外文翻译---变电站电缆自动化系统的有效计划-plc设计(编辑修改稿)

外文翻译---变电站电缆自动化系统的有效计划-plc设计(编辑修改稿)内容摘要：

int. 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 ˆI is a leader then the sum of all connections including the connectionˆi and its followers is less than the capacity requirement of the cable type j to whichˆi 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 leaderˆi 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 instances with nine cable types. The number of connections N in each sub problem instance is varied from 10 to 50. Each cable type has a cable cost which is discrete uniformly distributed between 1 and 2 and has a total number of conductors which is discrete uniformly distributed between 1 and 5. Each connection is allowed to be assigned to M out of the nine cable types, where M is discrete uniformly distributed between 3 and 6. Furthermore, the number of connection pairs which 214 T. Sivanthi and J. Poland Fig. 2. Performance obtained with different solvers cannot b。