Observability analysis and bad data processing for state estimation with equality constraints
TL;DR: In this article, a factorization-based observability analysis and normalized residual-based bad-data processing are extended to state estimation with equality constraints, and the normalized residuals are calculated using the sparse inverse of the gain matrix.
Abstract: A factorization-based observability analysis and the normalized residual-based bad-data processing have been carried out for state estimation using the normal equation approach. The observability analysis is conducted during the process of triangular factorization of the gain matrix. The normalized residuals are calculated using the sparse inverse of the gain matrix. The method of Lagrange multipliers is applied to handle state estimation with equality constraints arising from zero injections, because of its better numerical robustness. The method uses a different coefficient matrix in place of the gain matrix at each iteration. The factorization-based observability analysis and normalized residual-based bad-data processing are extended to state estimation with equality constraints. It is shown that the observability analysis can be carried out in the triangular factorization of the coefficient matrix, and the normalized residuals can be calculated using the sparse inverse of this matrix. Test results are presented. >
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01 Feb 2000
TL;DR: In this article, the state of the art in electric power system state estimation is discussed, which is a key function for building a network real-time model, a quasi-static mathematical representation of the current conditions in an interconnected power network.
Abstract: This paper discusses the state of the art in electric power system state estimation. Within energy management systems, state estimation is a key function for building a network real-time model. A real-time model is a quasi-static mathematical representation of the current conditions in an interconnected power network. This model is extracted at intervals from snapshots of real-time measurements (both analog and status). The new modeling needs associated with the introduction of new control devices and the changes induced by emerging energy markets are making state estimation and its related functions more important than ever.
778 citations
Cites methods from "Observability analysis and bad data..."
...The Hachtel method was first applied to power system state estimation in [39] and was further studied in [ 41 ], which extended the normalized residuals approach to Hachtel state estimators....
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...The largest normalized residual method was extended to the normal equations approach with equality constraints [ 41 ] and to the blocked sparse matrix approach [42]....
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01 Jan 2010
TL;DR: It is shown that it is necessary and sufficient to protect a set of basic measurements to detect false data injection attacks in state estimation and by having a way to independently verify or measure the values of a strategically selected set of state variables.
Abstract: State estimation is an important power system application that is used to estimate the state of the power transmission networks using (usually) a redundant set of sensor measurements and network topology information. Many power system applications such as contingency analysis rely on the output of the state estimator. Until recently it was assumed that the techniques used to detect and identify bad sensor measurements in state estimation can also thwart malicious sensor measurement modification. However, recent work by Liu et al. [1] demonstrated that an adversary, armed with the knowledge of network configuration, can inject false data into state estimation that uses DC power flow models without being detected. In this work, we explore the detection of false data injection attacks of [1] by protecting a strategically selected set of sensor measurements and by having a way to independently verify or measure the values of a strategically selected set of state variables. Specifically, we show that it is necessary and sufficient to protect a set of basic measurements to detect such attacks.
436 citations
Cites methods from "Observability analysis and bad data..."
...Until recently, it was generally assumed that the techniques used to detect, identify and correct [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16] bad sensor measurements in state estimation are sufficient to detect and recover from sensor measurement manipulation....
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TL;DR: In this paper, a comparative study of five methods, namely, the normal equations method, the orthogonal transformation method, hybrid method, normal equations with constraints, and Hachtel's augmented matrix method for state estimation has been conducted.
Abstract: Ill-conditioning in the gain matrix of the classical normal-equations-approach for state estimation has created a numerical stability problem for large power systems. Several methods have been proposed to circumvent the problem. A comparative study of five methods, namely, the normal equations method, the orthogonal transformation method, the hybrid method, normal equations with constraints, and Hachtel's augmented matrix method for state estimation has been conducted. The comparison is made in terms of their (i) numerical stability, (ii) computational efficiency, and (iii) implementation complexity. A theoretical analysis indicates that the orthogonal transformation method is numerically most stable. But the orthogonal transformation method cannot be implemented in the efficient fast decoupled version. It is shown that the hybrid method and Hachtel's method are both good compromises between numerical stability and computational efficiency. >
206 citations
TL;DR: In this paper, a two-step approach is proposed for parameter error estimation, where the first step is to estimate a bias vector which combines the effects of parameter errors and the state of the system.
Abstract: Any error of network parameters affects the value of the measurement residuals calculated in state estimation. Explicit mathematical expressions relating the residuals to the parameter errors are derived. A two-step approach is proposed for parameter error estimation. The first step is to estimate a bias vector which combines the effects of parameter errors and the state of the system. A least-square approach using the measurement residuals calculated in each state estimation run is proposed for the first step. After several state estimation runs, a sequence of such bias vectors is obtained. The second step is to estimate the parameter errors from the sequence of bias vectors. A recursive least-square estimation method is proposed for this step. Theoretical and computational issues of the proposed method are addressed. Test results are presented. >
152 citations
TL;DR: In this article, a recursive Tabu search (RTS) method is proposed to solve the optimal PMU placement problem, which aims to find the minimum number of PMUs and their corresponding locations in order to achieve full network observability.
Abstract: Phasor measurement units (PMUs) are essential tools for monitoring, protection and control of power systems. The optimal PMU placement (OPP) problem refers to the determination of the minimal number of PMUs and their corresponding locations in order to achieve full network observability. This paper introduces a recursive Tabu search (RTS) method to solve the OPP problem. More specifically, the traditional Tabu search (TS) metaheuristic algorithm is executed multiple times, while in the initialisation of each TS the best solution found from all previous executions is used. The proposed RTS is found to be the best among three alternative TS initialisation schemes, in regard to the impact on the success rate of the algorithm. A numerical method is proposed for checking network observability, unlike most existing metaheuristic OPP methods, which are based on topological observability methods. The proposed RTS method is tested on the IEEE 14, 30, 57 and 118-bus test systems, on the New England 39-bus test system and on the 2383-bus power system. The obtained results are compared with other reported PMU placement methods. The simulation results show that the proposed RTS method finds the minimum number of PMUs, unlike earlier methods which may find either the same or even higher number of PMUs.
145 citations
References
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TL;DR: On etend la methode frontale pour resoudre des systemes lineaires d'equations en permettant a plus d'un front d'apparaitre en meme temps.
Abstract: On etend la methode frontale pour resoudre des systemes lineaires d'equations en permettant a plus d'un front d'apparaitre en meme temps
956 citations
TL;DR: This paper considers stable numerical methods for handling linear least squares problems that frequently involve large quantities of data, and they are ill-conditioned by their very nature.
Abstract: A common problem in a Computer Laboratory is that of finding linear least squares solutions. These problems arise in a variety of areas and in a variety of contexts. Linear least squares problems are particularly difficult to solve because they frequently involve large quantities of data, and they are ill-conditioned by their very nature. In this paper, we shall consider stable numerical methods for handling these problems. Our basic tool is a matrix decomposition based on orthogonal Householder transformations.
764 citations
TL;DR: In this article, the state estimation problem in electric power systems consists of four basic operations: hypothesize structure; estimate; detect; identify, which is addressed with respect to the bad data and structural error problem.
Abstract: The state estimation problem in electric power systems consists of four basic operations: hypothesize structure; estimate; detect; identify. This paper addresses the last two problems with respect to the bad data and structural error problem. The paper interrelates various detection and identification methods (sum of squared residuals, weighted and normalized residuals, nonquadratic criteria) and presents new results on bad data analysis (probability of detection, effect of bad data). The theoretical results are illustrated by means of a 25 bus network.
608 citations
TL;DR: In this article, a complete theory of network observability is presented, starting from a fundamental notion of the observability of a network, a number of basic facts relating to network observations, including unobservable states, observable branches, observable islands, relevancy of measurements, etc.
Abstract: A complete theory of network observability is presented. Starting from a fundamental notion of the observability of a network, a number of basic facts relating to network observability, unobservable states, unobservable branches, observable islands, relevancy of measurements, etc. are derived. Simple and efficient algorithms can be developed based on these basic facts to (i) test network observability, (ii) identify observable islands and (iii) place measurements for observability.
315 citations
TL;DR: Two algorithms are presented; one for testing the observability of a network and identifying the observable islands when the network is unobservable, and the other for selecting a minimal set of additional measurements to make the network observable.
Abstract: Two algorithms are presented; one for (i) testing the observability of a network and (ii) identifying the observable islands when the network is unobservable, and the other for selecting a minimal set of additional measurements to make the network observable. The two algorithms are based on triangular factorization of the gain matrix and are characterized by (i) being extremely simple, (ii) using, subroutines already in a state estimation program, and (iii) incurring very little extra computation. The design and testing of the algorithms are presented in this paper.
237 citations