Study on Demand Response of Residential Power Customer

Transcription

1 Journal of Power and Energy Engneerng Publshed Onlne July 06 n ScRes. htt:// htt://dx.do.org/0.46/jee Study on Demand Resonse of Resdental Power Customer Xu Cao Hayong Jang Le Huang Xueng Wang Xu Zhang School of Comuter Scence Fudan Unversty Shangha Chna Engneerng Research Center of Cyber Securty Audtng and Montorng Mnstry of Educaton Shangha Chna Xnneng Kabo Industral Co. Ltd. Shangha Chna Receved 9 March 06; acceted 6 July 06; ublshed 9 July 06 Abstract In order to otmze the ladder-rcng scheme n Shangha we resent a mult-objectve otmzaton model (MOOM). To buld ths model frst we use rce elastcty theory; dvde the ladder rcng nto eak electrcty bll and valley electrcty bll n the tme dmenson to model the sngle-user demand resonse. Second based on the sngle-user demand resonse model combned wth the overall users electrcty dstrbuton densty functon we buld an all-users demand resonse model. The roosed model has two objectves: mnmze energy consumton and maxmze resdents satsfacton. Smulaton results confrm that the roosed model can otmze the ladder-rcng scheme. Keywords Demand Resonse Ladder Prcng Prce Elastcty Ladder Prcng Otmzaton. Introducton Over a longer erod of tme as a result of a untary low rce has been mlemented n Chna whch had a roblem of cross-subsdzaton [] [] there was a serous contradcton between ndustral (commercal) users and resdental users. To allevate ths roblem n recent years our country carred out a seres of bll reforms and has mlemented TOU ladder-rcng whch s also known as cumulatve rce ladder and so on. The ladder rcng not only can ease the cross-subsdzaton roblem off [] but also can nhbt the resdents from wastng electrcty. Snce 0 the ractce of ladder rcng the exstng ladder rogram reures constant otmzaton [4] to adjust to changes n dfferent factors for examle resdental customer ncome energy envronment etc. Ladder rcng s based on Ramsey rule [5]. Takng advantage of Ramsey rule s a way to make the ladder rcng scheme [6]. Accordng to the analyss of factors whch affect the electrc rce such as resdents affordablty resdental electrcty demand the cost of electrcty and so on the authors [7] has roosed ter uantty otmal model and the ter range otmal model. Rank-Sum Rato method and round-robn algorthm are aled n [8] to fnd the best tered electrc uantty settng. The authors [9] frst dscuss the dfference n elastcty How to cte ths aer: Cao X. Jang H.Y. Huang L. Wang X.P. and Zhang X.Q. (06) Study on Demand Resonse of Resdental Power Customer. Journal of Power and Energy Engneerng 4-7. htt://dx.do.org/0.46/jee

2 of consumers based on Stone-Geary Functon and then develo an otmzaton model to determne the otmal tered levels. The author [0] takes advantage of Ramsey rcng rncle and elastcty matrx of elastcty demand and bulds a jont otmzaton model of resdental tme-of-user block electrcty rate. The dscussons and analyss n ths aer are based on the above lterature. In ths aer we construct a sngle-user demand resonse model for users wth dfferent stalls n ladder rcng. Then combned the overall users electrcty dstrbuton densty functon an all-users demand resonse model s establshed. Fnally we roose a mult-objectve otmzaton model whose objectves are to mnmze energy consumton and maxmze resdents satsfacton. The rest of ths aer s organzed as follows. We ntroduce elastcty n Secton. The sngle-user demand resonse model and all-users demand resonse model are formulated n Secton. The mult-objectve otmzaton model s resented n Secton 4. In Secton 5 smulaton results are shown.. Elastcty In mcroeconomcs the elastc theory s manly used for researchng the measurement of how an economc varable s to change n another []... Prce Elastcty of Demand Prce elastcty of demand s one of elastcty commonly referred to as the rce elastcty. Prce elastcty of demand rmarly used to reresent a erod of tme the extent of the relatve change n the demand for commodty reactons wth the relatve changes n the rce of the commodty tself. Prce elastcty of demand usually reresented by the followng formula: ΔQ Q Q P = = () ΔP P Q P where s the rce elastcty of demand coeffcent ΔQ s change n uantty demanded ΔP s change n rce Q s uantty demanded P s rce... Cross-Prce Elastc Under normal crcumstances the demand for a commodty s not only concerned wth ts own rce but also related to the rce of smlar roducts. Also n the electrcty market as n the TOU condtons the energy n the tme dmenson of eak valley flat can be seen as three dfferent goods user demand for electrcty usually deends not only on the flat erod rce but also related to eak and valley tme rce []. In order to characterze ths relatonsh ntroduced the cross elastcty of demand []. Cross elastcty of demand mathematcal exresson s as follows: ΔQX QX ΔQX PY xy = = () ΔPY ΔPY QX P Y where XY s the cross-rce elastcty of demand coeffcent ΔQ X s change n X s uantty demanded P s change n Y s rce Q s X s uantty demanded P s Y s rce. Δ Y.. Elastc Matrx for Electrcty Prce Defnes rce elastcty matrx: where X E v = v vv E s the rce elastcty matrx of the -ter user y () s the Prce elastcty of demand of the eak e-

3 rod vv s the Prce elastcty of demand of valley erod v s the cross-rce elastcty of demand between eak erod and valley erod s the cross-rce elastcty of demand between valley erod and eak erod.. Demand Resonse.. Sngle-User Demand Resonse v Changes n user reurement matrx can be formulated as follows: Δ (Δ Δ ) v Δ = v (Δ vv Δ v ) where Δ s change n electrc energy demanded at eak erod Δ v s change n electrc energy demanded at valley erod Δ s change n electrc energy demanded at eak erod of the -ter user caused by change n eak rce Δ v s change n electrc energy demanded at eak erod of the -ter user caused by change n valley rce Δ vv s change n electrc energy demanded at valley erod of the -ter user caused by change n valley rce Δ v s change n electrc energy demanded at valley erod of the -ter user caused by change n eak rce. Take ()-() nto (4) we can get: E = v v where s the -ter eak electrc energy consumton s the -ter valley electrc energy consumton s the frst-ter eak rce ( Δ ) s the new -ter eek rce v s the frst-ter valley rce ( Δ v ) s the new -ter valley rce. Ladder rcng n Shangha s dvded nto three levels by user electrc energy consumton assume the lowest level consumton n the ( 0 x ) range the mddle level consumton n the ( x x ) range the hghest level n the ( x ) range. For each user n three levels we have v v = v v v vv v v v v x ; v ( ) = v vv v v v = x 0 < x x ; v v ( ) = v vv v v v v v v = x = x - x > 0; (6) where s the -ter user energy demand after resondng to change n rce. From (6) we can see the frst-ter user only resonds to the frst-ter rcng changes the second-ter user needs to resonds to the frst-ter and second ter rcng changes and the thrd-ter user needs to resonds to all the three ters rcng changes. In ths aer we suose that all the users do not shft from one ter to another after they resond to the rcng changes. The rcng changes and the user has regulated ther demand the electrcty bll can be obtaned as: ( v ) ( ) ( vv v v ) ( v v ) c = (4) (5)

4 where ( v ) ( ) ( vv v v) ( v v) = c ( ) ( ) ( ) ( ) c (7) = v v v c s the -ter user electrcty bll after resondng to change n rce.. All-Users Demand Resonse We have formulated sngle-user demand resonse now the ueston s: How to get the all-users demand resonse? To answer ths ueston we aled the overall users electrcty dstrbuton densty functon. Defne f(x) as the eak electrc energy consumton f(y) as the valley electrc energy consumton and: ( ) 0 0 < < F = f ( x) dx ( ) 0 0 < < F = f ( y) dy (8) Gven f(x) f(y) the electrc energy consumton and electrcty bll can be derved as: γ ( ( ) ( v ) v v ) (9) Q = U f d f d 0 0 γ ( ( ) v ( v ) v v ) (0) C = U f d f d 0 0 where Q s electrcty energy demand of all the users after resondng to change n rce C s electrcty bll of all the users after resondng to change n rce U s the total number of users γ the roorton of -ter users f ( ) s the eak energy consumton densty functon of -ter users f ( v ) s the valley energy consumton densty functon of -ter users s eak electrcty energy demand of -ter users after resondng change n the rce v s valley electrcty energy demand of -ter users after resondng change n the rce s -ter new eak rce s -ter new valley rce. v 4. Mult-Objectve Otmzaton Model 4.. Satsfacton The satsfacton of the resdental customer can be modeled as: C C θ = () C 0 s.t. 0 η C C ηc where θ s the satsfacton of resdents η s uer bound coeffcent of the growth of electrcty gross roceeds. Clearly the lower C s the hgher satsfacton the customer wll get. If C s eual to C satsfacton wll aroach the uer bound. If C s twce than C satsfacton wll be close to Energy Consumton Imlementaton ladder rcng olcy an mortant goal s to guder resdent users to reduce electrcty consumton mrove ower effcency to ncrease the utlzaton of electrc ower system []. In ths aer we name ρ as electrcty coeffcent to reresent the raton of the amount of total electrcty after resonse to that before resonse. The electrcty coeffcent s as: ρ ( Q Qv )/( Q Qv) = () where Q s eak electrcty energy demand of all the users after resondng to change n rce Q v s valley electrcty energy demand of all the users after resondng to change n rce Q s eak electrcty energy demand of all the users Q s valley electrcty energy demand of all the users. v 4

5 On consderng only rce nfluence of factors on resdental electrcty consumton condton when the electrcty rce ncreases the overall resdental users electrcty consumton should show a negatve trend. It s reasonable to assume that we always have the followng constrant: 4.. Otmzaton Model Q Q Q Q 0 () v v So far we are ready to formulate the ladder rcng otmzaton roblem as the followng mult-objectve otmzaton roblem: mn ρ maxθ Q Qv ρ = Q Qv C C θ = C 0 C C ηc 0 η 4 s.t Δ < 5 0. Δ 6 Δ Δ v = 7 Δ Δ v = 8 From (4) 4 guara guarantee electrcty bll growth after user resonse wthn a certan range. 56 a- refer to gu tonal Develoment and Reform Commsson. 78 refer to t that valley electrcty bll s half of the eak electrcty bll. In the above otmzaton roblem the two objectves conflct wth each other we cannot fnd the otmal soluton to meet these two objectves. So n ths artcle we wll use genetc algorthm to fnd the Pareto set of ths model. 5. Smulaton Result 5.. Data Accordng to the gudance of NDRC ths aer suoses that the frst-ter electrcty rce wll not change the second-ter eak electrcty rce relatve to the frst-ter eak wll ncrease Δ RMB/kWh the second-ter valley electrcty rce wll ncrease Δ / RMB/kWh the thrd-ter eak electrcty rce relatve to frst-ter electrcty eak rce wll ncreaseδ RMB/kWh and the thrd-ter valley electrcty rce wll ncreaseδ / RMB/kWh. The electrcty energy consumton standard for each ter n Shangha wll reman the same. The exermental data are actual consumton data of 487 resdents n an area of Shangha n 0. From these data statstcal results show that: ) There are 4 resdents belongs to frst-ter user. Average electrcty consumton er month s 67 kwh. Rato between eak and valley s 0.69:0.08; ) There are 7 resdents belongs to frst-ter user. Average electrcty consumton er month s 9 kwh. Rato between eak and valley s 0.69:0.09; ) There are 8 resdents belongs to frst-ter user. Average electrcty consumton er month s 80 kwh. Rato between eak and valley s 0.694:0.06. Takng the lmted electrcty hstorcal data nto account the data of electrc ower elastcty matrx refer- (4) 5

6 ences that n [0]. Table fgures out that the frst-ter resdent and the thrd-ter resdent has a small rce elastc lack of elastc to the contrary the second-ter resdent has a large rce elastc and s senstve to electrovalence. 5.. Densty Dstrbuton Functon By usng R to test the dstrbuton of eak and valley ower consumton for each ter customer the result shows that they are all belongs to lognormal dstrbuton. The lognormal dstrbuton s as follows: f ( lnx µ ) /σ ; = e (5) xσ ( x µσ) The arameters of these densty functons can be worked out through the hstory ower data of 47 resdents whch are shown n Table. 5.. Result and Analyss We use Matlab to solve the mult-objectve otmzaton model () by genetc algorthm. Fnally the result of ths otmzaton roblem s shown as follows: From the result we can see when s and s.46 energy consumton s lowest but the resdents satsfacton s hghest. On the ooste when s and s 0.40 energy consumton s hghest but the resdent satsfacton s lowest. If we take the current ladder rcng olcy of Shangha nto (7) the result shows the 478 resdents can conserve kwh energy the whole year the extra electrcty bll s RMB and the resdent satsfacton s Now f the ladder rcng decson makers want to save more energy relatvely when s 0.0 and s 0.8 the savng energy wll mrove from kwh to kwh. On the other hand someday they want to mrove the resdent satsfacton relatvely from the Fgure when s and s 0.50 the resdent satsfacton can mrove from to Table. Prce elastc and cross-rce elastc. User Perod Prce Elastc ( ) Cross-Prce Elastc ( ) vv v v Frst-ter Resdent Second-ter Resdent Thrd-ter Resdent Peak Valley Peak Valley Peak Valley Table. The arameters of the densty functon. Densty Functon µ σ v v v 6

7 Fgure. Pareto otmal solutons. 6. Conclusons and Future Work In ths aer we have frst analyzed the sngle-user demand resonse and all-users demand resonse. Based on these and combned wth the densty functon of energy consumton we have roosed a mult-objectve otmzaton model. Through the otmzaton model the desgn makers can formulate dfferent ladder rcng scheme for varous urose n dfferent erod. Here we have just focused on otmal the rce of ladder rcng. A hgher research on otmal both the rce and the ter range of ladder rcng may be done n the future. References [] Zhang L.Z. (00) Dscusson of Resdents Steed Tarff System Increments. Prce Theory and Practce 9-0. [] Zhu C.Z. (00) The Ladder Prcng Is the Ladder of Tarff Reform. Chna Power Enterrse Management No.. [] Gao Y. (0) Research Tmesharng Ladder Prcng Based on TOU and Ladder Prcng. Journal of Schuan Unversty of Scence & Engneerng: Natural Scence Edton 5. [4] L C.R. and Yu J.M. (00) Korean Resdents of the Ladder Prcng Exerence and Enlghtenment. Electrc Power Technologc Economcs No [5] Ln B.Q. (00) Controversy of Ladder Prcng. Chna Power Enterrse Management No. 7 [6] Brown S.J. (986) Sbley Davd Sumner. The Theory of Publc Utlty Prcng. Cambrdge Unversty Press Cambrdge. htt://dx.do.org/0.07/cbo [7] Wang W.L. and Lu J.C.(0) Influence Factors of Ladder Prcng and Analyss of Otmzaton Model. Foregn Investment n Chna No. 8. [8] Zhu K.D. and Song Y.H. (0) Tan Zhognfu. Resdents Ladder Prcng Desgn Otmzaton Model. East Chna Electrc Power No. 6. [9] L Y. Luo Q. and Song Y.Q. (0) Study on Tered Level Determnaton of TOU & Tered Prcng for Resdental Electrcty Based on Demand Resonse. Power Protecton and Control System No. 8. [0] Huang H.T. (0) A Jont Otmzaton Model of Resdental Tme-of-Use Block Electrcty Rate. Grd Technology No. 0. [] Economcs. htt://en.wkeda.org/wk/elastcty_ [] Qn Z.F. Yue S.M. and Yu Y.X. (004) End Retal Electrcty Market Electrcty Prce Elastcty Matrx. Automaton of Electrc Power Systems No. 5. [] Lu Y. Tan Z.F. and Q J.X. (005) TOU Prcng Desgn Otmzaton Model. Chna Management Scence No. 5. 7