Bayesian Probabilistic Power Flow Analysis Using Jacobian Approximate Bayesian Computation

A probabilistic power flow (PPF) study is an essential tool for the analysis and planning of a power system when specific variables are considered as random variables with particular probability distributions. The most widely used method for solving the PPF problem is Monte Carlo simulation (MCS). Although MCS is accurate for obtaining the uncertainty of the state variables, it is also computationally expensive, since it relies on repetitive deterministic power flow solutions. In this paper, we introduce a different perspective for the PPF problem. We frame the PPF as a probabilistic inference problem, and instead of repetitively solving optimization problems, we use Bayesian inference for computing posterior distributions over state variables. Additionally, we provide a likelihood-free method based on the Approximate Bayesian Computation philosophy, that incorporates the Jacobian computed from the power flow equations. Results in three different test systems show that the proposed methodologies are competitive alternatives for solving the PPF problem, and in some cases, they allow for reduction in computation time when compared to MCS

Physics-guided Residual Learning for Probabilistic Power Flow Analysis

Probabilistic power flow (PPF) analysis is critical to power system operation and planning. PPF aims at obtaining probabilistic descriptions of the state of the system with stochastic power injections (e.g., renewable power generation and load demands). Given power injection samples, numerical methods repeatedly run classic power flow (PF) solvers to find the voltage phasors. However, the computational burden is heavy due to many PF simulations. Recently, many data-driven based PF solvers have been proposed due to the availability of sufficient measurements. This paper proposes a novel neural network (NN) framework which can accurately approximate the non-linear AC-PF equations. The trained NN works as a rapid PF solver, significantly reducing the heavy computational burden in classic PPF analysis. Inspired by residual learning, we develop a fully connected linear layer between the input and output in the multilayer perceptron (MLP). To improve the NN training convergence, we propose three schemes to initialize the NN weights of the shortcut connection layer based on the physical characteristics of AC-PF equations. Specifically, two model-based methods require the knowledge of system topology and line parameters, while the purely data-driven method can work without power grid parameters. Numerical tests on five benchmark systems show that our proposed approaches achieve higher accuracy in estimating voltage phasors than existing methods. In addition, three meticulously designed initialization schemes help the NN training process converge faster, which is appealing under limited training time.Comment: Probabilistic power flow, data-driven, residual learning, neural network, physics-guided initializatio

Lightweight Probabilistic Deep Networks

Even though probabilistic treatments of neural networks have a long history, they have not found widespread use in practice. Sampling approaches are often too slow already for simple networks. The size of the inputs and the depth of typical CNN architectures in computer vision only compound this problem. Uncertainty in neural networks has thus been largely ignored in practice, despite the fact that it may provide important information about the reliability of predictions and the inner workings of the network. In this paper, we introduce two lightweight approaches to making supervised learning with probabilistic deep networks practical: First, we suggest probabilistic output layers for classification and regression that require only minimal changes to existing networks. Second, we employ assumed density filtering and show that activation uncertainties can be propagated in a practical fashion through the entire network, again with minor changes. Both probabilistic networks retain the predictive power of the deterministic counterpart, but yield uncertainties that correlate well with the empirical error induced by their predictions. Moreover, the robustness to adversarial examples is significantly increased.Comment: To appear at CVPR 201

Probabilistic load flow in systems with high wind power penetration

This paper proposes a method for solving a probabilistic load flows that takes into account the uncertainties of wind generation, but also of load and conventional systems. The method uses a combination of methods including cumulant, point estimate and convolution. Cornish Fisher expansion series are also used to find the CDF. The method is of especial application to estimate active power flows through lines

Randomized Dynamic Mode Decomposition

This paper presents a randomized algorithm for computing the near-optimal low-rank dynamic mode decomposition (DMD). Randomized algorithms are emerging techniques to compute low-rank matrix approximations at a fraction of the cost of deterministic algorithms, easing the computational challenges arising in the area of `big data'. The idea is to derive a small matrix from the high-dimensional data, which is then used to efficiently compute the dynamic modes and eigenvalues. The algorithm is presented in a modular probabilistic framework, and the approximation quality can be controlled via oversampling and power iterations. The effectiveness of the resulting randomized DMD algorithm is demonstrated on several benchmark examples of increasing complexity, providing an accurate and efficient approach to extract spatiotemporal coherent structures from big data in a framework that scales with the intrinsic rank of the data, rather than the ambient measurement dimension. For this work we assume that the dynamics of the problem under consideration is evolving on a low-dimensional subspace that is well characterized by a fast decaying singular value spectrum

Point estimate method for voltage unbalance evaluation in residential distribution networks with high penetration of small wind turbines

Voltage unbalance (VU) in residential distribution networks (RDNs) is mainly caused by load unbalance in three phases, resulting from network configuration and load-variations. The increasing penetration of distributed generation devices, such as small wind turbines (SWTs), and their uneven distribution over the three phases have introduced difficulties in evaluating possible VU. This paper aims to provide a three-phase probabilistic power flow method, point estimate method to evaluate the VU. This method, considering the randomness of load switching in customers’ homes and time-variation in wind speed, is shown to be capable of providing a global picture of a network’s VU degree so that it can be used for fast evaluation. Applying the 2m + 1 scheme of the proposed method to a generic UK distribution network shows that a balanced SWT penetration over three phases reduces the VU of a RDN. Greater unbalance in SWT penetration results in higher voltage unbalance factor (VUF), and cause VUF in excess of the UK statutory limit of 1.3%