Yang Weng

Semidefinite programming for power system state estimation

State Estimation (SE) plays a key role in power system operation and management. For AC power system state estimation, SE is usually formalized mathematically as a Weighted Least Square or Weighted Least Absolute Value problem, and solved by Newtons method. Although computationally tractable, Newtons method is highly sensitive to the initial point, as it is essentially a local search algorithm. In this paper, we propose a Semidefinite Programming (SDP) approach to effectively obtain a good initial state to improve the performance of the existing Newtons method. Our simulation results not only show that the SDP initial guess is much better than the currently used flat start on the IEEE standard bus systems, but also demonstrates approximately globally optimal results, with a lower bound provided in this paper.

Historical data-driven state estimation for electric power systems

This paper is motivated by major needs for accurate on-line state estimation (SE) in the emerging electrical energy systems; accurate state and topology are needed to support operators decisions as system conditions vary both during normal conditions for enhanced efficiency and during contingency conditions to ensure reliable operations. We propose a new SE method which is based on a combined use of informative historical data with the extended state space formulation for managing the nonlinear nature of AC power flow equations and related numerical problems. Specifically, the approach comprises two stages. First, based on historical data maximum-likelihood parameter estimation is conducted to update model parameters. The second stage utilizes these estimated model parameters and on-line measurements to estimate the state. Instead of using the extended Kalman Filter we are using a Kalman Filter in a model-based physically meaningful kernel feature space. This leads to ax two-stage Kalman Filter which can overcome problems created by the occasional missing data or data available at different rates (SCADA and PMU data); therefore, we claim that its performance is highly robust. This claim is confirmed by the simulation results performed for several IEEE test systems which show significant improvements over the performance of both the static SE with Newtons method and the extended Kalman Filter SE approach; once the parameters are learned, the computational time is smaller than the currently used SE, making it feasible in operations.

Outage Analysis of Block-Fading Gaussian Interference Channels

This paper considers the asymptotic behavior of the outage probability of a two-source block-fading single-antenna Gaussian interference channel in the high-SNR regime by means of the diversity-multiplexing tradeoff. A general setting where the user rates and the average channel gains are not restricted to be symmetric is investigated. This asymmetric scenario allows to analyze networks with “mixed” interference, i.e., when different sources are at different distance from their intended destination, that are not possible under the commonly used symmetric assumption. Inner and outer bounds for the diversity are derived. The outer bound is based on the recent “to within one bit” capacity result of Etkin for the unfaded Gaussian channel and is a re-derivation of a known bound for which an error is pointed out. The inner bound is based on the Han and Kobayashi achievable region both without rate splitting and with a rate spitting inspired by the “to within one bit” capacity result. An analytical comparison of the diversity upper and lower bounds for a general channel seems difficult; by numerical evaluations, the two bounds are shown to coincide for a fairly large set of channel parameters.

Graphical model for state estimation in electric power systems

This paper is motivated by major needs for fast and accurate on-line state estimation (SE) in the emerging electric energy systems, due to recent penetration of distributed green energy, distributed intelligence, and plug-in electric vehicles. Different from the traditional deterministic approach, this paper uses a probabilistic graphical model to account for these new uncertainties by efficient distributed state estimation. The proposed graphical model is able to discover and analyze unstructured information and it has been successfully deployed in statistical physics, computer vision, error control coding, and artificial intelligence. Specifically, this paper shows how to model the traditional power system state estimation problem in a probabilistic manner. Mature graphical model inference tools, such as belief propagation and variational belief propagation, are subsequently applied. Simulation results demonstrate better performance of SE over the traditional deterministic approach in terms of accuracy and computational time. Notably, the near-linear computational time of the proposed approach enables the scalability of state estimation which is crucial in the operation of future large-scale smart grid.

Robust Data-Driven State Estimation for Smart Grid

A grand challenge for state estimation in newly built smart grid lies in how to deal with the increasing uncertainties. To solve the problem, we propose a data-driven state estimation approach based on recent targeted investment on sensors, data storage, and computing devices. An architecture is proposed to use power system physics and pattern to systematically clean historical data and conduct supervised learning, where historical similar measurements and their states are used to learn the relationship between the current measurement and the state. In order to deal with nonlinearity, kernel trick is used to produce linear mapping in a carefully selected higher dimensional space. To speed up the data-driven approach for online services, we analyze power system data set and discover its clustering property due to the periodic pattern of power systems. This leads to significant dimension reduction and the idea of preorganizing data points in a tree structure for inquiry, leading to 1000 times speedup. Numerical results show that the proposed data-driven approach works well in a smart grid setting with increasing uncertainties and it produces an online state estimate excelling current industrial approach.

Probabilistic baseline estimation via Gaussian process

Demand response aims at utilizing flexible loads to operate power systems in an economically efficient way. A fundamental question in demand response is how to conduct a baseline estimation to deal with increasing uncertainties in power systems. Unfortunately, traditional baseline estimation lacks the ability to characterize uncertainties due to their deterministic modeling. This deficiency often results in erroneous system operations and miscalculated payments that discourage participating customers. In this paper, we propose a Gaussian process-based approach to mitigate the problem. It features the ability to use all historical data as a prior knowledge, and adjust the estimation according to similar daily patterns in the past. To characterize the uncertainties, this method provides a probabilistic estimate that can be used to not only increase estimation confidence for system operators but also to fairer treatment to customers. Finally, simulation results from Pacific Gas and Electric Company data show that this new method can produce a highly accurate estimate, which dramatically reduces the uncertainties inherent in the distribution power grid. Such a work opens the door for power system operation based on probabilistic estimate.

On the Han-Kobayashi achievable region for Gaussian interference channels

This work analyzes a particular achievable region for Gaussian interference channels (IFC) derived from the general Han-Kobayashi region. By reformulating the Han-Kobayashi achievable region as the sum of two sets, we characterize the maximum achievable sum-rate with Gaussian inputs and without time-sharing in closed from for any channel parameter. We then show that the computed sum-rate meets the upper bound by Kramer for any IFC with mixed interference, and not only for IFC with strong interference. We then show that for a certain subclass of IFCs with mixed interference, the capacity region contains a line segment of slope -1 of which we characterize the extreme points in term of the power allocation among private and common messages.

A search method for obtaining initial guesses for smart grid state estimation

AC power system state estimation process aims to produce a real-time “snapshot” model for the network. Therefore, a grand challenge to the newly built smart grid is how to “optimally” estimate the state with increasing uncertainties, such as intermittent wind power generation or inconsecutive vehicle charging. Mathematically, such estimation problems are usually formulated as Weighted Least Square (WLS) problems in literature. As the problems are nonconvex, current solvers, for instance the ones implementing the Newtons method, for these problems often achieve local optimum, rather than the much desired global optimum. Due to this local optimum issue, current estimators may lead to incorrect user power cut-offs or even costly blackouts in the volatile smart grid. To initialize the iterative solver, in this paper, we propose utilizing historical data as well as fast-growing computational power of Energy Management System, to efficiently obtain a good initial state. Specifically, kernel ridge regression is proposed in a Bayesian framework based on Nearest Neighbors search. Simulation results of the proposed method show that the new method produces an initial guess excelling current industrial approach.

Robust state-estimation procedure using a Least Trimmed Squares pre-processor

Based on real-time measurements, Static State Estimation serves as the foundation for monitoring and controlling the power grid. The popular weighted least squares with largest normalized residual removed, gives satisfactory performance when dealing with single or multiple uncorrelated bad data. However, when the bad data are correlated or bounded, this estimator has poor performance in detecting bad data, which leads to erroneous deleting of normal measurements. Similar to the Least Trimmed Squares(LTS) method of robust statistics, this paper considers a state estimator built on random sampling. However, different from previous robust estimators, which stop after estimation, we regard the LTS estimator as a pre-processor to detect bad data. A subsequent post-processor is employed to eliminate bad data and re-estimate the state. The new method has been tested on the IEEE standard power networks with random bad data insertions, showing improved performance over other proposed estimators.

Urban distribution grid topology reconstruction via Lasso

The growing integration of distributed energy resources (DERs) in urban areas raises various reliability issues. To ensure robust distribution grid operation, grid monitoring tools are needed, where the topology reconstruction serves as the first step. However, the topology reconstruction is hard in distribution grid. This is because 1) the branches are difficult and expensive to monitor since most of them are underground in urban areas; and 2) the assumption of radial topology in many studies is inappropriate for meshed urban grids. To address these drawbacks, we propose a new data-driven approach to reconstruct distribution grid topology by utilizing the newly available smart meter data. Specifically, a graphical model is built to model the probabilistic relationships among different voltage measurements. With proof, the topology reconstruction problem is formulated as a regularized linear regression problem (Lasso) to deal with meshed network structures. Simulation results show highly accurate estimation in IEEE standard distribution test systems with and without loops using real smart meter data.