Table 3: Operating time of P/B relays for an IEEE 8-bus test system (LP problem).

Proposed NM-PSO method
Backup relayPrimary relayConstraint value
No.Operating timeNo.Operating time

60.313410.11300.2004
91.042280.11100.9312
70.341380.11100.2303
11.633820.14121.4926
100.387590.18750.2000
70.341320.14120.2001
20.355130.15510.2000
110.3762100.17600.2002
50.952260.12030.8319
140.643960.12030.5236
80.3320130.13130.2007
91.0422140.08080.9614
50.952270.05150.9007
11.6338140.08081.5530
131.675870.05151.6243
30.358540.15840.2001
120.3848110.15780.2270
40.400050.20000.2000
131.6758120.19431.4815
140.6439120.19430.4496