Research On Taylor Series Algorithm Of Numerical Simulation For Power System Transient Stability

With the gradual formation of China's ultra-large-scale interconnected power system, it is a strong growing demand to analyze and calculate the power system transient stability. Since the higher-order Taylor series method was introduced for power system stability, the research of transient stability simulation using the Taylor series method was never interrupted. In this paper, based on the recursive calculation of the high-order derivatives of the power network, the transient simulation of Taylor series algorithm is studied to develop the aspects of the computing efficiency, numerical stability and etc.This paper investigates the high-order Taylor series solution of ordinary differential equations from the calculation of ordinary differential equations, purposes its conditions and disposal methods to form the higher derivative recursive formula. And on this basis, the author analyzes the power system electromechanical transient simulation and the recursive time derivatives rules of the power system state variables such as the angle of generators, which is the underlying reasons for obvious efficiency and high speed of Taylor series method. Have researched the high-order recursive rules of constant differential equations, the author provides a mathematical basis for the development of the fast high-order Taylor series method and further improves its theoretical system info for transient stability analysis.Have an in-depth research on the order selection of the algorithm design in order to improve the calculating efficiency of high-order Taylor series method for transient stability. The main computation of Taylor series method for transient stability analysis is concentrated in the higher-order derivative of the recursive calculation,therefore the highest Taylor series order plays an important role for the calculating efficiency.In this paper, the dynamic multi-dimensional control taylor series order has been approached. And the paper points out that the taylor series method can adopt different order for the various time constant sectors in accordance with transient stability simulation accuracy, in order to achieve maximum compression of redundant calculation in the calculating process and thereby enhance the computational efficiency. On the other hand, In order to fully use the information contained in higher derivatives of the earlier step, a method of explicit multi-step and multi-derivative integration transient stability calculation is proposed. The integral formula contains the higher derivative values of more than one time step, so the accuracy order of algorithm is improve by the multi-step information and the recursive calculation consumption of the derivatives in each time step is reduced correspondingly. The new multi-step method of transient stability calculation retains the advantages of the original Taylor series method such as fast, recursive, etc. The algorithm is simple and convenient to achieve by the design of the new integral formula. The new method can be used by combination with single-step Taylor series method, it is easy to shift from the two methods. Therefor, both the flexibility and the computational efficiency is achieved.Finally, the numerical stability of Taylor series method is studied. As a explicit algorithm, the numerical stability of Taylor series method is limited. In simulation of more than one swing or longer time period, the application of high-order Taylor series method has been confined. Based on the recursive system for calculating high-order derivatives in the Taylor series method and the integration formula of multi-step and high-order derivative, a new time-domain simulation algorithm is proposed with both high-order and large numerical stability region. Through the rational design of calculation parameters, the numerical stability region of the implicit Taylor series method proposed by this paper can contain the negative half-plane of the domain plane ofμ= hλ. According to Hmathematical model of transient stability calculation, the algorithm processes of implicit multi-step multi-derivative Taylor series method is presented.The implicit Taylor series method has accurate, rapid and simple recursive and easy programming advantages, while its numerical stability region can include the left half plane in the complex plane. The new method with the single-step and multi-step Taylor series method can be unified as a whole, which is an effective algorithm for time domain simulation.In this paper, the algorithm presented above is testified through numerical examples and the results are satisfactory. Through the time-domain simulation of transient stability of the Taylor series algorithm, the analysis of the electromechanical transient process of the power system is analysed from the angle of high-order derivatives of the power grid variables on the time; the computing efficiency of the transient stability simulation is improved by the design of dynamic order selection strategy and multi-step multi-derivative integration formula; and the application of the Taylor series algorithm is expanded by the implicit multi-step Taylor series method.