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Transient Analysis Of Electrical Circuits Using Runge-Kutta Method

Transient analysis is an analysis of transient response of an electrical circuit. The purpose of transient analysis is to analyse the performance of an electrical circuit. Transient is a sudden application of source to a circuit or a brief increase in current or voltage in a circuit which cause damage to some sensitive components and instruments. Electrical transient phenomena can be generated due to some natural events and switching operations. In order to solve the transient analysis of electric circuit, numerical techniques for utilization in the companion analytical method of transient circuit analysis are used to solve second-order differential equations which generated from circuit equations of RLC circuit. The objective of this project is to solve the transient analysis of electric circuit using analytical method and Runge-Kutta method. Fourth-order Runge-Kutta method is chosen as the numerical method to solve transient analysis of electric circuit due to its high accuracy of approximations. In this project, transient analysis of RLC circuit is simulated using MATLAB and visualised in a graphical form. Next, the results of transient analysis obtained from analytical method and Runge-Kutta method are tabulated and analysed by using Microsoft Excel. Besides that, the aim of this project is to compare the transient analysis obtained form Runge-Kutta method with the analytical solution. There are two numerical simulations conducted in this project. First numerical simulation is to solve transient analysis of electric circuit on three different types of response which are underdamped response, critically damped response and overdamped response. Another numerical simulation is to solve transient analysis of a RLC circuit using different step sizes. The results obtained are analysed and compared in term of error in order to determine the accuracy of Fourth-order Runge-Kutta method. In the first simulation, Fourth-order Runge-Kutta method has a high degree of accuracy which is up to 99.99%. Besides, the accuracy of Fourth-order Runge-Kutta method can be improved as the time step size decimates. Fourth-order Runge-Kutta method provides an alternative solution for transient analysis of electrical circuits.