@et.aau.d; fbl@et.aau.d). Θ Set of branche wth tranformer Set of bue for reactve power compenator D Set of bue for hunt capactor/reactor () Set of all parent of bu () Set of all chldren of bu Confdence et of the probablty dtrbuton Y Feable regon of contnuou varable under -th cenaro Parameter M A large number me horzon N w Cardnalty of Θ N c Cardnalty of D N r Cardnalty of D N Number of cenaro K Number of obervaton for uncertan parameter n Number of tap rato at tranformer branch (, ) r, x Retance/reactance of branch (, ) b, Shunt uceptance from to ground C /C Upper/lower bound of hunt capactor/reactor capacty at bu W / W Upper/lower bound of tranformer rato lmt at branch (, ) c, Specfed operatonal tme for hunt capactor/reactor at bu w, Specfed operatonal tme for tranformer (, ) Step ze of hunt capactor/reactor at bu w, ap rato on -th level of the tranformer (, ) U /U Upper/lower bound of voltage magntude at bu I l Current capacty lmt of branch (, ) Q c, / Q c, Upper/lower bound of reactve power compenaton for contnuou reactve power compenator at bu u Uncertan parameter u Uncertan parameter under -th cenaro Number of auxlary bnary varable,0,...,, p 0 H, G Probablty from the htorcal data A parameter that can control the ze of the confdence et ung -norm to control the ze of the confdence et ung nf-norm to control the ze of the confdence et Confdence level Varable Actve/reactve power flow from bu to
U Voltage magntude of bu P, Q Inected actve/reactve power of bu l Squared branch current at branch (, ) w ap rato of the tranformer branch (, ) C Value of hunt capactor/reactor at bu o Optmal 0- decon on -th level of the tranformer (, ) ρ Optmal tep of hunt capactor/reactor at bu Q c, Value of reactve power compenaton for contnuou reactve power compenator at bu v Squared voltage magntude of bu z Dcrete decon varable y Contnuou decon varable y Contnuou decon varable under -th cenaro,0,..., Auxlary bnary varable to expre the nteger, varable ρ by bnary code D I. INRODUCION ISRIBUED networ, characterzed by ther motly radal topology, are featured wth heavly fluctuatng load, whch may lead to large power loe and voltage drop near the end of feeder, adverely affectng ndutral manufacture and daly lve. o mprove the power qualty, reactve power optmzaton, ervng for tertary voltage control (VC), am to mze the total tranmon loe and mprove the voltage profle by controllng reactve power compenator and tranformer tap rato over everal perod, whle atfyng pecfc phycal and operatng contrant. Generally, the controlled equpment can be clafed a contnuou and dcrete controllable devce. he dcrete controllable devce are controlled va wtchng on/off and they hould not be aduted qute frequently due to ther ervce lfetme and extng manufacture technque. hu, the total number of operatng tme of dcrete controllable devce lmted, whch lead to the development of the dynamc reactve power optmzaton (DRPO) model [-3]. h model actually a large-cale mxed-nteger nonlnear programg and everal technque ncludng ntellgent earche and tandard branch-and-bound/cut method were propoed to olve th complex model [4]-[6]. Wth a propoal of a two-tage mult-perod mxed-nteger convex model, [7] analyzed the tradeoff between r mtgaton and nvetment cot mzaton. In [8], a voltage ecurty contraned mult-perod optmal reactve power flow model wa propoed baed on the generalzed Bender decompoton method wth an optmal condton decompoton approach to olve t. However, the ze of data are a a reult of large-cale mxed-nteger nonlnear programg problem wth mult-perod, ncreang the computatonal burden and tme. Recently, the conc relaxaton technque wa tuded n dtrbuton networ, whch gve a ound oluton whle gnfcantly mprovng the computatonal performance [9]-[]. For ntance, n [], the econd-order cone to relax the non-convex power flow equaton were propoed n order to obtan a mxed nteger econd order coned programg model, after whch a entvty-baed relaxaton and decompoton method wa ntroduced to further mprove the computaton. After deterng the total ze of the dtrbuted energy torage (DES, e.g., battere) and optmal locaton for the DES, [3] appled the econd order cone programg relaxaton to obtan the globally optmal oluton and avod the problem of NP-hardne. Furthermore, [4] dealt wth a ont problem of reactve power optmzaton and networ reconfguraton to mze power loe and mprove the voltage profle, the orgnal non-convex model of whch wa converted nto a mxed nteger econd order cone programg model ung the econd-order cone relaxaton, the bg-m method and the pecewe lnearzaton technque. Neverthele, an ncreang number of dtrbuted generator (DG) ncludng wnd power and photovoltac (PV) cog nto dtrbuted networ nowaday. he dtrbuted networ ntegrated wth DG, termed a actve dtrbuted networ, are facng crtcal techncal challenge to tradtonal operaton due to the tochatc nature of DG, whch may reult n uncertan output, and thu everer voltage volaton. o cope wth the uncertan output of DG n the optmzaton operaton n actve dtrbuton networ, tochatc programg [5-7], chance-contraned baed tochatc programg [8-0] and robut optmzaton [-3] have been extenvely explored. For example, a mult-cenaro framewor for optmal power flow under the wort wnd cenaro and tranmon N- contngency to properly addre the uncertan wnd power generaton wa propoed n [4]. A tochatc mult-obectve framewor for dtrbuton feeder reconfguraton wa employed n [5], frtly convertng t nto pecfc detertc cenaro among random cenaro of wnd/load forecat varaton and then mplementng mult-obectve formulaton for each detertc cenaro n the frt tage. In [6], a chance-contraned programg for optmal power flow under uncertanty conderng nonlnear model wth multple uncertan nput wa tuded, where a bac-mappng approach and lnear approxmaton of nonlnear model equaton were performed. Furthermore, [7] converted the chance-contraned tochatc programg formulaton nto a lnear detertc problem and a decompoton-baed method to olve the day-ahead chedulng problem. Although lnearzed model enable to mprove computatonal effcency, the accuracy of lnearzaton hould be enured. Generally, tochatc programg method cannot cover all the poble realzaton of uncertante. In order to addre th problem, robut optmzaton wa propoed to mmunze agant the oluton wthn a gven uncertanty et. A preented n [8], a two-tage robut reactve power optmzaton to coordnate the dcrete and contnuou reactve power compenator wa et up, whle hedgng agant any poble realzaton wthn uncertan wnd power output. A mxed-nteger two-tage robut optmzaton formulaton and a decompoton algorthm n a mater-lave tructure to acheve mum networ loe were dcued n [9], conderng the wort condton over uncertanty et. Although the robut optmzaton can protect the ytem agant a pre-defned uncertanty et, t alway gve a more conervatve oluton than the tochatc approach. In practce, htorcal data of DG output may be avalable at ISO/RO. herefore, t poble to derve a more effcent oluton that robut whle le conervatve, whch ncorporate the uperorty of both tochatc and robut approache. Accordng to the htorcal data, a confdence et contructed for the probablty dtrbuton of the uncertante to fnd an optmal oluton under the wort probablty dtrbuton [30]-[35]. herefore, a data-drven two-tage tochatc dynamc reactve power optmzaton model developed n th wor to coordnate the dcrete and contnuou controllable
3 devce, whle addreng the uncertan DG output. he contrbuton of the paper are ummarzed a follow: ) It the frt tme to et up a data-drven tochatc programg model n the dtrbuton networ, where the econd order cone programg relaxaton utlzed to relax the nonconvex feable regon caued by the branch flow equaton. Furthermore, the dynamc reactve power optmzaton can be termed a a large-cale mxed-nteger econd order cone programg model. ) It found that the propoed model ha a pecal tructure n the econd-tage b-level model, where the feable regon of the uncertanty et dont wth the operatng regon. A a reult, a new column-and-contrant generaton algorthm propoed to decompoe the b-level problem nto everal mall-cale ub-problem to be handled n parallel, whch doe not requre the dualty nformaton a the tradtonal method. he ret of the paper organzed a follow: Secton II preent a general dynamc reactve power optmzaton baed on econd order cone programg relaxaton for actve dtrbuton networ. In Secton III, a data-drven tochatc reactve power optmzaton model propoed wth the conderaton of uncertan DG output. Furthermore, a new dualty-free baed column-and-contrant generaton algorthm preented to olve the propoed reactve power optmzaton model n Secton IV. In Secton V, numercal reult obtaned on a 33-bu ytem demontrate the effectvene of the propoal, whch alo compared wth the two tradtonal approache. Fnally, concluon are drawn n Secton VI. II. REACIVE POWER OPIMIZAION MODEL IN ACIVE DISRIBUION NEWORKS A. Formulaton of Reactve Power Optmzaton Model Dtrbuton networ, dfferent from tranmon networ, have the property that the topology radal, o t very common to utlze the branch flow formulaton for decrbng the power flow n dtrbuton networ [], [8], [36]. P H H r l, B Q G G xl + b, U B U U r H xg r x l,, E \ () U U r H xg r x l,, w H G lu,, E where, E \ denote, E, but,. he frt and econd equaton decrbe the actve and reactve power balance at each bu; the thrd and fourth equaton decrbe the voltage drop at each lne and tranformer; the lat equaton decrbe the relatonhp among voltage, current and power. he reactve power optmzaton problem eentally am to mze total power loe by controllng the reactve power compenator and tranformer tap rato over a gven number of tme horzon whle atfyng varou phycal contrant. Here, the reactve power compenator can be clafed a contnuou adutment equpment uch a DG output, and dcrete adutment equpment ncludng capactor ban. It common that the electrc devce ncludng tranformer tap rato and wtched capactor ban cannot be aduted very frequently due to the lmtaton of ther ervce lfetme and extng manufacture technque. herefore, the mum allowable operatonal tme hould be condered n the model and the reactve power optmzaton model can be exactly wrtten a follow Q t, t, ot c r l t () t, E.t, PDG, t PL, t H t H t r l t B, t,..., (3) U tc t+ Qc, t QL, t, B, G t G t xl t+ b, U t t,..., (4) n 0 U t U t r H t x G t r x l t, o t U t U t, w,, E /, t,..., (5),, t r H t x G t r t x t l t,,,,..., (6) H t G t l t U t E (7) n o, t,, 0 (8) U U t U, B (9),, 0 l t I E (0) Qc, Qc, t Qc,, \ D () n t 0 C t C t, D () C C t C, D (3) t t c,, D t o t o t, (4) w,, (5) t Z o, t 0,,,, (6), D (7) where () am to mze total networ lo over tme perod; (3)-(4) denote the power balance at each bu; (5)-(7) how the Ohm' law for each branch, ncludng (6) for tranformer branch; (8) how a choce contrant by whch only one trap rato level choen; (9)-(0) are contrant for voltage
4 magntude and branch current; () the contrant for the contnuou reactve power compenator; ()-(3) are the contrant for dcrete reactve power compenator; (4)-(5) are retrcton that the total allowable operatonal tme by dcrete adutment equpment hould be lmted. However, the model ()-(7) a mxed nteger nonlnear nonconvex programg whch very dffcult to olve. However, the non-convexty come only from the nonlnear power flow contrant. o addre th ue, the em-defnte programg (SDP) and econd order cone programg (SOCP) were propoed to convexfy the feable regon encloed by the power flow contrant [9]-[0]. It wa hown n [9]-[0] that SOCP and SDP relaxaton method are equvalent for the radal networ, but the computatonal tme from the former one much le than the latter one. h becaue both SOCP and SDP are olved by the tandard prmal-dual nteror pont method, but SOCP ha much better wore-cae complexty than SDP [37]. heoretcally, the complexty of SOCP O(n 3 ) wherea O(n 4 ) of SDP. Here, n the number of varable. hu, for a large power ytem wth numerou varable, SOCP would perform much fater than SDP and thu elected n th wor. B. SOCP Relaxaton for Reactve Power Optmzaton Model At frt, let U t v t (4)-(7), (9) wll become v t C t + Qc, t QL, t for B and then contrant +, G t G t xl t b v t, B, t,..., (8) v t v t r H t x G t r x l t, n 0, E /, t,..., (9) o t v t u t r H t x G t r t x t l t, w,, t,..., (0),,,, H t G t l t v t E () U v t U, B () he contrant n () a nonlnear equalty, reultng n the nonconvex problem. o addre th ue, the econd order cone relaxaton performed by relaxng the quadratc equalty nto nequalty, yeldng H t G t l t v t l t u t,, E (3) After th relaxaton, the orgnal reactve power optmzaton model wll lead to be a mxed nteger econd order cone programg model, but not a tandard mxed nteger econd order cone programg model nce there are tll many blnear term n the above model, and we can mplfy them by reformulaton n the appendx, leadng to (A0)-(A). Subequently, the reactve power optmzaton model n can be mathematcally formulated a a general problem a a y (4).t. zy, Y Az b, z 0, (5) y Cy f, Q y q c,,..., y d n Y (6) Dy g Gz, Ey u where C, Q, q, c, D, g, G, E and d are matrx/vector form wth repect to the orgnal model. III. DAA-DRIVEN SOCHASIC REACIVE POWER OPIMIZAION CONSIDERING UNCERAINIES In the lat ecton, the reactve power optmzaton model only conducted under a gven load demand curve over multple tme perod. However, to addre the uncertan generaton output of the dtrbuted generator (.e., u n (6)), the tochatc programg employed to coordnate the dcrete and contnuou reactve power compenator. Specfcally, the dcrete decon varable (.e., z n (4)) hould be detered before the uncertanty revealed nce uch equpment hould not be aduted qute frequently, wherea the contnuou decon varable (.e., y n (4)) can be flexble wth the revealed uncertanty. h framewor gve a two-tage framewor and for the N cenaro of uncertante from dcretzng the gven N u and the corre- ). he obectve functon probablty dtrbuton, uch that pondng probablty ( p,, N p u,, mze the total expected networ lo. hen, the general data-drven tochatc reactve power optmzaton model formulated a.t. zy, Y N p a y (7) Az b, z 0, (8),,,..., y Cy f Q y q c y d n Y (9) Dy g Gz, Ey u Due to the lmted nformaton from the htorcal data, the probablty dtrbuton of uncertante cannot be exactly detered by the data. A a reult, we allow the probablty dtrbuton of uncertante to be arbtrary wthn a pre-defned confdence et contructed from the htorcal data. hu, the propoed data-drven tochatc reactve power optmzaton model am to fnd the optmal oluton under the wort-cae probablty dtrbuton, uch that.t. z p yy N p a y (30) Az b, z 0, (3),,,..., y Cy f Q y q c y d n Y (3) Dy g Gz, Ey u
5 In [35], two popular confdence et baed on norm- and norm-nf were preented for, whch can be expreed a N N N p R p p0 R p 0, p p (33) N N R 0 R p p 0, N p p p p (34) Suppong N cenaro from K obervaton, we have the followng relatonhp between the number of htorcal data and : K / 0 Ne K 0 Ne N Pr p p (35) Pr p p (36) It can be found that the rght-hand de of (35)-(36) actually the confdence level of the confdence et. hen, the relatonhp between confdence level (.e., the rght-hand de of (35)-(36)) and the value of gven by N N ln (37) K N ln K (38) Furthermore, (37) and (38) how that wth the ncreae of the number of htorcal data,.e., M, the etmated probablty dtrbuton wll be cloer to t true dtrbuton. hat mean, wll become maller untl to zero. Moreover, for the ame, maller than. IV. COLUMN-AND-CONSRAIN GENERAION ALGORIHM he propoed data-drven tochatc reactve power optmzaton model can be cat a a two-tage optmzaton problem whch generally can be olved by the Bender decompoton method or tandard column-and-contrant generaton method (C&CG). hee method are mplemented n a mater-ubproblem framewor: ub-problem (SP) am to fnd the crtcal cenaro of the uncertan et for a gven frt-tage decon varable that provde an upper bound; then new varable and contrant are added to the mater problem (MP) to obtan a lower bound. he MP and SP are olved teratvely and the method top untl the gap between the upper and lower bound maller than a pre-et convergence tolerance. A. C&CG-Sub-problem For a gven pecfc frt-tage varable n the -th teraton a z, we can et up a econd-tage b-level - model from (30)-(3) to fnd the wort-cae cenaro, yeldng p y Y N p a y (39),,,..., y Cy f Q y q c y d n.t. Y Dy g Gz, Ey u,..., N (40) It can be oberved that the model (39)-(40) ha ome pecal properte: () the ub-feable regon (Y,,Y,,Y N ) are eparable; () the decon varable p are all nonnegatve; () the feable regon of and Y are abolutely dont. For the frt and econd properte that the ub-feable regon (Y,,Y,,Y N ) are eparable and the decon varable p are all nonnegatve, we can exchange the ummaton operator and operator, o the econd-tage - problem can be reformulated a p N p a y (4) y Y,,,..., y Cy f Q y q c y d n.t. Y Dy g Gz, Ey u,..., N (4) For convenence, let become.t. h p N y Y arg h ph a y and the above model y Y (43) a y (44),,,..., y Cy f Q y q c y d n.t. Y Dy g Gz, Ey u,..., N (45) Accordng to the property (), the feable regon Y for varable y and the feable regon for varable p are abolutely dont. hat mean, the feable regon of upper-level model doen t affect the lower-level model and for any gven value p, the optmal oluton y unque. A a reult, the blevel model can be olved by equentally olvng upper-level and lower-level model, repectvely. Moreover, the frt property tell that the ub-feable regon (Y,,Y,,Y N ) are eparable, o lower-level model of the b-level model can be further decompoed nto N ndependent optmzaton model. h gve the fact that the b-level model can be decoupled by the followng tructure: For each u, t generate a econd order cone programg model, uch that arg a y (46) h y Y,,,..., y Cy f Q y q c y d n.t. Y (47) Dy g Gz, Ey u It can be oberved that the above econd order cone programg model are N mall model, comparng to the orgnal model (43)-(45), nce (46)-(47) only contan varable y for each model wherea (43)-(45) contan (y,,y,,y N ) multaneouly n one model. Moreover, the N mall model can be handled n parallel. After obtanng the optmal oluton ( h,, h above N mall model, we have p N hp N ) for the (48)
6 hu, we can ee that the orgnal b-level model can be olved by N mall econd order cone programg model that can be handled n parallel and one mall lnear programg. When the SP olved, an optmal value Q z and the wort-cae probablty p are obtaned, whch n fact gve an upper bound for the orgnal model. hen, a et of extra varable y,+ and aocated contrant are generated and added nto mater problem by fxng the optmal probablty p from the above model n (48). If the SP feable, we can create varable, y and agn the followng contrant to C&CG-mater problem, whch called optmalty cut. N p a y (49), Cy f, Q y q c y d,,..., n (50),,, N (5),, Dy g Gz, Ey u,,..., where a dummy contnuou varable. If the SP nfeable, t poble to create varable x and agn the followng contrant to C&CG-mater problem, whch called feablty cut. Cy f, Q y q c y d,,..., n (5),,, N (53),, Dy g Gz, Ey u,,..., B. C&CG-Mater Problem he MP am to relax the orgnal optmzaton model and provde a lower bound. After K teraton have been preceded, the mater problem can be decrbed a follow: (54).t. N z Az b, z 0, (55) p a y,,,... K (56), Cy f, Q y q c y d,,..., n,,,,,,... K,,..., N (57),, Dy g Gz, Ey u,,,... K,,..., N (58) he above MP a tandard mxed nteger econd order cone programg model that can be ealy handled by the off-the-hell commercal olver, uch a MOSEK, CPLEX, GUROBI, etc.. Solvng the MP gve the optmal dcrete varable z and optmal contnuou varable (y,,,y, ) that are generated n SP for the uncertanty et. he SP and the MP are olved teratvely untl the gven convergence crtera atfed and thu the global optmal oluton obtaned. A preented n [4], the column-and-contrant generaton algorthm can be converged n fnte teraton where all poble realzaton of are needed to be enumerated [4]. However, t hould be noted that the propoed column-and-contrant generaton algorthm a lttle dfferent from that n [4], where the propoed model ha a pecal tructure, o that there no need a [4] to dualze the nner - b-level model nto a ngle level model to olve t. Wth repect to the pecal tructure, we propoe a novel C&CG decompoton method wth the nformaton of dualty. For the gven convergence error, the mplementaton tep of the propoed algorthm are gven n able I. ABLE I PROCEDURE OF C&CG ALGORIHM C&CG algorthm. Set LB=, UB=, =0;. Solve the mater problem (54)-(58). Derve an optmal oluton z and (, y,,,y,+ ) for =,,N. hen, update the Update UB={UB, lower bound LB c y ; 3. Fx z and olve the ubproblem (46)-(47) n parallel, yeldng an optmal value Q( z ) and wort-cae probablty p. 4 c z Q z }. If UB-LB<, terate; ele, go to tep 5. 5 Generate varable ( y,,, y,,, y N, ). Add the new varable and contrant to mater problem accordng to (49)-(53). Update =+, and go to tep. V. NUMERICAL ANALYSIS A. et Sytem and Data Collecton In th ecton, a 33-bu dtrbuton networ that plotted n Fg. analyzed to verfy the propoed method. We conder the tep of tap rato (R) of the tranformer n the ubtaton 0.0 and the range [0.94,.06]. wo wtchable capactor/reactor (SCR) are connected to bue {#3, #9} whoe capacty are both [-0.0, +0.0] MVar, where the tep are 0.00 and 0.005 MVar. he mum operatng tme over 4 hour for SCR are 8 and 6, repectvely. Bede, fve DG are ntalled at bue {#9, #5, #8, #3, #33} wth the capacty beng 0. MW, 0. MW, 0.3 MW, 0.3 MW and 0.3 MW repectvely. he forecated load demand and DG generaton factor over 4 hour are depcted n Fg.., where t aumed that the uncertan DG output follow a multvarate normal dtrbuton wth the varance equvalent to /5 of the mean value (a..a., forecated value). We randomly generate 000 ample by Monte Carlo mulaton to mulate the et of the htorcal data. ang the detered by (37) for example, the relatonhp among, N and hown n Fg. 3. h reveal that for the gven number of ample, wth the ncreae of the number of cenaro N and confdence level, become larger and the uncertanty et wll become larger a well. It obvou that the ze of uncertanty et wll affect the optmal oluton, o n the followng tudy, we wll chooe dfferent N and to how the mpact of uncertanty et on the reactve power optmzaton model. he computatonal ta were performed on a.0 GHz peronal computer wth 4 GB RAM, and the propoed method wa programmed n MALAB where the mxed nteger econd order cone programg were olved ung CPLEX.5.
7 Load/Generaton Factor 9 0.5 0.5 3 4 5 6 7 8 9 0 3 4 5 6 7 8 3 4 5 6 7 8 9 30 3 3 33 Fg.. opology of 33-bu ytem Load Factor DG Factor at bue #9, #5, #8 DG Factor at bue #3, #33 0 0 5 0 5 0 5 me Perod (hour) 0.04 0.03 0.0 0.0 0 Fg.. Load/Generaton factor over 4 hour. 0.5 0.60.7 0.8 7 8 0.9 5 6 0.95 3 4 0.99 N Fg. 3. he relatonhp among, N and. B. Reult and Comparon on A 33-Bu et Sytem he propoed method compared wth the tradtonal two popular method, two-tage tochatc and robut optmzaton approache, denoted by S and R repectvely. o compare wth the tradtonal tochatc programg model wth the detertc multvarate normal dtrbuton, we olve the tradtonal model and fx the frt-tage decon varable. hen, we randomly chooe 0000 dfferent probablte from the uncertan et and olve the econd-tage problem for each gven probablty, where t found that the oluton wth the mum networ lo erved a the wort-cae cenaro for the tochatc approache, denoted a Swt. Furthermore, the comparon of the three method preented n able II. he reult how that the two-tage robut optmzaton method yeld the hghet networ lo (.8545 MW) and the two-tage tochatc optmzaton method arrve at the lowet networ lo (.07 MW). he two-tage robut 9 SCR DG 0 optmzaton method optmze the optmal oluton under the wort-cae for all the poble realzaton, whch lead to the larget optmal oluton. he two-tage tochatc optmzaton method neglect the uncertanty of probablty of each cenaro, whch lead to the mallet optmal oluton. Moreover, he two method alway yeld the ame oluton for dfferent. he propoed method under both and gve a mld optmal oluton and can be termed a a budget that can control the ze of uncertanty et and further affect the optmal oluton. Moreover, the networ lo from the wort cae of tochatc approach (.e, Swt) conderng uncertan probablty dtrbuton about 0%~30% larger than the tradtonal two-tage tochatc programg. Increang confdence level lead to a larger uncertanty et, o that the wort-cae oluton wll become larger. Comparng the propoed method wth the tradtonal tochatc approach, t can be oberved that the networ lo from the propoed method under both uncertan et nf and larger than the tradtonal tochatc programg, whle t maller than that from the wort cae of tochatc approach. In partcular, a maller confdence level lead to a larger gap between Swt and the propoed method. Bede, the networ lo by the propoed method under dfferent uncertanty et gve dfferent value, but for the ame confdence level, the optmal oluton very cloe and the optmal oluton under lghtly maller than that under nf. Fnally, the dcrete control acton by the three method are tuded and compared. ae the frt SCR for llutraton and Fg. 4 depct that four and eght operatng tme of SCR are obtaned by robut and tochatc optmzaton method, wherea the propoed method operated between 4 and 8 tme. Here, we only chooe =0.5 and =0.99 for comparon due to the lmted pace. It oberve that wth the ncreae of, the optmal control acton over 4 hour cloer to that of robut optmzaton method. h becaue the ncreae of wll enlarge the uncertanty et, whch cloer to the uncertanty et of robut optmzaton approach. able II. Comparon of networ lo by three method under dfferent nf Networ Lo (MW) R S Swt 0.5.083.0575.8545.07.3888 0.6.80.076.8545.07.4305 0.7.70.5.8545.07.473 0.8.409.0.8545.07.570 0.9.307.94.8545.07.568 0.95.370.364.8545.07.6076 0.99.5066.5088.8545.07.6309
8 Locaton of SCR 6 5 4 Robut Optmzaton Method Stochatc Optmzaton Method Propoed Method wth =0.99 Propoed Method wth =0.5 3 0 5 0 5 0 5 me Perod/Hour Fg. 4. Comparon of SCR on the three method C. Comparon of Computatonal Performance Between the Propoed Method and radtonal Approache he comparon of computatonal performance among the three approache hown n able III, preentng the teraton (Iter.) and computatonal tme (me) of each method. For the two-tage tochatc prograg model, t need to olve a large-cale mxed nteger econd order cone programg, whch actually a ngle-level model that can be drectly handled by the off-the-helf olver. However, the computatonal tme ncreae gnfcantly wth the ncreae of the number of cenaro. For the two-tage robut optmzaton model, the number of teraton only 3, where a new wort-cae cenaro dentfed at each teraton. It very tme-conug becaue olvng the nner b-level - problem need to tae dual and furthermore to olve a large-cale mxed nteger econd order cone programg model. In contrat, the propoed data-drven tochatc programg model ha a very pecal tructure, n whch the feable regon of econd-tage problem dont wth the uncertanty et, o a new column-and-contrant generaton algorthm propoed to decompoe the SP nto N mall-cale SP that can be olved n parallel. Meanwhle, the SP are everal econd order cone programg model, dfferent from the robut optmzaton model where the SP a large-cale mxed nteger econd order cone programg. he computatonal tme can be further reduced gnfcantly. It oberved from able III that the propoed method much fater than the two-tage robut optmzaton method. Moreover, when N mall, two-tage tochatc programg model a lttle fater than the propoed method, but wth ncreang N, the two-tage tochatc programg model become gnfcantly lower due to the large number of varable and contrant from the cenaro, wherea the computatonal tme of the propoed model ncreae only lghtly than to the decompoton method. herefore, the propoed method perform fater than the two-tage tochatc programg model epecally for the cae wth a large number of cenaro. Another tet ytem from a 3-bu tet ytem wth 0 DG and fve wtchable capactor/reactor (SCR) connected to bu, 35, 54, 76, and 08, whch hown n Fg. 5. he detaled nformaton can be avalable from [8]. he comparon of computatonal performance among the three approache hown n able IV, where t can be oberved that the robut optmzaton need x teraton for convergence by ue of column-and-contrant generaton algorthm and the total tme about 473. he computatonal tme of the tochatc optmzaton wll ncreae gnfcantly wth ncreang the number of cenaro. h becaue the tochatc optmzaton model contan N et of decon varable and contrant. Large N wll gnfcantly ncreae the number of total decon varable and contrant and thu need more computatonal tme. A for the propoed method, the computatonal peed more than 0 tme fater than the robut and tochatc optmzaton model when N large. Snce the ncreae of N wll enlarge the uncertanty et. herefore, t need more teraton for convergence and the total computatonal tme wll ncreae a well. Fnally, t hould be mentoned that the mum gap of conc relaxaton for any tet ytem maller than 0-4 MW, uggetng that the econd order cone programg relaxaton alway exact to the orgnal nonconvex model. able III. Comparon of computatonal effcency by three method on 33-bu tet ytem Propoed Robut Stochatc N Iter. me () Iter. me () Iter. me () 5 3.3 3 8.5 0 3 6.6 3 3.4 5 3 3.5 3 897.4 50.3 0 4 9.9 3 56.8 5 4 37.5 3 363.7 3 9 30 5 6 5 0 3 4 50 33 3 8 48 47 49 09 07 64 6 45 5 46 08 06 7 44 65 3 43 66 63 05 0 03 04 8 00 7 4 4 0 99 4 40 6 7 98 69 70 97 8 9 35 39 68 75 38 9 74 36 60 0 37 4 59 58 57 67 73 78 7985 7 77 0 9 0 5 53 54 55 56 6 3 80 7 8 Subtaton 76 94 84 3 34 5 6 7 96 9 90 88 8 3 5 4 6 95 93 9 89 87 86 8 83 Fg. 5. opology of 3-bu ytem able IV. Comparon of computatonal effcency by three method on 3-bu tet ytem Propoed Robut Stochatc N Iter. me () Iter. me () Iter. me () 5 6 76.5 6 5.3 0 7 08. 6 33.4 5 7 3.9 6 473 987.6 0 8 08.8 6 09. 5 8 35.4 6 5754.3
9 VI. CONCLUSIONS h wor propoe a data-drven tochatc reactve power optmzaton model to addre uncertan dtrbuted generator ntegrated nto actve dtrbuton networ. Accordng to the htorcal data, the propoed method contruct a confdence et for the probablty dtrbuton of the uncertante and am to fnd an optmal oluton under the wort probablty dtrbuton. Furthermore, conc relaxaton employed to utlze to relax the feable regon encloed by power flow equaton. It noted that the propoed model ha a pecal tructure, o that a new column-and-contrant generaton algorthm propoed to decompoe the econd-tage b-level nner problem nto everal mall-cale ubproblem that can be handled n parallel. he comparon wth the tradtonal two-tage tochatc and robut approache on two tet ytem how that the propoed model can acheve better optmal oluton and computatonal performance than tradtonal method. APPENDIX A dcued n Secton II, the orgnal reactve power optmzaton model not a tandard mxed nteger econd order cone programg model nce there are tll many blnear term n the above model. Now, we can mplfy them o a to contruct a tandard mxed nteger econd order cone programg model. () Reformulaton for contrant n ()-(4) and (8) he dcrete reactve power compenator n ()-(4) and (8) are nonnegatve nteger, rather than 0- bnary varable. For the tandard mxed nteger programg model, t expected to formulate the model wth bnary varable. herefore, we hould reformulate each nteger varable t nto a combnaton of 0- bnary varable. Snce any nteger number ha a unque bnary code, the bnary code of t can be expreed by the combnaton of bnary varable t, t,..., t a,0,, 0 t t t t,0,..., (A) Accordng to the bound contrant n () and (3) that C C t C C t C t, we can derve 0,0,, t t... t C C (A) Snce t, t,..., t 0,, the mum value,0,, hould be. herefore, the mum value of hould be C C C C log log (A3) v t C t become Accordng to (A) and (), v t C t v t C t 0,0,, C v t t v t v t... t v t (A4), (8) derve For convenence, let, t, tv t 0,0, C t t..., t + Q c, t QL, t +, G t G t xl t b v t Furthermore, t tv t,, mean of the bg-m approach, uch that, t,..., (A5) can be lnearzed by,,, M t t M t M t t v t M t gve,,, For (A6), nce, t 0,,, t 0 0, t 0 0, t v t 0, t gve M t M, we can fnd that D,,.., (A6) M t v t M, D,,, t 0 ; t v t. herefore, (A6) equvalent to t tv t,, and ()-(4) and (8) can be expreed a (A5) wth addtonal contrant (A6). Meanwhle, tang (A) nto (4) lead to, t, t c,, D t 0 (A7) () Reformulaton for contrant n (0) Smlar to the method for lnearzng blnear term o t v t can be alo lnear- v tc t, the blnear term, zed ung the bg-m approach. Let h, t o, tv t the contrant (0) contanng blnear term and o t v t wll become n h, t v t r H t xg t r t x tl t, 0 w,,,,, Mo, t h, Mo, t,,, t,..., (A8) M o t h t v t M o t,,.., n (A9) Accordng to the above reformulaton and relaxaton n ecton II, the reactve power optmzaton model can be cat a a tandard 0- mxed nteger econd order cone programg a follow:,,
0 Q t, t, ot c r l t (A0) t, E.t (3), (8), (0)-(), (5)-(6), (9), ()-(3), (A5)-(A9) (A) t0,, o t0,, Q c t Contnou (A) REFERENCES [] S. Cor, P. Marannno, N. Lognore, G. Morechn et al., Coordnaton between the reactve power chedulng functon and the herarchcal voltage control of the EHV ENEL ytem, IEEE ran. Power Syt., vol. 0, no., pp. 686-694, 995. []. Dng, Q. Guo, H. Sun, et al., "A quadratc robut optmzaton model for automatc voltage control on wnd farm de," IEEE Power and Energy Socety General Meetng, Vancouver, Canada, 03, pp. -5. [3]. Dng, Q. Guo, H. Sun, et al., A robut two-level coordnated tatc voltage ecurty regon for centrally ntegrated wnd farm, IEEE ran. Smart Grd, vol. PP, no. 99, pp. -, 05. [4] J. Zhao, L. Jud n Z. Da, et al., Voltage tablty contraned dynamc optmal reactve power flow bed on branch-bound and prmal-dual nteror pont method, Int. J. Electr. Power Energy Syt., vol. 7, no.3, pp. 60-607, 05. [5] B. Zhao, C. X. Guo, Y. J. Cao, A multagent-baed partcle warm optmzaton approach for optmal reactve power dpatch, IEEE ran. Power Syt., vol. 0, no., pp. 070-078, 005. [6]. Dng, R. Bo, F. L, et al., A b-level branch and bound method for economc dpatch wth dont prohbted zone conderng networ loe, IEEE ran. Power Syt., vol. 30, no. 6, pp. 84-855, 05. [7] J. Lopez, J. Contrera and J. R. S Mantovan, Reactve power plannng under condtonal-value-at-r aement ung chance-contraned optmzaton, IE Gener. ranm. Dtrb., vol. 9, no. 3, pp. 3-40, 04. [8] A. Rabee and M. Parnan, Voltage ecurty contraned mult-perod optmal reactve power flow ung bender and optmalty condton decompoton, IEEE ran. Power Syt., vol. 8, no., 03. [9] M. Farvar, and S. H. Low, Branch Flow Model: Relaxaton and Convexfcaton-Part I, IEEE ran. Power Syt., vol. 8, no. 3, pp. 554-564, 03. [0] M. Farvar, and S. H. Low, Branch Flow Model: Relaxaton and Convexfcaton-Part II, IEEE ran. Power Syt., vol. 8, no. 3, pp. 565-57, 03. [] B. Mohamadreza, H. M. Reza and G. Mehrdad, Second-order cone programg for optmal power flow n VSC-type-AC-DC grd, IEEE ran. Power Syt., vol. 8, no. 4, pp. 48-49, 03. []. Dng, S. Lu, Z. Wu and Z. Be, Sentvty-baed relaxaton and decompoton method to dynamc reactve power optmzaton conderng DG n actve dtrbuton networ, IE Gener. ranm. Dtrb.,vol. PP, no. 99, pp. -, 06. [3] Q. L, R. Ayyanar and V. Vttal, Convex optmzaton for DES plannng and operaton n radal dtrbuton ytem wth hgh penetraton of photovoltac reource, IEEE ran. Sutan. Energy, vol. 7, no.3, 06. [4] Z. an, W. Wu, B. Zhang and A. Boe, Mxed-nteger econd-order cone programg model for VAR optmzaton and networ reconfguraton n actve dtrbuton, IE Gener. ranm. Dtrb., vol. 0, no. 8, pp. 938-946, 06. [5] J. Brge and F. Louveaux, Introducton to tochatc programg, New Yor, NY,USA: Sprnger-Verlag,997 [6] A. Papavalou, S. Oren and R. O Nell, Reerve requrement for wnd power ntegraton: a cenaro-baed tochatc programg framewor, IEEE ran. Power Syt., vol. 55, no. 4, pp.97-06, 0. [7] C. Sahn, M. Shahdehpour and I. Ermen, Allocaton of hourly reerve veru demand repone for ecurty-contraned chedulng of tochatc wnd energy, IEEE ran. Sutan. Energy, vol. 4, no., pp.9-8, 03. [8] A. Charne, W. W. Cooper, Chance-contraned programg, Manage. Sc., vol. 6, no., pp. 73-79, 959. [9] L. Roald, S. Mra,. Kraue and G. Anderon, Correctve control to handle forecat uncertanty: a chance contraned optmal power flow, IEEE ran. Power Syt., vol. PP, no. 99, pp. -, 06. [0] H. Heaz and H. M. Rad, Energy torage plannng n actve dtrbuton grd: a chance-contraned optmzaton wth non-parametrc probablty functon, IEEE ran. Smart Grd, vol. PP, no. 99, pp. -, 06. [] J. Lopez, D. Pozo, J. Contrera and J. Mantovan, A mult-obectve regret robut VAr plannng model, IEEE ran. Power Syt., vol. PP, no. 99, pp. -, 06. [] R. A. Jabr, Adutable robut OPF wth renewable energy ource, IEEE ran. Power Syt., vol. 8, no. 4, pp. 474-475, 03. [3] L. Zhhuan, Y. Ln and X. Duan, Non-doated ortng genetc algorthm-ii for robut mult-obectve optmal reactve power dpatch, IE Gener. ranm. Dtrb., vol. 4, no. 9, pp. 000-008, 00. [4] X. Fang, F. L, Y. We, R. Azm and Y. Xu, Reactve power plannng under hgh penetraton of wnd energy ung Bender decompoton, IE Gener. ranm. Dtrb., vol. 9, no. 4, pp. 835-844, 05. [5]. Nnam, A. Kavoufard and J. Aghae, Scenaro-baed mult-obectve dtrbuton feeder reconfguraton conderng wnd power ung adaptve modfed partcle warm optmzaton, IE Renewable Power Gener., vol. 6, no. 4,pp. 36-47, 0. [6] H. Zhang and P. L. Chance contraned programg for optmal power flow under uncertanty, IEEE ran. Power Syt., vol. 6, no. 4, pp. 47-44, 0. [7] H. Wu, M. Shahdehpour, Z. L and W. an, Chance-contraned day-ahead chedulng n tochatc power ytem operaton, IEEE ran. Power Syt., vol. 9, no. 4,pp. 583-59,04. [8]. Dng, S. Lu, W. Yuan Z. Be and B. Zeng, A two-tage robut reactve power optmzaton conderng uncertan wnd power ntegraton n actve dtrbuton networ, IEEE ran. Sutan. Energy, vol. 7, no., pp. 30-3,06. [9] H. Haghghat and B. Zeng, Dtrbuton ytem reconfguraton under uncertan load and renewable generaton, IEEE ran. Power Syt., vol. 3, no. 4, pp.666-675, 06. [30] Z. Wang, Q. Ban, H. Xn and D. Gan, A dtrbutonally robut co-ordnated reerve chedulng model conderng CVaR-baed wnd power reerve requrement, IEEE ran. Sutan. Energy, vol. 7, no., pp. 65-636, 06. [3] P. Xong, P. Jruttaroen and C. Sngh, A dtrbutonally robut optmzaton model for unt commtment conderng uncertan wnd power generaton, IEEE ran. Power Syt., vol. PP, no. 99, pp.-, 06. [3] Y. Zhang, S. Shen and J. L. Matheu, Dtrbutonally robut chance-contraned optmal power flow wth uncertan renewable and uncertan reerve provded by load, IEEE ran. Power Syt., vol. PP, no. 99, pp. -, 06. [33] W. We, F. Lu and S. Me, Dtrbutonally robut co-optmzaton of energy and reerve dpatch, IEEE ran. Sutan. Energy, vol. 7, no., pp. 89-300, 06. [34] Q. Ban, H. Xn, Z. Wang, D. Gan and K. P. Wong, Dtrbutonally robut oluton to the reerve chedulng problem wth partal nformaton of wnd power, IEEE ran. Power Syt., vol. 30, no. 5, pp. 8-83, 05. [35] C. Zhao and Y. Guan, Data-drven tochatc unt commtment for ntegratng wnd generaton, IEEE ran. Power Syt., vol. 3, no. 4, pp. 587-596, 06. [36] N. L, L. Chen, S. H. Low, Exact convex relaxaton of OPF for radal networ ung branch flow model, IEEE hrd Internatonal Conference on Smart Grd Communcaton (SmartGrdComm), pp. 7-, 0. [37] M. S. Lobo, L. Vandenberghe, S. Boyd and et al, Applcaton of econd-order cone programg, Lnear algebra and t applcaton, vol. 84, no., pp. 93-8, 998. ao Dng (S 3 M 5) receved the B.S.E.E. and M.S.E.E. degree from Southeat Unverty, Nanng, Chna, n 009 and 0, repectvely, and the Ph.D. degree from nghua Unverty, Beng, Chna, n 05. Durng 03~04, he wa a vtng cholar wth the Department of Electrcal Engneerng and Computer Scence, he Unverty of enneee, Knoxvlle (UK), N, USA. He receved the excellent mater and doctoral dertaton from Southeat Unverty and nghua Unverty, repectvely, and outtandng graduate award of Beng Cty. Dr. Dng ha publhed more than 60 techncal paper and authored by Sprnger hee recognzng outtandng Ph.D. reearch around the world and acro the phycal cence Power Sytem Operaton wth Large Scale Stochatc Wnd Power Integraton. He currently an aocate profeor n the State Key Laboratory of Electrcal Inulaton and Power Equpment, the School of Electrcal Engneerng,
X an Jaotong Unverty. H current reearch nteret nclude electrcty maret, power ytem economc and optmzaton method, and power ytem plannng and relablty evaluaton. QngrunYang receved the B.S. degree from the School of Electrcal Engnee rng, X an Jaotong Unverty, X an, Chna, n 07. He currently purun g the M.S. degree at X an Jaotong Unverty. H maor reearch nteret n clude power ytem optmzaton and demand repone. Yongheng Yang (S - M 5) receved the B.Eng. degree n 009 from Northwetern Polytechncal Unverty, Chna and the Ph.D. degree n 04 from Aalborg Unverty, Denmar. He wa a potgraduate wth Southeat Unverty, Chna, from 009 to 0. In 03, he wa a Vtng Scholar wth exa A&M Unverty, USA. Snce 04, he ha been wth the Department of Energy echnology, Aalborg Unverty, where currently he an Atant Profeor. H reearch nteret are focued on grd ntegraton of renewable energy ytem, power converter degn, analy and control, harmonc dentfcaton and mtgaton, and relablty n power electronc. Dr. Yang ha publhed more than 80 techncal paper and co-authored a boo Perodc Control of Power Electronc Converter (London, UK: IE, 07). Dr. Yang a Member of the IEEE Power Electronc Socety (PELS) Student and Young Profeonal Commttee, where he erve a the Global Strategy Char and reponble for the IEEE PELS Student and Young Profeonal Actvte. He erved a a Guet Aocate Edtor of IEEE JOURNAL OF EMERGING AND SELECED OPICS IN POWER ELECRONICS, and ha alo been nvted a a Guet Edtor of Appled Scence. He an actve revewer for relevant top-ter ournal. Cheng L receved the B.S. degree from the School of Electrcal Engneerng, X an Jaotong Unverty, X an, Chna, n 06. He currently purung the M.S. degree at X an Jaotong Unverty. H maor reearch nteret nclude power ytem optmzaton and renewable energy ntegraton. Zhaohong Be (M 98 SM ) receved the B.S. and M.S. degree from the Electrc Power Department of Shandong Unverty, Jnan, Chna, n 99 and 994, repectvely, and the Ph.D. degree from X an Jaotong Unverty, X an, Chna, n 998. Currently, he a Profeor n the State Key Laboratory of Electrcal Inulaton and Power Equpment and the School of Electrcal Engneerng, X an Jaotong Unverty. Her man nteret are power ytem plannng and relablty evaluaton, a well a the ntegraton of the renewable energy. Frede Blaaberg (S 86 - M 88 - SM 97 - F 03) wa wth ABB-Scanda, Rander, Denmar, from 987 to 988. From 988 to 99, he wa a Ph.D. Student wth Aalborg Unverty, Aalborg, Denmar. He became an Atant Profeor n 99, an Aocate Profeor n 996, and a Full Profeor of power electronc and drve n 998 at Aalborg Unverty. H current reearch nteret nclude power electronc and t applcaton uch a n wnd turbne, PV ytem, relablty, harmonc and adutable peed drve. Prof. Blaaberg ha receved 7 IEEE Prze Paper Award, the IEEE Power Electronc Socety (PELS) Dtnguhed Servce Award n 009, the EPE-PEMC Councl Award n 00, the IEEE Wllam E. Newell Power Electronc Award n 04 and the Vllum Kann Ramuen Reearch Award n 04. He wa an Edtor-n-Chef of the IEEE RANSACIONS ON POWER ELECRONICS from 006 to 0. Prof. Blaaberg wa noated n 04 and 05 by homon Reuter to be between the mot 50 cted reearcher n Engneerng n the world.