A network synthesis based approach for frequency dependent network equivalents

Abstract

Transient simulation of large electric power systems is resource-intensive and it is often prohibitive to model the entire network in the simulator. To save computational resources, only a part of the network is modelled in detail and the remainder is modelled as an equivalent from the point of connection. To derive this equivalent, a frequency scan of the network portion is obtained either through measurements made on the actual network or via measurements on a highly detailed simulation model; and stored as a table of frequency versus impedance (magnitude and phase). Such a model is called a Frequency Dependent Network Equivalent (FDNE). Using curve-fitting, the frequency scan is fitted by a rational function, which can then readily be converted into a time-domain simulation model. Using the FDNE instead of modelling a whole network in detail, greatly reduces the computer simulation time, which is critical, and reduces the cost of computing resources particularly in real-time simulators. One of the major challenges in the current state of the art in implementing FDNEs is that the fitted rational function is often not passive. In other words, the model generates energy in some ranges of frequencies which may lead to instability in the simulation.

In this work, a new method is explored to go directly from the frequency scan (tabulated function) to the time domain model without fitting the response by rational functions. In this technique, using network realization methods, an electric network made up of RLC branches and ideal transformers are used to fit the response while preserving the passivity of the network. Brune's realization method for the single-port network and Tellegen's extension for multi-port networks are adapted to implement numerically on tabulated functions. The most desirable feature of these techniques is that the realized network is always passive. So, unlike the current methods, there is no possibility whatsoever of violation of passivity in the resulted network.