基于非参数核密度估计的扩展准蒙特卡洛随机潮流方法

扩展蒙特卡洛方法将随机潮流的误差转化为可控量,并可在样本数增加时保留已知的潮流计算结果。基于扩展拉丁超立方抽样的方法效率比简单随机抽样高,但仍存在两方面的问题:第一,扩展拉丁超立方抽样无法保证序列的差异性,这成为计算效率提高的瓶颈;第二,当输出变量偏离正态分布时,扩展拉丁超立方抽样方法缺乏性能良好的收敛判据。针对以上两个问题,采用基于Sobol序列的扩展准蒙特卡洛方法进行随机潮流计算,并提出基于非参数核密度估计方法的收敛判据。对IEEE 30和IEEE 118节点系统的仿真结果表明,所述方法比扩展拉丁超立方抽样方法更加方便、准确,同时效率更高、收敛更快;而基于非参数核密度估计的收敛判据直观、适应性强,对变量的概率分布没有附加条件,可准确指导扩展随机潮流的收敛。

An Extended Quasi Monte Carlo Probabilistic Load Flow Method Based on Non-parametric Kernel Density Estimation

The extended Monte Carlo method is capable of translating the error in the probabilistic load flow into controllable parameters and retaining the power flow results already obtained with the sample size increased. The conventional method based on the Latin hypercube sampling is more efficient than simple random sampling, but still have two main drawbacks: firstly, the Latin hypercube sampling method is of low accuracy for its incapability of generating sampling sequences of low discrepancy, which constitutes the bottleneck of convergence; secondly, there is no suitable convergence criterion that can be adopted in the non-normal distribution scenarios. In order to overcome these two drawbacks, a probabilistic load flow method based on Sobol sequence is proposed. Furthermore, a convergence criterion based on non-parametric density estimator is employed. The simulation results on IEEE 30-bus system and IEEE 118 bus system demonstrate the validity of the proposed method. In contrast to the method based on Latin hypercube sampling, the proposed method is of high efficiency, accuracy and speed. And the adoption of the convergence criterion is more direct and flexible, and better able to guide the convergence in extended probabilistic load flow. This work is supported by State Key Program of National Natural Science Foundation of China (No. 51337005) and National Basic Research Program of China (973 Program) (No. 2014CB23903).