Reliability optimization design of distribution systems via multi-level hierarchical procedures and generalized reduced gradient method

This paper develops an optimization method for reliable design of substations. Reliability indices used are failure rate and interruption duration, which are commonly used in the distribution systems. Through applying the proposed method, the optimal reliability indices of apparatus are obtained, which minimize the total cost comprising apparatus investment cost and interruption cost, and also satisfy reliability constraints of load point. Three kinds of interruption cost including initial interruption cost, outage frequency cost and interruption duration cost are considered. The optimization technique employed in this paper to solve the nonlinear programming problems is the generalized reduced gradient (GRG) method. For simplification of computation of large or complex systems, the multi-level hierarchical optimization is applied. It starts by dividing the system into several subsystems, and finds the optimal reliability indices for subsystems. Then by repeatedly taking the previous “subsystem” as the following “system” and the previous “constituent” as the following “subsystem”, and applying the GRG method, we can finally find the desired reliability indices for components of the primitive system. To demonstrate the application of the method, a secondary substation of the Taiwan Power Company is taken as an example, computation results of the application example show that the interruption cost is effectively reduced. The proposed method is applicable to existing substation expansion and new substation establishment