Abstract: Power grid system is the key infrastructure for the development of modern society. The interconnectivity between different lines in a power grid makes the operation of a power system with long-distance transmission more efficient, but it also causes transmission failures. Due to the inherent characteristics and physical mechanism of transmission, the cascading failures result in large-scale power outages. Cascade failures have fast propagation speed and wide range, which leads to huge social and economic losses.
In order to describe the impact of dynamic changes of traffic in the grid system on the grid operation and to analyze more precisely the reliability of different lines at different moments, this paper establishes a multi-state cascade failure Markov model with dynamic failure rates. It sorts out a variety of methods used in the study of cascade failure of power grid system, and gives the topology structure, the calculation method of flow and the initial state of power grid system. Based on the state space of the lines, the sets of lines in different states of the power grid system are defined respectively. The classical two-state model (operating state and fault state) is expanded into a multi-state one including normal operating state, safe fault state and dangerous fault state. A new multi-state cascade failure Markov model is established to analyze the transition probability of lines and the transition probability of the whole system in the power grid system. Combined with the characteristic that the flow is redistributed with the process of cascade failures, the calculation methods of safety failure rate, dynamic dangerous failure rate, line reliability and system reliability are given. This method can more accurately describe the influence of dynamic flow change on the operation of power grid system and analyze the reliability of different lines at different moments. Finally, the reliability analysis process of power grid system is given by the numerical example, and the differences in reliability of the same power grid system under the fixed failure rate and dynamic one is compared, which shows the effectiveness and accuracy of the model.
This paper expands the classical two-state model into a multi-state model including normal operating state, safe fault state and dangerous fault state. Considering the line failure rate with the dynamic change of flow load, the breakthrough failure rate is often approximately the error caused by fixed constant value. This paper establishes a multi-state cascade failure Markov model with dynamic failure rates, the related reliability indexes are analyzed, and the calculation methods of safe failure rate, dangerous failure rate, most vulnerable line index and system reliability are given, so as to analyze the reliability of multi-state cascade failure power grid system with dynamic failure rate more accurately.

Key words: power network, cascade failure, Markov, reliability

摘要： 电网中不同线路之间的互连性使远距离传输的电力系统运行效率提高的同时也会造成传输故障,发生级联失效从而造成大规模停电。为了描述网络系统中流量的动态变化对电网运行的影响,更精准的分析不同线路在不同时刻的可靠度,本文建立了动态故障率的多状态级联失效马尔可夫模型,将经典的二态 模型(运行状态和故障状态)拓展成包括正常运行状态、安全故障状态和危险故障状态的多态模型,并考虑了线路故障率随流量载荷的动态变化,对相关的可靠性指标进行了分析,给出了安全故障率、危险故障率、最脆弱线路指标以及系统可靠度的计算方法。

关键词: 电力网络, 级联失效, 马尔可夫, 可靠性