| Time domain simulation is an important method to study the transient stability of power systems.The time domain simulation method mainly involves the numerical solution of differential-algebraic equations.At present,the most commonly used method for power system transient stability simulation is to first use the implicit trapezoidal method to discretize ordinary differential equations,and then use the quasi-Newton method to solve the nonlinear equations.This simulation method requires multiple iterations during each step of the integration process,so it consumes a lot of time in the application of large-scale power systems.In order to solve the above problems,this paper relies on the National Grid Corporation of Science and Technology Project Funding(XTB17201800225),and firstly applies the Kahan method to the calculation of power system transient stability,which is called the quadratic vector field method in this paper.Through theoretical analysis,Kahan method is a second-order,A-stable numerical calculation method.The Kahan method not only has the same computational accuracy and numerical stability as the implicit trapezoidal integration method.The transient stability simulation method based on Kahan method is linear implicit,and the integral of each time step can be calculated by solving a single linear system.This thesis uses the state variable dimension increase method to describe the electromechanical transient characteristics of the power system in the second differential algebraic system.The governor,exciter,voltage stabilizer(PSS)and other power system component models and algebra will be established using differential equations.The network equation established by the equation is transformed into the form of a quadratic vector field.Then the Kahan method is used to solve the nonlinear equations of differential-algebraic equations.Through the classical model and the detailed model of the 5-machine 18-node example and the IEEE145-node example,the implicit trapezoidal method is used as the contrast method to verify the quadratic vector field method.The simulation results show that under the same step size,the difference between the results of the quadratic vector field method and the implicit trapezoidal method is very small,that is,the calculation accuracy is the same;but the quadratic vector field method has a faster calculation speed,that is,a higher calculation efficiency.Therefore,the quadratic vector field method as a whole is a simple and reliable new implicit simultaneous solution method,which is suitable for the numerical calculation of power system transient stability and similar problems. |
