Multiscale simulation of frequency dependent line models and network equivalents

Abstract

The evaluation of power systems encompasses phenomenon of distinct timeframes and so leads to the adoption of different simulation tools. For instance, fast transients related to switching maneuvers require time-steps of microseconds while slow transients, related to energy exchange between generators, demand timesteps of milliseconds. However, the need to assess conditions where slow frequency oscillations might be combined with fast transients is becoming more common. This research evaluates the use of frequency dependent admittance-based models in the development of multiscale algorithms for phase-coordinate modeling of overhead lines, subsea cables and frequency dependent network equivalents. Unlike the modeling with the Method of Characteristics, the direct fitting of the nodal admittance matrix and two alternative schemes are considered to cope with the trade-off between time-step and traveling times, namely: the Folded Line Equivalent and Idempotent Decomposition. The concept of Latency is also addressed in a distinct way to provide more efficient realization frequency dependent models to allow the so-called multirate simulation. The major advantage of the designed models is the straightforward implementation in EMTP-like programs such as PSCAD, EMTP-RV and ATP since they attain the same Norton-type structure. In addition, dynamic phasors allowed the unification of electromagnetic and electromechanical modeling into a single model. Both numerical performance and accuracy of the proposed schemes are evaluated through several test cases. The Method of Characteristics and the Numerical Laplace Transform are used for comparison. The computational burden is considerably reduced without significant loss of accuracy and with no numerical oscillations or discontinuities in the waveforms.