TABLE OF CONTENTS The integration methods based on a truncated Taylor's series are prone to numerical oscillations when simulating step responses.
An interesting alternative to numerical integration substitution that has already proved its effectiveness in the control area, is the exponential form of the difference equation. The implementation of this method requires the use of root-matching techniques and is better known by that name.
The purpose of the root-matching method is to transfer correctly the poles and zeros from the s -plane to the z-plane, an important requirement for reliable digital simulation, to ensure that the difference equation is suitable to simulate the continuous process correctly.
This chapter describes the use of root-matching techniques in electromagnetic transient simulation and compares its performance with that of the conventional numerical integrator substitution method described in Chapter 4.
The application of the numerical integrator substitution method, and the trapezoidal rule, to a series RL branch produces the following difference equation for the branch:
| (5.1) |  |
Careful inspection of equation 5.1 shows that the first term is a first order approximation of e -x, where x = ?tR/ L and the second term is a first order approximation of (1 - e -x)/2 [1]. This suggests that the use of the exponential expressions in the difference equation should eliminate the truncation error and thus provide accurate and stable solutions regardless of the time step.
Equation 5.1 can be expressed as:
