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研究复杂的电力系统,尤其是考虑了系统中设备修复的多状态过程的可靠性,应该采用状态分析的方法。马尔可夫过程是一个有力的数学工具。该过程的基本原理是研究系统所处的各种状态的概率和各状态之间的转移关系。其特点是“无记忆性的”,即过程的下一个未来状态,只取决于它当前所处的状态或前有限次的状态,而与过去的历史状态无关。马尔可夫过程可以分为空间上和时间上都是离散型的、空间上是离散而时间是连续型的以及空间上和时间上都是连续型的三种。同时,又可根据其状态转移概率是恒定的还是随时间变化的函数,分为平稳的和非平稳的马尔可夫过程。在电力系统可靠性研究中,应用最多的是空间上离散状态,而时间上连续的平稳马尔可夫过程,它常具有以下性质:
Research on complex power systems, especially considering the reliability of multi-state process of equipment restoration in the system, should adopt the method of state analysis. Markov process is a powerful mathematical tool. The basic principle of this process is to study the probabilities of the various states in which the system is located and the relationships between states. It is characterized by “memorylessness,” that the next future state of the process depends only on its current state or its formerly limited state, irrespective of past history. The Markov process can be divided into three types: discrete in space and time, discrete in space, continuous in time and continuous in space and time. At the same time, it can be divided into stationary and non-stationary Markov process according to the function whose state transition probability is constant or time-varying. In the study of power system reliability, the most widely used is the stationary Markov process, which is spatially discrete but time-continuous, and often has the following properties: