Wide-area Transmission System Fault Analysis Based on Three-Phase State Estimation with Considering Measurement Errors

A three-phase state estimation in active distribution networks

In this paper a new approach for a three-phase Distribution System State Estimator (DSSE) is presented. It utilizes the most types of analog real time measurements (including voltage and current magnitude, active and reactive power measurements). The correct utilization is supported by topology analysis and creation of measurement areas. Loads are modeled based on historical or AMR information. The estimation problem is solved by weighted least squares error method. Applying traditional state estimation on distribution networks, by using load data as pseudo measurement, causes state estimation formulations that have very large size. Approach presented in this paper is based on network reduction which reduces size of the problem. The approach is very fast and provides feasible results.

Power system state estimation is heavily subjected to measurement error, which comes from the noise of measuring instruments, communication noise, and some unclear randomness. Traditional weighted least square (WLS), as the most universal state estimation method, attempts to minimize the residual between measurements and the estimation of measured variables, but it is unable to handle the measurement error. To solve this problem, based on random matrix theory, this paper proposes a data-driven approach to clean measurement error in matrix-level. Our method significantly reduces the negative effect of measurement error, and conducts a two-stage state estimation scheme combined with WLS. In this method, a Hermitian matrix is constructed to establish an invertible relationship between the eigenvalues of measurements and their covariance matrix. Random matrix tools, combined with an optimization scheme, are used to clean measurement error by shrinking the eigenvalues of the covariance matrix. With great robustness and generality, our approach is particularly suitable for large interconnected power grids. Our method has been numerically evaluated using different testing systems, multiple models of measured noise and matrix size ratios.

In allusion to the defect that conventional weight least squares (WLS), when applied to the power system state estimation, generally takes the same weight. It causes large state estimation error. A state estimation method combining optimal weight setting with weighted least squares is proposed. On the basis of weighted least squares state estimation models, through the theoretical analysis of different kinds of voltage measurements, power injection measurements and power flow measurements data, which impact differently on the results, different weights are set corresponding to their measurement sensitivity in order to reduce the estimation errors. Finally, the algorithm is tested on IEEE14 bus system by MATLAB. Compared with the traditional weighted least squares, this method is similar with regard to iteration time. However, the voltage and phase angle state estimation accuracy can be improved by about 0.16 and 4.66 percentage points. Therefore, the algorithm has certain advantages and application value.

Decoupled State-Estimation in Energy Control Centres

The paper presents a method for estimating the parameters of an untransposed transmission line, which can be represented by an equivalent π-model, in real-time. The estimation of parameters is performed using the Weighted Least Squares (WLS) method, which utilizes three sets of synchronized phasor measurements of voltages and currents at both ends of the transmission line, with at least one measurement containing a sufficient zero-sequence voltage component. This method could be used in general case - for both transposed and untransposed lines, that have balanced or unbalanced load. By applying this method, it is possible to calculate the values of self-impedances and mutual impedances, as well as the values for susceptances. By transforming these values into the system of symmetrical components, the impedances and susceptances of positive, negative, and zero sequences, as well as mutual impedances between the positive, negative, and zero sequences, are also determined. The parameters of the untransposed line were determined in two different cases. Voltage and current measurements at both end of the transmission line were generated using MATLAB Simulink software, where phasors were determined and later used as data input for the calculations. In the first idealized case, measurement errors were not considered, while in the second case, measurement error was modelled in the input data. In both cases, two methods were applied: the first one which estimates the unknown parameters of the untransposed line using equations for an untransposed transmission line, and the second one which estimates the unknown parameters based on equations for a transposed line.

Robust three-phase state estimation for PV-Integrated unbalanced distribution systems

For analysis, operation and planning of a power system, state estimation and power flow analysis are important tools. Accurate state estimation enables active monitoring of power systems. The state estimation with minimum data is important for reducing the complexity in the state estimation process. In this paper, a state estimation based on the Weighted Least Squares (WLS) method with minimum data (12 measurement) is considered. The state estimation is done with different measurement data that is 62 measurement data, 18 measurement data and 12 measurement data for 6 bus test system. A comparison between these different measurements data is also analyzed in terms of the state estimated.

ABSTRACTThe power system state estimator based on the support vector machine (SVM) and the weighted least squares (WLS) method is presented in the paper. The WLS provides state estimations necessary for creating SVM model which is then used for state estimation. The developed algorithm was tested on the IEEE systems, and the performance indicators were calculated in order to compare the accuracy of estimation and the measurement error filtering. The results indicate that the proposed hybrid model outperforms the classical WLS-based state estimation in terms of accuracy and improves measurement error filtering in comparison to the classical estimator.

State estimation is often a challenging task in distribution systems due to deploying a limited number of measurement devices. Moreover, the integration of precise distribution-level phasor measurement unites, a.k.a micro-PMUs, along with inaccurate pseudo-measurements in state estimation introduces another challenge. These issues might decrease the efficiency of traditional standard weighted least squares (WLS) for distribution system state estimation. This paper proposes a novel linear distribution system state estimation based on limited number of synchrophasor measurements and pseudo-measurements. To involve pseudo-measurements into the linear state estimation, Taylor's approximation is adopted to reformulate pseudo-measurement functions in a linear form. The results obtained via numerical simulations demonstrate that the proposed linear state estimation method performs as good as the standard nonlinear WLS estimator. Moreover, the sensitivity analyses results show that our method has a better performance compared to WLS once a limited number of highly precise micro-PMUs are accompanied with inaccurate pseudo-measurements in state estimation.

An observable microgrid may become unobservable when sensors are at fault, sensor data is missing, or data has been tampered by malicious agents. In those cases, state estimation cannot be performed using traditional approaches without pseudo-measurements. To address the lack of observability, this article presents the design and implementation of a novel three-phase state estimation method for unobservable and unbalanced AC microgrids, using machine learning techniques, without pseudo-measurements, and under heteroscedastic (i.e., non-constant variance) noise. The proposed machine learning state estimation (MLSE) makes full use of multiple candidate models trained with a small number of power flow simulations via OpenDSS, through random levels of demand and renewable generation in every simulation, enhanced through a proposed Tikhonov regularization operator. To deal with the heteroscedastic nature of measurements, a recursive average model is proposed to accurately estimate the state variables. Results are obtained using real data from a microgrid located on the main campus of the State University of Campinas (UNICAMP), in Brazil. The method can be easily adapted to microgrids with different configurations, distributed energy resources, and measurements. It is shown that the proposed MLSE outperforms the traditional weighted least square (WLS) state estimator.

State estimation (SE) is an important task allowing power networks to monitor accurately the underlying system state, which is useful for security-constrained dispatch and power system control. For nonlinear AC power systems, SE amounts to minimizing a weighted least-squares cost that is inherently nonconvex, thus giving rise to many local optima. As a result, estimators used extensively in practice rely on iterative optimization methods, which are destined to return only locally optimal solutions, or even fail to converge. A semidefinite programming (SDP) formulation for SE has been advocated, which relies on the convex semidefinite relaxation (SDR) of the original problem and thereby renders it efficiently solvable. Theoretical analysis under simplified conditions is provided to shed light on the near-optimal performance of the SDR-based SE solution at polynomial complexity. The new approach is further pursued toward complementing traditional nonlinear measurements with linear synchrophasor measurements and reducing computational complexity through distributed implementations. Numerical tests on the standard IEEE 30- and 118-bus systems corroborate that the SE algorithms outperform existing alternatives, and approach near-optimal performance.

Inferential measurement of SAG mill parameters II: state estimation

Due to the insufficient measurements in the distribution system state estimation (DSSE), full observability and redundant measurements are difficult to achieve without using the pseudo measurements. The matrix completion state estimation (MCSE) combines the matrix completion and power system model to estimate voltage by exploring the low-rank characteristics of the matrix. This paper proposes a robust matrix completion state estimation (RMCSE) to estimate the voltage in a distribution system under a low-observability condition. Tradition state estimation weighted least squares (WLS) method requires full observability to calculate the states and needs redundant measurements to proceed a bad data detection. The proposed method improves the robustness of the MCSE to bad data by minimizing the rank of the matrix and measurements residual with different weights. It can estimate the system state in a low-observability system and has robust estimates without the bad data detection process in the face of multiple bad data. The method is numerically evaluated on the IEEE 33-node radial distribution system. The estimation performance and robustness of RMCSE are compared with the WLS with the largest normalized residual bad data identification (WLS-LNR), and the MCSE.

This paper investigates how the efficiency of Weighted Least Squares (WLS) State Estimation changes according to both the uncertainty of network parameters and the uncertainty of measurements. Performance of State Estimator based mainly on the accuracy of its inputs and it is very important for the power system planners to improve the state estimation by determining whether to invest on increasing the measurement preciseness or improve the power network model. For this purpose, an algorithm for simulation of the uncertainty effects on the state estimator is proposed and tested on IEEE 14-Bus power network test case. The implementation of this algorithm enables us to analyze how much the state estimator's output is affected according to the network parameters uncertainty by means of state errors distribution versus the network parameters uncertainty. On the other hand, a serious defect in an estimator is the lack of unbiasedness. Hence a new prominent analysis is performed to find how network parameters uncertainty can affect the state estimator's bias by using distribution of the ratio between the absolute value of state errors mean and the related standard deviations versus the network parameters uncertainty and comparing it with a predefined threshold. Moreover, this analysis is also performed considering correlation in the network parameters, to investigate the effect of parameters correlation on the state estimator.