Reliability Analysis of a Home-scale Microgrid Based on a Threshold System

The reliability of a microgrid power system is an important aspect to analyze so as to ascertain that the system can provide electricity reliably over a specified period of time. This paper analyzes a home-scale model of a microgrid system by using the threshold system model (inadvertently labeled as the weighted k-out-of-n:G system model), which is a system whose success is treated as a threshold switching function. To analyze the reliability of the system, we first proved that its success is a coherent threshold function, and then identified possible (non-unique) values for its weights and threshold. Two methods are employed for this. The first method is called the unity-gap method and the second is called the fair-power method. In the unity-gap method, we utilize certain dominations and symmetries to reduce the number of pertinent inequalities (turned into equations) to be solved. In the fair-power method, the Banzhaf index is calculated to express the weight of each component as its relative power or importance. Finally, a recursive algorithm for computing system reliability is presented. The threshold success function is verified to be shellable, and the non-uniqueness of the set of weights and thresholds is demonstrated to be of no detrimental consequence, as different correct sets of weights and threshold produce equivalent expressions of system reliability.