A Regional Time-of-Use Electricity Price Based Optimal Charging Strategy for Electrical Vehicles

Transcription

1 energies Aricle A Regional Time--Use Elecriciy Price Based Opimal Charging Sraegy for Elecrical Vehicles Jun Yang, Jiejun Chen, *, Lei Chen, Feng Wang 2, Peiyuan Xie 3 Cilin Zeng 3 School Elecrical Engineering, Wuhan Universiy, Wuhan 432, China; JYang@whu.edu.cn (J.Y.); sclchen982@63.com (L.C.) 2 Compuer School Wuhan Universiy, Wuhan 432, China; fengwang@whu.edu.cn 3 Sae Grid Hunan Power Supply Company, Changsha 4, China; xie_peiyuan@63.com (P.X.); clzenghus@26.com (C.Z.) * Correspondence: chenjiejun@whu.edu.cn; Tel.: Academic Ediors: Michael Gerard Pech Ximing Cheng Received: 3 May 26; Acceped: 8 Augus 26; Published: 24 Augus 26 Absrac: Wih popularizaion elecric vehicles (EVs), ou--order behaviors large numbers EVs will bring new challenges o safe economic operaion power sysems. This paper sudies an opimal sraegy for EVs. For ha a ypical urban is divided ino four regions, a regional ime--use (RTOU) elecriciy model is proposed o guide EVs when where o charge considering spaial emporal characerisics. In ligh elasic coefficien, user response o RTOU elecriciy is analyzed, also a bilayer opimizaion sraegy including regional-layer node-layer models is suggesed o schedule EVs. On one h, regional layer model is designed o coordinae EVs locaed in differen ime space. On or h, node layer model is buil o schedule EVs o charge in cerain nodes. According o simulaions an IEEE 33-bus disribuion nework, performance proposed opimal sraegy is verified. The resuls demonsrae ha proposed bilayer opimizaion sraegy can effecively decrease cos users, miigae peak-valley load difference nework loss. Besides, RTOU elecriciy shows beer performance han ime--use (TOU) elecriciy. Keywords: elecric vehicles; user responsiviy; opimizaion scheduling; RTOU elecriciy model; regional layer model; node layer model. Inroducion EVs represen a promising echnology due o ir environmenal friendliness poenial o reduce dependence on fossil fuels []. However, inegraion massive numbers EVs is sill regarded as a grea challenge for elecric power sysems. The rom behaviors large-scale EVs in spaial emporal domains may lead o a series problems in power grid, such as power congesion, under-volage, grid insabiliy [2,3]. Considering ha EVs can represen disribued mobile power dems in near fuure, i s meaningful valuable o sudy opimal sraegy EVs [4,], so as o promoe large-scale applicaion EVs. A presen, sudies on opimal scheduling EVs are generally performed considering spaial emporal characerisics. Some opimizaion models have been proposed o coordinae EV users in emporal domain [6 9]. In [6], o opimize objecive funcions including loss cos purchased energy, an opimizaion approach o devise an efficien managemen sraegy is proposed for EVs. In [], a muli-objecive scheduling EVs in a smar disribuion sysem is proposed, so as o minimize oal operaion cos emissions. In [8], o improve securiy economics grid operaion, a model concerning wih opimal power flow, saisic characerisics EVs, Energies 26, 9, 6; doi:.339/en996

2 Energies 26, 9, EV owners degree saisfacion, power grid cos is suggesed. In [9], opimal sraegy EVs is suggesed o smooh daily curve, resuls can confirm is effeciveness. Regarding opimizaion models which can coordinae EV users in spaial domain, a few works have been done o dae [ 2]. In [], o reduce impacs disordered behaviors on disribuion nework, muli-objecive opimizaion including ime, disance dispaching load is invesigaed, complee EV load spaial allocaion can be achieved. In [,2], corresponding auhors discuss sraegies plug-in EVs o improve economic operaion power grid highligh users benefis. In [3,4], opimizaion sraegies are based on bilayer opimizaion a ransmission disribuion sysem levels, herein opimizing peak-valley difference reducing nework loss can be achieved, respecively. However, ineress EV saions are ignored in aforemenioned works, incenive measures guiding EVs o charge are no aken ino accoun. In fac, elecriciy is an effecive means o guide orderly behaviors EVs. The pricing scheme conveys quaniy informaion o load aggregaor o conrol plug-in EV flee [,6]. To apply peak shaving for power grid by scheduling behaviors EVs, peak-valley TOU elecriciy is discussed in []. The TOU elecriciy is discussed in [8], opimal scheduling models EVs based on TOU is proposed in [9,2]. The coordinaion sraegies plug-in EVs in smar grids based on real-ime elecriciy are proposed in [2,22], his sraegies are able o minimize power losses improve volage priles. However, wih developmen elecriciy marke, saions will arrange cerain elecriciy policy o arac EVs o charge, meanwhile elecriciy policy will be differen in emporal spaial domains. Noe ha, radiional elecriciy can saisfy his requiremen. Therefore, a new elecriciy policy considering emporal spaial characerisics mus be sudied. In addiion, behaviors EVs may be absoluely sochasic for saion in realiy, so only parial EVs will respond o elecriciy o charge in relaed saions. Consequenly, EV user responsiviy o elecriciy mus be considered in opimal sraegy EVs. Table generalizes objecives aforemenioned works on opimal scheduling EVs. In his paper, our research group proposes a regional ime--use (RTOU) elecriciy -based opimal sraegy for EVs considering user responsiviy. For ha a ypical urban is divided ino four regions, RTOU elecriciy model can guide EVs when where o charge, also a bi-layer opimizaion sraegy including regional-layer node-layer models is suggesed o schedule EVs. The paper is organized as follows: a RTOU elecriciy model is buil in Secion 2. Secion 3 analyses user responsiviy o RTOU elecriciy. A bi-layer opimizaion model for coordinaing EVs is proposed in Secion 4. Secion is devoed o simulaions an IEEE 33-bus disribuion nework, performance proposed opimal sraegy is verified. Finally, conclusions are drawn in Secion 6. Table. The researches on opimal scheduling EVs. Research Perspecive Lieraure Objecive Funcion Scheduling Sraegy Temporal domain Spaial domain [6] () power losses (2) cos purchased energy [] () oal operaional coss emissions [8] () power loss (2) adjusmen frequency for power grid conrol equipmen (3) smoohness for power daily load curve (4) EV owners degree saisfacion [9] () peak-valley difference [] [] () sysem ime (2) sysem capaciy (3) dispaching load () generaion cos (2) nework losses [2] () uilizaion exising neworks

3 Energies 26, 9, Table. Con. Research Perspecive Lieraure Objecive Funcion Scheduling Sraegy Incenive Measures Conclusions Temporal Spaial domain Peak-Valley TOU TOU Real-Time [3] [4] () Firs level: dis cos EV, saion corresponding ransformer loading (2) Second level: nework Losses () ransmission sysem: fuel cos; PM 2. emission a rmal uni; sar-up shu-down cos rmal uni; cos; wind curailmen cos (2) disribuion sysem: nework Losses [] () peak-valley difference [9] () energy cos [2] () cos [2] () difference beween load curve ideal load curve (2) nework Losses [22] () oal cos for all EVs wihin day The new elecriciy policy mus be sudied considering boh emporal spaial characerisics. Also, EV user responsiviy o elecriciy ineress EV saion mus be considered. 2. The Model RTOU Elecriciy Price In ligh commercial operaion dems EVs, differen saions may need differen elecriciy s [23]. Thus, a RTOU elecriciy model considering emporal spaial characerisics is discussed in his secion. Compared wih TOU elecriciy s, RTOU elecriciy s in differen regions are differen. In a cerain region, RTOU elecriciy consiss four elecriciy levels [24], following equaion can be obained: ρ P min P P ρ 2 P P P 2 ρ = ρ 3 P 2 P P 3 P 3 P P max ρ 4 where ρ is elecriciy ; ρ, ρ 2, ρ 3 ρ 4 are four-level elecriciy s, respecively; P is daily load; P min P max are minimum maximum daily loads in a day, respecively. The values ρ, ρ 2, ρ 3 ρ 4 should be limied in a cerain range according o levels user consumpion. ρ min is se o guaranee benefis power grid considering commodiy aribue elecric power; ρ max is se o guaranee benefis EV users considering user accepance for elecriciy. Meanwhile, revenue power grid mus be included: ρ min < ρ < ρ 2 < ρ 3 < ρ 4 < ρ max (2) M j= T = P a,j ρ j C (3) where ρ min ρ max are minimum maximum elecriciy s, respecively. P a,j is load a ime in j afer applicaion RTOU elecriciy s. M is number s, T is duraion, wih defaul value 24. C is revenue power grid before applicaion RTOU elecriciy : T C = P b ρ (4) = where P b ρ are load a ime elecriciy before applicaion RTOU elecriciy, respecively. ()

4 Energies 26, 9, The relaionship beween elecriciy levels elecriciy power is expressed as: P i+ = P i + P () Energies 26, 9, where P is difference lower or upper load boundary beween adjacen elecriciy level, where i can ΔP is be obained difference by invesigaing lower or upper local residens load boundary consumpion beween habis adjacen elecriciy paymen abiliies. Inlevel, a way, P i can canbe be obained simplified by invesigaing as: local residens consumpion habis paymen abiliies. In a way, ΔP can be simplified as: P = P max P min max Pmin P n (6) (6) where where n is n is number number elecriciy elecriciy levels, levels, is is value is se as Figure Figure shows shows RTOU RTOU elecriciy model. The load curve is isdivided ino ino four four levels levels according according o o maximal maximal minimal values load level. Power/MW Load Level 4 Load Level 3 Load Level 2 Load Level Base load Toal load EVs charge load Figure Figure. The. The divided divided sard RTOU elecriciy model. The four scenarios [2] include unconrolled, delayed, f-peak The four coninuous scenarios. [2] include The ypical unconrolled urban region, consiss delayed an indusrial,, f-peak a commercial coninuous, a residenial. Thean ypical fice. urban In region unconrolled consiss an, indusrial EVs sar, a commercial o charge, as soon a residenial as y are plugged in, an fice sop. when In baery unconrolled is fully charged. The, delayed EVs sar o charge as soon as is similar y are o plugged unconrolled in, sop when scenario. baery However, is fully i requires charged. only The a modes delayed infrasrucure is similar increase o o delay unconrolled iniiaion household scenario. However, unil p.m. ithe requires f-peak only a modes infrasrucure scenario can increase provide oa delay iniiaion signal o lead household EVs o charge unil opimal p.m. ime The for lower f-peak cos. For coninuous scenario, i assumes ha vehicle is coninuously charged scenario can provide a signal o lead EVs o charge in opimal ime for lower cos. whenever i is no in moion. In view four s four modes, re are 6 For coninuous scenario, i assumes ha vehicle is coninuously charged whenever i scenarios. Since analysis mehod for all scenarios is same, one scenario is seleced o is no invesigae in moion. In characerisics, view four s demonsraive four scenario modes, is shown re in Figure are 6 2. scenarios. Since analysis mehod for all scenarios is same, one scenario is seleced o invesigae characerisics, demonsraive scenario is shown in Figure 2.

5 Energies 26, 9, 6 8 Energies 26, 9, 6 8 Power/MW Base load EVs charge load Toal load Load Level 4 Load Level 3 Load Level 2 Load Level Power/MW Load Level 4 Load Level 3 Load Level 2 Load Level Base load EVs charge load Toal load power/mw (a) Toal load Base load EVs load Load Level 4 Load Level 3 Load Level power/mw Power/MW Base load EVs load Toal load Load Level 4 Load Level 3 Load Level 2 Load Level 6 Load Level (c) 2 2 (d) Figure The demonsraive scenario ypical regional load curves. (a) The residenial region load curve in in unconrolled mode; The fice region load curve in delayed mode; (c) The indusrial region load curve in f-peak mode; (d) The commercial region curve in coninuous mode The The User User Responsiviy Responsiviy o o RTOU RTOU Elecriciy Elecriciy Price Price In In fac, fac, many many facors facors will will affec affec behaviors behaviors EVs EVs [26], [26], such such as as policies, policies, EV EV scenarios, scenarios, user's user s driving driving habis, habis, SOC SOC baeries, baeries, exernal exernal environmen. environmen. However, However, purpose purpose EVs EVs changing changing habis habis is is o o gain gain more more economic economic benefis benefis [2], [2], se se ineress ineress are are refleced refleced in in elecriciy elecriciy.. In In his his secion, secion, elecriciy elecriciy is is poinedly poinedly aken aken ino ino accoun. accoun. Price Price elasiciy elasiciy [28] [28] indicaes indicaes relaionship relaionship beween beween elecriciy elecriciy number number responsive responsive EVs, EVs, so so phenomenon phenomenon EV EV users users response response o o elecriciy elecriciy can can be be described described as as follows: follows: N N ε () N = ε ρ () ρ where ρ Δ is is variaion elecriciy elecriciy,, ρ is original is original elecriciy elecriciy ; N, ; whichδn, represens which represens elecriciy consumpion elecriciy consumpion EVs, is EVs, variaion is variaion number number EVs. N isevs. original N is number original number EVs; ε is EVs; elasiciy is elasiciy coefficien. coefficien. In general, EV users responses will be affeced by a curren ime s a or ime. Meanwhile, afer applicaion RTOU elecriciy s, differen regions have differen elecriciy s, so EV users responses are no only relaed o curren regional, bu also affeced by or regions. Therefore, regional self-elasiciy coefficiens cross-elasiciy coefficiens are expressed as follows:

6 Energies 26, 9, bu also affeced by or regions. Therefore, regional self-elasiciy coefficiens cross-elasiciy coefficiens are expressed as follows: N jj N j N jj s N j N jh N j N jh s N j = ε jj ρ j ρ = ε jj ρs j s ρ = ε jh ρ h ρ = ε jh ρs h s ρ h = j h = j (8) To simplify calculaion, curren regional or regional muual-elasic coefficiens on differen periods are convered ino self-elasiciy coefficiens on a single period: ε jj ε jh = T ε jj s s= = T s= ρ j s ρ j ε jh ρs h s ρ j h = j (9) where ε jj ε jh are curren regional or regional elasiciy coefficiens a in j, respecively. The EVs elasiciy coefficiens curren region or regions are denoed as: N jj N j N jh N j = ε jj ρ j ρ j =, 2, 3, 4 = ε jh ρ j ρ h = j () where N j is original number EVs a ime in j. Considering influence curren regional or regional elasiciy coefficiens, number EVs responding o RTOU elecriciy is calculaed as follows: N j M = Nj + N jh = N j M + h= h= N j εjh ρ jj ρ () To quanify elasiciy coefficiens, riangular fuzzy number [29] is inroduced: ε = ε ε ε (2) where fuzzy cener ε represens average elasiciy coefficien; ε ε are minimum maximum elasiciy coefficiens, respecively. The minimum maximum number EVs N j Nj a ime in j are obained by Equaion () wih minimum maximum curren regional coefficien ε jj or regional elasiciy coefficiens ε jh. 4. The Bi-Layer Opimizaion Sraegy for EVs Charging 4.. The Framework Opimal Charging Sraegy for EVs The framework proposed opimal sraegy for EVs is shown in Figure 3.

7 Energies 26, 9, 6 8 Energies 26, 9, 6 8 Deermining RTOU based on load curve Minimizing cos users peak-valley difference by objecive funcion Considering consrains solving his model Regional model Oupuing resuls Evs ime region Minimizing nework losses by objecive funcion Nodel model Considering consrains solving his model Oupuing resuls Evs node Oupu resuls Figure Figure The The framework opimal opimal sraegy sraegy for for EVs. EVs Regional Layer Layer Model Model The The regional regional layer layer model model is ois minimize o minimize cos cos EV users EV users alleviae alleviae peak-valley peakvalley difference in disribuion in disribuion nework by nework coordinaing by coordinaing EVs a differen EVs a ime differen space. ime Thespace. oupus The difference oupus regional layer regional model layer are model are cos peak-valley cos peak-valley difference by difference guiding by guiding ime ime region region EVs. EVs Objecive Funcion.. Charging cos cos users users Regarding fac fac ha ha cos cos users users is is seleced as as objecive funcion, is is expression is: is: M T ) f = min min M (ρ T j j j f P cn j P N (3) j= = c (3) j where P c is average power EVs. is lengh ime inerval, herein i is se as where Pc one hour. is average power EVs. Δ is lengh ime inerval, herein i is se as one hour. 2. Peak-valley difference 2. Peak-valley difference To realize economic operaion power grid, peak valley difference is also considered as an opimal To realize objecion economic [3]: operaion power grid, peak valley difference is also considered as an opimal objecion [3]: f 2 = min(l max L min ) (4) where L max L min are peak load valley 2 load, maxrespecively. min f min( L L ) (4) A linear weighing mehod is used o calculae muli-objecive funcion: where Lmax Lmin are peak load valley load, respecively. A linear weighing mehod is used o calculae ( muli-objecive ) f funcion: F = min λ f + 2 λ f 2 () f f 2 F min λ f λ 2 2 f f () 2

8 Energies 26, 9, where F is oal objecive funcion. λ λ 2 are weigh coefficiens, respecively. f f 2 is base cos peak-valley difference o eliminaion physical dimension. The value λ λ 2 can be deermined by balancing ineress grid users, herein λ =. λ 2 =. are adoped Consrains. Consrain hours To charge sufficien energy o EVs, ime should be long enough: M T j= = N j N max c (6) where c is average ime EVs, N max is maximum number available EVs. 2. Consrain oal EVs number in The number available EVs in a every ime can be consrained as follows: 3. Consrain user responsiviy M N j N max T () j= N j Q j (8) Afer adjusing elecriciy, some EVs will be guided o charge in special saions, meanwhile re are sill some EVs ha do no respond o RTOU elecriciy. According o user responsiviy model suggesed in Secion 3, consrain user responsiviy o RTOU elecriciy can be consrained as follows: 4.3. Node Layer Model N j Nj Nj (9) The node layer model opimizaion is o minimize loss disribuion nework. Meanwhile, pris users saion are aken ino consideraion [3]. The oupus node layer model are EVs node nework loss by guiding node EVs Objecive Funcion For objecive funcion relaed o power loss, i is expressed as: where P Loss, is denoed as: P Loss, = K K k= m= f 3 = min T = P Loss, (2). ( Vk, 2 Gkm + V m, 2 G km 2 Vk, V m, G km cosθ km, ) (2) where K is se all nodes excep slack node. V k, V m, are volages node k node m, respecively. G km is real par admiance marix; θ km, is phase angle difference beween node k node m a ime.

9 Energies 26, 9, Consrains. Consrain acive reacive power balance The acive reacive power balance mus be saisfied a each node: Pk, G PD k, P cn k PT k, = k K, T (22) Qk, G QD k, QT k, = k K, T (23) where Pk, G QG k, are acive reacive power node k a ime, respecively. PD k, QD k, are acive reacive power load node k a ime, respecively. Pk, T QT k, are ransmied acive reacive power node k a ime, respecively: Pk, T = V k, V m, (G km cosθ km, + B km sinθ km, ) m K Qk, T = V k, V m, (G km sinθ km, B km cosθ km, ) m K (24) where B km is imaginary par admiance marix. 2. Consrain node volage The node volage should mee following consrain condiions: V k,min V k, V k,max k K, T (2) where V k,min V k,max are lower upper limis node volage, respecively. 3. Consrain securiy To ensure securiy disribuion nework, ransmission capaciies lines mus be limied in a safe range: P km, P km,max k K, T (26) where P km,max is maximum ransmission capaciy line k m, P km, is power flow ransmission line k m a ime : 4. Consrain saion revenue Pkm, = Vk, V m, (G km cosθ km, + B km sinθ km, ) V k, G km (2) Afer RTOU elecrical is used, revenues charge saions are no less han before: S k = { N k > N k = (28) where S k is revenue coefficien charge saion accessed o node k: S k = C C % = T ρ j P cn k = (29) T ρ P c N k = where C C are revenues wih wihou RTOU elecrical, respecively.. Consrain for oal number EVs in regional

10 /CNY /CNY Energies 26, 9, 6 8 The number available EVs in a cerain can be consrained as follows: N k = N j T (3) k j Energies 26, 9, Consrain Energies 26, 9, 6 saion service capaciy 8 6. Consrain saion service capaciy The 6. EV Consrain saions saion are divided service ino capaciy four differen grades [32]: The EV saions are divided ino four differen grades [32]: The EV saions are divided ino four N k differen grades [32]: k N (3) Qk (3) k N Qk (3). Case Sudies. Case Sudies In. Case his secion, Sudies numeral simulaions are carried ou o illusrae effeciveness proposed In his secion, numeral simulaions are carried ou o illusrae effeciveness proposed sraegy for EVs. As shown in Figure 4, an IEEE 33-bus disribuion nework is divided ino In his sraegy secion, for numeral EVs. As simulaions shown in Figure are carried 4, an ou IEEE o 33-bus illusrae disribuion effeciveness nework is divided proposed ino four regions consising an indusrial, a commercial, a residenial an fice. four regions sraegy consising for EVs. an As indusrial shown, Figure a 4, commercial an IEEE 33-bus, disribuion a residenial nework is an divided fice. ino Nodefour Node inregions IEEE consising IEEE 33-bus 33-bus sysem an sysem indusrial is ais slack a, slack bus. a bus. commercial In In his his disribuion disribuion, a residenial sysem, sysem, base base an power fice power is. se isas se as MVA Node MVA in IEEE base base 33-bus volage volage sysem is se is se is asa as 2.66 slack 2.66 bus. kv. kv. In The The his parameers disribuion sysem, lines lines base maximum power maximum is load se load as nodes nodes aremva obained are obained from base from volage lieraure is [33]. se [33]. as 2.66 kv. The parameers lines maximum load nodes are obained from lieraure [33] Commercial Commercial Office Office Residenia Residenia l l Indusrial Indusrial The disribuion nework The disribuion nework Figure Figure 4. An 4. An IEEE 33-bus disribuion nework. Figure 4. An IEEE 33-bus disribuion nework. During simulaions, ρ is se as ρ2 is se as.6 CNY/kWh; ρ3 During simulaions, ρ is se as.6 is se as. CNY/kWh; ρ 2 is se as.6 CNY/kWh; ρ 3 is se as CNY/kWh; During ρ4 is simulaions, se as. CNY/kWh. ρ is se as The. TOU CNY/kWh; elecriciy ρ2 is se as.6 CNY/kWh; RTOU elecriciy ρ3 is se as.6 are.6 CNY/kWh; CNY/kWh; ρ 4 is se as. CNY/kWh. The TOU elecriciy RTOU elecriciy shown in Figures ρ4 is se as. 6, respecively. CNY/kWh. The TOU elecriciy RTOU elecriciy are are shown in in Figures 6, 6, respecively Figure. The TOU elecriciy prile. Figure. The TOU elecriciy prile. Figure. The TOU elecriciy prile.

11 Price/CNY Energies 26, 9, 6 8 Energies 26, 9, Residenial region Commercial region Indusrial region Office region Figure 6. The RTOU elecriciy priles. Figure 6. The RTOU elecriciy priles... Opimizaion Resuls Regional Layer Model.. Opimizaion Resuls Regional Layer Model Four s are sudied in his secion as follows: Four s are sudied in his secion as follows: Case : re are 2 EVs wih unconrolled mode, elecriciy in his is se as.6 CNY/kWh. Case : re are 2 EVs wih unconrolled mode, elecriciy Case 2: re are 2 EVs wih proposed opimizaion sraegy, user in his is se as.6 CNY/kWh. responsiviy is considered. The priles in his are shown in Case 2: re Figure are 6. 2 EVs wih proposed opimizaion sraegy, user Case 3: responsiviy re are 2 is considered. EVs The wih proposed priles opimizaion in sraegy, his are shown user in Figure responsiviy 6. isn considered. The priles in his are shown in Case 3: re Figure are 6. 2 EVs wih proposed opimizaion sraegy, user Case 4: responsiviy re are 2 isn EVs considered. wih The proposed prilesopimizaion sraegy, his are shown user in responsiviy is considered. The priles in his are shown in Figure 6. Figure. Compared wih user responsiviy o RTOU elecriciy, Case 4: re are 2 EVs wih proposed opimizaion sraegy, user phenomenon EVs in cross-region can be ignored. responsiviy is considered. The priles in his are shown in Figure. The opimizaion regional model is a mixed-ineger linear programming (MILP) problem Compared wih user responsiviy o RTOU elecriciy, phenomenon EVs which can be solved by GMP-CPLEX solver in AIMMS [34]. The expecaions objecive in cross-region can be ignored. funcion, peak-valley difference cos for four s are shown in Table 2, load curves are shown in Figure. Compared wih, peak-valley difference user The opimizaion regional model is a mixed-ineger linear programming (MILP) problem cos are decreased in s 2, 3, 4. Wihou considering user responsiviy in 3, performance which can be solved by GMP-CPLEX solver in AIMMS [34]. The expecaions objecive peak-valley difference user cos will be beer han ha in 2, because all funcion, EVs peak-valley are dispached difference o charge by RTOU cos elecriciy for four. s Compared are shown wih in Table 4 using 2, TOU load curves elecriciy are shown, in Figure opimal. Compared resuls wih 2 using, RTOU peak-valley elecriciy difference will be beer. user cos are decreased in s 2, 3, 4. Wihou considering user responsiviy in 3, performance peak-valley difference Table 2. The user simulaion resuls cos will EVs opimizaion. be beer han ha in 2, because all EVs are dispached o charge Case by RTOU elecriciy Case. Case 2 Compared Case 3 wih Case 4 4 using TOU elecriciy, peak-valley opimal resuls difference (MW) 2 using.43 RTOU.2 elecriciy will be beer. cos (CNY) 4, 3,6 2, 4,2 objecive Tablefuncion 2. The simulaion resuls 2.3 EVs 2.2 opimizaion The opimizaion Case resuls in regional Case layer model Case are 2shown Case in Figure 3 8. Case Compared 4 o rom peak-valley behaviors difference EVs (MW) in,.43 opimized.2 loads 8. EVs.43 are concenraed a ime when basic cos (CNY) load elecriciy 4, are 3,6 small in s 2, 2 4. The 4,2 impacs user responsiviy on objecive EVs schedule funcion are compared 2.3 beween Wihou considering 2.24 user The opimizaion resuls in regional layer model are shown in Figure 8. Compared o rom behaviors EVs in, opimized loads EVs are concenraed

12 Energies 26, 9, 6 Energies 26, 9, responsiviy in oal loads EVsare may concenrae :impacs a.m. : a.m. a ime when 3,basic load elecriciy small in s during 2 4. The user However, parial EVs prefer o charge a 8: a.m. : a.m. : p.m. 9: p.m. in 2. The responsiviy user Energies on 26,EVs 9, 6 schedule are compared beween 2 3. Wihou considering 2 8 impacs differen priles on EVs scheduling are compared 2 4. responsiviy in 3, oal loads EVs may concenraebeween during : a.m. : a.m. responsiviy in 3, oal loads, EVs may concenrae during load : a.m. : a.m. a Compared wih 2 using RTOU elecriciy more EVs concenraes However, parial EVs prefer o charge a 8: a.m. : a.m. : p.m. 9: p.m. in 2. However, parial EVs preferisosmall. charge a 8: a.m. : a.m. : p.m. 9: p.m. in 2. The imeimpacs when The elecriciy differen onevs EVsscheduling scheduling compared beween 2 impacs differen priles priles on are are compared beween Compared wih using RTOU elecriciy moreevs EVs concenraes Compared wih-32 2 using RTOU elecriciy,, more loadload concenraes a a x elecriciy ime when is small. ime when elecriciy is small x Power/MW Power/MW Figure. The load curvesbefore before afer regional dispach. Figure. The The load curves Figure. load curves before afer afer regional regional dispach. dispach Commerical Indusrial Commerical Office Indusrial Residenial Office number EVs number EVs 2 6 Commercial Indusrial 4 3 Commercial 4 2 Office 3 Residenial Indusrial 2 3 (a) Residenial 9 Office (a) 8 Commercial Indusrial Office Residenial number EVs EVs number Commercial Residenial Indusrial Office (c) Residenial number EVs EVs number number EVs number EVs Commercial 8 4 Indusrial 3 Office 2 6 Residenial Commercial (d) Indusrial Office Residenial Figure 8. The opimizaion resuls regional dispach for EVs. There are four panels, y should be lised as: (a) Case ; Case 2; (c) Case 3; (d) Case 4. (c) resuls are analyzed when differen RTOU elecriciy (d) The regional simulaion s elasiciy coefficiens are considered, so as o verify his paper s viewpoin. Figure The resuls regional dispach dispach for for EVs. EVs. There are four panels, should Figure The opimizaion opimizaion are. four panels, y y When ρ is se as. resuls CNY/kWh; ρ2regional is se as.6 CNY/kWh; ρ3 There is se as CNY/kWh; ρ4 isshould se be lised as: (a) Case ; Case 2; (c) Case 3; (d) Case 4. be lised (a) Case ; Case 2; (c) Case 3; (d) four Cases 4. are shown as Figure 9. as.9as: CNY/kWh, simulaion resuls The regional simulaion resuls are analyzed when differen RTOU elecriciy s The regional simulaion resuls are analyzed when differen RTOU elecriciy s elasiciy coefficiens are considered, so as o verify his paper s viewpoin. elasiciy coefficiens are considered, so as o verify his paper s viewpoin. When ρ is se as. CNY/kWh; ρ2 is se as.6 CNY/kWh; ρ3 is se as. CNY/kWh; ρ4 is se When ρ is se as. CNY/kWh; ρ2 is se as.6 CNY/kWh; ρ3 is se as. CNY/kWh; ρ4 is se as.9 CNY/kWh, simulaion resuls four s are shown as Figure 9. as.9 CNY/kWh, simulaion resuls four s are shown as Figure 9.

13 number EVs number Evs number EVs number Evs Energies 26, 9, Energies 26, 9, Commerical Indusrial Office Commerical Indusrial Office Residenial /h Residenial (a) Commerical Indusrial Office Residenial Commerical Indusrial Office Residenial /h /h (c) (d) Figure The Theopimizaion opimizaionresuls resuls differen differen RTOU RTOUelecriciy elecriciy s. s. There There are four are four panels, panels, y y should should be lised be lised as: (a) as: Case (a) Case ; ; Case Case 2; (c) 2; Case (c) Case 3; (d) 3; Case (d) Case From Table 3, i is concluded ha change ariff may only affec specific values From Table 3, i is concluded ha change ariff may only affec specific values scheduling resuls, bu no change qualiaive conclusions shown in his paper. When driving scheduling resuls, bu no change qualiaive conclusions shown in his paper. When driving habis, SOC baeries exernal environmen change, number responsive EVs will change habis, SOC baeries exernal environmen change, number responsive EVs will change accordingly. In his paper, i means ha elasiciy coefficiens will change. Table 4 shows accordingly. In his paper, i means ha elasiciy coefficiens will change. Table 4 shows simulaion resuls differen elasiciy coefficiens. In Table 4, change elasiciy simulaion resuls differen elasiciy coefficiens. In Table 4, change elasiciy coefficiens may only affec specific values scheduling resuls, bu no change qualiaive coefficiens may only affec specific values scheduling resuls, bu no change qualiaive conclusions. Moreover, driving habis, SOC baeries exernal environmen have no effec on conclusions. Moreover, driving habis, SOC baeries exernal environmen have no effec on proposed scheduling sraegy. proposed scheduling sraegy. Table 3. The simulaion resuls differen RTOU elecriciy s. Table 3. The simulaion resuls differen RTOU elecriciy s. Case Case Case 2 Case 3 Case 4 Case Case Case 2 Case 3 Case 4 peak-valley difference (MW) peak-valley difference (MW) cos (CNY) 4, 2,92 2, 3,4 cos (CNY) 4, 2,92 2, 3,4 objecive funcion Table 4. The simulaion resuls differen elasiciy coefficiens. Case Case Case 2 Case 3 Case 4 Case Case Case 2 Case 3 Case 4 peak-valley difference (MW) peak-valley difference (MW) cos cos (CNY) (CNY) 6, 6,2,96 2,96 2,3 2,3 3,8 3,8 objecive funcion The Opimizaion Resuls Node Layer Model Four s are sudied in his secion as follows: Case : : The The number EVs in in four regionsis is same as, behaviors EVs EVsare are unconrolled. Case 6: 6: The The number number EVs EVs in in four four regions regionsis is opimizaion opimizaionresuls resulsin in Case Case : : The The number number EVs EVs in in four four regions regions is is opimizaion opimizaion resuls resuls in in Case 8: The number EVs in four regions is opimizaion resuls in 4.

14 number EVs number EVs number number EVs EVs number EVs number EVs number number EVs EVs Energies 26, 9, Energies Case 26, 8: 9, 6 The number EVs in four regions is opimizaion resuls in Energies The 26, opimizaion 9, 6 problem is a mixed-ineger nonlinear programming (MINLP) which 4 can 8 be solved by GMP-AOA solver in AIMMS [34]. The opimizaion resuls in node layer model are shown The in in Figure opimizaion.. Figure problem shows shows is a mixed-ineger EVs EVs spaial spaial disribuion nonlinear disribuion programming a a : : a.m. a.m. in (MINLP) in 6. From 6. which From Figures can Figures be solved,, by conclusion conclusion GMP-AOA can can solver be be drawn in drawn AIMMS ha ha [34]. The opimized opimizaion spaial spaial resuls disribuions node layer model EVs are are concenraed shown in Figure in. nodes Figure, 8, shows, 6,, EVs 2, 3, spaial 2, 26, disribuion 2 28 a close : a.m. o in beginning 6. From bus Figures each region. Thus,, if conclusion can be drawn saions ha are opimized locaed in spaial aforemenioned disribuions nodes, EVs nework are losses concenraed caused by EVs nodes, 8, loads, can 6, be, 2, well 3, 2, 26, 2 28 close o beginning bus each reduced. region. Thus, if saions are locaed in aforemenioned nodes, nework losses caused by EVs loads can be well reduced N N2 N4 N23 N6 N9 N2 N N N2 N2 N28 N4 N23 N3 N6 N9 Nodes N2 N N2 N28 N Nodes (a) (a) N N2 N4 N N2 N23 N6 N4 N9 N23 N6 N2 N9 N N2 N2 N N28 N2 N3 Nodes N28 N3 Nodes (c) (c) N N2 8 9 N4 6 N23 N6 N9 N N N N2 N2 N28 N3 8 N N23 N6 N9 9 2 Nodes N2 N N N28 N (d) (d) Figure... The The opimizaion resuls node dispach for for EVs. EVs. There There are are four four panels, panels, y y should should be be be lised lised as: as: (a) (a) Case ; ; Case 6; 6; 6; (c) Case ; ; (d) Case Commercial Nodes N 3 N N4 N N23 N2 N6 N9 9 N4 N2 N N23 N6 N9 N2 N2 N N28 N N N28 Nodes N Nodes Office Residenial Charge Charge Indusrial Indusrial Figure. The spaial disribuions EVs a a.m. in 6 in nework. Figure. The spaial disribuions EVs a a.m. in 6 in nework. Figure 2 shows nework losses before afer opimizaion. The oal nework losses in Figure 2 shows nework losses before afer opimizaion. The oal nework losses in Figure, 2 6, shows nework 8 losses will be before.43 MW, afer.33 opimizaion. MW,.39 The MW, oal nework.46 MW, losses in, 6, 8 will be.43 MW,.33 MW,.39 MW,.46 MW, respecively., Regarding 6, 2 8 will3 be where.43 user MW, responsiviy.33 MW, are respecively.39 MW, considered.46 MW, respecively. respecively. ignored, ir Regarding Regarding impacs on where where are analyzed, user user responsiviy responsiviy respecively. are are Since respecively respecively more considered concenraion considered ignored, ignored, EVs ir ir impacs impacs loads on on in ime-domain 6 6 in are are analyzed, 3 analyzed, causes respecively. respecively. loads decenralizaion Since Since more in more spaial concenraion concenraion domain, EVs opimizaion loads resuls in ime-domain in 6 show in beer performance 3 causes han loads ha decenralizaion in. For in spaial 2 domain, 4 where opimizaion RTOU resuls elecriciy in 6 show beer TOU performance elecriciy han ha are in adoped,. For respecively, 2 ir 4 where RTOU elecriciy TOU elecriciy are adoped, respecively, ir

15 Energies 26, 9, 6 8 EVs Energies 26, 9, loads 6 in ime-domain in 3 causes loads decenralizaion in spaial domain, 8 Energies 26, 9, 6 8 opimizaion resuls in 6 show beer performance han ha in. For 2 4 where impacs RTOU on elecriciy node layer model TOU are analyzed elecriciy in 6 are adoped, 8. From respecively, figure, ir impacs oal nework on impacs on node layer model are analyzed in 6 8. From figure, oal nework node losses layer in model 6 are analyzed smaller han in ha 6 in In From addiion, figure, curves oal nework nework losses losses in have losses in are smaller han ha in 8. In addiion, curves nework losses have 6 aredifferen smaller peak han ha ime, in 8. reason In addiion, is ha curves emporal disribuion nework losses have differen EVs is differen peak ime, in differen peak ime, reason is ha emporal disribuion EVs is differen in four reason s. four s. is ha emporal disribuion EVs is differen in four s. Figure Figure Figure shows shows shows volage volage volage disribuions disribuions under under under differen differen differen s. s. s. Compared Compared Compared wih wih wih, i, is, i found is i is ha found found ha 6, 6, 6, 8 will show 8 will will beer show show performance beer beer performance performance on volage on on levels volage volage levels end levels nodes. end end Regarding nodes. nodes. Regarding Regarding 2 3 where 2 user 3 responsiviy where where user user responsiviy responsiviy are respecively are are respecively respecively considered considered considered ignored, ir ignored, ignored, impacs ir ir on impacs 6 on are 6 sudied, respecively. are are sudied, sudied, respecively. respecively. 3 x Power/MW Figure 2. The nework losses before afer afer opimizaion dispach. dispach. Figure 2. The nework losses before afer opimizaion dispach. voalge voalge voalge voalge nodes nodes (a) (a) 2 nodes nodes(c) nodes (d) (c) (d) Figure 3. The volage disribuions disribuion nework. There are four panels, y should Figure Figure be lised The as: The (a) volage volage Case ; disribuions disribuions Case 6; (c) Case disribuion ; disribuion (d) Case 8. nework. nework. There There are are four four panels, panels, y y should should be lised be lised as: (a) as: Case (a) Case ; ; Case Case 6; (c) 6; Case (c) Case ; (d) ; Case (d) Case In view ha more concenraion EVs loads in ime-domain in 3 causes loads In view decenralizaion ha more in concenraion spaial domain, EVs opimizaion loads resuls in ime-domain in 6 in show 3 beer causes loads decenralizaion in spaial domain, opimizaion resuls in 6 show beer voalge voalge voalge.. voalge nodes nodes nodes

16 Energies 26, 9, In view ha more concenraion EVs loads in ime-domain in 3 causes loads decenralizaion in spaial domain, opimizaion resuls in 6 show beer performance han ha in. For 2 4 where RTOU elecriciy TOU elecriciy are used, respecively, ir impacs on node layer model are analyzed in 6 8. I is observed ha, volage levels end nodes in 6 are more preferable. 6. Conclusions This paper s main conribuion is o propose a RTOU elecriciy -based bilayer opimizaion sraegy for EVs, herein benefis disribuion nework users are boh aken ino accoun. To analyze impacs RTOU elecriciy on behaviors EVs, user responsiviy is invesigaed by mehod elasic coefficien. From simulaions an IEEE 33-bus disribuion nework, performance proposed opimal sraegy is verified, some conclusions are drawn as follows: () The effeciveness proposed opimizaion sraegy can be confirmed. For regional layer model which is designed o coordinae EVs locaed in differen ime space, i can shave peak fill valley load priles, cos users is well reduced. Concerning node layer model which is buil o schedule EVs o charge in cerain nodes, is applicaion can decrease nework losses o a cerain exen. (2) Compared wih TOU elecriciy, RTOU elecriciy can obain beer opimizaion resuls. (3) When user responsiviy o RTOU elecriciy is aken ino consideraion, opimal scheduling resuls are more similar o realiy. (4) If saions are locaed in nodes being close o beginning bus each region, disribuion nework can poenially obain beer economic benefis. In near fuure, opimal RTOU elecriciy, real ime ariff feasible incenive measures will be sudied furr. Besides, some follow-up works relaed o node layer model will be performed, EVs scheduling sraegy based on inegraion ransporaion nework power grid will be aken ino accoun. The resuls will be repored in laer aricles. Acknowledgmens: The work is funded by Naional Science Foundaion China (23, 2, ), Sae Grid Corporaion China (226K) Fundamenal Research Funds for Cenral Universiies (242kf4). Auhor Conribuions: Jun Yang conceived srucure research direcion paper; Jiejun Chen wroe paper compleed simulaion for sudies; Lei Chen revised wriing enire manuscrip; Feng Wang provided algorihms; Peiyuan Xie wroe programs; Cilin Zeng analyzed daa. Conflics Ineres: The auhors declare no conflic ineres. Abbreviaions Index:, s Se ime j, h Se region k, m Se Nodes Lis Main Variables: N j N k V k P Loss, Number EVs a ime in region j Number EVs a ime in node k Volage in node k Nework loss disribuion nework a ime

17 Energies 26, 9, 6 8 Lis Main Parameers: ρ j Q j Q k P km, Elecriciy a ime in region j Maximum number available EVs in region j Service capaciy saion in node k Power flow on ransmission line k m a ime References. Gradii, G.; Langella, G.; Laerza, C.; Valeni, M. Convenional elecric vehicles: A complee economic environmenal comparison. In Proceedings ICCEP 2, h Inernaional Conference on Clean Elecrical Power, Taormina, Ialy, 6 8 June 2; pp Foley, A.; Tyr, B.; Calnan, P.; Gallachóir, B.Ó. Impacs Elecric Vehicle under elecriciy marke operaions. Appl. Energy 23,, [CrossRef] 3. Fernes, C.; Frías, P.; Laorre, J.M. Impac vehicle-o-grid on power sysem operaion coss: The Spanish sudy. Appl. Energy 22, 96, [CrossRef] 4. Soromme, E.; Hindi, M.M.; MacPherson, S.J.; Venkaa, S.S. Coordinaed plug-in hybrid elecric vehicles o minimize disribuion sysem losses. IEEE Trans. Smar Grid 2, 2, [CrossRef]. Lopes, J.A.P.; Soares, F.J.; Almeida, P.M.R. Inegraion elecric vehicles in elecric power sysem. Proc. IEEE 2, 99, [CrossRef] 6. Di Silvesre, M.L.; Sanseverino, E.R.; Zizzo, G.; Gradii, G. An opimizaion approach for efficien managemen EV parking los wih baeries re faciliies. J. Ambien Inell. Hum. Compu. 23, 4, [CrossRef]. Zakariazadeh, A.; Jadid, S.; Siano, P. Muli-objecive scheduling elecric vehicles in smar disribuion sysem. Energy Convers. Manag. 24, 9, [CrossRef] 8. Yang, J.; He, L.; Fu, S. An improved PSO-based sraegy elecric vehicles in elecrical disribuion grid. Appl. Energy 24, 28, [CrossRef] 9. Yao, Y.; Gao, W.; Li, Y. Opimizaion PHEV Charging Schedule for Load Peak Shaving. In Proceedings ITEC Asia-Pacific 24 Conference-Expo, Beijing, China, 3 Augus 3 Sepember 24; pp. 6.. Tian, W. Elecric Vehicle Baery Swapping Saion Coordinaed Charging Dispach Mehod Based on Temporal Spaial Double Dimensions. Ph.D. Thesis, Beijing Jiao Tong Universiy, Beijing, China, 23.. Deilami, S.; Masoum, A.S.; Moses, P.S.; Masoum, M.A. Real-ime coordinaion plug-in elecric vehicle in smar grids o minimize power losses improve volage prile. IEEE Trans. Smar Grid 2, 2, [CrossRef] 2. Richardson, P.; Flynn, D.; Keane, A. Opimal elecric vehicles in low-volage disribuion sysems. IEEE Trans. Power Sys. 22, 2, [CrossRef] 3. Yagciekin, B.; Uzunoglu, M. A double-layer smar sraegy elecric vehicles aking rouing charge scheduling ino accoun. Appl. Energy 26, 6, [CrossRef] 4. He, L.; Yang, J.; Yan, J.; Tang, Y.; He, H. A bi-layer opimizaion based emporal spaial scheduling for large-scale elecric vehicles. Appl. Energy 26, 68, [CrossRef]. Roering, N.; Ilic, M. Opimal charge conrol plug-in hybrid elecric vehicles in deregulaed elecriciy markes. IEEE Trans. Power Sys. 2, 26, [CrossRef] 6. Xi, X.; Sioshansi, R. Using Price-Based Signals o Conrol Plug-in Elecric Vehicle Flee Charging. Smar Grid 24, 3, [CrossRef]. Shaoyun, G.; Huang, L.; Liu, H. Opimizaion peak-valley TOU power ime-period in ordered mode elecric vehicle. Power Sys. Pro. Conrol 22, 4,. 8. Ferruzzi, G.; Gradii, G.; Rossi, F.; Russo, A. Opimal operaion a residenial microgrid: The role dem side managemen. Inell. Ind. Sys. 2,, [CrossRef] 9. Dubey, A.; Sanoso, S.; Cloud, M.P.; Waclawiak, M. Deermining Time--Use Schedules for Elecric Vehicle Loads: A Pracical Perspecive. Power Energy Technol. Sys. J. 2, 2, 2 2. [CrossRef] 2. Cao, Y.; Tang, S.; Li, C.; Zhang, P.; Tan, Y.; Zhang, Z.; Li, J. An opimized EV model considering TOU SOC curves. IEEE Trans. Smar Grid 22, 3, [CrossRef] 2. Solani, N.Y.; Kim, S.J.; Giannakis, G.B. Real-ime load elasiciy racking pricing for elecric vehicle. IEEE Trans. Smar Grid 2, 6, [CrossRef]

18 Energies 26, 9, He, Y.; Venkaesh, B.; Guan, L. Opimal scheduling for dis elecric vehicles. IEEE Trans. Smar Grid 22, 3, 9. [CrossRef] 23. Yan, Q.; Manickam, I.; Kezunovic, M.; Xie, L. A muli-iered real-ime pricing algorihm for elecric vehicle saions. In Proceedings ITEC 24, IEEE Transporaion Elecrificaion Conference Expo, China, Beijing, 3 Augus 24; pp Song, Y. Opimzaion Model for Design Tired Pricing for Household Elecriciy in China. Maser s Thesis, Norh China Elecric Power Universiy, Beijing, China, Arks, K.; Denholm, P.; Markel, A.J. Coss Emissions Associaed wih Plug-in Hybrid Elecric Vehicle Charging in Xcel Energy Colorado Service Terriory; Naional Renewable Energy Laboraory: Golden, CO, USA, Li, R.; Wu, Q.; Oren, S. Disribuion locaional marginal pricing for opimal elecric vehicle managemen. IEEE Trans. Sys. 24, 29, [CrossRef] 2. Falvo, M.C.; Gradii, G.; Siano, P. Elecric vehicles inegraion in dem response programs. In Proceedings 24 Inernaional Symposium on Power Elecronics, Elecrical Drives, Auomaion Moion (SPEEDAM 24), Ischia, Ialy, 8 2 June 24; pp Koroleva, K.; Kahlen, M.; Keer, W.; Rook, L.; Lanz, F. Tamago car: Using a simulaion app o explore elasiciy dem for elecriciy elecric vehicle users. In Proceedings Inernaional Conference on Informaion Sysems, Auckl, New Zeal, 4 December Li, Y.; Luo, Q.; Song, Y.Q.; Xu, J.; Cai, L.; Gu, J. Tiered pricing mechanism based on fuzzy dem response. Eas China Elecr. Power 22, 4, Bae, S.; Kwasinski, A. Spaial emporal model elecric vehicle dem. IEEE Trans. Smar Grid 22, 3, [CrossRef] 3. Acha, S. Impacs Embedded Technologies on Opimal Operaion Energy Service Neworks. Ph.D. Thesis, Imperial College, London, UK, Beijing Qualiy Technology Supervision Bureau. Technical Specificaion Elecriciy Supply Assure for Elecric Vehicle: Elecric Vehicle Charging Saion; DB/Z28 2; Beijing Qualiy Technology Supervision Bureau: Beijing, China, Venkaesh, B.; Ranjan, R.; Gooi, H.B. Opimal reconfiguraion radial disribuion sysems o maximize load abiliy. IEEE Trans. Power Sys. 24, 9, [CrossRef] 34. The AIMMS Websie. 24. Available online: hp://aimms.com/english/developers/resources/solvers/ (accessed on 2 December 24). 26 by auhors; licensee MDPI, Basel, Swizerl. This aricle is an open access aricle disribued under erms condiions Creaive Commons Aribuion (CC-BY) license (hp://creaivecommons.org/licenses/by/4./).