Numerical Stability and Compensation Method for Equivalent Controlled Source in Electromagnetic Transient Simulation

In electromagnetic transient simulation, equivalent controlled source is usually used as an alternative of the original circuit element, such as a controlled voltage source to replace the modular multilevel converter(MMC). Since a time-step delay between the control and circuit system solution, there may be numerical stability problem. By deducing the delay differential equation and calculating its characteristic values, the causes of numerical instability are explained. Finally the numeric compensation method to solve the numerical stability problem is proposed by studying the delay function through Taylor's series and Laplace transformation.