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.

Electric power system state estimation

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.

/pdf/detecting-false-data-injection-attacks-on-dc-state-3ormqqgezs.pdf

Detecting False Data Injection Attacks on DC State Estimation

In this paper, we analyze the cyber security of state estimators in Supervisory Control and Data Acquisition (SCADA) systems operating in power grids. Safe and reliable operation of these critical infrastructure systems is a major concern in our society. In current state estimation algorithms there are bad data detection (BDD) schemes to detect random outliers in the measurement data. Such schemes are based on high measurement redundancy. Although such methods may detect a set of very basic cyber attacks, they may fail in the presence of a more intelligent attacker. We explore the latter by considering scenarios where deception attacks are performed, sending false information to the control center. Similar attacks have been studied before for linear state estimators, assuming the attacker has perfect model knowledge. Here we instead assume the attacker only possesses a perturbed model. Such a model may correspond to a partial model of the true system, or even an out-dated model. We characterize the attacker by a set of objectives, and propose policies to synthesize stealthy deceptions attacks, both in the case of linear and nonlinear estimators. We show that the more accurate model the attacker has access to, the larger deception attack he can perform undetected. Specifically, we quantify trade-offs between model accuracy and possible attack impact for different BDD schemes. The developed tools can be used to further strengthen and protect the critical state-estimation component in SCADA systems.

/pdf/cyber-security-analysis-of-state-estimators-in-electric-2fcdogsjx1.pdf

Cyber security analysis of state estimators in electric power systems

This paper deals with the problem of network parameter errors in state estimation. First of all, some experimental results are presented showing the influence of these errors on the performance of weighted least squares state estimators. Secondly, the preliminary step of identifying suspicious network parameters is briefly discussed. A classification of the techniques proposed in the literature to estimate parameter errors is then suggested, followed by a description of the main ideas behind each method. Finally, a discussion is included on the possibilities and limitations of every class of methods.

Power system parameter estimation: a survey

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. >

Comparison of different methods for state estimation

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. >

Estimation of parameter errors from measurement residuals in state estimation (power systems)

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. >

W.-H.E. Liu

Papers

Estimation of parameter errors from measurement residuals in state estimation (power systems)

Observability analysis and bad data processing for state estimation with equality constraints