大系统马尔可夫模型状态转移概率矩阵的快速形成方法

An Effective Method to Formulate State Transition Probability Matrix of Markov Model of Large-Scale System

提出马尔可夫模型状态转移概率矩阵的快速形成方法.定义元件状态转移率矩阵和系统状态数组,将系统状态转换为便于计算机存储与处理的数组,有效地描述了系统状态之间的转移;基于元件状态转移率矩阵和系统状态数组提出不受系统状态和元件状态数目限制快速准确计算状态转移率的方法,通过挖掘状态转移概率矩阵中非零元素的分布规律提出非零元素的快速定位方法,进而快速形成状态转移概率矩阵的稀疏存储;针对由两状态元件组成的系统,提出基于给定系统状态排序和服务状态集数组快速定位状态转移概率矩阵中非零元素的方法.将其应用于电力系统概率安全性评估,以新英格兰10机39节点系统为例,证实了方法的有效性和实用性.

An effective method to formulate state transition probability matrix was presented. Component state transi- tion rate matrix and system configuration array were defined. Consequently, system configurations were expressed in terms of arrays which can be conveniently stored and processed by computer, and transitions between system con- figurations were described efficiently. An effective method to calculate state transition rate without the limitation of the number of system states and component states was presented. A method to fast locate the non-zero elements was pre- sented according to the rule of the distribution of non-zero elements, and then, sparse storage of the state transition probability matrix was formulated swiftly. In the case that components only have two states, the location of non-zero elements was straightly obtained based on given order of system state and service set array. Application to probabilistic security assessment, taking New England 10 generators and 39 buses system as example, verifies the effectiveness and availability of the method.