Network Reduction With Unknown Transmission Line Status

A network reduction method for a network with unknown transmission line statuses is presented. This method could have wide applications in optimal transmission maintenance scheduling and transmission network planning. These problems are complicated and difficult to solve since transmission line's status will change the system's topology and consequently shifting factors. In general, voltage angle variables at all buses, and corresponding constraints, need to be introduced to solve these problems. However, this will make the problem practically insolvable due to the huge number of variables and constraints. The proposed method will dramatically decrease the number of variables and constraints needed in transmission line maintenance problem. The most important and inspiring point is that the number of necessary variables and constraints is proportional to the number of transmission lines with unknown status and the number of lines being monitored, and is independent of the size of the system. A six-bus system is used to illustrate the proposed methods.