EE236C. Energy Management for EV Charge Station in Distributed Power System. Min Gao

Transcription

1 EE236C PROJEC Repor Energy Manageen for EV Charge Saon n Dsrbued Power Syse Mn Gao Prof. Leven Vandenberghe Sprng 22

2 . nroducon Mos radonal power syses generae elecrcy by hea power plans, hydropower plans and nuclear plans, whch are all cenralzed large elecrcy generaon facles. he benefs by dong so s obvous,.e. has fully-fledged auoac conrol ehod such ha safey of he grd could be ensured, would generae elecrcy wh fxed frequency5hz n Asa, Europe and 6Hz n Norh Aerca so as o anan he sably of he whole syse and would have a low cos of every kwh of elecrcy. However, radonal generaon ehod s hard o acheve peak regulaon ncely, would lose los of energy durng long dsance ranssson and cause severe envronenal ssue. On he oher hand Dsrbued Power SyseDPS generaes elecrcy fro any sall energy sources. Usng DPS could su he need for he sall area near where has been locaed, reduce he long dsance ranssson loss and eco-frendly snce os of he generaon ehod would no produce as uch polluon as he convenonal one. he ajor concern abou DPS s he relavely poor elecrcy qualy copared wh he radonal one. n os cases, power copanes are relucan o le power flow fro DPS sources flow no her sable power grds. Snce fossl fuels becoe ore and ore expensve and have been regarded as he an ssue for global warng, people sared o fnd alernave ways o subsue fossl fuels. Wh he er of clean and cheap, elecrcy has becoe a good alernave n auooble ndusry. Many auooble anufacures began o produce HEV and EV nsead of radonal cars. Usually, Chargng process for EV would be done n a charge saon jus lke gas saon for noral vehcles. Snce elecrcy generaed by dsrbued generaor gh no sasfy he need of elecrcy qualy for he convenonal power grd, a feasble soluon s o buld a DPS specal for EV saon, opology could be seen as follow for exaple.

3 Fg Chargng Saon opology hs opology s conss of few baeres whch conneced o he DPS generaor, super capacorsor oher energy sorage devce whch can be regarded as back up energy sorage and a swch connecs o convenonal grd n case of he oal aoun of he generaed elecrcy could no sasfy he need of he EV charge saon. ypcally chargng profle for a EV s a cobnaon of consan curren chargng, consan volage chargng and PWM conrolled curren chargng. ypcally here are wo dfferen knds of chargng ehod. he frs ehod would have wo chargng sage. he frs sage s o charge he baery a consan C-rae unl reaches nonal volage value, he second phase s o charge a consan volage unl chargng curren becae. e of curren value n he frs sage. he second ehod s o charge he baery wh soe pulse curren and gradually decrease he chargng curren when baery volage reaches soe hreshold. he perforance of hs opology would have a srong rely on baeres and oher sorage devce, hus an opal elecrcy anageen ehod for hs opology s of grea deand o be developed. 2. Model Forulaon n hs proble, by gven load curren over e, capacy, SOC and oher paraeers of baeres and super capacors, we wan o oban an opal baery and super capacor dschargng schedule fro dsrbued power source so as o prolong baery lfe and

4 nze he energy loss n a dsrbued generaon based EV chargng saon. We have followng general assupons. Frs s a hgh saple frequency, curren/volage value beween each e sep s consan. hen he second one s convenonal power grd wll only conneced o super capacors and charge he when needed. hrd one s all he baery and super capacor curren are dynacally conrol by power elecronc devce. Oher nor assupons are descrbed n dealed case. 2. aery Lfe Opzaon Generally for a baery, he hgher he dscharge rae s, he less he baery lfe wll be. he hgher Deph of DschargeDOD of a baery s, he hgher baery capacy degradaon wll be.hgh curren value would ncrease baeres' nernal ressance ore rapdly and hus would ake baeres' lfe becoe shorer. Also noe ha for ceran gven dscharge rae, baery cells whch s cycled a hgh level DODs were shown o reach he defned end of lfe,.e. only 7% capaccy of a fresh baery could hs baery be charged, uch sooner han hose cycled a lower DODs <5%. hs observaon s llusraed n Fg. 2 Fg 2 aery Cycle Lfe VS DOD o acheve he goal of long baery lfe, we wll conrol he curren value flows hrough he baeres and ry o ake as sall as possble, also we would lke o conrol he flucuaon of curren value so as o ake hngs easy for conroller chps o conrol he crcu. We assue ha he volage and curren are easured usng dscree sgnals wh a suffcenly sall saplng perod. he baery has a capacy n ap-hour uns. he agnude of he baery curren and he curren flucuaon of he baery can be denoed as and, respecvely.

5 For he whole dschargng perod, we wan o nze he suaon of curren a each e sep and suaon of flucuaon, whch s denoed as and., For each baery, we wan he curren flows ou fro would no be greaer han soe value bu no srcly less han. So a penaly funcon could play a role here o nze he objecve and ensure os of he value would be less han desred value. n hs proble, we wll choose Huber penaly funcon. 2 z ϕ z 2 z z < z Snce he Deph of Dscharge s a grea concern durng he EV chargng process, a SOC lower bound for each baery wll be added o ensure hey wll no be over-dscharged. Case aery Only opology wh dencal Paraeers hs gh be he sples case aong all he possble opologes. he objecve funcon as o ake curren as sall as possble and res devae curren flucuaon. he only consran gh be Krchhoff's Crcu Law whch s he curren flows ou fro he baery should be equal o hose flows no EV. he opzaon proble s shown as below. n s.. ϕ, λ n N, loadn ϕ, λ 2 Where ϕ f x, b s huber penaly funcon hs s obvously a convex opzaon proble. Case2 aery Only opology wh Dfferen paraeers n hs case he dfference beween he case s ha each baery would have dfferen capacy and dfferen nal SOC value. y dong so we could sulae each baery's condon n a ore praccal anner. For he purpose of SOC balancng beween each baery so ha we could fully use every baery and avod he case ha one of he baery dranes ou bu oher baeres sll rean pleny of charge, he objecve funcon would need o keep he dfference of each baery's SOC n a sall value besdes acheveng he funconaly n case.

6 n s.. ϕ, λ G.3 n N, loadn ϕ, λ FG 2 where F Q soc G Q n he forulaon above, F s eoplz arx and G represens for SOC of each baery a every e sep. he second consran eans ha DOD for every baery should no be greaer han 7% whch s ang o prolong he baery lfe. hs s also a convex prograng proble. Case3 aery and Super Capacor opology Fg 3 s he equvalen crcu for super Capacors. Denoe ernal volage, capacor curren, equvalen seral ressanceesr, and capacance as v Fro basc crcu heory we have vs s d k k C k Fg 3 Super Capacor Equvalen Crcu s s, R k k s, k, C respecfully. One benef for us o use super capacor s ha could accep huge curren change beween e seps and hs wll provde he possbly o ake baery curren have less flucuaons. Here we also assue ha ha he nal capacor volage should rean he sae o he k

7 fnal capacor volage such ha durng he whole EV chargng process, he energy change n he whole EV saon s. Model forulaon s shown as below n s.. ϕ V V, λ V V G. p j C, end ϕ n N j R loadn S, λ FG 2 p ϕ, λ 3 he objecve funcon as o conrol boh curren of baery and super capacor and SOC saus for each baery. he frs consran s Krchhoff Curren Law. he second consran s ganed by he characersc equaon of super capacor a each e sep. hrd Consran s o ensure ha nal capacor volage should rean he sae o he fnal capacor volage such ha durng he whole EV chargng process. Fourh consran s o ensure capacor's volage should be a posve value. Las consran s he DOD consran jus he sae as wha n case and case 2. For prograng convenence n solver, we need o ransfor he proble no a proper way. y usng arx represenaon and changng varables, we could have followng opzaon odel n α s.. ϕ A V EV > < V G., λ β p K, n N ϕ R S loadn, λ γ FG ε 2 p ϕ, λ 3 where

8 [,,,] A n K n E [,,,,, ] F Q soc G Q Marx A coes fro processng wh one e sep and he nex e sep of he consran of super capacy volage recursvely. hs forulaon s obvously a convex opzaon proble. Noe ha wh soe hgh curren value, frs wo huber penaly funcon would reurn sgnfcan large value whch wll lower he nfluence of oher ers. We would pu soe wegh o all he coponens o adjus hs phenoenon. 2.2 Energy Loss Opzaon n EV chargng saon syse, energy loss fro power sde s anly generaed by equvalen seral ressance n super capacors. Especally durng he chargng and dschargng of he s. Alhough an energy loss can be nduced by he baery snce also has nernal ressance, we wll gnore because ressance n baery s relavely sall copared o ESR n super capacors. Denoe Power loss as Q loss and Q loss 2 Rd. n proble forulaon, we wll sply use R nsead of Q loss o ake calculaon easer snce nze hese wo funcons wh he sae consran would reurn he sae opal soluon. he opzaon odel s shown as follows, he only dfference beween hs forulaon and prevous one s he change n objecve funcon.

9 ... n < > G V EV R K V A s R S N n load p s n 2.3 Mul-crera Forulaon wo objecves enoned above are needed o be consdered sulaneously,.e., he nzaon of agnude and flucuaon for baery and nzaon of oal energy loss. A cobned forulaon s shown as follows...,,, n 3 2, < > G V EV R K V A s R FG S N n load p p s n µ λ ϕ ε γ λ ϕ β λ ϕ α where ] [,,,,, [,,,] Q soc Q G F E K A n n 3. Nuercal Resul

10 For nuercal calculaon we wll use 5 loads, 5 baeres and 3 super capacors. npu load curren would be gven by user. Each baery would have dfferen capaces and nal SOC values. Also each super capacor would have dfferen capaces and equvalen seral ressances. We assue each load would have a curren daa wh ean 5A and sandard devaon of, each baery wll have a capacy value wh ean 8Ahconsss of any cascaded sall baery packs and sandard varaon and nal SOC value wh ean 9% and sandard devaon 2 and each super capacor wll have cap value of ean and sandard varaon 25 and equvalen seral ressance wh.oh ean and. sandard varaon. y dong so we wan o sulae a relavely exree case n he chargng syse. For scalng ssue of every coponen n he objecve funcon and avod solver runnng no nuercal probles whle dealng wh large value nuber, we se he wegh wh e-6, e-6, e-2, e-6, e-2 respecvely. Fgure 4 below shows he curren profle of all 5 loads,

11 Fg 4 Load Curren Profle Fgure 5 below s he resul of baery curren for dsrbued power source afer opzaon. All he currens flow ou fro hese baeres are relavely becoe consan value. Also noe ha curren values for all he baeres are nearly he sae because copared wh he capacy of each baery C-rae s very low roughly around 3/8.375~%. f we decrease he capacy of one or ore of hese baeres,.e., ncrease C-rae grealy, curren value would dffer a lo bu paern would sll be he sae.

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13 Fg 5 aery Oupu Curren Fgure 6 below s super capacor curren, super capacors end o be charged before he loads requre large aouns of power o he energy sorage devces. eans ha n realy f we could predc he fuure profles of he load curren,a uch ore effecve real-e energy anageen could be scheduled n he chargng syse. Fg 6 Super Capacor Curren Nex fgure s super capacor volage. We can see ha durng he EV chargng process, he volage change of he super capacors n he whole syse s equal o zero. Fg 7 Super Capacor Volage \ SOC change a each e sep s shown n he followng fgure. We could see ha each

14 baery's SOC has a lnear decreasng rend so ha curren flucuaon s nzed here and wh a relavely low curren value, baery's lfe wll be prolonged. Fg 8 SOC Saus for Each aery 4. Concluson n hs repor we acheved opal conrol sraegy o prolong he baery lfe of he power source sde and nze energy loss of an EV dsrbued chargng saon syse. Opzaon resul showed ha baery fro dsrbued power source could supply nearly consan power o anan s longevy and nze he oal loss n he syse even n rando load curren profle.

15 Reference. S. oyd and L. Vandenberghe, Convex Opzaon. Cabrdge, U.K.,: Cabrdge Unv. Press, S.M. Lukc, S.G. Wrasnga, F. Rodrguez, J. Cao, and A. Ead, "Power Mangeen of an Ulracapacor/aery Hybrd Energy Sorage Syse n an HEV," n EEE Veh. Power Prop. Conf., Sep. 26, pp J. Wang, P. Lu, J. Hcks-Garner, E. Sheran, S. Soukazan, M. Verbrugge, H. aarab, J. Musserc, and P. Fnaorec, "Cycle-lfe odel for graphe-lfepo4 cells,"journal of Power Sources, vol. 96, ssue 8, pp , Apr C. Cho, J. Jeon, J. K, S. Kwon, K. Park, S. K, "Acve Synchronzng Conrol of a Mcrogrd", Power Elecroncs, EEE ransacons on, vol. 26, ssue: 2, pp Dec Y. Zhang, Z. Jang, and X. Yu, "Conrol Sraeges for aery/super Capacor Hybrd Energy Sorage Syses, " n Proc. EEE Energy 2 Conf., Nov. 28, pp -6.

16 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %EV Chargng Saon Modelng %Mul-objec funcon s now workng %Could also coen ou oher cases o see resul of such easer case %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% clear all clc %%nalzaon %nsaple pons; %5baery %p2 5; n; k4; p2; Czeros,n-;C; Rzeros,n;R;R2-; Mzeros,-;M; Pzeros,; P;P2-; oeplzc,r;foeplzm,p; loadnorrnd5,,5,n; % %%Case % cvx_begn % varable baery,n; % nze susuhuberbaery,7susuhuber*baery',3 % subjec o % %KCL % for :n % subaery:,-suload:,; % cvx_end % %%Case2 % capacynorrnd8,,,; % socnorrnd9,6,,; % whle axsoc> nsoc< % socnorrnd9,6,,; % Qcapacy.*soc/; % for : % Sga,:capacy*.*ones,n; % % cvx_begn % varable baery,n; % nze susuhuberbaery,sga/e6susuhuber*baery',5/e6norf*q-subaery' *../Q', % subjec o % %KCL % for :n % subaery:,-suload:,; % Q-subaery'*../Q>.*ones,; % cvx_end % Case3_

17 % capacynorrnd8,,,; % socnorrnd9,6,,; % whle axsoc> nsoc< % socnorrnd9,6,,; % Qcapacy.*soc/; % for : % Sga,:capacy*.*ones,n; % A[,zeros,n;eyen,zerosn,]; % eyen; % K./*[zeros,n;eyen]; % Rs.*[zeros,n;eyen]; % E[,zeros,n-,-]; % % cvx_begn % varables baery,n capacy,n Vcapacyn,n; % nze.5*susuhuberbaery,65/e6.5*susuhuber*baery',5/e6.25*norf*q-su baery'*../q',.*susuhubercapacy,2/e6 % subjec o % for :n % subaery:,sucapacy:,-suload:,; % A-*Vcapacy-K*capacy'-Rs*'; % E*Vcapacy; % % <capacy; % >-capacy; % % Q-subaery'*../Q>.*ones,; % cvx_end %Case3_2 % C3; % capacynorrnd8,,,; % socnorrnd9,6,,; % whle axsoc> nsoc< % socnorrnd9,6,,; % Qcapacy.*soc/; % for : % Sga,:capacy*.*ones,n; % A[,zeros,n;eyen,zerosn,]; % eyen; % K.*[zeros,n;eyen]; % sccapacynorrnd,3,,c; % G[zeros,n;eyen]; % Rsnorrnd,.,,C % E[,zeros,n-,-]; % % cvx_begn % varables baery,n capacyc,n Vcapacyn,C C,n; % nze.5*susuhuberbaery,65/e6.5*susuhuber*baery',5/e6.25*norf*q-su baery'*../q',.*susuhubercapacy,2/e6 % subjec o % %KCL % for :n % subaery:,sucapacy:,-suload:,; % for j:c

18 % A-*Vcapacy:,j-K/scCapacyj*capacyj,:'-Rsj*G*j,:'; % E*Vcapacy:,j; % <capacy; % >-capacy; % Q-subaery'*../Q>.*ones,; % cvx_end %%Mul-objecs C3; capacynorrnd8,,,; socnorrnd9,2,,; whle axsoc> nsoc< socnorrnd9,2,,; end Qcapacy.*soc/; for : Sga,:capacy*.*ones,n; end A[,zeros,n;eyen,zerosn,]; eyen; K.*[zeros,n;eyen]; sccapacynorrnd,25,,c; G[zeros,n;eyen]; Rsnorrnd.,.,,C; E[,zeros,n-,-]; load daa cvx_begn varables baery,n capacyc,n Vcapacyn,C C,n; nze susuhuberbaery,4/e6susuhuber*baery',.5/e6norf*q.*soc/-sub aery'*../q',/e2susuhubercapacy,2/e6surs* capacy/e2*. subjec o %KCL for :n subaery:,sucapacy:,-suload:,; end for j:c A-*Vcapacy:,j-K/scCapacyj*capacyj,:'-Rsj*G*j,:'; E*Vcapacy:,j; end <capacy; >-capacy; Vcapacy>; Q.*soc/-subaery'*../Q>.3*ones,; cvx_end fgure ploload' fgure plobaery';axs[ 9];ylabel'CurrenA'; fgure plocapacy';axs[ 5 4];ylabel'CurrenA'; fgure plovcapacy;ylabel'volagev'; for :n SOCb:,Q.*soc/-subaery:,:'*../Q; end fgure plosocb';ylabel'soc';