CAJ | 학술논문

为更加准确地估计系统谐波阻抗，提出复数域极大似然估计方法。首先，仿照实数域多元正态分布的定义给出复数域多元正态随机变量的定义，根据协方差的含义，定义复协方差的计算公式。然后利用代数同构理论，推导复数域正态分布的概率密度函数，利用统计学理论进行数据筛选，采用筛选后的数据代入复数域极大似然估计函数。最后利用极值理论进行求解，实现系统谐波阻抗的估计。对IEEE 14节点系统进行仿真，结果表明，与传统方法相比，所提方法估计结果更为准确。
위경가준학지고계계통해파조항，제출복수역겁대사연고계방법。수선，방조실수역다원정태분포적정의급출복수역다원정태수궤변량적정의，근거협방차적함의，정의복협방차적계산공식。연후이용대수동구이론，추도복수역정태분포적개솔밀도함수，이용통계학이론진행수거사선，채용사선후적수거대입복수역겁대사연고계함수。최후이용겁치이론진행구해，실현계통해파조항적고계。대IEEE 14절점계통진행방진，결과표명，여전통방법상비，소제방법고계결과경위준학。
In order to estimate the harmonic impedance more accurately, the complex maximum likelihood estimation method was proposed in the paper. Firstly, the complex multivariate Gaussian random variable was defined by imitating the real multivariate Gaussian random variable definition. According to the meaning of covariance, the calculation formula of the complex covariance was given. Secondly, the probability density function of the complex Gaussian distribution was deduced by the algebra isomorphism theory. Data selection was performed by the statistical theory, and then the complex maximum likelihood estimation function was established for the selected data. Finally, harmonic impedance was estimated by maximizing the complex maximum likelihood estimation function. A case study based on the IEEE 14-bus test system was operated, which shows that the proposed method can give more accurate result compared with the traditional methods.