Smart Grid Congestion Management Through Demand Response

Transcription

1 Smart Grd Congeston Management Through Demand Response J. Hazra, Kaushk Das, and Deva P Seetharam IBM Inda Research Emal:{jahazra1,kausdas8,dseetharam}@n.bm.com Abstract Ths paper proposes a novel cost-effectve congeston management (CM) scheme for smart grds through demand response(dr). In ths congeston management, two objectves.e. acceptable congeston and congeston cost ncludng DR are optmzed by choosng optmal mx of generaton reschedulng and DR of partcpatng buses by mnmzng the mpact on revenues and customer satsfacton. Partcpatng generators for reschedulng and loads for DR are selected usng an senstvty ndex whch combnes both bdng cost and senstvty to allevate the congeston. The scheme employs a meta-heurstc optmzaton technque called Ant Colony Optmzaton to optmze the ndvdual optons and uses a fuzzy satsfyng technque to choose the best compromse soluton from the set of Pareto optmal solutons. The proposed system has been evaluated on benchmark IEEE 30 bus test systems and the results of ths evaluaton are presented n ths paper. I. INTRODUCTION Congeston n smart grd s a very common problem manly because of ncreased penetraton of ntermttent renewable sources and dmnshng spare capacty of the grd due to extensve usuage of transmsson system. In a compettve energy market, most of the tme grd operates very close to t s capacty. Therefore, congestons may occur frequently due to unexpected lne outage, generator outage, sudden ncrease of demand, falures of equpments, lack of co-ordnaton among generaton and transmsson, etc. Sometmes, such congestons are not allevated ntentonally due to economc reasons whch not only decreases asset lfe tme, but also trggers the large blackouts. In fact, several blackouts have happened from congeston [1]. Hence, network congeston has become a major concern for smart grds and there s a growng demand for fast, transparent, and cost effectve congeston management solutons for smart grds. In the lterature, many methods are reported for congeston management n power systems. For example, n references [2], [3] congestons are managed through cost-free means such as network reconfguraton, operaton of transformer taps and operaton of flexble alternatng current transmsson system (FACTS) devces. Generaton reschedulng and load sheddng are used n [4], [5] for allevaton of congeston. In these methods system operator has no choce of selectng the partcpatng generator and/or load buses. Reference [6] proposed a mathematcal model of bus Senstvty Factors (SFs) whch relate the bus njectons to change n lne currents. These SFs are used to allevate the congeston by selectng hgh senstve generator and/or load buses. However, ths method does not consder the cost of generaton reschedulng and/or load sheddng. Reference [7] proposed a drect method for allevaton of congeston where both cost of load sheddng and generaton reschedulng are consdered. Consderng slow dynamcs of the grd, a congeston management method has been proposed n [8]. Reference [9] proposed a congeston management technque consderng the rsk of cascadng falures due to malfunctonng of protecton system. Most these methods manage congeston by ether generaton schedulng and/or by load sheddng whch s determned by Independent System Operators (ISOs) where loads have no optons to act. Recently several prcng schemes such as real tme prcng, tme of use prcng, peak prcng, peak reducton credt, etc are proposed for demand response whch enables loads to drectly partcpate n managng the grd. Demand response shows to have several benefts ncludng better utlzaton of renewable resources, network relablty enhancement, mprovng the loadablty of the transmsson lnes, etc. Recently, a combnaton of demand response and FACT control s proposed n [10] for congeston management. However, ths method may not provde optmal soluton as t does not consder cost senstvty whle selectng DR partcpants. In ths paper, a novel congeston management scheme s proposed through demand response. In ths method, a tradeoff has been made between tolerable congeston and the cost of operaton whle managng the congeston. A Senstvty Index (SI) whch combnes the cost and senstvty s proposed to use for selecton the partcpatng loads for DR and generators for reschedulng. Congeston s managed through optmal mx of generaton schedulng and demand response. A mult objectve Ant Colony Optmzaton (ACO) method has been used to generate the trade-off solutons and a fuzzy satsfyng method has been used to select the best compromse soluton from the set of Pareto optmal solutons. Rest of the paper s organzed as follows. Secton II brefly presents the congeston management formulaton. Secton III descrbes the senstvty ndex used for load and generaton selecton n CM and Secton IV descrbes the ant colony optmzaton method. Secton V presents the fuzzy approach for selectng the best compromse soluton, and secton VI descrbes the congeston management strategy. Secton VII presents the smulaton results whereas Secton VIII concludes the proposed work.

2 II. SYSTEM ARCHITECTURE Electrc power market s consdered to have three categores of partcpants.e. the bdders, the schedulng coordnators and the ndependent system operator. Responsblty of each of these partcpants s descrbed as follows: A. The Bdders Generaton and dstrbuton companes form ths group. Ths group encompasses both the load and generaton sde of the market. Bdders may have ther own physcal assets, or act as aggregators for other producers or consumers. Durng congeston n power network they offer ther bd prce to the schedulng coordnator to manage the congeston. B. The Schedulng Coordnator The functon of the schedulng coordnator s to match load and generaton bds to produce a balanced transacton for submsson to the system operator. By aggregatng the curves on the supply and demand sde, the schedulng coordnator calculates a market clearng prce whch s awarded to all accepted bds. C. The Independent System Operator Schedulng coordnators pass on balanced load generaton transactons to the system operator. The ISO then carres out congeston management, before returnng the revsed schedules to the schedulng coordnators. III. PROBLEM FORMULATION The objectve of the proposed congeston management s to mnmze the congeston as well as the cost of operaton. Mathematcally t can be represented as follows: Objectve 1: Mnmze congeston nl MnmzeOL= (S S max ) 2 (1) =1 where, OL s cumulatve overload, nl s number of overloaded lne, S s MVA flow on lne, and S max s MVA capacty of lne. Objectve 2: Mnmze cost of operaton MnmzeTC = ng =1 [(a +b. P g +c. P g 2 ) + e sn(f (P g P mn )) ] + pl k=1 (a k +b k. D k +c k. D k 2 ) (2) where, TC s total operaton cost, ng s number of partcpatng generators, pl s number of partcpatng loads, P g s the amount of generaton change at bus generator, P mn s mnmum generaton of th generator, D k s amount of load change at bus k, a,b,c are cost coeffcents of generator, a k,b k,c k are cost coeffcents demand response at load bus k and e,f are coeffcents of generator reflectng valve pont loadng effect. Constrants Equalty constrants Network power flow equatons: NB P g P d = V V j Y j cos(δ δ j θ j ) (3) j=1 NB Q g Q d = V V j Y j sn(δ δ j θ j ) (4) j=1 where, P g,q g real and reactve power generaton at bus ; P d,q d real and reactve power demand at bus ; N B number of buses; V, V j voltage magntude at bus and j respectvely; Y network admttance matrx; δ,δ j voltage angle of bus and bus j respectvely; θ j admttance angle of lne between buses and j. Inequalty constrants Inequalty constrants are operatng and physcal lmts of each transmsson lne, transformer and generator as follows: where, V mn,v max Flow,Capacty P mn,p max Q mn,q max Flow Capacty (5) V mn V V max (6) P mn P g P max (7) Q mn Q g Q max (8) mnmum and maxmum voltage lmt power flow on lne and lne capacty mnmum and maxmum actve power generaton lmts of generator ; mnmum & maxmum reactve power generaton lmts of generator. IV. SELECTION OF PARTICIPATION NODES For any congeston, utltes nterested n partcpatng congeston management may not be be equally cost effectve and/or senstve n managng congeston. For example, n any congested place, local utltes are expected to be more effectve than remote ones n allevatng t. On the other hand, remote utltes may be cheaper than local utltes. Hence, t s essental to select the optmal mx of utltes so that total operaton cost s mnmzed. In ths paper, a senstvty ndex called SI s used to select the partcpatng buses where SI s defned as follows: SI = f IC (9)

3 where IC s ncremental cost of generaton (IC g ) or load (IC l ) defned as follows: IC g = b +2c P g + e f cos(f (P g P mn )) ] IC l = b k +2ć k D k and (f ) s the senstvty of the change n lne flow wth respect to njecton defned as follows [11]: f = I km P = I km X k δ k V + I km X m δ m V ( Ikm Y k + β V k V + I km Y m V m V ) (10) where, I km s change n lne current from bus k to m, P s change n real power njecton at bus,x/y s element of admttance matrx, V s voltage magntude and δ s voltage phase angle. Partcpatng generators are selected on the bass of SI values. As the power output from a generatng staton can be ncreased or decreased (wthn the operatng lmts) accordng to requrements, generator buses wth hgh postve or negatve SI value can be selected as a partcpatng generator n congeston management. On the other hand as demand s assumed to be decreased only, buses wth hgh negatve senstvty values are consdered for DR. For non-partcpatng buses the senstvty values are assgned as zero. V. ANT COLONY OPTIMIZATION (ACO) In ths paper a mult-objectve ant colony optmzaton technque proposed n [12] s used. The algorthm conssts of four stages.e. soluton constructon, pheromone update, local search and pheromone re-ntalzaton as descrbed follows: 1) Soluton Constructon: In ths method, ntal poston of each ant.e. ntal soluton vectors are generated randomly n the feasble search regon. In each teraton artfcal ant construct the soluton by generatng a random number for each varable usng the normal dstrbuton N(µ,σ 2). Mean (µ ) and standard devaton (σ 2 ) for each varable changes wth teraton number based on the experence of the colony. 2) Pheromone update: For mult-objectve the real dffculty les n the defnton of the best solutons of the canddate set. In ths paper the best solutons wth respect to each objectve are selected to update the pheromone nformaton. Then, when multple pheromone nformaton s consdered, each pheromone matrx assocated wth each objectve s updated by the soluton wth the best objectve value for the respectve objectve. Pheromone matrx for any objectve s updated as follows: µ (t) = µ (t)+ρ 2 x gb σ (t) = σ (t)+ρ 2 x lb µ (t 1) (11) where ρ 2 [0,1] s the ntensfcaton parameter, a unform random number between 0 and 1 and x lb s the local best soluton (Pareto optmal) found n last (t-1) teraton. 3) Local Search: In ths paper Pareto Local Search (PLS) proposed n [13] s mplemented. PLS starts from a soluton and examnes ts neghborhood. Next, any nondomnated soluton found s added to an archve and the domnated ones are removed from t. PLS termnates when all the neghborng solutons of all solutons n the archve have been explored. 4) Pheromone Re-ntalzaton: To avod premature convergence or gettng trapped nto local mnma pheromone re-ntalzaton s done lookng at a convergence factor cf defned as follows [14]: n 2σ b a cf = n The pseudo code for ACO s shown n Table I. TABLE I PSEUDO CODE FOR ACO Randomly generate ntal solutons wthn search space and ntalze pheromone trals Repeat Construct soluton for each ant usng normal dstrbuton Identfy global best and local best ant Conduct local search on them Update pheromone Check the convergence factor. If below threshold re-ntalze pheromone Untl some convergence crtera s satsfed Provde the set of Pareto optmal solutons VI. SELECTION OF COMPROMISE SOLUTION (12) In order to chose a sutable soluton from the set of pareto optmal solutons, a fuzzy satsfyng method s used to fnd the best compromse soluton from a set of Pareto optmal solutons. For each objectve fuzzy membershp s defned by lnear functon as follows: µ = 1 f f f mn f max f f max f max f f mn 0 f f f max < f < f max (13) where µ s membershp value of objectve ; f mn s the value of objectve whch s completely satsfactory; f max s the value of objectve whch s completely unsatsfactory. For each Pareto soluton normalzed membershp functon s found as follows: µ k = Nobj =1 µk M k=1 Nobj =1 µk (14) where, N obj s the number of objectve functons; M s number of Pareto optmal solutons; µ k s membershp value of non domnated soluton k. The non-domnatng soluton that attans the maxmum membershp µ k s chosen as the best compromse soluton.

4 VII. CONGESTION MANAGEMENT STRATEGY In ths method set of partcpatng loads and generators s selected based on senstvty ndex as descrbed n Secton III. Wth the selected partcpants congeston s managed by optmal mx of generaton reschedulng and/or demand response based on requred level of congeston allevaton. In case of multple lne overloads, congestons are solved smultaneously to avod oscllatory soluton and non-convergence due to conflct. Per unt values of load and generaton are taken as state varables. Computatonal steps of the proposed congeston management scheme s summarzed as follows: 1) Identfy the congested lnes and transformers n the grd. 2) Collect bddng from generators and loads nterested n congeston management. 3) Calculate senstvty Indces (SIs) for nterested generators and loads wth respect to change n current flow on each congested lne. 4) Select hgh senstve generators and loads for CM. 5) Mnmze cost of operaton and congeston usng Ant Colony Optmzaton. 6) Check whether congeston s managed. a) If not, select more partcpants and goto step 5. b) Else, go to step 7. 7) Select the best compromse soluton from the set of Pareto optmal solutons usng fuzzy approach. 8) Present the soluton to the decson maker. VIII. SIMULATION RESULTS Proposed congeston management method s evaluated on benchmark IEEE 30 bus test systems. For smulaton purpose, cost coeffcents as gven n Appendx were chosen for DR whle cost coeffcents for generators were chosen from reference [11]. Wth the gven cost functons, an experment was done to optmze the colony sze whle optmzng the precongeston generaton cost. Convergence characterstcs wth dfferent sze of colony are gven n Fgure 1. From ths fgure, t s clear that colony of 10 ants provdes satsfactory convergence characterstc. From ths experment t seems that optmal number of ants n the colony s proportonal to the dmenson of the optmzaton problem. Hence, for congeston management, colony sze was chosen as the number of varables to be optmzed. In order to evaluate the proposed congeston management technque, congestons were smulated by settng reduced value for the lne lmts of a few lnes. Detaled smulated cases are gven n Table II. Test system IEEE 30 Bus 1A 1B 1C TABLE II SIMULATED CASES Smulated cases Overload smulaton by reducng capacty of lne 1-2 to 70 MVA Overload smulaton by reducng capacty of lnes to 10 MVA respectvely Overload smulaton by reducng capacty of lnes 2-5 and 5-7 to 40 MVA and 10 MVA respectvely Cost (Rs/h) Fg x 105 P=5 P=10 P=15 P=20 P= Iteraton number Convergence characterstcs wth dfferent colony sze For case 1A, congeston was created by reducng capacty of lne 1-2 from 130 MVA to 70 MVA. Senstvty ndces of generators and loads wth respect to change n flow on lne 1-2 are gven n Table III and Table IV, respectvely. In ths case all the senstvtes are negatve whch ndcate congeston can be allevated ether by ncreasng the generaton or by reducng load. As generator senstvtes are more or less equal, all the generator buses are selected for CM. In ths case, there are several load buses havng hgh senstvty ndex. All the load buses havng senstvty ndex SI are selected for congeston management. In ths case, though few loads such as buses 2, 5 and 7 are hghly senstve to allevate the congeston, got lower rank n the SI table as ther ncremental costs are very hgh. Wth the selected partcpants ACO was run and obtaned Pareto optmal solutons are presented n Fgure 2. Fgure 2 clearly shows Pareto solutons are unformly dstrbuted accrross the Pareto font. Non-domnated solutons wth mnmum cost, mnmum congeston and a trade-off from these Pareto optmal solutons are presented n Table V. From Table V t s clear that n ths case demand response partcpaton s not economcal and hence congeston s managed only wth generaton reschedulng. In ths case, f the operator wants to allevate the overload completely he wll choose the soluton 1 and for ths case congeston cost wll be as hgh as Rs/h But f the operator allows some overload ( 10%) and chooses soluton 2, congeston cost wll be as low as Rs/h Ths motvates utltes to allow some overload. However, sometme such overload may not be acceptable due to relablty threat. In such case utltes always can chose a compromse soluton where tradeoff s made between cost and congeston. Solutons 1, 2 and 3 clearly show that f the operator wants to allevate the over load completely he has to sacrfce the cost a lot. TABLE III GENERATOR SENSITIVITIES W.R.T CONGESTED LINES Bus

5 TABLE IV LOAD SENSITIVITIES W.R.T CONGESTED LINES Bus Senstvty Index w.r.t Bus Senstvty Index w.r.t Bus Fg. 2. Pareto optmal solutons for congeston case 1A For congeston case 1B, generator senstvtes are very low as shown n Table III and hence are not very effectve n managng the congeston. Ths s not surprsng because generators are far away from the congeston locaton. On the other hand, loads at buses 21, 23, 24 and 26 are hghly senstve and hence, are selected for demand response n ths congeston management. In ths partcular case at least one generator needs to be selected as slack because f congeston s managed by load reducton through DR, at least one generator should reduce the generaton to balance the total load and generaton. In ths case generator at bus 11 s selected as slack as t has the hghest senstvty ndex and s close to the congeston locaton. Pareto optmal solutons wth selected partcpants are presented n Table V. In ths case f the operator wants to allevate the congeston completely he needs to reduce total MW load through DR. In ths case 9.75MW, 0.45 MW, 0.81 MW and 1.06 MW loads are reduced at buses 21, 23, 24 and 26, respectvely. In response to MW of DR, MW of generaton s backed down at bus 11 to balance the grd. Though load s reduced by MW, generator needs to be reduced by MW because transmsson loss s reduced by 0.3 MW due to load reducton n the grd. For the gven scenaro, operator needs to pay Rs as DR ncentve and Rs for generaton back down ncentve. Hence total congeston cost becomes Rs It s nterestng to note that for the gven scenaro demand response cost s much lower than the ncentve gven to the generator only for balancng the grd. Even though hgh ncentve s pad to one generator, overall congeston cost through DR s better than the congeston management through generaton reschedulng. It s also obvous that congeston cost can be low f some overload s tolerated. These smulaton results clearly show that demand response could be an effcent means of managng congeston n smart grd. For case 1C, congeston was created on two lnes.e. 2-5 and 5-7. In ths case, senstvty ndces wth respect to each lne are conflctng. For example, for bus 2 generaton SI s postve (0.0014) w.r.t. flow on lne 2-5 whereas t s negatve ( ) w.r.t. flow on 5-7. On both the lne power flow s towards bus 5. If generaton at bus 2 s ncreased flow on lne 2-5 ncreases whereas flow on 5-7 decreases and vce versa. In order to acheve a trade-off generators and loads are selected based on absolute value of SI. In ths congeston case, t s assumed that most senstve generator at bus 5 s not nterested to partcpate n the congeston management. Hence, remanng generators and hgh senstve loads (at buses 5, 7, 26 and 29) are selected for congeston management. Pareto optmal solutons for ths case are presented n Table V. Table V shows that n ths case congeston can not be allevated by generaton reschedulng only. Therefore, demand response has to be carred out on partcpatng loads. To allevate the overload completely operator needs to reduce MW load only at bus 5 where MW of load reducton s compensated by generaton reducng of MW at bus 2, 1.08 MW at bus 8, 2.19 MW at bus 11, and 1.03 MW at bus 13. For ths case congeston cost becomes as hgh as Rs ncludng demand response cost of Rs and generaton reschedulng cost of As expected, for subsequent solutons congeston cost reduces wth hgher tolerable overload. All these case studes clearly shows that a combnaton of DR and generaton schedulng could be very effectve for allevatng the congeston n smart grd. IX. CONCLUSION In the era of grd restructurng, congeston n power network s qute common. Ths paper proposes a congeston management method through demand response. Smulaton results presented n ths paper clearly show that wth demand response, congeston management becomes more flexble and

6 Case TABLE V SIMULATED CASES FOR IEEE 30 BUS SYSTEM Over loaded Intal generaton/ Pareto optmal solutons condton load* at Mn congeston Mn cost Compromse Partcpatng buses MVA Cap. Lne Bus Pg/ Cong. Pg/ Cong. Pg/ Cong. Pg/ Cong. code Pd Cost Pd Cost Pd Cost Pd Cost Rs/h Rs/h Rs/h Rs/h MW MW MW MW 1A B * * * C * * * * economcal as loads can drectly partcpate n congeston management. Smulaton results also show that proposed senstvty ndex could be very effectve n selectng approprate partcpaton generaton and demand for managng the congeston most economc way. It was also dentfed that sometmes lttle overload could reduce the congeston cost sgnfcantly. REFERENCES [1] R. C. Hardman, M. Kumbale, and Y. V. Makarov, An advanced tool for analyzng multple cascadng falures, n Proc. Intl Conf. Probablstc Methods Appled to Power Systems, Sept. 2004, pp [2] N. Acharya and N. Mthulananthan, Locatng seres facts devces for congeston management n deregulated electrcty markets, Electr Power Syst Res, vol. 77, pp , [3] T. Nguyen and V. Nguyen, Applcaton of wde-area network of phasor measurements for secondary voltage control n power systems wth facts controllers, n n Proc. Power engneerng socety general meetng, vol. 3, 2005, pp [4] T. K. P. Medcherla, R. Bllnton, and M. S. Sachdev, Generaton reschedulng and load sheddng to allevate lne overloads-analyss, IEEE Trans. Power Apparatus and Systems, vol. PAS 98, no. 6, pp , Nov [5] A. Shandlya, H. Gupta, and J. Sharma, Method for generaton reschedulng and load sheddng to allevate lne overloads usng local optmsaton, IEE Proc. C Gener. Trans. and Dst., vol. 140, no. 5, pp , Sept [6] D. Hazarka and A. K. Snha, Method for optmal load sheddng n case of generaton defcency n a power system, Int. J. Electr. Power Energy Syst., vol. 20, no. 6, pp , Aug [7] B. K. Talukdar, A. K. Snha, S. Mukhopadhyay, and A. Bose, A computatonally smple method for cost-effcent generaton reschedulng and load sheddng for congeston management, Int. J. Electr. Power Energy Syst., vol. 27, no. 5-6, pp , June-July [8] J. Hazra and A. K. Snha, Congeston management usng multobjectve partcle swarm optmzaton, n IEEE Trans. Power Systems, vol. 22, no. 4, 2007, pp [9] J. Hazra and D. P. Seetharam, A network congeston management approach consderng the rsk of cascadng falures, n Proc. PEDES & POWER INDIA CONF, [10] A. Yousef, T. T. Nguyen, H. Zarepour, and O. P. Malk, Congeston management usng demand response and facts devces, Electrcal Power and Energy Systems, [11] J. Hazra, A. K. Snha, and Y. Phulpn, Congeston management usng generaton reschedulng and/or load sheddng of senstve buses, n Proc. Thrd Internatonal Conference on Power Systems, [12] M. Lpez-Ibez, Multobjectve ant colony optmzaton, Master s thess, Technsche Unverstat Darmstadt, Germany, [13] L. Paquete and T. Stutzle, A study of local search algorthms for the bobjectve qap wth correlated flow matrces, European Journal of Operatonal Research, [14] M. Kong and P. Tan, Ant Colony Optmzaton and Swarm Intellgence. Sprnger-Verlag, 2006, vol. 4150/2006, ch. A Drect Applcaton of Ant Colony Optmzaton to Functon Optmzaton Problem n Contnuous Doman, pp APPENDIX TABLE VI DR COST COEFFICIENTS Amount of load p q r n the bus(mw) Rs/h Rs/MWh/h Rs/MW 2 /h >