Reliability analysis and optimization of multi-state tree-structured systems with performance sharing mechanism

Existing studies on reliability modeling of performance sharing systems (PSSs) have primarily focused on common bus or series structure. However, in some practical PSSs, units are organized in a tree structure. This paper addresses the research gap in reliability optimization of tree-structured PSSs. In such systems, units with random performance and demand are arranged in different layers. The surplus performance of each unit can be shared by the connected units located in adjacent layers. The system fails if there exists performance deficiency. A recursive method is proposed to determine the state of connected units. Additionally, a reliability evaluation algorithm is developed based on universal generating function. We further investigate the optimization of transmission capacity allocation to maximize system reliability. To streamline the search for the optimal solution, a strategy space reduction approach is introduced to derive the more appropriate value range of each decision variables, thereby simplifying the optimization process. Genetic algorithm (GA) is employed to identify the optimal solution within the optimized strategy space. Validation through two power systems demonstrates that the proposed reliability evaluation method accurately evaluates the system reliability, and the improved GA efficiently finds a superior transmission capacity allocation strategy compared to the conventional GA.