基于交叉熵的大电网可靠性序贯蒙特卡洛仿真研究

发布时间：2018-01-01 01:22

本文关键词：基于交叉熵的大电网可靠性序贯蒙特卡洛仿真研究　出处：《重庆大学》2016年硕士论文　论文类型：学位论文

【摘要】：电网可靠性评估能够从概率风险视角为电力系统规划、运行和管理等提供风险决策的参考依据,成为当前研究热点之一。在电网可靠性评估中,序贯蒙特卡洛仿真法由于能有效模拟系统运行和故障恢复过程的时序特征,因此不但能得到电网可靠性指标的期望值指标,还能有效获取电网可靠性指标的概率密度分布,由此得到广为关注。但是,序贯蒙特卡洛仿真计算精度与计算成本的矛盾严重限制了其工程实用性,因此研究序贯蒙特卡洛仿真的收敛性加速方法具有重要的学术与实际意义。方差削减技术是加快蒙特卡洛仿真收敛速度的有效方法,其中重要抽样法已得到较多研究,而交叉熵算法作为一种新兴的重要抽样法,在电网可靠性非序贯蒙特卡洛仿真中取得了较好的收敛性加速效果。但在序贯仿真框架下,如何实现交叉熵算法和序贯仿真的有机结合,同时实现可靠性指标期望值和概率分布的准确计算,值得深入探索。本文的主要研究内容:(1)系统研究了基于交叉熵的非序贯蒙特卡洛仿真法的基本原理。在电网可靠性非序贯蒙特卡洛仿真中,元件的两状态可靠性模型采用二项分布来描述,交叉熵法可有效估计该二项分布对应的最优重要抽样概率密度分布(IS-PDF)的参数,从而实现方差减小和收敛性加速的目的。(2)在基于交叉熵的非序贯蒙特卡洛仿真法基础上,提出了计算最优IS-PDF参数的序贯交叉熵法。推导了序贯仿真中计算最优不可用度的迭代公式,根据元件不可用度与故障率和修复率的关系,给出故障率和修复率三种不同计算方式,从而能够利用故障率和修复率进行电网可靠性评估的序贯仿真。与已有方法相比,本文最优不可用度估计阶段及其之后的电网可靠性评估阶段,都处于序贯仿真框架中,并且这两个阶段抽样得到的系统状态序列样本都可用于最终的可靠性指标计算,从而进一步提高了可靠性评估的效率。(3)基于交叉熵的序贯蒙特卡洛仿真必须采用似然比对系统状态序列的影响后果进行修正,本文推导了修正系统状态持续时间的四种似然比公式和修正系统失负荷频率的似然比公式,并且证明了仅利用系统状态概率之比修正系统状态序列的序贯仿真实际上仍是非序贯仿真。为获得可靠性指标准确的概率分布,提出了基于交叉熵的IS-PDF参数估计的基本原则:交叉熵算法将改变抽样概率密度分布的参数,但参数改变前后系统故障状态的频率变化越小越好。
[Abstract]:Power network reliability assessment can provide reference for power system planning, operation and management from the perspective of probabilistic risk. It has become one of the current research hotspots. Sequential Monte Carlo simulation method can effectively simulate the time series characteristics of system operation and fault recovery process, so it can not only get the expected value index of power network reliability index. The probability density distribution of power network reliability index can also be effectively obtained, which has been widely concerned. However, the contradiction between the accuracy of sequential Monte Carlo simulation and the calculation cost seriously limits its engineering practicability. Therefore, it is of great academic and practical significance to study the convergence acceleration method of sequential Monte Carlo simulation. Variance reduction is an effective method to accelerate the convergence speed of Monte Carlo simulation. Among them, the important sampling method has been more studied, and the cross-entropy algorithm is a new important sampling method. In the power network reliability non-sequential Monte Carlo simulation, a good convergence acceleration effect has been achieved, but in the framework of sequential simulation, how to realize the organic combination of cross-entropy algorithm and sequential simulation. At the same time, the expected value and probability distribution of reliability index can be calculated accurately. The main research content of this paper is: 1) the basic principle of non-sequential Monte Carlo simulation method based on cross-entropy is studied systematically in the power network reliability non-sequential Monte Carlo simulation. The two-state reliability model is described by binomial distribution. The cross-entropy method can effectively estimate the parameters of the optimal important sampling probability density distribution (IS-PDF) corresponding to the binomial distribution. Therefore, the aim of reducing variance and accelerating convergence is realized based on the non-sequential Monte Carlo simulation method based on cross-entropy. A sequential cross entropy method is proposed to calculate the optimal IS-PDF parameters. An iterative formula for calculating the optimal unavailability in sequential simulation is derived according to the relationship between the component unavailability and the failure rate and repair rate. Three different calculation methods of failure rate and repair rate are given so that the sequential simulation of power network reliability evaluation can be carried out by using failure rate and repair rate. In this paper, the optimal unavailability estimation stage and the subsequent power network reliability evaluation stage are in the sequential simulation framework. And the system state series samples obtained by the two stages sampling can be used to calculate the final reliability index. Therefore, the efficiency of reliability evaluation is further improved.) the sequential Monte Carlo simulation based on cross-entropy must be modified by using likelihood alignment of the effect of system state sequence. In this paper, four kinds of likelihood ratio formulas for modifying the state duration of the system and the likelihood ratio formula for correcting the out-of-load frequency of the system are derived. And it is proved that the sequential simulation which only uses the ratio of the system state probability to modify the system state sequence is still non-sequential simulation in order to obtain the accurate probability distribution of the reliability index. The basic principle of IS-PDF parameter estimation based on cross-entropy is put forward: the cross-entropy algorithm will change the parameters of sampling probability density distribution, but the frequency change of system fault state before and after the change of parameters is as small as possible.
【学位授予单位】：重庆大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TM732;TM743

【相似文献】