Study On Numerical Calculation Method Of Transient Stability Based On Compact Finite Difference Scheme

The transient stability analysis of the power system is described by a group of ordinary differential equations or a set of joint equations of ordinary differential equations and algebraic equations.These equations are often without analytical solutions,so finding a numerical method with good stability,high accuracy and fast computation is the main task of this paper.In this paper,two fast numerical methods are proposed based on the finite difference scheme,and are applied to the numerical calculation of power system transient stability.These two methods are respectively GBDF and ETR₂ that constructed methods in this paper.To sum up,from the construction of finite difference scheme to the fast numerical calculation method and the application of it to the transient stability calculation of power system,this paper is a theoretical deduction and a new process to put into practice.Using classic differential quadrature formulae and uniform grids,this paper systematically constructs a variety of high-order finite difference schemes,and some of these schemes are consistent with the so-called boundary value methods include GBDF GAMs and ETRs.The derived difference schemes enjoy the same stability and accuracy properties with correspondent differential quadrature method s but have more simple form of calculation,thus,they can be seen as a compact format of classic differential quadrature methods.Through systematic Fourier stability analysis,the characteristics such as the dissipation,dispersion and resolution for the different schemes has been studied and compared.Using Fourier stability analysis method,the characteristics such as the dissipation,dispersion and resolution for the different schemes ha ve been studied and compared.The proposed algorithm uses GBDF and ETR₂to carry on the continuous time discretization to the differential equations,and then uses the Newton method to solve the whole nonlinear system of the discretized nonlinear equations.Based on the band structure characteristic of the global Jacobian matrix,a special matrix equation split-combination technique is used to avoid the triangular factorization of the global Jacobian matrix or multiple block sub-matrices,thus to improve the efficiency of numerical calculation of transient stability.In this paper,the new fast numerical calculation method is applied to the numerical calculation of power system transient stability,and a new numerical method for transient stability is proposed.As a finite difference compact scheme,the GBDF method and the ETR2 method have the advantages of high order and good numerical stability.The new method proposed in this paper is simulated and verified by IEEE145 node system and Poland 2000 systems.