Lissajous curve methods for the identification of nonlinear circuits: Calculation of a physical consistent reactive power

This paper presents a novel analysis of nonlinear circuits useful for the computation of the reactive power from only terminal measurements. The method computes the reactive power of unknown circuits based on the physical understanding of Maxwell equations. The proposed method is able to identify instantaneous quantities (circuit parameters, powers, etc.) for two physical equivalent models: series and parallel circuits. The parallel equivalent model shows advantages for multi-subsystems. Several numerical examples are provided for validation of the proposed method and to illustrate step-by-step the calculation details. To be compatible with digital instrumentation, a time discrete formulation is used for all calculations. All examples are simulated in MATLAB and the EMTP (Electro-Magnetic Transients Program).