基于广义柯西分布的系统侧谐波阻抗估计

An Assessment Method of Power System Harmonic Impedance Based on Generalized Cauchy Distribution

从波动量法的基本理论入手,研究波动量比值符号的概率统计特征,通过理论分析提出当谐波源受到多种随机因素影响时波动量比值的实部和虚部的概率密度服从广义柯西分布,并选取Pearson VII公式对此进行描述。然后,给出利用概率统计和非线性曲线拟合估计谐波阻抗的具体方法及步骤。进而分析影响波动量法误差的各种因素,推导理论误差表达式并提出修正误差的措施。与各类依赖判据进行数据过滤的方法相比,概率法的数据处理过程更为简便,具有较好的通用性、可靠性及抗干扰性,同时,概率法能更全面地分析波动量比值的概率统计特征,避免数据的误处理。蒙特卡洛仿真及实例应用分析验证了所提方法的有效性和实用性。

Starting from the basic theory of fluctuation method, this paper studied probability characteristics of the ratio of harmonic voltage fluctuation to harmonic current fluctuation. Through theoretical analysis, it was proved that the probability density of both real and imaginary part of the ratio follow the generalized Cauchy distribution if the harmonic source is affected by many random factors. So the Pearson VII formula was selected to describe the above distributions. An approach and its specific steps of using probability statistics and nonlinear curve-fitting were proposed to be used for estimation of power system harmonic impedances. Furthermore, this paper analyzed the factors affecting the estimated error of fluctuation method, and then gave out a set of error formulas and measured to reduce the error. Compared with the methods depending on data filtering strategies, the probability approach is more simple and convenient in data processing. And it has more advantages such as universality, reliability and noise immunity. Meanwhile, it can reduce failure rate of data processing by considering the probability characteristics in a wide perspective. Monte Carlo simulation and field test data analysis show that the proposed approach is practical and effective.