Reliability assessments for two types of balanced systems with multi-state protective devices

•Two balanced systems with protective devices (PDs) are built for the first time.•New triggering policies of PDs based on the system characteristics are proposed.•The protective effects of PDs differ when they are in different operation stages.•Markov process imbedding methods are built to evaluate reliability of two models. In the existing studies, the positive effects of a protective device on the reliability of balanced systems have not been attached importance, and the research on protective devices is limited and insufficient with respect to the triggering and protection mechanisms. Driven by practical engineering applications, this paper establishes two reliability models for balanced systems with multi-state protective devices from the perspectives of dynamic and static balanced concepts, respectively. The rebalanced mechanisms are considered in the proposed dynamic balanced system, and system imbalance is included in the failure criteria of the proposed static balanced system. In both models, new triggering mechanisms of protective devices are proposed based on the respective characteristics of the balanced systems. Moreover, variable protection mechanisms of the devices are proposed by introducing different reduction factors when the protective device operates in different stages. The protective devices reduce the integrated impact of shocks and internal degradation exerted on the units in the new models. The Markov process imbedding method combined with Monte-Carlo simulation is employed to derive the reliability of the proposed models. The applicability of proposed systems and correctness of the method are validated by practical engineering applications.