基于重要抽样函数参数解析优化的电网可靠性评估

重要抽样(IS)法可显著提高电网可靠性的蒙特卡罗仿真(MCS)速度.作为一种有效的IS法,交叉熵法(CEM)以迭代方式实现重要抽样概率密度函数(IS-PDF)的交叉熵参数优化,然而迭代寻优存在较大计算成本.针对此问题提出一种全新的IS-PDF参数解析优化方法.首先将故障系统状态的理论最优IS-PDF用非线性方程组进行解析表达,并将IS-PDF的参数(即元件的最优无效度)作为方程组待求变量.由于系统故障状态数目庞大,导致方程组中方程数目太多而无法求解,为此引入最小割集概念对系统故障状态进行合并,在不改变理论最优IS-PDF等式方程约束的前提下,大大降低了方程数目;最后对削减后的方程组采用最小二乘估计实现元件最优无效度的解析求解.该方法的有效性和高效性通过MRBTS(modified Roy Billinton Test System)和IEEE-RTS79(IEEE-Reliability Test System 1979)可靠性测试系统的仿真计算进行了验证.

Analytical parameter optimization based on importance sampling for power-system reliability evaluation

Importance sampling (IS) can effectively speed up the Monte Carlo simulation (MCS) of power-system reliability evaluation. As a promising IS method, the cross-entropy method (CEM) can estimate the parameters of the IS probability density function (IS-PDF) by using an iterative parameter optimization procedure; nevertheless the iterative parameter optimization incurs high computation burden. A novel analytical approach for IS-PDF parameters optimization is proposed in this paper to reduce the computation cost. Firstly, the theoretically optimal IS-PDF for failure system states is formulated by a set of nonlinear equations where the PDF parameters, i.e. the optimal component unavailabilities, are to be solved. Because these equations are too many to be solved, the concept of minimum cut set identification is introduced to reduce the number of equations significantly while keeping the equality constraint for the theoretically optimal IS-PDF. Finally, to derive the optimal component unavailabilities, the least square estimation is used to solve these equations. The effectiveness and efficiency of the proposed method are verified by MRBTS and IEEE-RTS79.