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

Malicious attacks against power systems are investigated, in which an adversary controls a set of meters and is able to alter the measurements from those meters. Two regimes of attacks are considered. The strong attack regime is where the adversary attacks a sufficient number of meters so that the network state becomes unobservable by the control center. For attacks in this regime, the smallest set of attacked meters capable of causing network unobservability is characterized using a graph theoretic approach. By casting the problem as one of minimizing a supermodular graph functional, the problem of identifying the smallest set of vulnerable meters is shown to have polynomial complexity. For the weak attack regime where the adversary controls only a small number of meters, the problem is examined from a decision theoretic perspective for both the control center and the adversary. For the control center, a generalized likelihood ratio detector is proposed that incorporates historical data. For the adversary, the trade-off between maximizing estimation error at the control center and minimizing detection probability of the launched attack is examined. An optimal attack based on minimum energy leakage is proposed.

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Malicious Data Attacks on the Smart Grid

The placement of a minimal set of phasor measurement units (PMUs) so as to make the system measurement model observable, and thereby linear, is investigated. A PMU placed at a bus measures the voltage as well as all the current phasors at that bus, requiring the extension of the topological observability theory. In particular, the concept of spanning tree is extended to that of spanning measurement subgraph with an actual or a pseudomeasurement assigned to each of its branches. The minimal PMU set is found through a dual search algorithm which uses both a modified bisecting search and a simulated-annealing-based method. The former fixes the number of PMUs while the latter looks for a placement set that leads to an observable network for a fixed number of PMUs. In order to accelerate the procedure, an initial PMU placement is provided by a graph-theoretic procedure which builds a spanning measurement subgraph according to a depth-first search. From computer simulation results for various test systems it appears that only one fourth to one third of the system buses need to be provided with PMUs in order to make the system observable. >

Power system observability with minimal phasor measurement placement

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.

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Detecting False Data Injection Attacks on DC State Estimation

This paper addresses itself to the problem of topological observability in Power System State Estimation. After giving a brief theoretical background a new observability algorithm using a network flow technique is presented. The algorithm is explained with reference to the IEEE-5 bus system and its performance is evaluated using the IEEE-30 and IEEE-118 bus systems.

Observability Determination in Power System State Estimation Using a Network Flow Technique

A power system is observable if the measurements made on it allow determination of bus voltage magnitude and angle at every bus of the network. This paper outlines the theoretical basis for an algorithm for determining observability. Based on this theory, an algorithm for networks containing both bus injection and line flow measurements is presented.

Power System Observability: A Practical Algorithm Using Network Topology

A power system static-state estimator has the ability to detect and purge some measurement errors. This paper develops the theoretical basis for determining the bad measurement detectability properties of the state estimator from the topology of the 1-line diagram and the locations of the measurements. Based on this theory, an algorithm is described that: 1) identifies those measurements that have detectable error residuals; and 2) determines the regions of measurement error residual spread.

Power System State Estimation Residual Analysis: An Algorithm Using Network Topology

Measurement system failures may make it impossible for the power system state estimator to estimate bus voltage angles and magnitudes at all buses in the power system. When confronted with such a measurement deficiency, the state estimator can estimate bus voltages over only a portion of the entire network. This paper presents an algorithm that determines the largest region where bus voltages may be estimated-the maximum observable subnetwork. The theoretical basis of the algorithm is developed, and the underlying concepts are illustrated on an example network.

Power System State Estimation with Measurement Deficiency: An Algorithm that Determines the Maximal Observable Subnetwork

Power system state estimation is usually formulated as a weighted least-squares problem and solved iteratively by the normal equations method. The normal equations solution method is well-known to exhibit a tendency to be numerically unstable on some networks. A manifestation of this numerical instability is an ill-conditioned set of linear equations that are to be solved at each iterative step. Recent papers have presented orthogonal factorization methods as remedies for this instability. Experience shows, however, that these methods tend to suffer from excessive fill-in when confronted with networks that have a high measurement redundancy. The folklore of power-system state estimation says that large numbers of bus injection measurements (as opposed to line flow measurements) tend to aggrevate the instability, no explanation for this observation, however, has appeared in the literature. This paper presents an analysis of the sources of ill-conditioning in the power system state estimation problem and offers an alternative solution method, due to Peters and Wilkinson, that overcomes this ill-conditioning without losing matrix sparsity.

The Solution of Ill-Conditioned Power System State Estimation Problems Via the Method of Peters and Wilkinson

This paper extends the authors' topological theory of network observability to develop an algorithm for the evaluation of the reliability of a measurement system for state estimation. This reliability evaluation algorithm is designed both to meet the demands of life-size systems and to provide information necessary for measurement system design improvement. The algorithm is applied to a 137-bus, 200-line system to demonstrate its effectiveness.

G. R. Krumpholz

Papers

Power System Observability: A Practical Algorithm Using Network Topology

Power System State Estimation Residual Analysis: An Algorithm Using Network Topology

Power System State Estimation with Measurement Deficiency: An Algorithm that Determines the Maximal Observable Subnetwork

The Solution of Ill-Conditioned Power System State Estimation Problems Via the Method of Peters and Wilkinson

State Estimator Measurement System Reliability Evaluation -- An Efficient Algorithm Based on Topological Observability Theory