Bayesian Inference of Parameters in Power System Dynamic Models Using Trajectory Sensitivities

We propose an analytically tractable Bayesian method to infer parameters in power system dynamic models from noisy measurements of bus-voltage magnitudes and frequencies as well as active- and reactive-power injections. The proposed method is computationally appealing as it bypasses the large number...

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Bibliographic Details
Published in:IEEE transactions on power systems 2022-03, Vol.37 (2), p.1253-1263
Main Authors: Nagi, Rubinder, Huan, Xun, Chen, Yu Christine
Format: Article
Language:English
Subjects:
Bayes factor
Bayes methods
Bayesian analysis
Bayesian inference
Bayesian model selection
Case studies
Computational modeling
Data models
Differential equations
dynamic model
Dynamic models
Linearization
Load modeling
Mathematical model
Nonlinear systems
parameter estimation
Parameter sensitivity
Sensitivity
Sensitivity analysis
Statistical inference
System effectiveness
Trajectory
trajectory sensitivities
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Summary:We propose an analytically tractable Bayesian method to infer parameters in power system dynamic models from noisy measurements of bus-voltage magnitudes and frequencies as well as active- and reactive-power injections. The proposed method is computationally appealing as it bypasses the large number of system model simulations typically required in sampling-based Bayesian inference. Instead, it relies on analytical linearization of the nonlinear system differential-algebraic-equation model enabled by trajectory sensitivities. Central to the proposed method is the construction of a linearized model with the maximum probability of being (closest to) the actual nonlinear model that gave rise to the measurement data. The linear model together with Gaussian prior leads to a conjugate family where the parameter posterior, model evidence, and their gradients can be computed in closed form, markedly improving scalability for large-scale power systems. We illustrate the effectiveness and key features of the proposed method with numerical case studies for a three-bus system. Algorithmic scalability is then demonstrated via case studies involving the New England 39-bus test system.
ISSN:0885-8950
1558-0679
DOI:10.1109/TPWRS.2021.3104536