The Application of Tabu Search Algorithm on Power System Restoration

Transcription

1 The Applcaton of Tabu Search Algorthm on Power System Restoraton FANG Xn-yan,CAI Xao-y, Jang Chuan-wen Dept.of Electrcal Eng.., Shangha Jaotong Unv., Shangha , Chna Abstract:-The essay s just accordng to the part of the Shangha Electrc System, whch s n accdent. The Breadth Frst Search (BFS) and The Depth Frst Search (DFS) wll be used to solve the problem of the early search of the net, then The Tabu Search wll be used to search for the fastest restore path. After these searches, C++ wll be used to comple the BFS and the DFS; also t wll be used to establsh the tabu lst. The result shows that the optmal restore path wll be selected n power system restoraton. Key Words:- restoraton; tabu search ; power system 1 Introducton The control of power system restoraton refers to load rejecton after urgent regulaton when there s an accdent n power system; or measures of regulatng the system to normal condton to the largest extent n shortest tme when the system s separated. In dstrbuton systems, accdents manly ndcate that a fault occurrng n a certan component (lne, transformer, etc) causes protecton actons and the break of relatve relays, thus causng loss of power n the regons supported by the equpment whle segregatng the fault source, or the operaton of the equpment under overloaded condton. The task of restoraton s to restore load as much as possble n power loss regons n shortest tme and to shft load from overloaded equpment reasonably. The paper analyzes some factors based on power system restoraton takng the status of separated system as ts object. (1) Start Power Supply The key of successful restoraton s start power supply. But not all the power supply can be used as the start power supply, whle only those unts wth self-start, or black-start capabltes can work as the start power supply n separated system. The unts wth self-start capabltes mean that they can restore power supply rapdly wthout external help and transmt start power to other unts through lnes. Among the start power supply, the water turbne generators such as pumped storage generatng unts are the most convenent. (2) Restore Path After an accdent n the power system, the restoraton process should be n order and n lne. Inapproprate order may cause another accdent, so the establshment of restore path s an mportant part n restorng power system. The restore path ncludes: The restore path of power plant: restore path of the power plant wthout self-start capabltes n the system. Several factors such as hgh supply relablty, beng closest to the start power supply, fewest swtch operands etc, should be consdered comprehensvely whle determnng the path. The attrbutes of the power plant may also be taken nto account that accordng to the mportance of power plant, nuclear power plant should be restored frst, then s the water power plant, the gas power plant, and the coal-fred power plant s the last. The restore of load: restore path of the load

2 n power system. Whle comprehensvely consdered the factors as hgh supply relablty, beng closest to the start power supply, fewest swtch operands etc, the mportance of load should also be consdered. Frst class load whch concerns the development and securty of natonal economy must be restored frst, then s the second and thrd class load. Restore load. Load should be restored accordng to the order of power transmsson. Statc stablty of the system, frequency stablty of the net, voltage stablty of the bus, actve and reactve power matchng and other factors should be consdered. Swtch operatng sequence and swtch operand. Another factor concernng the process of power system restoraton f swtch operatng sequence and swtch operand. The power of load n the system should be restored rapdly whle the securty and accuracy s guaranteed. Thus the operaton order of the swtch operatng sequence should be gven out correctly and rapdly so the operator may operate on the swtches n order. 2 The Prncple and Applcaton of Breadth Frst Search (BFS) and Depth Frst Search (DFS) 2.1 The Prncple of Breadth Frst Search (BFS) Breadth Frst Search (or Wdth Frst Search) s one of the most convenent graphc search algorthms and also the prototype of many mportant graphc algorthms. Djkstra sngle-source shortest path algorthm and Prm least tree algorthm also take the smlar dea as BFS. Whle graph G and source pont s are known, BFS tres to explore the border of G by a systematc way so as to fnd out all the ponts s can reach, and calculate the dstance from s to these ponts (the least number of borders). The algorthm can create a breadth frst tree that takes s as ts root and can reach all the ponts. If v s any pont that s can reach, the path from s to v n the breadth frst tree corresponds to the shortest path from s to v n graph G,.e. the path ncludes the least number of borders. The algorthm apples to both drectonal and nondrectonal graphs. Breadth Frst Search get ts name because the algorthm always extends outwards through borders connectng the found and unfound ponts. It means that the algorthm frst explores all the ponts whch are at a dstance of k from s, then explores other ponts that are at a dstance of k+1 from s. To keep the search track, BFS colors up every pont: whte, grey or black. At the begnnng, all the ponts are whte. Wth the search, the ponts gradually become grey, and then black. The frst tme a pont s reached, t becomes nonwhte. So grey and black ponts means they have be found. But BFS dstngush them to ensure that the search s carred out accordng to breadth frst prncple. If (u,v) E and pont u s black, pont v s grey or black (u and v are two search ponts, E s ponts collecton of G). That s to say all the ponts adjonng black ponts have been found. Grey ponts can adjon some whte ponts and they represent the borders the found and unfound ponts. In the process of BSF, a breadth frst tree s created whch only ncludes the root pont,.e. source pont s. When scannng the adjonng table of found pont u, f a whte pont v s found, v and the border (u, v) are added to the tree. In the tree, pont u s called elder or parent pont of v. Snce one pont can be found only once, t can have only one parent pont. To root pont, the defnton of ancestor and descendant relatons s the same as usual: f u s n the path from root s to pont v, u s called ancestor of v and v s the descendant of u. The nput graph G s supposed to be

3 expressed by adjonng table n BFS. For each pont u V, ts color s stored n the varable color[u] and the parent ponts of u are stored n varableπ[u]. If u has no parents (for example, u=s or u hasn t been found), π[u] s empty. The calculated dstance from source s to pont u s stored n varable d[u]. A FIFO queue s used to store the grey ponts collecton. 2.2 The Prncple of Depth Frst Search (DFS) Just as ts name tells, the strategy DSF follows s to search the graph as deep as possble. In DFS, f a newly found pont has an unexplored border, exploraton should be carred out through ths border. When all the borders of the pont v have be explored, the search wll go back to the start pont that connects v by that border. The process wll keep on untl all the ponts that can be reached from source pont are found. If there are some unfound ponts, one of them should be selected as a source pont to repeat the above process. The process should be repeated untl all the ponts are found. Smlar as BFS, when scannng the adjonng table that contans the found pont u and fndng a new pont v, DFS wll makeπ[v] (the parent collecton of v) u. The dfference between BFS and DFS s that the parent chld graph of the former algorthm forms a tree whle that of the latter one can be composed of several trees as the search may be repeated from several source pont. So the defnton of DFS s parent chld graph s slghtly dfferent from BFS s: G ( V, E ), E = {( π [] v ) E v V [ v] NIL} = π π π π : DFS s parent chld graph forms a depth frst forest composed of several depth frst trees. The borders of Eπ are called branches. Just lke BFS, DFS also colors up the ponts n the process of search to represent the ponts status. Each pont s whte at the begnnng, becomes grey when found and set black at the end (.e. when the adjonng table s thoroughly searched). The technque can ensure that the search of each pont ends n one depth frst tress, so these trees are separated. Besdes creatng a depth frst tree, DFS sets tme mark for every pont. Each pont v has two tme mark: the frst tme mark d[v] s set when v s frst found (and v s set to grey), the second mark f[v] s set when fnshng checkng the adjonng table of v. The tme marks are used n many graphc algorthms and they are very helpful to DFS. 2.3 The Applcaton of Combnng BFS, DFS wth Tabu Search Algorthm The effcency and smplcty of BFS and DFS makes them an effectve method of operatng path before usng tabu search algorthm. Concretely, t means that n the net graph where connectng relatons and node attrbutes are know, BFS algorthm s used frst to search the net graph so as to fnd out those power supples wthout self-start capablty. The DFS algorthm s carred out to fnd out all the trees, takng each power supply as a start pont. At the same tme a search depth should be set accordng to the actual net graph. The search should stop when reachng ths search depth to prevent the problem of low restore speed of the net graph that s caused by one tree s long restore path and the subsequent long power restore tme of the load at the end of the tree. Fnally a group of ndependent trees connected by drectonal lnes between nodes can be formed by DFS. Those selected nodes are taken as publc nodes through whch the ndependent trees can be connected wth each other to form a net graph of power restoraton as necessary preparatons for tabu search algorthm. 3 The Introducton of Tabu Search Algorthm s Prncple Tabu search (TS)s a unversal nner heurstc optmal technque n the use of solvng large-scale combnaton optmal problems. By

4 flexble memory, t prevents search plungng nto partal optmzaton. The basc concept of TS manly ncludes neghbor and reservaton perod. Usually, TS starts searchng from an ntal soluton whch s created randomly or by an exstng heurstc method. By movng the applcaton operators, TS operates on the current soluton and forms a group of neghbor testng solutons. In ths process, the soluton whch best mproves the judge functon wll be chosen as the new current optmal soluton. If none of the movements can mprove the judge functon, t ndcts the current soluton s the partal optmal soluton. To avod plungng nto partal optmzaton, a tabu lst wth a length s set n TS. The tabu lst stores the recently realzed movements and ant- movements, and t must be updated n each teraton. When formng a new movement, the movements n tabu lst must be restraned snce they wll make the search process return to the vsted space. Repeat the TS search process untl the stop rule s satsfed. 4 The Applcaton of Tabu Search Algorthm n power system restoraton 4.1 The Mathematcal Descrpton of Power System Restoraton The problem can be solved by two aspects: the shortest tme of power supply restoraton and the shortest tme of load restoraton Power Supply Restoraton (1) Objectve functon mn F, ( y z) = ( t y + t jz j ) Where y s swtch collecton; y =1 when swtch closes from dsconnecton, otherwse y =0; t s the operaton tme y needs; t j s the warm-up start tme of the power plant; z s load collecton; z =1 when the current plant s n power supply restoraton, otherwse z =0. (2) Restrctons Capacty restrcton: t refers to the capacty of total load allocated for a swtch as well as the load of the branches connectng to t. It s descrbed as: x j s Where j M k x j s connecton coeffcent of relevant swtches and branches, x j =1 when load z j s suppled by y, otherwse x j =0; s j s the load of the mono-branch connectng to the swtch, M k s load capacty. j =1,2,. Voltage decent restrcton: certan reactve compensaton must be carred out when puttng nto load to mantan the node voltage n the ratng level. It s descrbed as: V V mn t V max Where V t s node voltage Load Restoraton (1) Objectve functon mn G Where ( x ) = t x x shows swtch s status, x =1 when swtch closes from dsconnecton, otherwse x =0; t s operaton tme of swtch. (2) Restrctons The capacty restrcton and voltage descent restrcton are smlar as that of the power plant restoraton. Connecton restrcton: one load needs at

5 least one power supply. Power balance: at a tme, the power that all load absorbs equals the power that all plants sends out mnus the power those plants consumes. Accumulator s lastng tme: t s descrbed as: t x < T Where x T x s the lastng tme of swtch s accumulator,.e. swtch s lastng tme should be longer than swtch s operaton tme. The power plant and the load should be consdered comprehensvely to get matched n solvng the problem of power supply and load restoraton. 4.2 Instance Analyss The New Baogang systematc graph of Shangha electrcal net(fg.1) s taken as the example to llustrate how to use tabu search algorthm n determnng the restore path after system separaton. SDK 2131 XBG above object, tabu search algorthm can be used to change the power supply of each load so as to fnd out the best supply path. The search result,.e. the power supply of each load, should be placed n a status lst. So the expresson of each change should be easy for storage and usage. The structure characterstcs of the status lst are as follows: The length of the lst should be equal to the number of load that hasn t restored ts power supply. The statstc ncludes all nodes of the power plant and load. Each locaton of the lst represents the upper load or the power supply of the load. So, the lst shows the unrestored load s supported by whch power supply respectvely. Fgure 2 shows the net graph after BFS and DFS algorthm of New Baogang systematc graph. Table 1 s the start status lst of fgure 2. It s easy to establsh the tabu lst gven the status lst s establshed, snce the functon of tabu lst s to prevent the search return to the status that have been reached. The storage content of tabu lst s as follows: BG 2135 YH BG XBG YH WR WCB TB 2191 WR WCB SDK Fg.2 The power net after search TB Tab.1 The start status table Fg.1 New Bao Steel power net The realzaton of tabu lst To realze optmzaton n power system restoraton, the essental s to realze fastest power supply restoraton. And to realze the Load YH WR TB WCB Power Supply XBG SDK SDK XBG

6 Net structure (status lst); The current status s tabu length; Table 2 s the tabu table of fgure 2. Objectve functon. Tab2. Tabu table Net Structure Tabu Length Objectve Functon XBG YH WCB BG SDK WR TB 5 F(X1) XBG YH BG WCB SDK WR TB 6 F(X2) Where F(X1) and F(X2) are general expresson of the objectve functon. Start Form ntal net structure Form neghbor net structure (status) Keep searchng next net strructure Amend tabu length when needed Release a search when needed Reach fnal status No End Yes Fg.3 The flow chart of optmal restore path The realzaton of search method (status change) The search for neghbor status can be realzed by change the power supply of the load n the current net. And the load whose power supply can be changed must meet the condton

7 that ts former and subsequent load s not supported by the same power supply, otherwse the load can t change ts power supply. The steps of the search method are as follows: Select the load whose power supply can be changed n the current net structure. Form the neghbor status by changng the selected load n 1. The status are canddate status for 3. Select the status that s most sutable to the object functon and sn t tabooed. Export the restore path graph of the chosen method. Fgure 3 s the flow chart of optmal restore path by tabu search algorthm.s 5 Concluson Based on TS algorthm s advantages on searchng optmal power system restore path and dscussons on BFS and DFS as well as how ther combnaton provdes search path wth TS algorthm, the paper dscusses the applcaton of TS algorthm on power system restoraton, and gves out the system structure of power system restoraton based on TS algorthm. Program codes of searchng net structure by combnaton of BFS and DFS as well as searchng restore path were wrtten by C++. Program codes of tabu lst n TS algorthm were also fnshed. Complemented by the TS programs, these codes can solve the optmzaton problem of restore path of target net restoraton n power system. Reference [1]ZHOU Lng,WANG Xng-nan,DING Xao-qun,et al. Applcaton of genetc algorthm tabu search combnaton algorthm n dstrbuton network structure plannng[j].power System Technology, 1999,23(9): [2] HAN L-mn,WEI You-shuang, FENG Yun-cheng. The Convergence esu lts for TabuSearch Algorthm[J].The Practce and Theory of System Engneerng, 1998,(10):6-10. [3]ZHANG Xue-song, LIU Zuo, YU Er-kan. The strategy of dstrbuton capactor scheme based on tabu search[j].power System Technology, 1998,22(2): [4] LIU Da-peng, TANG Guo-qng, CHEN Hen. Tabu search based etwork parttonng for voltage control [J].Power System Automaton, 2002,(3):18-22 [5] CHEN Gen-jun, LI J-guang, WANG Le. Dstrbuton system plannng by Tabu search approach[j].power System Automaton, 2001(4): [6]WANG Hong-zhang, XIONG Xn-geng, WU Yao-wu. Power system reactve power optmzaton based on modfed tabu search algorthm[j].power System Technology, 2002,26(1): [7]HAN Zhen-xang, QIAN Yuan-png,WEN Fu-shuan. Tabu search approach to fault dagnoss s n power systems usng fuzzy abductve nference.journal of Tsnghua Unversty, 1993,39(3): [8] Zhu Yong-l. Applcaton actualty and latency applance doman analyss n electrc power systems by expert systems[j].power Informaton, 1996, (3):5-9. [9 ] ZHOU Yun-ha, MIN Yong, YANG Bn. Fault calculaton n expert system of relay coordnaton management[j].power System Automaton, 2001, (15): [10]QIU Xao-yan, TANG Ha-png. Power system restoraton based-on expert system and numbercal computaton[j].journal of Electrcal Machne Engneerng of Chna, 1996,16(6) : [11]Krschen, D.S.; Volkmann, T.L. Gudng a power system restoraton wth an expert system, IEEE Transactons on Power Systems, Volume: 6 Issue: 2, 1991 Page(s): [12]T.Sakaguch,K.Matsumoto,Development of a Knowledge Based System for Power System Restoraton, IEEE Transactons on Power Apparatus and Systems, Vol.PAS-102, No.2,

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