Optimal location and size of distributed energy resources using sensitivity analysis-based approaches

This paper introduces an analytical approach based on sensitivity analyses of various objective functions with respect to load constraints to determine optimum locations and sizes of distributed energy resources (DERs). This method is based on sequentially calculating Lagrange multipliers of the dual solution of an optimization problem for various load buses. Determining the best candidate locations based on the sensitivity analyses with the assumption that an active constraint would remain active for all source sizes could produce inaccurate results. The reason is that buses that are ranked as the best candidates based on Lagrange multipliers may not be valid for large DERs since Lagrange multipliers change with the change in the system loading. In this work, locations and sizes are jointly determined in a sequential manner based on the validity of the active constraints. The proposed method can be applied with any objective function; however, in this paper, minimum generation cost is used as an objective function in the optimization problem. The method is demonstrated on several test systems including the IEEE RTS, IEEE 14, 30, 57, 118 and 300 bus test systems and the results showed the effectiveness of the proposed method against the traditional sensitivity analysis methods. Also, the results of the proposed method are validated using genetic algorithm.