基于贝叶斯定理的系统谐波阻抗估计

Utility Harmonic Impedance Estimation Based on Bayes Theorem

提出了基于贝叶斯定理计算系统侧谐波阻抗的方法。首先根据最大熵原则,系统侧谐波阻抗的先验分布设为均匀分布;其次利用核密度估计获得停机时刻的真实背景谐波电压的概率分布,从而得到先验阻抗值对应的背景谐波电压条件概率;然后根据贝叶斯定理,利用已求得的条件概率修正先验分布,得到后验分布;最后以损失函数最小化为准则求得系统侧谐波阻抗。该文方法适用于任意背景谐波分布,且背景谐波干扰较大时,仍具有较高的准确性。此外,从概率的角度分析系统侧谐波阻抗,提出利用信息熵减量和可信区间宽度,为计算的可靠性评估提供依据。仿真分析和现场数据计算表明,该文方法具有有效性和准确性。

This paper proposed a method to calculate the utility harmonic impedance based on Bayes theorem. Firstly, according to the maximum entropy principle, prior distribution of utility harmonic impedance was a uniform distribution. Secondly, the real probability distribution of utility harmonic voltage at the downtime was estimated by kernel density estimation, thus conditional probability of utility harmonic voltage corresponding to the prior impedance was obtained. Thirdly, the posterior distribution was corrected from prior distribution by use of conditional probability on the basis of Bayes theorem. Finally, the utility harmonic impedance was calculated by minimizing the loss function. The proposed method is applicable to arbitrary background harmonic distribution and still accurate under large interference of background harmonic. In addition, the reliability of results was quantified by comentropy decrement and width of confidence interval from a probabilistic perspective. Based on analysis of simulation results and field test cases, it proves that the proposed method is effective and accurate.