An Adaptive Bayesian Parameter Estimation of a Synchronous Generator Under Gross Errors

• Published in: IEEE transactions on industrial informatics Vol. 16; no. 8; pp. 5088 - 5098
• Main Authors: Xu, Yijun, Mili, Lamine, Korkali, Mert, Chen, Xiao
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 01.08.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptation models; Bayes methods; Bayesian analysis; Bayesian approach; Conditional probability; Distribution functions; Gaussian distribution; generator parameter estimation; Generators; Importance sampling; importance sampling (IS); Iterative methods; Mathematical models; Measuring instruments; multifidelity surrogate; Parameter estimation; Parameter uncertainty; Phasor measurement units; polynomial chaos expansion (PCE); Polynomials; Power system dynamics; Probability density function; Probability distribution functions; Sampling methods; Statistical inference; Synchronous machines
• ISSN: 1551-3203; 1941-0050; 1941-0050
• DOI: 10.1109/TII.2019.2950238

Polynomial-chaos-expansion-based surrogate models have recently been advocated in the literature for power system dynamic parameter estimation. Regarding the estimation of the uncertain generator parameters, a Bayesian inference framework has been proposed based on a polynomial-based reduced-order representation of the synchronous machines using assumed parameter values. Then, the non-Gaussian posterior probability distribution functions (pdfs) of these parameters are recovered through the stochastic sampling approach efficiently. However, facing very large parameter errors, the reliability of the surrogate model decreases, yielding biased estimation results. To overcome this problem, this article develops a hierarchical Bayesian inference framework that processes the measurements provided by phasor measurement units, while making use of multifidelity surrogates together with the importance sampling method. The latter allows us to estimate in an efficient manner the posterior pdfs of the uncertain parameters through the normalized weights of the prior samples. To improve the accuracy of the posterior pdfs, an adaptive procedure is further adopted in the importance sampling for the gradual evolution of its proposal functions. The new proposals assist in fine-tuning the sample space and thereby help to construct surrogates with higher fidelity. Through an iterative process, this approach is able to estimate accurately and efficiently non-Gaussian posterior pdfs of the uncertain generator parameters subject to gross errors.