George N. Korres

Taxonomy of PMU Placement Methodologies

Utilization of phasor measurement units (PMUs) in the monitoring, protection and control of power systems has become increasingly important in recent years. The aim of the optimal PMU placement (OPP) problem is to provide the minimal PMU installations to ensure full observability of the power system. Several methods, based on mathematical and heuristic algorithms, have been suggested for the OPP problem. This paper presents a thorough description of the state of the art of the optimization methods applied to the OPP problem, analyzing and classifying current and future research trends in this field.

A Distributed Multiarea State Estimation

This paper presents a new distributed state estimation method for multiarea power systems. Each area performs its own state estimation, using local measurements, and exchanges border information (estimated boundary states and measurements) at a coordination state estimator, which computes the system-wide state. Furthermore, observability and bad data analysis are accomplished in a distributed manner. The proposed method is illustrated with the IEEE 14-bus system. Test results with the IEEE 118-bus system are given.

A reduced model for power system observability: analysis and restoration

An algorithm for observability analysis and restoration in power system state estimation is presented. The problem of P- delta , Q-V and complete observability is addressed. In the proposed algorithm, groups of buses are represented by supernodes and the problem of observability analysis and restoration is examined with a reduced network. The proposed algorithm is easily implemented and it is independent of the state estimation solution algorithm. In case of unobservability, the proposed methodology identifies directly the maximal islands and determines the number and the placement of the required pseudomeasurements for observability restoration. Results from several test cases are presented. >

Numerical observability analysis based on network graph theory

This paper presents a numerical method for topological observability analysis of a measured power system. By floating-point operations on the echelon form of a rectangular test matrix, which is based on network graph properties, observability and maximal observable islands are determined. A minimal set of pseudo measurements, which make an unobservable network barely observable, is selected in a noniterative manner. The existing numerical methods are based on the number of zero pivots that may appear during the factorization of the measurement Jacobian or the gain matrix. Due to round-off errors, the zero pivots may be misclassified. The problem becomes more severe when the number of injection measurements is large, resulting in a great disparity of values in Jacobian or gain matrix. In the proposed method, the test matrix consists of +/-1 values, it is numerically better conditioned and zero pivots are identified more accurately. By topological processing of the flow measured branches and by removing the redundant injection measured nodes that are incident only to flow measured branches or branches which form loops with flow measured branches, a reduced test matrix is created with fewer nonzero elements than the Jacobian or the gain matrix, resulting in less computational effort. The method details are illustrated by various test systems.

Decoupled Optimal Load Flow Using Linear or Quadratic Programming

The Optimal Load Flow problem is a constrained optimization problem of large size and great complexity. For on-line implementation fast execution times and minimum computer storage are required. The proposed iterative scheme, reported in this paper, decomposes the Optimal Load Flow problem into real and reactive subproblems. At each iteration the two subproblems are solved using quadratic programming. If the valve point loading is to be considered, the two subproblems are solved using linear programming. In our scheme, linearization of the non-linear constraints of the problem is succeeded by utilizing Z-matrix techniques and sensitivity analysis.

A reduced model for bad data processing in state estimation

A reduced model theory for bad data processing is proposed which utilizes the concept of error residual spread areas. Based on the reduced model theory, statistical indices can be defined for each error residual spread area, and therefore existing detection and identification techniques can be applied separately for each error residual spread area. In this way, errors can be isolated in smaller regions of the system, making it possible to avoid the search for bad data in the global system. Results from several test cases on power systems show the effectiveness and robustness of the method. >

A Novel Algorithm for Locating Faults on Transposed/Untransposed Transmission Lines Without Utilizing Line Parameters

This paper puts forward a novel algorithm for locating faults on power transmission lines without requiring line parameters. The algorithm utilizes unsynchronized measurements of voltages and currents from both ends of a transmission line and is formulated in terms of the fundamental frequency phasors of the measured signals. Both prefault and postfault phasors are processed for determining the sought distance to fault and the synchronization angle. The calculations are performed initially for a lumped parameter line model with neglecting shunt capacitance. Then, these results are used as starting values for an iterative process, where the impacts of the shunt capacitance of the line are considered. The proposed two-stage fault-location algorithm is applicable for transposed and untransposed transmission lines and is independent of the fault resistance and source impedances. Evaluation studies using reliable Alternate Transients Program-Electromagentic Transients Program simulation data verify that the proposed algorithm can yield quite accurate results.

Identification and updating of minimally dependent sets of measurements in state estimation

A new algorithm for the identification and updating of minimally dependent sets of measurements is presented. The technique implemented in the algorithm is a mixed numerical-symbolic method based on a reduced model and graph theory. As a byproduct of the algorithm, critical measurements and error residual spread areas are provided. Emphasis is placed in the updating of the above quantities when one or more measurements are eliminated from the measurement set. Computational aspects of the proposed algorithm are discussed, and results from an illustrative example and test cases are reported. >

A Weighted Least Squares Algorithm for Optimal PMU Placement

This letter presents a new method for optimal placement of phasor measurement units (PMU) for complete power system observability. The optimal PMU placement (OPP) problem is formulated as a quadratic minimization problem with continuous decision variables subject to nonlinear observability constraints. The optimal solution is obtained by an unconstrained nonlinear weighted least squares (WLS) approach. Simulations are conducted on different IEEE systems (14-bus, 30-bus, 57-bus, and 118-bus) to prove the validity of the proposed algorithm.

Optimal placement of phasor measurement units: A literature review

The increasing availability of phasor measurement units (PMUs) at substations enables the synchronized measurements to various applications, such as the monitoring of system state under normal operations or the protection and control of power systems during abnormal operation. The objective of the optimal PMU placement (OPP) problem is to determine a minimal set of PMUs such that the whole system is observable. To solve the OPP problem, mathematical programming, heuristic, and meta-heuristic optimization techniques, have been proposed. This paper provides a comprehensive literature review on the OPP problem and the solution methodologies. Due to the vast number of publications in this field, the most representative papers are reviewed.