第4卷第6期 智能系统学报 Vol.4 No.6 2009年12月 CAAI Transactions on Intelligent Systems Dec.2009 doi:10.3969/j.issn.16734785.2009.06.014 Optimal coordination of directional over current relays using evolutionary programming M.Geethanjali,S.Mary Raja Slochanal (Department of Electrical and Electronics Engineering,Thiagarajar College of Engineering,Madurai-625015,India) Abstract:Co-ordination of directional over current relays (DOCR)requires the selection and setting of relays so as to se- quentially isolate only that portion of the power system where an abnormality has occurred.The problem of coordinating protective relays in electrical power systems consists of selecting suitable settings such that their fundamental protective function is met,given operational requirements of sensitivity,selectivity,reliability and speed.Directional over current relays are best suited for protection of an interconnected sub-station transmission system.One of the major problems asso- ciated with this type of protection is the difficulty in coordinating relays.To insure proper coordination,all the main/back up relay pairs must be determined.This paper presents an effective algorithm to determine the minimum number of break points and main/back up relay pairs using relative sequence matrix(RSM).A novel optimization technique based on ev- olutionary programming was developed using these main back up relay pairs for directional over current relay coordination in multi-loop networks.Since the problem has multi-optimum points,conventional mathematics based optimization tech- niques may sometimes fail.Hence evolutionary programming (EP)was used,as it is a stochastic multi-point search opti- mization algorithm capable of escaping from the local optimum problem,giving a better chance of reaching a global opti- mum.The method developed was tested on an existing 6 bus,7 line system and better results were obtained than with conventional methods. Keywords:power system protection;protection coordination;directional over current relay;evolution- ary programming;optimization technique CLC Number:TP18 Document code:A Article ID:1673-4785(2009)06-0549-12 The main function of power system protection is to Since it is very difficult to find a proper relay setting isolate only the faulty component or a minimal set of to meet the requirements by traditional methods,partial components as soon as the fault occurs.Since the main optimization of OC relay settings based on predetermined protection system may sometimes fail(relay fault or pick-up current settings were developedis6.Since they breaker fault),there must be back up either in the cannot take all system conditions into consideration the same station (local back up)or in neighboring lines results may get trapped at local optimum relay settings. (remote back up)with time delay according to the se-Therefore some of the different multi-point search algo- lectivity requirement.The determination of the time rithms such as genctic algorithms and evolutionary delays of all the back up relays,in the main/back up programming (EP)are used to reach global optimum in relay pairs,is known as coordination of the protection a better way.Thus recently the problem of coordinating system.Generally,in meshed networks with multiple DOCR in power systems was stated and solved in the generation buses,directional protection relays are framework of optimization theory.For this paper,a used.Among those,directional over current relays novel approach using EP for optimal coordination of (DOCR)are the major protection devices in distribu- DOCR was developed.The work done involved the fol- tion systems.The major problems associated with lowing two stages: DOCR are relay setting calculations and coordination. 1)Determination of a minimum set of break points Received Date:2008-11-24. and the main/back up relay pairs using relative se- Corresponding Author:M.Geethanjali.E-mail:mgeee@tce.edu. quence matrix (RSM)
·550. 智能系统学报 第4卷 2)Development of a DOCR coordination algorithm dal method.But in these methods the solution obtained based on EP using the main/back up relay pairs deter- may not be taken as a global optima because there is a mined in 1). chance of getting trapped in local optima.Hence in Thus an effective "optimal"solution to the co- this proposed method EP which gives global optima is ordination problem was obtained. used to optimize the problem. 1 DOCR coordination 2 Development of optimal DOCR co- Directional over current relays are best suited for ordination algorithm protection of interconnected sub-system transmission systems or as secondary protection of main transmission The method developed for optimal co-ordination of systems.Co-ordination of these protective relays in- directional over current relays consists of the following volves their selection and setting so as to sequentially i- steps: solate only that portion of the power system where the 2.1 Determination of main/back up relay pairs abnormality occurs.To achieve this isolation,it is nec- The relay which clears the fault in the protected essary to set protective devices so that only the device section as quickly as possible is called the main relay. nearest to the fault opens and isolates the faulty circuit The relay which operates after a slight time delay,if from the system.The problem of coordinating protec- the main relay does not operate to trip its circuit break- tive relays in electrical power systems consists of selec- er,is known as the back up relay.In order to obtain ting suitable settings such that their fundamental pro- proper co-ordination,it is very important to find all the tective function is met given requirements of sensitivi- main-back up relay pairs.Each main-back up relay ty,selectivity,reliability and speed.The setting of pair is set according to the coordination interval.All DOCRs has to satisfy all possible network configura- main-back up relay pairs are found using break points tions subject to type and location of all possible faults. and a relative sequence matrixs,10 Back up protective devices are set to operate at 1)Determination of break points. some predetermined time interval after the primary de- The starting points of sequences that ensure coor- vices fails to operate.When remote back up protection is dination are called break points.Determination of break required,then coordination should be done for all possi- points(BPs)yields the minimum set of relays to start ble main/back up relay pairs at corresponding stations. the co-ordination process.They are determined using a Since the relays are directional ones,the mesh should run simple loop matrix (L)which is determined by using in both directions to include all of the relays.It is neces- the network topology. sary to determine a set of starting relays which would The simple loop matrix L is determined using the break all the meshes of the network when they are simul- following steps: taneously open.Those relays are known as"Break Points" DFormation of network graph,edges and verti- (BPs)tio」 ces:A network graph is obtained from the network by Conventionally,the co-ordination of directional o- replacing the nodes with vertices and the lines with the ver current relays (DOCR)is done using interactive edges of the network.The edges are numbered from 1 methods,wherein the co-ordination engineer runs dif-to e and vertices from 1 to v. ferent cases for distinct faults and configurations,until 2Numbering of relays:The relays are numbered an acceptable solution is reached.Unfortunately the in the correct manner.For example,if the relay on solution found by these procedures is not optimal in any line"i"is located at the initial vertex of the edge, strict sense,but simply the best of the possible solu- and is numbered as "i"then the relay at the final tions tried [s6.Later,optimality was obtained using vertex of the edge is numbered as e+i. conventional optimization methods like the Gauss-Sei- 3Formation of sub matrix F:Any circuit of the
第6期 M.Geethanjali,et al:Optimal coordination of directional over current relays using evolutionary programming ·551· graph is a linear combination of some fundamental circuits mined using break points and the augmented incidence of the graph.The maximum number of circuits of any matrix,which includes all buses and in which each re- graph is2-1.Then all simple loops of the network can lay is treated as a line. be determined by considering every "g"in the interval 3)Determination of main-back up relay pairs. 1 <g<2-1.Let the binary representation of "g" To ensure proper coordination,all main-back up contain entry 1 in the digital positionsj,j2,etc.Then a relay pairs must be determined.The main-back up re- sub matrix F is formed by rowsj,j,. lay pairs are determined using RSM and an augmented 4Procedural steps for determination of matrix L: incidence matrix.The procedure is explained in the .The set (S)of columns F which have even numb- flowchart given in Fig.1 and a Matlab coding was de- esr of non-zero entries are determined.This set is repre- veloped.The inputs to this program are the edge list, sented as S=C,C:,C..If no such column exists,the specifying the lines,number and the two buses to linear combination is not a simple loop and next g is con- which it is incident.Thus all main/back up relay pairs sidered.If F has only one row,then it is a loop. can be determined. The second step is to select a column k of F such that k is an element ofS and the N entry in the first row Start of that column is not zero. Enter network details .Each row i of F(i not equal to l)which has a non zero entry in column k is replaced by its sum with Determine break points the first row if F(i,k)=F (,k).The first row is then deleted.Then the procedure is repeated from step Determine relative sequence matrix two. .When F contains only one row,it represents the Select the element in RSM relevant oriented circuit of the network graph.The pro- (This is a back up relay) cedure is repeated for every g in the interval I<g< Find the bus in which this 21-1.Each circuit corresponds to one row of the ma- relay is looking towards trix L.This matrix L is called the "all circuits matrix" Find the relay which is looking away of the network graph. from this bus or adjacentrelay. (This is a main relay.〉 5Formation of augmented matrix Lp: 吃1 Check whether all the elements are in RSM where L is the matrix obtained by setting every -1 entry of L to zero.L2 is the matrix obtained by setting Y Stop every +1 entry of the L to zero and then replacing every -1by+1. Fig.1 Flow chart to determine the main/back up relay pairs The break points are determined using the matrix 2.2 Formulation of optimization problem for Lp.The set of columns of Lp which covers it are the DOCR coordination break points of the network.A set of columns is said to After finding the main/back up relay pairs co-or- cover the matrix Lp if each row of Lp has at least one dination is optimized.The optimization problem is stat- non-zero entry in one of the columns of the chosen set. ed as follows: Thus break points are determined. Objective: 2)Determination of relative sequence matrix [RSM]. To find TDS and ip for all relays such that the to- The sequence for setting the relays is displayed by tal operating time is minimized and the constraints are a“relative sequence matrix”（RSM).This is deter- satisfied
.552. 智能系统学报 第4卷 Objective function: Min∑I. 3 Evolutionary programming-a so- 自 lution for an optimal problem Bounded Constraints: ip血≤in≤in’ Evolutionary programming (EP)creates artificial TDSin≤TDS≤TDS, intelligence based optimization algorithms using the Taia≤T≤Tnm mechanics of natural selection:mutation,competition, Co-ordination constraints: and evolution.The process of evolution inevitably leads Thackp-Tm>co-ordination interval (C)for to the optimization of "behavior"within the context of each of the main/back up relay pairs given criteria.It has been seen that artificially simula- 2.3 Determining the solution to the optimization ting evolutionary processes provides a generalized prob- problem using an optimization technique lem-solving technique.Optimization with evolutionary By using any optimization technique an optimal programming has been demonstrated to proceed more solution can be searched in both the subspaces(ie. efficiently and effectively than a gradient based tech- TDS and i,)simultaneously and global optima can be nique.Thus EP offers a new tool for optimization of obtained. complex power system problems. The detailed flowchart for the proposed optimal In EP,each individual competes with some other DOCR coordination algorithm is given in Fig.2. individuals in a combined population of older genera- Start tions and mutations of the older generations.The re- sults of competition are evaluated using probabilistic Enter network rules.The winners in the old generation constitute the details next generation.The number of individuals in the new generation will be the same as in the old generation. Determine break points The general process of EP is described as follows: 1)Initialization Determine relative The initial variable population is selected by ran- sequence matrix domly selecting P:=1,2,..,m from sets of uniform distribution,ranging over a maximum and minimum Determine main/backup limit where m is the population size.Then the fitess relay pairs scoref:is calculated for each P:. 2)Statistics Enter relay details The maximum fitness,minimum fitness,sum of fitness and average fitness of this generation is calculat- Form coordination constraints ed using Equ.(1),(2),(3)and (4)respectively. using main/backup relay-pairs f=fie(1,,msuch that ∫≥f,j=1,…,m}, (1) Optimize the coordination using any optimization technique fmin=f,ie(1,,m such that f≤f,Hj={1,…,m, (2) Obtain relay settings and T fm=∑f, (3) (4) Stop fos =fam/m. 3)Mutation. Fig.2 Flow chart for proposed optimal DOCR coordination Each P:is mutated and assigned to Pm in accord- algorithm ance with Equ.(5)
第6期 M.Geethanjali,et al:Optimal coordination of directional over current relays using evolutionary programming ·553· P+nd=Pu+N(0,B(m-i血） tionary programming for the optimal co-ordination prob- lem as formulated.The optimization is done in the fol- j=1,2,…,n. (5) lowing steps. Then the corresponding fitnessfm is obtained.A 1)Initialization. combined population is formed with the old generation The variables in the optimal co-ordination problem and the mutated old generation. are pickup current (i)and time dial setting (TDS). 4)Competition. Hence the initial variable population is selected and Each individual P:in the combined population has [ipl p2… iplm to compete with some other individuals to get its chance im to be transcribed to the next generation.A weight val- given as for pickup current ue Wis assigned to the individual according to the com- im2 petition,as given in Equ.(6). Lipl [TDSu TDS2 TDSim (6) 台 TDS2 TDS2 TDS2m for time dial setting. where g is competition number and is from the set0, 1.As P:competes with a randomly selected individual P LTDS TDS TDS. in the combined population is calculated using Equ.(7). Then the operating time (T)is calculated for 「a=1,ifw<E+f each relay and for each individual by using the rela- (7) tionship given in Equ.(8). w=0,otherwise. T= K TDS (8) Where,u is randomly selected from a uniform distribu- -K) tion set U(0,1). When all individuals P:(i=1,2,.,2m)get Then the resultant operating time for all the relays will their competitive weights,they will be ranked in de- T Te Tim scending order of their corresponding value Wi.The be in the form of Tni,…,Tthe first m individuals are transcribed along with their cor- Ta… responding fitnessf:,to be the basis of next generation. operating time for all individuals 5)Determination. 2)Statistics. The convergence of maximum fitness to minimum The minimum value of total operating time is cal- fitness is checked.If the convergence condition is not culated for all relays as Tin n)=min T(n,i). obtained,then the mutation and competition process Where i=l,…,m. will run again.If it converges,the program will check 3)Mutation. limits of variables.If one or more variables exceed Each ip and TDS is mutated and assigned to their limits,the penalty factor of these variables will be j+m and TDS+m in accordance with the Equ.(9) increased,and then another loop of the process will and (10). start and it will run again. tm=+N(0,r(i,j》）, (9) 4 Proposed method of optimal co- TDS4m=TDS,+N(0,(i,J),(10) ordination of directional over where current relays using evolutionary programming r》=风ea)层 (11) (i》=B(TDss-TDSa)T点 (12) This section deals with the application of evolu-