Robust Matrix Completion State Estimation in Distribution Systems

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

Bad-data detection in pre-estimation can help to improve state estimation [Teeuwsen & Erlich, 2006]. Since transient and abnormal conditions may occur in a power system, measurements may be polluted by bad data to cause estimated errors. Hence, it is necessary to accurately detect the bad data. To ensure the reliability of the measured data, a practical state estimator should have an ability to detect and identify the bad data as well as to eliminate their effects on the estimation [Zhang & Lo, 1991]. Generally, bad-date detection is important to guarantee the reliability of the measured data. If one or more errors occur in power system measurements, the states of the estimated system may be biased and the safety of power supply may be potentially dangerous. To avoid this situation, several bad-data detection and identification schemes have been presented. For example, WLS (weighted least squares) was proposed in 1989 [EI-Keib et al., 1989]. The weighted sum of squares of the measurement residuals was chosen as the objective function to be minimized. But, WLS-based state estimators were only developed by using a linearized measurement function [Huang & Lin, 2003] with complicated computations. Then, linear programming (LP) was proposed to improve the identification method [Peterson & Girgis, 1988]. However, the LP estimator may fail to reject the bad data and it can be attributed to the existence of leverage in the power system model [Ali Abur, 1990]. Thus, Ali Abur had proposed hypothesis testing identification (HTI) to extend the case of the LP estimator. Nevertheless, it had caused computational burdens with taking the special properties of the LP estimation equations into account. Huang [Huang & Lin, 2003] proposed a changeable weighting matrix to identify the bad data but it only can apply for static state estimations. Nevertheless, Zhang had proposed recursive measurement error estimation identification (RMEEI) for bad-data identification [Zhang et al., 1992]. State variables, residuals and their parameters can be updated after removing a measurement from the suspected data set to the remaining data set by using a set of linear recursive equations. With splitting the raw measurements into some parts, a set of residual equations used by the traditional methods can only apply to linear systems and it may result the operation of calculation burden and complexity because each part consists of some measurements [Zhang et al., 1992]. Source: Kalman Filter, Book edited by: Vedran Kordic, ISBN 978-953-307-094-0, pp. 390, May 2010, INTECH, Croatia, downloaded from SCIYO.COM

Today's power system predominantly employing the weighted least squares (WLS) technique for estimating the state of the power system over robust state estimation techniques. The computational inexpensiveness of WLS made it a good choice for the operators compared to the robust state estimators. When the system is completely observable by PMUs, the relationship between measurements and state variables changes from non-linear to linear. This made robust state estimators computationally competitive with the WLS estimator (WLSE). In this paper, quadratic-constant (QC) robust estimator has been improved to make it suitable for linear state estimation. The constant part of the estimator after the break-even point is changed to decaying exponential. The proposed quadratically- decaying exponential criterion (QE) is tested on IEEE 14, 30, 57 and 118- bus systems for two cases. (a) measurement data having only Gaussian noise (b) with corrupt measurement data. It is demonstrated that the proposed estimator is able to suppress the bad data and exhibiting better estimation accuracy and computational performance compared to least absolute value (LAV) and WLSE.

Distribution system state estimation is essential for real-time monitoring and control of distribution systems. In recent years, an increasing number of Automated Meter Reading (AMR) systems have been installed to provide customer consumption information. The deployment of smart meters in low voltage (LV) distribution networks, within the context of Advanced Metering Infrastructure (AMI) systems, will enhance the electric energy consumption data storage, processing and analysis capabilities. Because of the limited number of real-time measurements in distribution systems, increased smart metering data availability from LV consumers is necessary to provide load estimates, which can be treated as pseudo-measurements to guarantee the network observability and estimate the system states. This paper presents two distinctive load estimation methods which utilize near real-time consumption data and short past consumption data, respectively. The accuracy of estimated loads is tested with a combined load and state estimation approach. Numerical results with a distribution system will show the effectiveness of the proposed algorithms.

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.

Detection and isolation of faulty line in an active distribution network using intelligent numerical relay

For real-time monitoring of distribution systems, distribution system state estimation (DSSE) methods have been developed. For accurate DSSE results, an accurate system model is needed. However, topology of a distribution network changes due to various reasons and some changes may not be monitored or known to the control center. This leads to an incorrect model used for the DSSE and thus causes incorrect estimation results. The contributions of this paper include an investigation on the capability of DSSE for bad data detection (BDD) in the presence of most common topology errors in practice, including capacitor bank failure and load balancing. Additionally, common measurement schemes are investigated to determine how a measurement scheme can be improved in order to improve topology error detection. Test results using a sample IEEE distribution feeder has been provided to illustrate the challenges associated with topology error detection using DSSE.

The State Estimation (SE) is one of the key elements of the monitoring activity of an active distribution network and is the basis for every control and management application. Distribution networks present their own features, requiring specific estimation methodologies. The most widespread algorithms for Distribution System State Estimation (DSSE) are based on a weighted least squares (WLS) minimization of the residuals of the measurements and usually compute the state in terms ofeither node voltages or branch currents. The DSSE relies on real measurements collected by the distributed measurement system and on other available information, mainly obtained from historical data, that help obtaining observability. The prior information (the so called pseudo-measurements) derived from expected power profiles of both loads and generators is crucial for the accuracy of the estimation process and has to be fully exploited. A degree of correlation can often be assumed among power consumptions or generations of some particular nodes. The influence of the correlation on the quality of the estimation is investigated in this paper using a branch current DSSE algorithm. The importance of including correlation in the WLS is discussed using both traditional and synchronized measurements. Results obtained on a 95-bus distribution network are presented and analyzed.

Decoupled State-Estimation in Energy Control Centres

The quality of measurement data directly determines the accuracy of the state estimation. In practice, erroneous measurement may exist due to various physical factors, and they are known as bad data. Moreover, the measured data may also be attacked by hackers. The existence of bad data and cyber attacks could cause the state estimation unable to estimate the actual system states. Therefore, it is of great significance to detect and differentiate bad data and cyber attacks in power system state estimation. To this end, a support vector machine was proposed in this paper. It was validated using IEEE 118 bus and IEEE 30 bus systems. Numerical results prove the effectiveness of the proposed method in identifying bad data and false data injection data.

This study presents a Distribution System State Estimation (DSSE) algorithm for unbalanced smart grids and evaluates its performance with special focus on the effect of the unavailability of measurements, which is a common problem on smart grids. The proposed DSSE algorithm is based on the Weighted Least Squares (WLS) method and the unbalanced power flow analysis and addresses several challenges such as unbalanced consumption, various configurations and types of loads, line couplings and lack of measurements. To validate the proposed algorithm’s performance, the IEEE 4-node test feeder and the IEEE European Low Voltage test feeder, comprising 907 nodes, are used as benchmarks. A detailed analysis of the DSSE state results, their deviations from the IEEE test feeders, and their sensitivity regarding measurements’ availability, demonstrates the accuracy and robustness of the proposed solution.

To adapt to the distribution network unobservable problem from the scarcity of real-time measurements, the distribution system state estimation (DSSE) method based on hybrid measurements of the supervisory control and data acquisition (SCADA) and the advanced metering infrastructure (AMI) is proposed. Firstly, the ratio of energy data from AMI is used to construct pseudo-measurements, which satisfies the observability of DSSE. Secondly, multiple SCADA acquisition snapshots joint state estimation model is constructed by the SCADA measurements and the energy data of AMI with multiple snapshots. In a rectangular coordinate system, the joint state estimation model and the weighted least squares (WLS) method are described in quadratic polynomial form, leading to a quadratic constraint quadratic estimation (QCQE) model. The QCQE model can decouple the modeling and algorithm implementation of state estimation and enhance the efficiency of algorithm implementation significantly. Otherwise, more state estimation mature algorithms can be adopted for the joint state estimation model in quadratic polynomial form. Simulations on the IEEE 33-bus system verify the accuracy and effectiveness of the proposed method.

This paper presents a new approach for detection and identification of ultiple bad data --- estimation-identification approach which has been developed in order to improve the performance of static-state estimators of power systems. It describes the important function of detection and identification of bad data which is of crucial importance in designing a static-state estimator as a basic element in power system real-time control; it also discusses tthe basic principle, method of solution and programing technique of so called "Estimation-Identificaition Approach" which is based on the better utilization of the resources of residues and the analysis of the property of its sensitivity matrix; and some test results of simulation on a model system and a practical searching system of doubtful data are given. Test results of identifying bad data is good, it is usually successful especially in the case of the occurence of multi-bad data. At the end of this paper comments concerning the advantages of this approach and its recommendation as a prospective practical approach in real-time applications are given.

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.

This article proposes a forecasting-aided medium-voltage (MV) distribution system state estimation (SE) method using a robust ensemble Kalman filter (REnKF). In the proposed solution, low-voltage (LV) measurements at the LV side of secondary substations are used together with the mathematical model of the MV/LV substations to derive new equivalent MV measurements. This yields the improvement of measurement redundancy and robustness of the REnKF to bad data and unknown system process noise. Specifically, we rely on the temporal correlations of the constructed innovation vector as well as the projection statistics (PS) to detect and modify the measurement error covariance matrix. Furthermore, the system process noise covariance matrix is updated adaptively to mitigate the impacts of uncertainties ON-state forecasting and measurement filtering. Extensive comparisons have been carried out with both the traditional EnKF and other SE formulations under balanced and unbalanced distribution system conditions. The results reveal that our proposed REnKF is able to obtain accurate SE results under various operation conditions, including the presence of intermittent renewable energy sources, bad data, and system unbalance.