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To address the challenge of solving the zero-pole of transcendental equation for distributed power station with simultaneous consideration of two factors， i.e.， dq-axis coupling and line distribution parameter， an impedance model for distributed power station considering the two factors is established. This paper proposes a matrix-determinant zero-pole solution method for transcendental equation using Padé approximation and provides detailed steps for calculating the zero-pole distribution of the transfer function. Furthermore，it analyzes the impact of the two factors on harmonic instability analysis in the system under different scenarios. The research demonstrates that the proposed method can accurately analyze harmonic instability issues when these two factors are considered simultaneously. And ignoring one of the two factors may result in the misjudgment of stability， and considering the line distribution parameter is a necessary prerequisite for solving the amplification point of high-frequency harmonics. The effectiveness of the proposed method is verified by simulation.

The existing methods for evaluating voltage sag severity do not sufficiently consider the effect of the multiple line characteristic factors on the line failure probability, which leads to a large error in the evaluation results. Therefore, an evaluation method for voltage sag severity based on multiple line characteristic factors fusion is proposed. Firstly, based on line historical fault data, the influence degree of multiple line characteristic factors on line fault which employ association rules to quantify is researched. Secondly, by improving the D-S evidence theory to fuse multiple line characteristic factors, an accurate line annual failure probability model is established, and the voltage sag severity of nodes by introducing maximum entropy into the method of fault positions are obtained. Finally, a comprehensive voltage sag severity index considering both voltage sag severity of power grid side and tolerance characteristics of sensitive equipment on the user side is proposed to evaluate node voltage sag severity. Based on the actual power quality monitoring data for validation and comparison with the evaluation cases that do not fully consider the line characteristic factors, the results show that the proposed method can effectively improve the accuracy of voltage sag severity evaluation.

To calculate the harmonic impedance on the system side is crucial for the safe and stable operation of the new power system. Existing algorithms for harmonic impedance estimation usually assume that the harmonic impedance on the system side is constant during the measurement period. However, the voltage on the system side always changes according to the working mode of the power grid or access of large power load demand, resulting in fluctuations of the harmonic impedance on the system side. Luckly, the harmonic impedance on the system side does not change much in the adjacent sampling time interval. On this basis, the paper proposes a new non-intervention solution for the variable harmonic impedance on the system side. In this method, the second-order change of the harmonic impedance and the second-order change of voltage in the adjacent sampling time interval are taken as the objective function. The harmonic impedance on the system side is solved by minimizing the target function. The proposed method is proved to be accurate and reliable by simulation and practical analysis, especially in the condition that the strong background harmonic or user-side harmonic impedance is not much stronger than the harmonic impedance on the system side.

The adjacent interharmonic pairs or single adjacent interhamonic symmetrical to the fundamental/harmonic component can be caused by the large-scale grid connection of renewable energy. It is usually necessary to confirm the type of adjacent interharmonics to build an accurate calculation model when estimating the frequency components in electric signal. However, the spectrum leakage interferences caused by the grid frequency deviation makes that requirement hard to achieve. Towards the problem, an effective criterion to confirm the type of the adjacent interharmonics and an accurate estimation method of the harmonics and adjacent interharmonics based on the criterion even there is frequency deviation are proposed. Firstly, the spectrum leakage interferences are suppressed to obtain the adjacent interharmonic spectral lines by analysing the relationship of the frequency deviation and spectral lines. Then, the type criterion of the adjacent interharmonics is proposed by comparing the spectrum difference between each type of adjacent interharmonics. Finally, the spectral line equation for each type of adjacent interharmonics are constructed according to the confirmed type to accurately estimate the harmonics and adjacent interharmonics. Even there is frequency deviation, the type of the adjacent interharmnics can be confirmed accurately and a more precise estimation of the harmonics and adjacent interharmonics can be achieved with the proposed method. The accuracy of the proposed method is verified by the simulation.

The distributed parameter model of the transmission line is a necessary premise for accurately analysing the harmonic instability of the wind farm. However, when the model is used for harmonic instability analysis, it causes difficulties in solving the zero and pole distributions of the transcendental equation of the system. Given this, the impedance model of the wind farm considering the line distribution parameters is established and verified. Next, a method based on Pade approximation to solve the zero and pole distributions of the transcendental equation is proposed. The exponential function is approximated to the rational fraction only by selecting the order of the rational fraction, without fitting coefficients. Further, the influence of different transmission line models on the harmonic instability under different line lengths and grid strengths is analyzed. Finally, the effectiveness of the proposed method is verified by the simulation case. The results show that the effect of distribution parameters cannot be ignored, otherwise, it may lead to the inaccurate analysis of stability and deviation or even omission of harmonic amplification points in the high-frequency band. The proposed method can not only accurately evaluate the stability of the system, but also analyze the harmonic amplification points.

Accurate calculation of harmonic impedance is the premise of harmonic control and reasonable division of harmonic responsibility. The existing harmonic impedance estimation methods should meet the conditions that the background harmonic fluctuations are small and the customer harmonic impedance is much larger than the utility harmonic impedance. However, the use of a large number of power electronics in power system makes those conditions are not be satisfied. Therefore, a utility harmonic impedance estimation method based on mutual information and data optimization is proposed. Firstly, the utility harmonic currents are solved by independent component analysis (ICA), and the data segments with small mutual information between the harmonic currents at the point of common coupling (PCC) and the utility harmonic currents are selected. Finally, the harmonic impedance of the screened data segment is estimated using the characteristic of zero covariance between the harmonic current at the PCC and the harmonic voltage on the utility. The effectiveness of the proposed method is tested by simulation and actual case analysis. Compared with existing methods, the proposed method is more accurate and widely applicable when the customer harmonic impedance is not much larger than the utility harmonic impedance.

Estimation of harmonic impedances and harmonic contributions is beneficial to harmonic control, and harmonic phasors data is necessary for the existing estimation methods. However, the phase angles of harmonic phasors are not recorded in some of current power quality measuring instruments (such as Fluke 1760 etc.), which makes the existing methods unavailable. To solve this problem, the Norton equivalent circuit model under harmonic frequency is improved and a new model composed of harmonic complex power sources and harmonic impedances is proposed. Based on the model, the harmonic impedance and harmonic contribution can be estimated by using independent component analysis algorithm, and the harmonic phasor data is no longer required. The superiority of the proposed model is verified through simulation and field cases. [ABSTRACT FROM AUTHOR]