Least Absolute Value Estimator Research Articles

Leverage Point Identification Method for LAV-Based State Estimation

In this article we enunciate and rigorously demonstrate a new lemma which, based on a previously proposed theorem, proves the identifiability of leverage points in state estimation with specific reference to the least absolute value (LAV) estimator. In this context, we also propose an algorithm for the leverage point identification in LAV estimators whose performance is validated by means of extensive numerical simulations and compared against the well-known approach of projection statistics (PS). The obtained results confirm that the proposed method outperforms PS and represents a significant enhancement for LAV-based state estimators as it correctly identifies all the leverage points in the measurement set.

Robust and Scalable Power System State Estimation via Composite Optimization

In today's cyber-enabled smart grids, high penetration of uncertain renewables, purposeful manipulation of meter readings, and the need for wide-area situational awareness, call for fast, accurate, and robust power system state estimation. The least-absolute-value (LAV) estimator is known for its robustness relative to the weighted least-squares (WLS) one. However, due to nonconvexity and nonsmoothness, existing LAV solvers based on linear programming are typically slow, hence inadequate for real-time system monitoring. This paper develops two novel algorithms for efficient LAV estimation, which draw from recent advances in composite optimization. The first is a deterministic linear proximal scheme that handles a sequence of convex quadratic problems, each efficiently solvable either via off-the-shelf algorithms or through the alternating direction method of multipliers. Leveraging the sparse connectivity inherent to power networks, the second scheme is stochastic, and updates only \emph{a few} entries of the complex voltage state vector per iteration. In particular, when voltage magnitude and (re)active power flow measurements are used only, this number reduces to one or two, \emph{regardless of} the number of buses in the network. This computational complexity evidently scales well to large-size power systems. Furthermore, by carefully \emph{mini-batching} the voltage and power flow measurements, accelerated implementation of the stochastic iterations becomes possible. The developed algorithms are numerically evaluated using a variety of benchmark power networks. Simulated tests corroborate that improved robustness can be attained at comparable or markedly reduced computation times for medium- or large-size networks relative to the "workhorse" WLS-based Gauss-Newton iterations.

Optimum Placement of Phasor Measurement Units in Power Systems

In this paper, we proposed to evaluate the optimal phasor measurement unit (PMU) placement based on the sum of variance (SV) of the robust estimators. Variance is traditionally used as a measure of the quality of estimates. In this paper, after satisfying the requirements of the minimum number of PMUs, maximum measurement redundancy, and observability, the placements obtained are further distinguished on the basis of the variance of the estimated states. Both the weighted least squares (WLS) and robust estimators are considered. Examples on the IEEE 30-bus system using least absolute value (LAV) estimation are given. The covariance of the state estimates from the WLS can be calculated using the existing formulas. However, there is no equivalent formula for the robust LAV estimator. A formula is derived in this paper using influence function to approximately calculate the covariance matrix of the state estimates from the robust LAV estimator. The optimum placement, i.e., the placement with the smallest SV, can be selected.

A Decentralization Method for Hybrid State Estimators

Hybrid state estimation determines the states of systems monitored both by conventional SCADA measurements and PMUs. This paper proposes a decentralization method in order to improve the computational performance of hybrid state estimators with minimum loss of accuracy. The proposed method utilizes sensitivity matrix that relates measurement errors to state estimates in order to form the so-called isolated bus groups and observable subislands. Although the proposed decentralization method can be applied to any state estimator, the paper is developed using a least absolute value (LAV) estimator for demonstration purposes, which is known to be robust against bad data. The high computational burden of LAV estimator compared to the well-known weighted least squares estimator is eliminated, thanks to the proposed decentralization method.

Robust wide‐area impedance‐based fault location method utilising LAV estimator

This study presents a robust method for detecting the location of fault in the wide-area power networks considering the limited number of synchronised phasor measurement units. In this manner, by employing the positive-sequence components in the governing equations at pre- and post-fault occurrence, the fault location (FL) problem is formulated as an optimisation problem. The constructed objective function consists of two terms that are dependent on the voltage and current changes so that each of them can be employed in the optimisation procedure, alone. Various factors, such as cyber attacks and measurement device failures, may lead to induce the bad data to the measurement set, and thus the results will not be valid. Automatic detection and elimination of erroneous measurements, contaminated with gross errors, from the measurement set, will be carried out utilising the least absolute value (LAV) estimator. This is the most important property of the LAV estimator, in which the bad measurements will be screened and suppressed during the iterative optimisation. An algorithm based on LAV estimation is presented to identify the FL. The efficiency of the proposed method is not affected by fault type and resistance. The method is tested on IEEE 14-bus, 57-bus and 118-bus case studies and simulation results indicate the accuracy of the developed technique.

A Robust PMU Based Three-Phase State Estimator Using Modal Decoupling

Power systems do not always operate under fully balanced conditions because of unbalanced loads and untransposed transmission lines. Under such conditions, commonly used positive sequence equivalent will no longer be valid. On the other hand, use of full three-phase model will add significant computational burden for the considered application. This paper describes a simple approach to address this issue for the specific application of state estimation. The main idea is to exploit the linearity of the estimation problem when the system is measured solely by phasor measurements. The linear problem lends itself to decoupling via modal transformation unlike the nonlinear formulation with SCADA measurements. A further improvement is introduced via the use of the least absolute value (LAV) estimator, which has the desirable property of automatic bad-data rejection. The paper illustrates how a robust LAV estimator designed for a positive sequence model can be efficiently used for the solution of an unbalanced three-phase state estimation problem.

LAV Based Robust State Estimation for Systems Measured by PMUs

The weighted least squares (WLS) estimator is commonly employed to solve the state estimation problem in today's power systems, which are primarily measured by SCADA measurements, including bus power injection, branch power flow and bus voltage magnitude measurements. Despite being widely used, WLS estimator remains to be non-robust, i.e., it fails in the presence of bad measurements. The so called least absolute value (LAV) estimator is more robust, but is not widely used due to its higher computational cost. LAV estimator has the desirable property of automatic bad-data rejection provided that the measurement set does not include any “leverage measurements”. There will be two important advantages to using LAV estimator when systems are observed by phasor measurements: 1) if the measurement set consists of only phasors, the leveraging effect of measurements can be easily eliminated by strategic scaling; 2) computational performance of LAV estimator will become competitive with that of WLS due to the linearity of the estimation problem for phasor measurements. This paper demonstrates these advantages and argues that the LAV estimator will be a statistically robust and computationally competitive estimator for those power systems that will be measured entirely by PMUs.

Minimization of Wet End disturbances during web breaks using online LAV estimation

During a Wet End break, the loss of paper feed through the paper machine causes loss of sensory information and the remaining parts of the process are operated in open-loop. This causes the stock composition in the Headbox to deviate substantially from the nominal specifications, causing paper quality (after start up) and paper machine runability issues. In this work, the Base Sheet Ash measurement of the scanner is estimated using a least absolute value (LAV) model which can then be used for control of the chalk valve during the breaks to keep the Headbox Ash within specified limits. The model is computed using a very fast optimization algorithm which is able to compute the LAV solution using only basic elementary operations. The proposed approach has been developed for a UK paper mill.

Role of Fuzzy Sets in Power System State Estimation

This paper presents an enhancement to the least median of squares (LMS) estimation in the power system state estimation. A weighted least square estimation may be used in conjunction with LMS, yet LMS could face difficulties for eliminating bad data in specific cases. The proposed method, denoted as fuzzy LMS+LAV estimation, employs the applications of fuzzy sets to improve the accuracy of LMS. The proposed method applies the LMS method to determine the bounds of residuals and then applies fuzzy sets to the least absolute value (LAV) estimator to eliminate bad data. The paper shows that the proposed method produces more accurate estimate of power system states than that of LMS. The complementary advantages of fuzzy LAV and LMS estimators without lengthy computational efforts, which are targeted by this paper include: * less computational effort than the fuzzy LAV. * better accuracy than LMS. * same if not better robustness than both estimators. A qualitative comparison illustrates the superior robustness of the proposed method in the presence of leverage bad data.

Estimation and testing in least absolute value regression with serially correlated disturbances

Least absolute value (LAV) regression provides a robust alternative to least squares, particularly when the disturbances follow distributions that are nonnormal and subject to outliers. While inference in least squares estimation is well-understood, inferential procedures in the context of LAV estimation have not been studied as extensively, particularly in the presence of non-independent disturbances. In this work, we study three alternative significance test procedures in LAV regression, along with two approaches used to correct for serial correlation. The study is based on large-scale Monte Carlo simulations, and comparisons are made based on both observed significance levels and power.

Identifying the unknown circuit breaker statuses in power networks

This paper describes an approach by which the circuit breaker status errors can be detected and identified in the presence of analog measurement errors. This is accomplished by using the least absolute value (LAV) state estimation method and applying the previously suggested two stage estimation approach by A. Monticelli (see ibid., vol.8, no.3, p.1143-9, 1993). The ability of the LAV estimators to reject inconsistent measurements, is exploited in order to differentiate between circuit breaker status and analog measurement errors. The first stage of estimation uses a bus level network model as in conventional LAV estimators. Results of stage 1 are used to draw a set of suspect buses whose substation configurations may be erroneous. In the second stage, the identified buses are modeled in detail using the bus sections and the circuit breaker models while keeping the bus level network models for the rest of the system. The LAV estimation is repealed for the expanded system model and any remaining significant normalized residuals are flagged as bad analog measurements, while the correct topology is determined based on the estimated flows through the modeled circuit breakers in the substations. The proposed approach is implemented and tested. Simulation results for cases involving circuit breaker status and/or analog measurement errors are provided.

Forecasting in least absolute value regression with autocorrelated errors: a small-sample study

Least absolute value (LAV) regression is a robust alternative to ordinary least squares (OLS) and is particularly useful when model disturbances follow distributions that are nonnormal and subject to outliers. The performance of the OLS estimator when the disturbances are autocorrelated has been studied extensively, but the performance of the LAV estimator in the presence of serial correlation is less well established. In this research, we study the forecasting performances of OLS- and LAV-based models for simple time series regression when the errors are autocorrelated. Monte Carlo simulation methods are used to compare the forecasting accuracies of the different models. A least absolute value analogue of the Prais-Winsten correction possesses an appealing robustness for the context under consideration.

Stochastic frontier production analysis: Measuring performance of public telecommunications in 24 OECD countries

This study presents a new use of least absolute value (LAV) estimation for obtaining parameter estimates of a stochastic frontier production function. The LAV estimation is combined with data envelopment analysis (DEA) and the resulting DEA/LAV estimates are examined by several statistical tests. As an important application, this study applies DEA/LAV stochastic frontier production analysis for measuring and predicting the performance of public telecommunications in 24 OECD (Organization for Economic Cooperation and Development) countries. This international comparison may serve as an empirical basis for understanding the telecommunications industries whose environments are now shifting from regulation to competition.

An example showing that a new technique for LAV estimation breaks down in certain cases

An example is given that shows how, in certain situations, a recently proposed technique to approximate the least absolute value (LAV) estimates of the unknown parameters of a linear model will break down, even though a well defined, but not unique, solution to the standard LAV estimation problem exists. Even if breakdown does not occur, examples can be constructed that cast doubts on the ability of the above mentioned technique to approximate LAV estimates with full generality.

Parameter estimation in linear static systems based on weighted least-absolute value estimation

In this paper, we present a new method for estimating a parameter vector of which measurements are carried out; however, these measurements are subjected to noise. First, we briefly consider least-square estimation of such vector to obtain some well-known results. Then, we proceed to formulate the problem in the least-absolute value (LAV) sense and show that we can obtain a set of overdetermined equations for the components of the unknown vector. These equations are solved using the least-square approach to ascertain which points give the least residuals. Having gained that information, we set to zero a number of residuals equal to the rank of the matrixH. Let this rank bek; then, the number of points which satisfy the LAV solution identically isk; this is a requirement that the LAV solution must satisfy (Refs. 1, 2). Several examples are presented in the paper.