Optimal allocation of multi-state performance sharing systems with multiple common buses

The reliability of performance sharing systems (PSSs) has received increasing research attention due to their practical importance. Early research mainly focused on the PSSs with one or two common buses. This paper investigates the reliability evaluation and allocation of a PSS with multiple common buses. The units in the system are organized into multiple clusters according to their connection to the common buses. Performance sharing is first performed in each cluster and then between the clusters. A UGF-based algorithm is developed to evaluate the system reliability based on the recursive analysis of each cluster. The optimization problem is further studied to find the optimal allocation strategy that maximizes the system reliability. To reduce the strategy space, a stochastic ordering based method is proposed to limit the value range of decision variables. The effectiveness of the reliability evaluation method is verified by an analytical example. In a numerical example, the proposed strategy space reduction method is embedded in the genetic algorithm (GA) and the improved GA outperforms the pure GA in allocation optimization.