Weighted Least Absolute Value Research Articles

A robust crow search algorithm based power system state estimation

The State Estimation (SE) computational procedure plays a crucial role in modern electric power system security control by monitoring and analyzing operational conditions and predicting any emergency. In order to estimate state variables, Power System State Estimation (PSSE) takes into account the magnitudes and phases of voltage on each bus. To address the state estimation challenges in power systems, in this paper, we propose a novel application of the Crow Search Algorithm (CSA) specifically tailored for the state estimation problem. We have assessed the introduced algorithm using the frameworks of both the IEEE 14-bus and IEEE 30-bus test systems. The first formulation is the Weighted Least Square (WLS) method, and the second is the Weighted Least Absolute Value (WLAV) method, both of which are objective function formulations. By comparing the results, it is clear that CSA-based SE is superior to the other metaheuristic algorithms considered, namely Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Artificial Bee Swarm Optimization (ABSO). As a point of comparison, we use the Newton–Raphson method for calculating load flow. It has been shown that the proposed CSA-based SE technique has better accuracy than the other two algorithms in all different test systems. With this study, the power system is operated more accurately and reliably by the operators operating the system.

Load-flow dependent twofold technique of tolerance selection for robust estimation of power system states

Accurate estimation of the voltage magnitudes, angles, and other states of the modern power system is essential for efficient monitoring. The precision of the meter readings affects the estimating procedure. However, the majority of traditional meter readings are incorrect, and some of them, known as bad-data, are far from the true levels. The estimation performance significantly declines when such poor measurements are present, either singularly or in multiple numbers. Some estimators have post-processing capabilities but are unable to deal with flawed data directly. One of the well-known robust estimators that can weed out faulty data during the estimating process is Least Measurement Rejected (LMR). For each measurement in the LMR formulation, a tolerance value must be carefully chosen. The performance of the estimation can be greatly enhanced by the careful selection of these numbers. The use of load-flow to choose the LMR tolerance values is recommended in this paper to prepare a twofold estimation process of robust nature. Several tests and analysis were done to determine how well the suggested load flow dependent LMR (LFLMR) estimator performed. It is contrasted with well-known estimators from the literature, including Weighed Least Square (WLS), its robust counterpart (RWLS), Weighted Least Absolute Value (WLAV), Iteratively Reweighted Least Square (IRLS), and seven distinct versions of LMR. Additionally, several load profile snapshots are simulated to test the LFLMR's robustness. In order to illustrate the effectiveness of the suggested estimator and to identify and estimate the wrongly measured values of the measurement series, IEEE standard 14, 30, and 118-bus power systems with various outlier scenarios are simulated.

Development of electrical power transmission system linear hybrid state estimator based on circuit analysis techniques

Electrical power systems are in rapid evolution, necessitating advanced monitoring, control, and protection aspects connected to an accurate knowledge of the state of the grid. State estimation is one-way such knowledge could be achieved by estimating voltage magnitudes and phase angles at all buses in electrical networks. Electric utilities are deploying advanced Phasor Measurement Units (PMUs) in grids with conventional Remote Terminal Units (RTUs). Integrating measurements from the two types of devices for state estimation is inevitable. In the past, hybrid state estimators have been based on nonlinear models associated with various challenges, such as using nonlinear state estimation algorithms with high computational time, slow convergence, and initialization problems. For this reason, there is a need to develop hybrid linear mathematical models that eliminate issues posed by nonlinearity models. This paper presents a novel mathematical formulation that gives a linear measurement model for hybrid state estimation based on the standard steady-state branch model. The developed model is then tested in MATLAB using three standard transmission test cases (IEEE 14-BUS, IEEE 30-BUS, and IEEE 57-BUS) with available measurements subjected to different errors. Notably, the performance of the developed model based on two different state estimation algorithms, Weighted Least Square (WLS) and Weighted Least Absolute Value (WLAV), are compared. The simulation results obtained for voltage magnitudes and phase angles for all buses in the three scenarios compare well with reference values. Using Normalized Cumulative Error (NCE) as a performance index, the developed linear measurement model gives less cumulative error than the conventional nonlinear model. With measurements subjected to bad data (such as negative values for measured variables), the developed model performs better using WLAV than the WLS estimation algorithm. The computational time for all three networks is notably less when using the WLAV algorithm than the WLS algorithm.

Evaluating Performance of a Linear Hybrid State Estimator Utilizing Measurements From RTUs and Optimally Placed PMUs

Synchro-phasor technology, using Phasor Measurement Unit (PMU), has improved the way power system data is collected for monitoring through state estimation. The placement of PMUs in a power system presents technical benefits, but it comes with high infrastructural costs. It is, therefore, necessary to install the minimum number of PMUs at optimal locations subject to power system observability, creating the Optimal PMU Placement Problem (OPPP). Some factors may be considered constraints in the OPPP, such as PMU outage. The main challenge with incorporating such constraints in the PMU placement problem is that the minimum number of PMUs required for system observation increases, contributing to the high infrastructural costs. This paper, therefore, proposes using a Linear Hybrid State Estimator (LHSE) that considers existing Remote Terminal Unit (RTU) measurements randomly distributed within the system and optimally placed Phasor Measurement Unit (PMU) measurements. The proposed LHSE addresses challenges associated with nonlinearity in state estimation. The LHSE is also based on the Weighted Least Absolute Value (WLAV) criterion, considered robust and able to detect and discard bad data during the estimation process. The proposed LHSE can address state estimation reliability and resiliency, specifically the PMU outage contingency, by employing existing RTU measurements and optimally placed PMU measurements based on the Artificial Bee Colony (ABC) optimization technique. The proposed approach also leverages RTU and PMU measurements to address PMU loss contingency instead of utilizing PMU measurements only as in existing studies. Three test cases (IEEE 14 Bus, IEEE 30 Bus, and IEEE 57 Bus) are considered, with the simulations performed in MATLAB using MATPOWER data. The performance of LHSE is evaluated considering PMU/RTU measurements and PMU measurements only scenarios. Both RTU/PMU measurements present a lower Normalized Cumulative Error (NCE) performance index than PMU measurements only. In case of a single PMU outage, the proposed LHSE can estimate all states based on RTU/PMU measurements instead of only PMU measurements that fail.

Most Valuable Player Algorithm Based State Estimation for Energy Systems

State estimation (SE) processes the real-time measurements and provides database to energy control centre for safety control of energy systems. Traditionally Weighted Least Square (WLS) and Weighted Least Absolute Value (WLAV) based algorithms have been suggested for SE but the development of very fast computers and parallel processing enable the system engineers to think of employing the computationally inefficient evolutionary algorithms, which are known to be robust and stable, in solving SE problems. This paper suggests a most valuable player algorithm based SE involving WLS and WLAV objectives one at a time, and presents results on four IEEE test systems for illustrating its superiority.

Adaptive State Estimation for Power Systems Measured by PMUs With Unknown and Time-Varying Error Statistics

Measurement error is a crucial factor that determines the accuracy of state estimation (SE). Conventional estimators have fixed models, and can yield optimal performance only when the measurement error statistics exactly meet the assumptions. In reality, however, the error distribution is usually unknown and time-varying, resulting in suboptimal state estimates in most cases. This paper develops the concept of adaptive SE for power systems measured by phasor measurement units (PMUs). First, the Gaussian-Laplacian Mixture (GLM) model is developed to fit the body and tail of unknown measurement error distributions. Then, an adaptive estimation framework is proposed based on the Expectation-Maximization (EM) algorithm. It is capable of tracking the actual error statistics online, and adjusting the parameters of SE to maintain near-optimality of state estimates under complex measurement error conditions. Simulation results demonstrate that the proposed adaptive estimator yields more accurate state estimates than the well-known Weighted Least Squares (WLS) and Weighted Least Absolute Value (WLAV) estimators by adapting itself to the variations of measurement error statistics.

A bilinear robust state estimation method for electric thermal integrated energy system

A bilinear robust state estimation method for electric thermal integrated energy system (IEHS) is proposed. First, the linear weighted least absolute value (WLAV) model of IEHS is constructed by introducing auxiliary variables, and then the state variables are estimated by solving a quadratic programming model with a nonlinear transformation. The advantage of the proposed method is that it has a high calculation efficiency. The effectiveness of the proposed method is verified on the IEHS test system.

A robust WLAV state estimation based on pseudo‐voltage measurements

This paper presents a robust state estimation (SE) based on weighted least absolute value (WLAV) criterion for power systems having both traditional remote terminal units (RTU) and synchronizing phasor measurement units (PMU). It is known that WLAV‐based SE performs poorly when bad data occurred in leverage measurements. To improve the robustness of WLAV‐based SE, a technique for converting actual measurements to pseudo‐voltage measurements is proposed in this paper. Using these pseudo‐voltage measurements, a measurement model containing no leveraging measurement point can be formulated. The SE problem is formulated as a constrained nonlinear optimization based on WLAV criterion and solved by using a primal‐dual interior point algorithm. Several IEEE test systems with mixed measurements have been used to demonstrate the robustness of the proposed method. The results indicate that the proposed method yields superior SE accuracy even under extremely bad data conditions. © 2020 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Physics-guided Deep Learning for Power System State Estimation

In the past decade, dramatic progress has been made in the field of machine learning. This paper explores the possibility of applying deep learning in power system state estimation. Traditionally, physics-based models are used including weighted least square (WLS) or weighted least absolute value (WLAV). These models typically consider a single snapshot of the system without capturing temporal correlations of system states. In this paper, a physics-guided deep learning (PGDL) method is proposed. Specifically, inspired by autoencoders, deep neural networks (DNNs) are used to learn the temporal correlations. The estimated system states from DNNs are then checked against physics laws by running through a set of power flow equations. Hence, the proposed PGDL is both data-driven and physics-guided. The accuracy and robustness of the proposed PGDL method are compared with traditional methods in standard IEEE cases. Simulations show promising results and the applicability is further discussed.

Determination of harmonic current contributions based on robust state estimation

In this paper, a state estimation based method is proposed to determine harmonic current contributions of plants supplied from a point of common coupling (PCC). This work mainly aims to reduce gross error of capacitive voltage transformer (CVT) measurements at harmonic frequencies using robust weighted least absolute value (WLAV) state estimation method, which provides the optimum state estimates for harmonic voltages in the presence of a redundant enough measurement set. Estimated harmonic voltages are then used to solve the harmonic current contribution problem based on superposition theorem. It has been shown that the proposed method can provide optimum harmonic estimates when CVTs are used. The use of the proposed method with proper measurement placement makes resistive-capacitive voltage transformers (RCVTs) redundant. Results of the proposed method are comparable with measurements of RCVTs, which have the disadvantages of having high costs and being cumbersome to install.

Power system state estimation solution using modified models of PSO algorithm: Comparative study

Abstract The objective of all power system state estimation (PSSE) is to determine, by statistical projections, the best estimate of state variables represented by the voltage magnitudes and voltage angles of all the buses. Due to the complexity and non-linearity of the power system (PS), it is necessary to use more advanced methods for its analysis and control in real-time environment. This research discusses the application and the comparison of hybrid models of one of the algorithm using artificial intelligence (AI) technique (particle swarm optimisation ‘PSO’) in minimising the raw measurement errors in order to estimate the optimal point of the PS when certain sensitive data are incomplete. The effectiveness of the hybrid models are demonstrated and compared with the original PSO, artificial bee swarm optimisation (ABSO) algorithm and genetic algorithm (GA) using IEEE 14, 30, 118 and 300 bus test systems. Newton-Raphson load flow solution is taken as benchmark. Two different objective function formulations assessed by PSWV (Particle swarm without velocity equation), EPSOWP (Enhanced particle swarm optimiser incorporating a weighted particle), PSO-RF (PSO with repulsion factor) and CLPSO (Comprehensive learning PSO). The first formulation is the Weighted Least Square (WLS) and the second one is the Weighted Least Absolute Value (WLAV).

Simultaneous estimation of state variables and network topology for power system real-time modeling

A combined Weighted Least Squares (WLS) and Weighted Least Absolute Value (WLAV) strategy is proposed to devise a joint state and network topology (S&T) estimator for power system real-time modeling. This is accomplished by formulating S&T coestimation as a multi-objective optimization problem combining both analog measurement residuals and operational conditions dictated by circuit-breaker statuses. The former are treated as arguments of a conventional WLS function, whereas the latter exploits the selective properties of the LAV criterion. The paper presents the theoretical framework for S&T coestimation, and proposes a specialized primal/dual interior point method to solve the corresponding optimization problem. Results obtained by applying the joint estimator to the IEEE 24-bus test system and to a real metropolitan system in Southern Brazil are reported in the paper. They indicate that S&T coestimation is a very promising approach to provide simultaneous solutions to both real-time modeling problems.

Particle swarm optimization for power system state estimation

Abstract The electrical network measurements are usually sent to the control centers using specific communication protocols. However, these measurements contain uncertainties due to the meters and communication errors (noise), incomplete metering or unavailability of some of these measurements. The aim of state estimation is to estimate the state variables of the power system by minimizing all measurement errors available at the control center. In the past, many traditional algorithms, based on gradient approach, have been used for this purpose. This paper discusses the application of an artificial intelligence (AI) algorithm, the particle swarm optimization (PSO), to solve the state estimation problem within a power system. Two objective functions are formulated: the weighted least square (WLS) and weighted least absolute value (WLAV). The effectiveness of PSO over another AI optimization algorithm, genetic algorithm (GA), is shown by comparing both two solutions to the true state variable values obtained using Newton–Raphson (NR) algorithm.

Power System State Estimation with Weighted Linear Least Square

Power system state estimation with conventional method, Weighted Linear Least (WLS), is performed in two steps. In the first stage the obsevability of system is done and then is system is observed state estimation is carried out. Otherwise estimator is disrupted and is not able to estimate the states. The another estimator, Weighted least Absolute Value (WLAV) has presented which is able to estimate the system states in all situations but this estimator have auxiliary variable which reduces the convergence rate estimator. In this paper, a new method, Weighted Linear Least Square (WLLS), is proposed for power system state estimation. The proposed method, WLLS, has fewer variables than WLAV. The objective function of the proposed method is linear therefore this estimator is able to estimate the states in unobservability situations. Case studies on IEEE 14 bus system show WLLS has good accuracy and speed and is able to estimate the states in all conditions. DOI: http://dx.doi.org/10.11591/ijece.v4i2.5874

A Robust State Estimation Method Based on Exponential Weight Functions

State estimation of power system is the basis of all the high level application and analysis for dispatch centers. Against the bad convergence of the WLAV (weighted least absolute value)-based state estimation method, a new robust state estimation method based on exponential weight function (E-LAV) is presented in the paper. This method uses an exponential weight function to replace discontinues weight function of WLAV to improve the poor convergence. The results of the sample system of 4-node system and the IEEE 118-node system show that the E-LAV-based state estimation method not only owns the similar convergence as WLS-based method, and also owns a strong robustness. Through modifying the weight matrix of the least squares, the proposed new method has good prospects for application in practical engineering.

Weighted least absolute value power system state estimation using rectangular coordinates and equivalent measurement functions

AbstractThis paper presents a new efficient computation technique for robust power system state estimation based on weighted least absolute value (WLAV) criterion. The proposed method employs rectangular form of state variables and equivalent measurements technique in order to obtain the linear measurement functions with linear constraints of state variables. The state estimation problem is then formulated as an optimization problem with a set of equality and inequality constraints. A solution method based on interior point algorithm is also proposed. Tests with several IEEE standard systems have been performed to investigate the performance of the proposed algorithm. Results indicate that the proposed state estimator gives promising performance compared with weighted least square (WLS) based estimation algorithms using state variables in polar forms. © 2011 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Iteratively reweighted least-squares implementation of the WLAV state-estimation method

An implementation of the weighted least absolute value (WLAV) method for obtaining an estimate of the state of the power system is presented. Most of the known WLAV methods use some form of linear programming software to find the best estimate. The paper shows that it is possible to obtain a WLAV estimate by simply applying the Newton-Raphson method to the set of equations that yield the critical points. The resulting iterative scheme corresponds to solving a sequence of linear weighted least-squares (WLS) problems. The proposed implementation enables the use of well-known techniques of WLS estimation and, consequently, facilitates the integration of the WLAV function in an energy management system. Test results on standard IEEE test systems reveal that the proposed implementation is competitive with a standard WLAV algorithm that uses a state-of-the-art implementation of an interior-point method.

Iteratively re-weighted least absolute value method for state estimation

A modified version of the weighted least absolute value (WLAV) method for the solution of the power system-state-estimation problem is presented. The WLAV method can be seen as minimising a linear objective function subject to a set of nonlinear constraints. The modification is aimed at producing a WLAV estimator that remains insensitive to bad data, even if they are associated with leverage-point measurements. This is achieved by bending the linear objective function, so that the residuals of bad measurements are allowed to grow without incurring much additional cost in the objective function. Consequently, the optimisation procedure would find an optimal solution where the residuals of all bad measurements are nonzero. The optimisation is carried out via sequential linear programming. It is shown that each linear program corresponds to a linearised WLAV problem with weights adjusted automatically during the iterations. To ensure fast execution time, the linear program is solved using a homogeneous interior-point method. Computational results show that the proposed method can identify bad data in leverage points.

SHORT-TERM LOAD FORECASTING USING WEIGHTED LEAST ABSOLUTE VALUE FILTER

ABSTRACT This paper presents results of a new application of the weighted least absolute value (WLAV) minimization criterion in a dynamic estimation algorithm to the problem of short-term load forecasting in electric power systems. The results are compared with those obtained using Kalman filtering and with an adaptive general exponential smoothing algorithm

Use of scaling in WLAV estimation of power system states

The authors present the results of employing a particular scaling strategy in weighted least absolute value (WLAV) state estimation of various test systems of sizes as large as 1500 buses. Apart from the effects of scaling on the leverage points and the robustness of the estimator, effects on computational speed and the dependence of these effects on the measurement types are also investigated. Simulation results indicate that scaling not only helps to reduce the leveraging effects but also improves the computational performance by decreasing the required number of Simplex iterations.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>