Data-Driven Learning-Based Optimization for Distribution System State Estimation

Abstract

Distribution system state estimation (DSSE) is a core task for monitoring and control of distribution networks. Widely used algorithms such as Gauss-Newton perform poorly with the limited number of measurements typically available for DSSE, often require many iterations to obtain reasonable results, and sometimes fail to converge. DSSE is a non-convex problem, and working with a limited number of measurements further aggravates the situation, as indeterminacy induces multiple global (in addition to local) minima. Gauss-Newton is also known to be sensitive to initialization. Hence, the situation is far from ideal. It is therefore natural to ask if there is a smart way of initializing Gauss-Newton that will avoid these DSSE-specific pitfalls. This paper proposes using historical or simulation-derived data to train a shallow neural network to 'learn to initialize' -that is, map the available measurements to a point in the neighborhood of the true latent states (network voltages), which is used to initialize Gauss-Newton. It is shown that this hybrid machine learning / optimization approach yields superior performance in terms of stability, accuracy, and runtime efficiency, compared to conventional optimization-only approaches. It is also shown that judicious design of the neural network training cost function helps to improve the overall DSSE performance. Index TermsDistribution network state estimation, phasor measurement units, machine learning, neural networks, Gauss-Newton, least squares approximation.

Physics-Aware Neural Networks for Distribution System State Estimation

“…The number of neurons representing each bus at the hidden layers is 48, 24, 12, and 6, respectively. Table II shows the average performance of the proposed physic-aware learning approach, the hybrid data-driven and optimization method [11] (SNN + G-N), and the Gauss-Newton (G-N) algorithm over 1000 cases of Scenario A. Simple feed-forward neural networks approaches require a lot of training data and computational resources.…”

“…It is often challenging to avoid exploding or vanishing gradients while training these feed-forward NNs, and thus the provided estimates are less accurate than any optimization-based approach. A joint optimization/learning approach was proposed in [11]. Since GN works very well when given a proper initialization, the key is to learn to initialize a Gauss-Newton solver.…”

Review of Learning-Assisted Power System Optimization

“…The supervised and transfer learning were applied in [41] to estimate the Pareto front that is made up with a series of initial values. This task was indeed more difficult than [38]- [40]. The numerical tests indicated that such estimation might cause large errors under specific conditions, so further validation and fine-tuning were extremely important.…”

Review of Learning-Assisted Power System Optimization

“…Many researches use machine learning approaches to estimate a good initial value, which is beneficial for a warmstart algorithm. Reference [38] proposed a "learn to initialize" strategy to improve the Gauss-Newton algorithm. The authors achieved this with a neural network, and designed a special loss function (only penalizing the maximized errors) to improve the overall performance.…”