【正文】 when true implies that the leader i is assigned to an instance of cable type j. _^, ),(,10 Kjiw he r eorX ji ?? (2) Table 1 illustrates all binary variables corresponding to the example shown in Figure 1 for the case with two cable types K1 and K2. It is assumed that connections C1 and C3 cannot be assigned to the same cable and K1 is not an allowed cable type for connection C3. As mentioned before all connections except the first connection, which must be a leader, can either be a leader or follower. This is ensured by the following constraint. CiYXKjiKj jiCii ii ???? ?? ??? ,1),(, ,),( ,^ ^ （ 3） A connection which is a leader in a cable cannot be a follower of a leader in another cable. This is expressed by the following constraint. _^*),( ,),(,1_^ ^^CiiXXCii iiii???? ?? （ 4） An implicit constraint of the cable planning problem is the capacity constraint which implies that the number of connections assigned to a cable must be less Table 1. Binary variables corresponding to Figure 1 example Efficient Planning of Substation Automation System Cables 213 than the capacity requirement . the total number of conductors in the cable minus the spare core requirement of the cable. Let Uj and Sj be the total number of conductors and the required spare core in cable type j, then the following equation expresses the capacity constraint. In this equation, if the connection ?I is a leader then the sum of all connections including the connection?i and its followers is less than the capacity requirement of the cable type j to which?i is assigned, otherwise the equation is by default satisfied. _^),( ,*),( ,),( , _^^_^ ^^ ^ ,)(1 CiYSUXXKji jijjCii iiCii ii??????? ?????? （ 5） In addition the problem formulation needs the following constraint to avoid indirect pairing of connections i and i? which have the same leader?i but (i, i?) is in X. .),(,)*,(),(,1 _**_^^*, ^^ Ciiiw he r e iCiiiiXX iiii ?????? （ 6） Similarly, the following constraint prohibits a follower to choose a leader whose selected cable type is not one of the allowed cable types of the follower. .),(,),(,)*,(),(,1 __^_^^, ^^ KjiKjiKw he r ejCiiiiYX jiii ??????? （ 7） Finally, the sub problem may include a set of preferred allocation rules which specify that all connections carrying certain signals should preferably be assigned to the same cable. This is achieved by introducing a penalty cost in the objective function. The penalty cost will increase when not all connections of any preferred allocation rule have the same leader or when there exists more than one leader among the connections within any preferred allocation rule. The constraints related to preferred allocation rules are not expressed due to space limitation. The objective of the cable planning problem is then specified as minimize ???_),( ,:m inKji jijYMim iz e （ 8） where Mj is the cost of cable type j. The optimization of the above problem results in a SAS cable plan with minimal total cable cost. 4 Results In order to conduct a meaningful experiment, due to the lack of sufficient real subproblem instances, we generated random sub problem