Power System State Estimation Problem Research Articles

An Improved Power System State Estimation Using A Dynamically Adapted JAYA Algorithm

State estimation is a central issue for power systems monitoring and control. Applying state estimation schemes ensures the accuracy of system real-time monitoring process. Due to the high nonlinearities and non-smoothness of the dynamic behavior of power systems, state estimation is getting more importance to lessen the error margins. In order to find the best estimate of the various variables of a power system, optimization-based and statistical techniques are applied. Classically, common metering devices are used to measure power system variables. Nevertheless, these devices are associated with errors, especially with the ongoing expansion of the power networks. These errors are linked to many issues related to operation and communication processes besides the errors caused by the metering device itself. The commonly applied technique to solve the power system state estimation problem is the Weighted Least-Squares (WLS) method. In this paper a dynamically adapted algorithm is introduced employing a WLS-based dynamic JAYA optimization technique. The algorithm was validated and applied on the well-known IEEE 14-bus network. The results proved the efficiency and advantages of the proposed algorithm when compared to other methods used for the state estimation problem.

Evaluation of time series methods for distribution system state forecasting.

High proliferation of DERs in the distribution system necessitates forecasting ability for state estimator. A dynamic state estimation is a fundamental tool for realizing distribution system automation. Selection of appropriate methodological framework is an essential step before implementing dynamic state estimation. We applied Vector Error Correction Model (VECM), Random Forest and Long Short Term Memory Network (LSTM) time series models to dynamic power system state estimation problem and found out that the LSTM model outperforms the other two in prediction accuracy.

Power system state estimation using teaching learning-based optimization algorithm

The main goal of this paper is to formulate power system state estimation (SE) problem as a constrained nonlinear programming problem with various constraints and boundary limits on the state variables. SE forms the heart of entire real time control of any power system. In real time environment, the state estimator consists of various modules like observability analysis, network topology processing, SE and bad data processing. The SE problem formulated in this work is solved using teaching leaning-based optimization (TLBO) technique. Difference between the proposed TLBO and the conventional optimization algorithms is that TLBO gives global optimum solution for the present problem. To show the suitability of TLBO for solving SE problem, IEEE 14 bus test system has been selected in this work. The results obtained with TLBO are also compared with conventional weighted least square (WLS) technique and evolutionary based particle swarm optimization (PSO) technique.

Artificial fish swarm optimization algorithm for power system state estimation

In this paper, the power system state estimation (SE) problem is formulated as a general non-linear programming problem with equality constraints and boundary limits on the state variables. The proposed SE problem is solved using an evolutionary based Artificial Fish Swarm Optimization Algorithm (AFSOA). The AFSOA is a global search algorithm based on the characteristics of fish swarm and its autonomous model. The detailed algorithm with its flow chart is presented in this paper. To show the effectiveness of the proposed SE approach, six bus test system is considered. The obtained results are compared with other algorithms reported in the literature.

Real-time equality-constrained hybrid state estimation in complex variables

The hybrid power system state estimation problem requires computing the state of the power network using data from both legacy and phasor measurements. Recent research has shown that the normal equations approach in complex variables is computationally advantageous, particularly in the presence of phasor measurement values, and that its software implementation is best suited to modern processors that employ single instruction multiple data (SIMD) processor extensions. The complex normal equations approach is however not ideal for handling zero injection measurements, as it requires their modeling as virtual measurements with high weights. This paper employs Wirtinger calculus for extending the complex normal equations approach to include equality constraints, and contrasts it with two previously published implementations: the normal equations approach in complex variables and the hybrid equality constrained state estimator in real variables. Numerical results are reported on transmission networks having up to 9241 nodes; they show that the complex variable equality constrained hybrid state estimator exhibits superior performance as compared to the above two techniques in terms of both computational time and accuracy. Moreover, the execution time on the largest network is less than 300 ms, which makes the proposed implementation commensurate with the requirements of real-time applications.

Artificial Bee Colony based Static State Estimation for Power Systems

This paper applies an artificial bee colony (ABC) based optimization, inspired from the foraging behavior of honey bees in searching foods, in solving the power system state estimation problem. The method does not require computation of Jacobian matrices but involves simply calculation of the objective function. In this approach each probable solution is represented by the position of food source. The proposed algorithm (PA) has been applied on IEEE-6, -14, -30 and -57 bus test systems and results are presented to exhibit its superiority in applying it in energy management systems.

Spurious Local Minima in Power System State Estimation

The power system state estimation problem computes the set of complex voltage phasors given quadratic measurements using nonlinear least squares. This is a nonconvex optimization problem, so even in the absence of measurement errors, local search algorithms like Newton/Gauss–Newton can become “stuck” at local minima, which correspond to nonsensical estimations. In this paper, we observe that local minima cease to be an issue as redundant measurements are added. Posing state estimation as an instance of the low-rank matrix recovery problem, we derive a bound for the distance between the true solution and the nearest spurious local minimum. We use the bound to show that spurious local minima of the nonconvex least-squares objective become far-away from the true solution with the addition of redundant information.

Convexification of Power Flow Equations in the Presence of Noisy Measurements

This paper is concerned with the power system state estimation (PSSE) problem that aims to find the unknown operating point of a power network based on a given set of measurements. We first study the power flow (PF) problem as an important special case of PSSE. PF is known to be nonconvex and NP-hard in the worst case. To this end, we propose a set of semidefinite programs (SDPs) with the property that they all solve the PF problem as long as the voltage angles are relatively small. Associated with each SDP, we explicitly characterize the set of all the complex voltages that can be recovered via that convex problem. As a generalization, the design of an SDP problem that recovers multiple nominal points and a neighborhood around each point is also cast as a convex program. The results are, then, extended to the PSSE problem, where the measurements used in the PF problem are subject to noise. A two-term objective function is employed for each convex program developed for the PSSE problem: 1) the first term accounting for the nonconvexity of the PF equations and 2) other one for estimating the noise levels. An upper bound on the estimation error is derived with respect to the noise level, and the proposed techniques are demonstrated on multiple test systems, including a 9241-bus European network. Although the focus of this paper is on power networks, yet the developed results apply to every arbitrary state estimation problem with quadratic measurement equations.

Enhancing Observability in Distribution Grids Using Smart Meter Data

Due to limited instrumentation, distribution grids are currently challenged by observability issues. On the other hand, smart meter data are communicated to utility operators from nodes with renewable generation and elastic demand. This paper employs grid data from metered buses toward inferring the underlying grid state. System nodes are partitioned into buses with time-varying injections that are assumed metered, and buses with relatively stationary conventional loads that are non-metered. Exploiting the variability at metered buses and the stationarity of conventional loads, the novel idea here is to solve the non-linear power flow (PF) equations jointly over consecutive time instants. By putting forth a coupled formulation of the PF problem (CPF), grid states can be recovered by metering fewer buses. An intuitive and easily verifiable rule pertaining to the locations of (non-)metered buses on the physical grid is shown to be a necessary and sufficient criterion for local observability in radial networks. To account for noisy smart meter readings, a coupled power system state estimation (CPSSE) problem is further devised. Both CPF and CPSSE tasks are tackled via augmented semi-definite program relaxations. The observability criterion along with the CPF and CPSSE solvers are numerically corroborated using randomly generated and actual solar and load data on the IEEE 34-bus benchmark feeder.

Conic Relaxations for Power System State Estimation With Line Measurements

This paper deals with the nonconvex power system state estimation (PSSE) problem, which plays a central role in the monitoring and operation of electric power networks. Given a set of noisy measurements, PSSE aims at estimating the vector of complex voltages at all buses of the network. This is a challenging task due to the inherent nonlinearity of power flows (PFs), for which the existing methods lack guaranteed convergence and theoretical analysis. Motivated by these limitations, we propose a novel convexification framework for the PSSE problem using semidefinite programming (SDP) and second-order cone programming (SOCP) relaxations. We first study a related PF problem as the noiseless counterpart, which is cast as a constrained minimization program by adding a suitably designed objective function. We study the performance of the proposed framework in the case where the set of measurements includes: 1) nodal voltage magnitudes and 2) branch active PFs over at least a spanning tree of the network. It is shown that the SDP and SOCP relaxations both recover the true PF solution as long as the voltage angle difference across each line of the network is not too large (e.g., less than $90^{\circ }$ for lossless networks). By capitalizing on this result, penalized SDP and SOCP problems are designed to solve the PSSE, where a penalty based on the weighted least absolute value is incorporated for fitting noisy measurements with possible bad data. Strong theoretical results are derived to quantify the optimal solution of the penalized SDP problem, which is shown to possess a dominant rank-one component formed by lifting the true voltage vector. An upper bound on the estimation error is also derived as a function of the noise power, which decreases exponentially fast as the number of measurements increases. Numerical results on benchmark systems, including a 9241-bus European system, are reported to corroborate the merits of the proposed convexification framework.

Extending the common information model for smart grids operational computations based on bus-branch models

In the modern smart grids (SGs), the heterogeneity of elements makes their interoperability difficult. In order to facilitate the integration and the interaction between different types of elements, the International Electrotechnical Commission (IEC) has introduced some standards (e.g., CIM, SCL), aimed at defining a common language for the communication among the different elements of a power system. However, without a harmonisation of these standards, the development and the implementation of systems and applications will result in a noticeable amount of single engineering design schemes. An ontology-based approach could collect knowledge from different applications, bridging the gap of harmonisation among such models. This paper deals with the implementation of a CIM ontology based on a bus-branch model that aims to support the power system state estimation problem. Resulting ontology has been instantiated by using a case study on a real power flow problem and evaluated by applying some well-known metrics.

Extending the common information model for smart grids operational computations based on bus-branch models

In the modern smart grids (SGs), the heterogeneity of elements makes their interoperability difficult. In order to facilitate the integration and the interaction between different types of elements, the International Electrotechnical Commission (IEC) has introduced some standards (e.g., CIM, SCL), aimed at defining a common language for the communication among the different elements of a power system. However, without a harmonisation of these standards, the development and the implementation of systems and applications will result in a noticeable amount of single engineering design schemes. An ontology-based approach could collect knowledge from different applications, bridging the gap of harmonisation among such models. This paper deals with the implementation of a CIM ontology based on a bus-branch model that aims to support the power system state estimation problem. Resulting ontology has been instantiated by using a case study on a real power flow problem and evaluated by applying some well-known metrics.

Power System State Estimation via Feasible Point Pursuit: Algorithms and Cramér-Rao Bound

Accurately monitoring the system's operating point is central to the reliable and economic operation of an electric power grid. Power system state estimation (PSSE) aims to obtain complete voltage magnitude and angle information at each bus given a number of system variables at selected buses and lines. Power flow analysis is a special case of PSSE, and amounts to solving a set of noise-free power flow equations. Physical laws dictate quadratic relationships between available quantities and unknown voltages, rendering general instances of power flow and PSSE nonconvex and NP-hard. Past approaches are largely based on gradient-type iterative procedures or semidefinite relaxation (SDR). Due to nonconvexity, the solution obtained via gradient-type schemes depends on initialization, while SDR methods do not perform as desired in challenging scenarios. This paper puts forth novel \emph{feasible point pursuit} (FPP)-based solvers for power flow and PSSE, which iteratively seek feasible solutions for a nonconvex quadratically constrained quadratic programming (QCQP) reformulation of the weighted least-squares (WLS) problem. Relative to the prior art, the developed solvers offer superior performance at the cost of higher complexity. Furthermore, they converge to a stationary point of the WLS problem. As a baseline for comparing different estimators, the Cram{\' e}r-Rao lower bound (CRLB) is derived for the fundamental PSSE problem in this paper. Judicious numerical tests on several IEEE benchmark systems showcase markedly improved performance of our FPP-based solvers for both power flow and PSSE tasks over popular WLS-based Gauss-Newton iterations and SDR approaches.

Power system static state estimation using a least winsorized square robust estimator

State estimation is the heart of the energy management system, primarily used for control and monitoring of electrical power systems. Commonly used conventional weighted least square estimator is not reliable, particularly in the presence of bad data. Subsequently, bad data processing techniques have been developed to detect, identify, and eliminate the bad data present in the measurement set. In the present paper, a robust least winsorized square (LWS) estimator is proposed for the power system static state estimation. One of the main advantages of this estimator is that it has an inbuilt outlier rejection property and is less sensitive to bad data (outliers) measurements. The power system state estimation problem has been solved as an optimisation problem using the jDE-self adaptive differential evolution algorithm. The proposed approach has been implemented and tested on standard IEEE test systems. The effectiveness of the LWS estimator has been demonstrated under different operating conditions, namely, normal operating condition, bad data condition, different operating points, different measurement condition, under the ill-conditioned system, and the presence of false data injection. The performance of the proposed approach has been compared with the conventional and the evolutionary based state estimation techniques. Based on the various performance indices, the results thus obtained show that the proposed technique has better accuracy, robustness, and reliability compared to the results obtained using conventional and evolutionary based state estimation techniques.

Hybrid power system state estimation using Taguchi differential evolution algorithm

Hybridising of different optimisation techniques provides a scope to improve global exploration capability of the resulting method. In this study, an enhanced differential evolution (DE) algorithm, called hybrid Taguchi-differential evolution (TDE) algorithm is proposed to solve power system state estimation problem as an optimisation problem. TDE combines the positive properties of the Taguchi's method to the classical DE algorithm for improving the accuracy and reliability of state estimation problem. The systematic reasoning ability of the Taguchi method is incorporated after crossover operation of DE algorithm to obtain the potential chromosome, better convergence rate and subsequently, to improve the robustness of the results. The proposed method is tested on IEEE test bus systems along with two ill-conditioned systems under different simulated conditions. The results reveal that solutions yield towards global optimum and it compares far better than conventional DE, particle swarm optimisation, gravitational search algorithm and weighted least square based state estimation techniques in terms of optimisation performance, solution quality and the statistical error analysis.

Gain Matrix Distributed Computing Technique for Power System State Estimation

The Electric Power System State Estimation problem involves large sparse matrices. The Jacobian matrix is highly sparse in nature and the computational efforts can be enhanced by avoiding arithmetic operations resulting in ‘zero’. The researchers have introduced sparse matrix techniques so as to store only non-zero elements of the matrix and thereby reducing the huge dynamic memory requirements, which intern reduce the computational time. A few such techniques [2],[3], [4] are listed in the reference. The primary focuses of these sparse techniques are on the memory/storage space reduction. This paper elaborates a different technique to obtain the “effective operation” with the focus on the computational time and the storage space reduction. The “effective operation” can be achieved without applying conventional compact storage techniques to find the Jacobian product. A different style for multiplication of two large sparse Jacobian matrices is adopted to obtain this novel approach. As a result, computational time is reduced and also Jacobian array size is reduced form two dimensional array to single dimensional array. The solution gives scope for distributed/parallel computing without disturbing the network structure [6].

Impact of Transformer Correlations in State Estimation Using the Unscented Transformation

This paper addresses the power system state estimation problem considering the correlations among instrument transformer signals. The correlations among processed measurements are estimated using the Unscented Transformation given the correlation and basic statistical information of internal measurements. In addition, the paper analyzes the impact of these correlations on the estimated states using the IEEE 118-bus test system under various operating conditions and measurement configurations.

Decomposition-Coordination Model and Algorithm for Parallel Calculation of Power System State Estimation Problem

Power system state estimation is the process of computing a reliable estimate of the system state vector composed of bus voltages’ magnitudes and angles from telemetered measurements on the system. This estimate of the state vector provides the description of the system necessary for operation, security monitoring and control. Many methods are described in literature for solving the state estimation problem, the most important of which are the classical weighted least squares and the non-quadratic method. However, both showed drawbacks when it comes to application to large-scale power system networks. In this paper, a new method in the name of decomposition-coordination approach using the weighted least squares is introduced in solving the large-scale power system state estimation problem. The estimation criterion is reformulated; voltage measurement, real and reactive power injections, real and reactive power flows, and real and reactive power flows in tie-line models of a decomposed system are developed. Two level structure of solving the estimation problem is introduced. The first level solves the sub-problem using gradient procedure methods while the second level determines the interconnection variables using predictive method. The positive characteristic of the method is that the coordinator has little work of predicting interconnection variables instead of solving the state estimation problem. The method can be used to solve a multi-area state estimation using parallel or distributed processing architectures.

Simultaneous identification and correction of measurement and branch parameter errors

The performance of the state estimation (SE) depends on the accuracy of the received measured data, as well as the parameter data of the power system. In this paper, a new algorithm is proposed for the simultaneous identification and correction of measurement and branch parameter errors (series and shunt admittances) in the power system SE problem. The proposed method uses Lagrange multipliers for the identification and correction of branch parameter errors without the need for a-priori specification of suspect parameter vectors. Erroneous measurements and branch parameter values can be corrected using the proposed method to estimate the measurement and branch parameter errors. Finally, IEEE 14-, 30-, and 57-bus test systems are used to show the validity and robustness of the proposed algorithm. Single, multiple, and simultaneous errors in the conventional measurements and branch parameters are considered for different case studies.

PMU Placement Based on Heuristic Methods, when Solving the Problem of EPS State Estimation

Creation of satellite communication systems gave rise to a new generation of measurement equipment – Phasor Measurement Unit (PMU). Integrated into the measurement system WAMS, the PMU sensors provide a real picture of state of energy power system (EPS). The issues of PMU placement when solving the problem of EPS state estimation (SE) are discussed in many papers. PMU placement is a complex combinatorial problem, and there is not any analytical function to optimize its variables. Therefore, this problem is often solved by the heuristic optimization methods. Depending on the chosen set of sensors (SCADA&PMU; only PMU; PMU placement based on the concept of depth of unobservability), one can obtain no less than 3 different variants of placing PMUs for one and the same system. The paper describes the PMU placement criteria suggested by the authors to solve the SE problem. Among them: improvement of bad data detection, maximum accuracy of estimates, transformation of the system graph into a tree, maximum number of measurements to be added, PMU placement during the decomposition of the power system SE problem. It is shown that the correct selection of PMU placement criteria can improve the solutions to these problems.