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.

/pdf/malicious-data-attacks-on-the-smart-grid-5ejbj8l4wt.pdf

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.

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

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 and modeling constraints may make it impossible for the power system state estimator to estimate bus voltage magnitudes and angles at every bus in the power system from the available real-time measurements. Such a measurement deficiency may be remedied by adding pseudo measurements of estimated bus loads. This paper presents a combined observability/measurement placement algorithm that both tests the measured network for observability and evaluates pseudo measurement sites as to the desirability of their inclusion into the measurement set.

Power System State Estimation with Measurement Deficiency: an Observability/Measurement Placement Algorithm

A method for detecting topology errors in electric power networks is developed by providing a geometric interpretation of the measurement residuals caused by such errors. A test for single topology errors is presented that is similar to the normalized residuals test for measurement errors. This test is generalized to multiple topology errors. The concept of critical network branches (where their removal renders the network unobservable) is introduced and extended to critical-branch k-tuples. It is shown that topology errors on critical branches cannot be detected from measurement residuals. An equation is developed for a matrix whose column linear dependencies determine topology error detectability and identifiability. An example for an IEEE 14 bus network is provided. >

Detection and identification of topology errors in electric power systems

A method for detecting and identifying multiple bad data in electric power networks is developed by providing a geometric interpretation of the familiar normalized residuals test for single bad data. This generalized multiple bad data test amounts to determining whether the residual vector lies in a subspace determined by the suspect measurements and whether any portions of that subspace are orthogonal to the residual vector. These tests can be performed efficiently using appropriate projection matrices. Thne notion of critical measurement (removal renders the network unobservable) is extended to critical k-tuples of measurements to determine which bad data hypotheses are actually testable. For example, gross errors in critical measurements are not detectable, and gross errors in a critical pair of measurements are detectable but not identifiable. More generally, k-2 gross errors in a critical k-tuple of measurements are identifiable while k or k-l gross errors are detectable but not identifiable. In essence, the set of testable hypotheses is determined by the geometry of the space spanned by all possible residual vectors. A procedure for selecting and pruning a suspect set of measurements is described. Examples for the IEEE 14 bus network are provided.

P. W. Davis

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 Observability/Measurement Placement Algorithm

Detection and identification of topology errors in electric power systems

Multiple Bad Data Detectability and Identifiability: A Geometric Approach