Using a Personal Computer to Teach Power System Transients

Because of the availability of low cost personal computers, students can use them as a computational tool in the study of power systems. This paper presents a technique for teaching power system transients using a personal computer. The technique allows the students to use their knowledge of network theory to develop a mathematical model for the power system. All components in the power system are represented by equivalent networks. For example, transmission lines are modeled by cascade connections of a finite number of pi-section segments. Each segment consists of a series resistance and inductance and a shunt conductance and capacitance. State equations are then formulated for the power system using the capacitor voltages and inductor currents as state variables. The result is a set of first-order, linear differential equations. Although the set is typically of high order, they are readily transformed to a set of linear difference equations by using trapezoidal integration. The resulting system of linear difference equations is quite manageable on the personal computer and the transient solution for system voltages and currents is readily obtained by linear algebra. Since this approach is based on network theory fundamentals, the modeling techniques can be taught to undergraduate students. The trapezoidal approach to the solution of the differential equations is intuitively appealing to undergraduates and may provide their first introduction to numerical integration. Therefore the student can develop the algebraic model and only needs a subroutine which solves a set of linear equations in order to obtain the transient solution.