This scientific paper presents a novel modified non-approximative method for instantaneously calculating state variables in a compact form. The method provides a direct solution in the discrete time domain, allowing for the specification of state variable values at any discrete time instant without requiring knowledge of previous variable values. This approach is useful for estimating voltage and current stresses of semiconductor elements and circulating energy within power electronic circuits, which is crucial for the correct design and operation of such systems. The paper utilized the z-transform with a long repetitive period to accelerate the calculation time and applies a method to solve the Steinmetz circuit using Matlab. The paper includes detailed simulations and a comparison of time consumption using both Euler implicit and the proposed direct non-approximative methods. Theoretical and simulation results were validated using Matlab/Simulink circuit simulator, demonstrating the effectiveness and efficiency of the proposed method.

This paper deals with the quasi-instantaneous determination (in a single-step response time) of apparent, active, and reactive (i.e., blind and distortion) power mean values including the total power factor, total harmonic distortion, and phase shift of fundamentals of a power electronic and electrical system (PEES) using the ip-iq method, which is the main contribution of the paper. The power components’ mean values are investigated during the transient and steady states. The power components’ mean values can be determined directly from phase current and voltage quantities, using an integral calculus over one period within the next calculation step and using moving average and moving rms techniques (or digital filtering). Consequently, the power factor can be evaluated with known values of a phase shift of fundamentals (using a Fourier analysis). The results of this study show how a distortion power component during transients is generated even under a harmonic supply and linear resistive–inductive load. The paper contains a theoretical base, modeling, and simulation for the three and single phases of the transients in power electronic systems. The worked-out results can be used to determine and size any PES. The presented approach brings a detailed time waveform verified by simulations in Matlab/Simulink 2022a and the Real-time HW Simulator Plecs RT Box 1.