TABLE OF CONTENTS A detailed representation of the complete power system is not a practical proposition in terms of computation requirements. In general only a relatively small part of the system needs to be modelled in detail, with the rest of the system represented by an appropriate equivalent. However, the use of an equivalent circuit based on the fundamental frequency short-circuit level is inadequate for transient simulation, due to the presence of other frequency components.
The development of an effective frequency-dependent model is based on the relationship that exists between the time and frequency domains. In the time domain the system impulse response is convolved with the input excitation. In the frequency domain the convolution becomes a multiplication; if the frequency response is represented correctly, the time domain solution will be accurate.
An effective equivalent must represent the external network behaviour over a range of frequencies. The required frequency range depends on the phenomena under investigation, and, hence, the likely frequencies involved.
The use of frequency dependent network equivalents (FDNE) dates back to the late 1960s [l] [3]. In these early models the external system was represented by an appropriate network of R, L, C components, their values chosen to ensure that the equivalent network had the same frequency response as the external system. These schemes can be implemented in existing transient programs with minimum change, but restrict the frequency response that can be represented. A more general equivalent, based on rational functions (in the s or z
