Reliability Analysis Of A Hydroelectric System With Different Failure States

The hydroelectric repairable degradation system is one of the key systems in reliability theory,and its theoretical results are crucial to the reliability of electric system operation.According to the actual situation,human error plays a major role when a hydroelectric plant fails,so it is very relevant to study the repairable degradation systems of hydroelectric power with different failure states caused by human error and major components failure.In this thesis,we study the reliability of a repairable degradation system of hydroelectric power with different failure states established by the supplementary variable method and Markov process.First,by selecting an appropriate state space and defining the operator of the system,the system of calculus equations of the hydroelectric repairable degradation system is transformed into an abstract Cauchy problem in Banach space.Second,we prove the system operator generates a positive C0 semigroup by using the resolvent positive operator and the cofinal theory,and obtain the existence and uniqueness of the dynamic solution of the system.Then,the exponential stability of the dynamic solution of the system is proved by spectral analysis of the system operator and by using C0 semigroup theory.Finally,the steady-state availability of the system is obtained from the perspective of eigenvectors of system operators.