Reliability Analysis of a Home-scale Microgrid Based on a Threshold System
Taufal Hidayat
Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, 21589, Saudi Arabia.
Ali Muhammad Rushdi *
Electrical and Computer Engineering, King Abdulaziz University, P.O.Box 80204 Jeddah 21589, Saudi Arabia.
*Author to whom correspondence should be addressed.
Abstract
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.
Keywords: Micro grid, k-out-of-n G system, threshold system, Banzhaf index, unity-gap, fair-power, shell ability, probability map