Bayesian probability

Deep learning

Mathematics

Gene

Algorithm

Machine learning

Econometrics

Artificial intelligence

Bayesian inference

Chemistry

Computer science

Unobservable

Bayes estimator

Variable-order Bayesian network

Artificial neural network

Biochemistry

Robustness (evolution)

IEEE Transactions on Power Systems

The problem of state estimation for unobservable distribution systems is considered. A deep learning approach to Bayesian state estimation is proposed for real-time applications. The proposed technique consists of distribution learning of stochastic power injection, a Monte Carlo technique for the training of a deep neural network for state estimation, and a Bayesian bad-data detection and filtering algorithm. Structural characteristics of the deep neural networks are investigated. Simulations illustrate the accuracy of Bayesian state estimation for unobservable systems and demonstrate the benefit of employing a deep neural network. Numerical results show the robustness of Bayesian state estimation against modeling and estimation errors and the presence of bad and missing data. Comparing with pseudo-measurement techniques, direct Bayesian state estimation via deep learning neural network outperforms existing benchmarks.

Bayesian State Estimation for Unobservable Distribution Systems via Deep Learning