6M.Geethanjali,et al:Optimal coordination of directional over current relays using evolutionary programming ·557· e number of elements (lines)=7, r14 1 v=number of nodes =6, 6 b number of tree branches =v-1 =6-1 =5, 7 9 number of links or chords 12 11 e-w+1=e-b=7-5=2. 93 For this system,node 3 is taken as reference.The details 11 3 about the network are given as the input to the Matlab program 1 10 for determining the main/back up relay pairs,and the following 38 results are obtained. Mb =Main/back up relay pairs 102 Input to the program 112 Γ1127 9 4 263 10 4 313 14 EFT =44 3 6 554 5 6 665 7 L762 1312 e =7(numbers of lines or elements), Even though twenty main/back up relay pairs were available for v=6 (numbers of nodes), this system only seventeen pairs were considered for the sake of V=6 (reference nodes). simplification. Output of the program: 5.2.2 Optimizing the co-ordination A incidence matrix The main/back up relay pairs obtained in the previous sec- Γ1010000 tion is used to form the co-ordination constraints.The optimiza -100000-1 tion problem for this example system can be formulated as fol- 0-1-1-1000, lows. 0 0001-10 Objective function: 00001-1 0 MinimizeT +T2 +T3+T+Ts +Ts+T+Ts+To+ B=fundamental circuit Matrix Tio+Tn+Ti2+Ti Tul. 「0-1011101 Where, 1-1-110001 Ka TDS T:= Lp =matrix of simple loops Γ0-1011107 Bounded constraints: -1-100011, inna≤in:≤nnr L-101-1-1-11 TDS≤TDS,≤TDS. Lp augmented simple loops matrix Tinn≤T≤Tis Γ00011100100000 i=1,2,…,14. 00100011100000 Co-ordination constraints 00100 1100000 T1-T4≥C,T,-T6≥C,T,-T,≥C, 001000 11001110 T1-T2≥C,T3-T,≥C,T3-T1≥C, 01000000001110 To-T1≥C,Ts-T3≥C,T2-T0≥C, 10011100010001 T2-T≥C,T4-T,≥C,T4-T0≥C, 10011100010001 T4-T2≥C,T4-T6≥C,T6-T≥Ci, break points =[1 9 11], T,-Tw≥C,T2-T13≥C RSM relative sequence matrix This non-linear optimization problem is solved using EP and the Γ19107 results are obtained and given in Table 6. 31000 6 Results and analysis 8240 -146712- The simulated results for sample system 1 are giv-