基于Bootstrap的负荷模型的小样本不确定性分析

Small sample uncertainty analysis of load model based on Bootstrap

电力系统不确定性分析中常对实测数据或模型参数的总体分布做出假定。实际上,概率分布的选取会造成计算结果的差异,影响判断和决策的制定。结合Bootstrap法和随机响应面法,提出了根据小样本数据的总体分布特性快速计算不确定性的策略:首先利用Bootstrap法估计小样本数据的经验概率分布,然后再估计不确定性分析所需的统计量,最后采用随机响应面法快速定量计算服从经验概率分布的参数所引起的不确定性。由于Bootstrap法可将小样本问题转化为大样本问题来估计未知参数的近似分布,该策略可充分利用现场实测的小样本数据,客观估计小样本空间下输出响应的不确定性。

The population distributions of the measured data or parameters are usually assumed during uncertainty analysis in power systems. In fact, the different probability distributions can bring different uncertain results, which will impact on judgements and planning. Combined with the Bootstrap and the Stochastic Response Surface Method （SRSM）, this paper proposes a new solution to calculating uncertainty according to the population distributions of small samples. Firstly, the empirical probability distribution of small samples is estimated by the Bootstrap. Secondly, the statistics for uncertainty analysis are estimated. Finally, the SRSM is adopted to quantitatively analyze the uncertainty arising from parameters that obey the empirical probability distributions. Since the Bootstrap estimates the approximate distribution of unknown parameter by converting the small-sample problem into the large-sample issue, the proposed solution can make full use of the measured data and objectively estimate the simulation uncertainties under small samples space.