Transient stability analysis is becoming increasingly important for power systems engineers and researchers. Accurate dynamic models are required, but aggregate load models are an area of weakness. Measurement-based system identification methods based on least-squares minimization have difficulty uniquely identifying the model parameters because the models exhibit parameter insensitivity and interdependency: vastly different model parameters can produce the same output waveform for a given disturbance. One could argue that the parameters of a model are unimportant, as long as the simulation output waveforms are correct. While this is true for the training set — the disturbance(s) we used to determine the parameters — we show that, when measurement noise exists, the model fails when we try to use it to predict the result of other disturbances. We present three methods for reducing the effect of parameter unidentifiability. First, we try increasing the size of the training data to include multiple disturbances, but this does not have a significant impact. Second, we present an algorithm based on a maximum a-posteriori (MAP) estimator, which can take advantage of prior knowledge of the parameters of the grid. The MAP estimator is both more accurate and more robust than least squares. Third, we make use of complex power measurements in addition to voltage. Complex power was found to be much more robust to noise, but many more monitoring devices would need to be deployed to provide the necessary measurements. We also consider the practical computational aspects of large-scale parameter estimation. We propose a geographical region of influence method to define zones where lower resolution models could be substituted to reduce the computational burden. We then investigate alternative metrics for defining the difference between two time series, because the Euclidean distance was shown to be inadequate.
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Improvements to power system dynamic load model parameter estimation