Research On Fast Numerical Calculation Methods Of Electromagnetic Transients In Power Systems

State space method and nodal analysis techniques are two basic methods of electromagnetic transient simulation.Among them,the nodal analysis method is the basis of electromagnetic transient programs(EMTP)and EMTP-type programs.The EMTP and its improved versions are quite mature and widely used for off-line simulation of electromagnetic transients in power systems.Currently,the EMTP-type programs face two problems,namely the numerical oscillation and lack of real-time.In view of these two specific problems,this paper uses several effective single or combined numerical methods with low-order or high-order and good numerical stability for electromagnetic transient simulation based on the state space method.In order to balance the accuracy and efficiency of electromagnetic transient simulation and suppress the numerical oscillation effectively,a three-step and fourth-order implicit Taylor series method is used for electromagnetic transient calculation in this paper.The method has A-stability and infinite stability,and its calculation accuracy is sixth-order,which has a fast decay rate to the truncation error and can effectively suppress the numerical oscillation.Considering that the three-step fourth-order implicit Taylor series method cannot completely avoid numerical oscillations from the origin of numerical oscillation,a new combined integration algorithm based on the new linear multistep formulae(LMF)for electromagnetic transient simulation is proposed.Inspired by the critical damping adjustment(CDA)method,this method uses two half-steps of three-step or four-step new LMF to perform numerical integration when experienced with sudden changes,and the implicit trapezoidal integration method is basically used.Whether EMTP-type programs or the new method above,they are essentially in serial computation mode.In order to further improve the efficiency of electromagnetic transient simulation in power systems,a new parallel-in-time algorithm for electromagnetic transient numerical simulation via matrix diagonalization or the real matrix eigenvalue decomposition is proposed based on the classical CDA method in strict mathematical sense.In addition,a coupled pseudospectral-differential quadrature method is proposed in this paper for high-precision and fast calculation of electromagnetic transient numerical simulation in transmission lines.In summary,from low-order to high-order numerical methods,this paper realizes the electromagnetic transient digital simulation from serial to parallel computation and proposes three new methods for electromagnetic transient simulations.Compared with the implicit trapezoidal integration method or the CDA method,the three methods proposed in this paper can solve the numerical oscillation or poor real-time problem in the existing electromagnetic transient simulation methods.And a coupled pseudospectral-differential quadrature method can improve the accuracy and efficiency of electromagnetic transients simulation for transmission line.The new methods proposed in this paper are expected to be further applied in practical engineering.