Compensating capacitor design for improving angle stability of DGs in a micro-grid using trajectory sensitivities approach

This paper presents an algorithm for locating and design of a capacitive compensator to improve angle stabilities of synchronous machine DGs in a micro-grid. The proposed algorithm uses the notion of trajectory sensitivities to determine the sensitivity of DGs rotor angles versus the susceptance of a compensator. Then, via the sensitivity analysis of the micro-grid subsequent to a pre-specified fault, the minimum required capacitor banks to maintain the angle stability of DGs is calculated. The algorithm formulations can be used for a micro-grid with an arbitrary number of DGs and under various fault scenarios. The algorithm also works for both grid-connected and autonomous (islanded) modes of a micro-grid. Capabilities of the algorithm are investigated using a modified benchmark system of the IEEE standard 399-1997. The validity of the algorithm is verified based on time-domain simulations of the benchmark study system using MATLAB software tools.