A harmonic instability analysis method for solving the zero and pole distributions of the transcendental equation

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.