Approximate Analytical Solution and Analysis of Power System Swing Equation
This paper studies the approximate analytical solution of the power system swing equation under large disturbance.Firstly,based on the inherent sinusoidal coupling characteristics of the swing equation itself,a generalized polynomial matrix description of its perturbation form is provided using the Taylor expansion formula.Secondly,considering the different stage of power system when suffered disturbance,the approximate analytical solutions of the swing equation in fault and after fault are obtained by using linear system theory and regular perturbation technique respectively.Then,the structure of the approximate solution is analyzed,revealing the mathematical foundation of the characteristic of the stable motion of the power grid,and the monotonicity of the amplitude of rotor angle is demonstrated.Finally,numerical examples of IEEE 3-machine 9-bus system and IEEE 10-machine 39-bus system verify the effectiveness of the results in this paper.
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