The existing methods estimating utility harmonic impedance usually require some assumptions such as the utility side is the dominant harmonic source and the harmonic impedance of customer side is much larger than that of the utility side, etc. However, these assumptions may not always hold in modern power grid. This paper proposes a novel method without any assumption, the estimation process only uses the correlation of the harmonic data measured at a point of common coupling (PCC). Through analysis of various field harmonic data, we find that measured data have short correlation characteristics, and there always exists a common weak correlation interval for the self-correlation and cross-correlation of the measured data. According to Norton equivalent circuit modal, it is easy to deduce that the utility harmonic current source is weak self-correlated in this interval. By selecting the self-correlation of the utility harmonic current source less than a small threshold, the utility harmonic impedance can be estimated accurately, whether the traditional assumptions are valid or not. In addition, the proposed method only requires a small sample size. Performance and effectiveness of the proposed method are verified through the simulation and field cases.

The traditional active power direction (APD) method has been proven to be unreliable to determine the dominant harmonic source at a point of common coupling (PCC), when both sides have the harmonic sources. In view of this shortcoming, this paper proposes an improved APD by imposing certain constraints to the traditional one. The constraints are developed based on the voltage and current measurements at the PCC and the impedance properties of the two sides. Through rigorous mathematical analysis, it has been proven that when those constraints are satisfied, the improved APD method is guaranteed to provide accurate results. Performance and effectiveness of the proposed method are demonstrated through simulation and field case verifications.

This article proposes a novel method for estimating multiharmonic sources in the underdetermined measurement system. In the proposed methodology, supposing that the number of harmonic measurements (HMs) is less than that of unknown state variables, the HM system can be mathematically described as underdetermined matrix equations, which has infinitely many solutions corresponding to all possibilities of the locations and the current emissions of the actual harmonic sources. Because the harmonic current emissions from nonharmonic source buses are approximately zero, by fitting the harmonic current emission of every possible nonharmonic source bus combinations and selecting the minimum fitting residual of all combination cases, thus, the true number, locations, and current emissions of harmonic sources are determined. Compared with the existing methods, the proposed method has less dependence on the placement of HMs and requires less prior information of harmonic sources. The effectiveness of the proposed method is verified by simulation and field case, with respect to a high correct location rate of more than 90%.

The existing noninvasive methods estimating utility harmonic impedance are usually based on the assumption that the impedance is constant during a time interval of concern. In fact, the utility harmonic impedance is variable due to various reasons such as possible short-circuit faults, grid operation changes, and capacitor switching. Thus, this paper proposes a novel method to estimate the variable utility harmonic impedance by minimizing the sum of the weighted impedance variations and the weighted variance of background harmonic voltage variations. The proposed method can track the continuous and abrupt changes of utility harmonic impedance. The effectiveness of the proposed method has been evaluated and verified through simulation and field cases.

For harmonic control of a power grid, it is prerequisite to accurately estimate and follow the utility harmonic impedance at the point of common coupling (PCC). The existing estimation methods generally consider that the utility harmonic impedance is constant, which causes the estimation error and fail in tracking of impedance fluctuations, since the utility harmonic impedance is fluctuant in practice. Actually, the harmonic impedance fluctuations will lead to the transient variation of the harmonic voltage and current which is bad for harmonic control. In this study, to follow the harmonic impedance fluctuations, a longer observation period is divided into a series of shorter period, and the fluctuations of the utility harmonic impedance over a short period are regarded as a stationary random process. Then, for each short period, the utility harmonic impedance is estimated by minimizing the fluctuation variance of the utility harmonic impedance. Besides the high estimation precision and good tracking performance of impedance fluctuations, other advantages of the proposed method are not limited by the traditional assumptions, such as the background harmonics are stable and small, the customer harmonic impedance is much larger than the utility, and the harmonic sources of both sides are independent, and so on.