·556· 智能系统学报 第4卷 B.=fundamental circuit matrix lays are used for ground protection. [1-11], Table 3 Relay data for sample system 2 L=matrix of simple loop Time dial Pick up current Operating time [1-11], relay setting/s setting/A /8 Lp augmented simple loops matrix rL1L21 Min Max Min Max Min Max 五 1 1.5 6 595 605 0.1 12 Therefore, 1.5 6 2995 3005 0.1 白 -690901 1.5 6 1495 1505 0.1 12 4 1.5 6 995 1005 0.1 3 5 1.5 6 95 105 0.1 Break points =[1 2], 12 6 1.5 295 305 0.1 12 127 1.5 145 155 0.1 12 RSM relative sequence matrix 45, 1.5 6 495 505 0.1 3 L3 6J 9 1.5 6 95 105 0.1 2 10 1.5 6 495 505 0.1 12 3 17 11 1.5 6 195 205 0.1 12 6 2 12 1.5 6 595 605 0.1 12 2 4 13 1.5 6 95 105 0.1 12 Mb main back up relay pairs 1 5 141.5 6 3900 4100 0.1 12 5 3 Table 4 Fault current data for sample system 2 LA 6 Main back up Main relay back up relay 5.1.2 Optimizing the coordination problem using EP relayrelay current/A current/A The main/back up relay pairs obtained in the previous step 14 7199 287.16830 is used to form the co-ordination constraints.The optimization 6 9 959 233.64100 > 9 1279 800.70810 problem for this sample system 1 can be formulated as follows. 12 11 2399 41.55701 Objective Function: 9 3 2599 1943.53900 Minimize Tu+Ta +Ts2 +T32 +Tss +T=sum of the 1 3 959 638.03350 operation times of the relays in their own zone,where, 1 10 609 40.000000 8 3430 56.000000 T= K·TDS 10 2 1439 88.000000 -K） 11 2 959 320.96450 9 4 2559 615.46110 Bounded constraints: 10 1439 556.36300 in≤≤n好， 4613 287.18830 TDS:h≤TDS:≤TDS:r, 6 14 4516 0.45160 5 6 959 233.64000 Tn≤T,≤Tinm 8 7 880 75.000000 i=1,2,…,6. 13 12 1439 556.000000 Co-ordination constraints: 5.2.1 Determination of main /back up relay pairs T1-T1≥C,T61-T41≥C,T2-Tn≥C, By using the software developed in MATLAB,all main/ T2-Ta≥C,Ta-Ta≥C,T8-Tg≥C back up relay pair for this system is found out.The graph and This non-linear optimization problem is solved using EP and the tree of this sample system are given in Fig.7. the results are obtained and given in section 6. ① 3®4④03>40 5.2 Sample system 2 This sample system is 6 bus,7 line (115 KV 2不 transmission system)practical system. This sample system 2 is a portion of the Puget Sound power and light company's 115 KV transmission Fig.7 The graph and the tree of sample system 2 system and in this system directional over current re- For this graph