A New Modified Non-Approximative Method for Dynamic Systems Direct Calculation

Abstract

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.

Keywords

• dynamical system
• numerical methods
• Laplace–Carson method
• Euler implicit method
• transient phenomena
• z-transformation