IEEE Transactions on Power Delivery · 2008 · 93 citations · 8 references
EngineeringComputational EngineeringElectrical EngineeringComputational ElectromagneticsElectromagneticsPower ElectronicsElectromagnetic PowerMaxwell's EquationsNumerical IntegrationNumerical Methods For Differential EquationsTime IntegrationTransient AnalysisCircuit Transient AnalysisElectromagnetic Transient SimulationElectromechanical TransientsNumerical Integration Methods For DynamicsNumerical Stability AnalysisPower System IntegrationStability Of Numerical SchemesTransient Electromagnetic Simulation
This paper proposes applying the two-stage diagonally implicit Runge-Kutta (2S-DIRK) method of numerical integration to the calculation of electromagnetic transients (EMTs) in a power system. The accuracy and the numerical stability of 2S-DIRK are almost the same as those of the trapezoidal method, while 2S-DIRK does not produce sustained numerical oscillation due to a sudden change of an inductor current or a capacitor voltage unlike the trapezoidal method. First, this paper reviews the 2S-DIRK integration scheme and derives the 2S-DIRK formulas of inductors and capacitors for both linear and nonlinear cases. Then, analytical comparisons of 2S-DIRK with the trapezoidal, backward Euler, and Gear-Shichman methods are carried out, and numerical examples which verify the analytical comparisons are shown. Finally, 2S-DIRK is compared with critical damping adjustment (CDA) implemented in electromagnetic transients program (EMTP) for some simulation cases.
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