The existing methods for estimating harmonic impedance usually assume that harmonic impedance is constant in a measurement period. However, for a variety of practical reasons, such as the load change of power grid, utility harmonic impedance may be changed. So a reasonable hypothesis is that utility harmonic impedance is time-varying, but the variation of the impedance is not large at adjacent sampling time. Thus, this paper proposes a novel method to estimate utility harmonic impedance by taking the criterion of minimum norm of impedance differences at adjacent sampling times with a measurement period. According to the proposed criterion, an objective function is built with the norm of the harmonic impedance differences and utility harmonic voltage differences of adjacent moments. And then, the utility harmonic impedance can be obtained by minimizing the objective function. The proposed method has high accuracy even while background harmonic emission level is high and harmonic impedance of customer side is not much larger than that of utility side. The effectiveness is verified by the simulation and field cases. In the simulation, the estimation errors of most cases are within 10% and the maximum error is not exceed 16%.

中文翻译：

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基于阻抗差最小范数的实用谐波阻抗估计研究

现有的估计谐波阻抗的方法通常假设谐波阻抗在一个测量周期内是恒定的。然而，由于各种实际原因，如电网负载变化，市电谐波阻抗可能会发生变化。所以一个合理的假设是公用事业谐波阻抗是随时间变化的，但在相邻采样时间阻抗的变化不大。因此，本文提出了一种新的方法，通过采用具有测量周期的相邻采样时间的阻抗差异的最小范数作为准则来估计公用事业谐波阻抗。根据提出的准则，以相邻时刻的谐波阻抗差和实用谐波电压差的范数构建目标函数。然后，可以通过最小化目标函数来获得实用谐波阻抗。即使在背景谐波发射水平较高且用户侧的谐波阻抗不大于公用侧的谐波阻抗时，所提出的方法也具有较高的准确度。通过仿真和现场案例验证了其有效性。在仿真中，大多数情况下的估计误差在10%以内，最大误差不超过16%。