Algorithm For Observability Analysis Research Articles

A Hybrid Observability Analysis Method for Power System State Estimation

For observability analysis algorithm of large-scale power system state estimation, the traditional topological algorithm is complicated and may experience combinatorial explosion problems. Meanwhile, the computation speed and numerical stability of the numerical algorithm are greatly affected by the scale of power systems. In an effort to solve these problems, this study proposed a topological-numerical hybrid observability analysis algorithm using SCADA measurements. In this paper, a basic conclusion that there is at most one unknown complex voltage of an observable island is presented; the theoretical basis and the concept of recursive combination of observable islands are described. Then, three combinability rules are proposed and recursively applied to directly judge whether the local observable islands can be combined or not. Moreover, a minimum number of equivalent branches with power flow pseudo-measurements are added inside the remaining islands to form a final simplified connected network. Finally, the numerical observability analysis method based on the decoupled DC model is carried out to obtain the final observability analysis results. Tests show that the proposed hybrid algorithm has obvious advantages in regard to the execution speed for large-scale systems and also avoids the numerical instability in large-scale power grids.

A Greedy Algorithm for Observability Analysis

This letter presents a numerical algorithm for observability analysis. The proposed algorithm is based on a greedy strategy combined with a Gram-Schmidt orthonormalization procedure of the rows of the measurement Jacobian matrix. The algorithm outputs the system is observable with the available measurements, and if not, it looks for the best candidate measurements to restore observability. Also, an efficient calculation of the null space of the Jacobian matrix can be obtained. The algorithm is an improvement with respect to other existing algorithms that calculate a factorization of the Jacobian matrix. Throughout the process it is not necessary to invert matrices, nor select pivots and the errors caused when dividing by values close to zero are avoided. Four examples are given to illustrate the effectiveness of the proposed method.

An integer-arithmetic algorithm for observability analysis of systems with SCADA and PMU measurements

This paper presents an efficient numerical method for observability analysis of systems including both conventional (SCADA) measurements and synchronized phasor (PMU) measurements, using integer preserving Gaussian elimination of integer coefficient matrices. The observable islands are identified in a noniterative manner, by performing backward substitutions on the integer triangular factors of the integer gain matrix. Multiple placement of conventional and phasor measurements for a system that is found to be unobservable is done by a direct method, using the integer triangular factors of a Gram matrix associated with a reduced size Jacobian matrix. Since all computations performed are exact, no round-off error, numerical instability, or zero identification problems occur. The IEEE 14-bus system is used to illustrate the steps of the proposed method. Test results for the IEEE 300-bus and the FRCC 3949-bus systems are provided to demonstrate the features of the proposed algorithms.

Transformer Tap Setting Observability in State Estimation

In conventional state estimation, transformer tap settings are treated as fixed network parameters. This may reduce the accuracy of state estimation algorithm, when a tap measurement is in error or an unmeasured tap is unknown. This paper presents a numerical observability analysis algorithm for a state estimation model which treats transformer tap settings as state variables and provides for turns ratio and phase-shift angle measurements. The proposed model is transformed to a conventional node frame of reference, by introducing one fictitious bus and one fictitious branch for each transformer with tap estimation enabled. For an unobservable system, observable islands are determined and additional measurements are directly provided for placement. Test results are presented.

Modelling and state estimation of power plant steam turbines

The development of a robust state estimator for ill-conditioned systems based upon the Levenberg-Marquardt algorithm in connection with Givens orthogonal row processing technique is described. The estimator works in two stages: the square-root-free Givens transformation is applied to the measurement Jacobian matrix to reduces it to the product of a unit upper triangular matrix and a diagonal matrix, then the square-root-free Givens transformation is again used to transform a diagonal matrix whose diagonal element is equal to the Levenberg-Marquardt parameter. The Levenberg-Marquardt parameter is adjusted so that the reduction in quadratic cost function is downhill in successive iterations and rapid convergence of the estimator is ensured. An observability analysis algorithm is also developed which is simple and easy to implement. Both description and implementation of the square-root-free Givens transformation are presented. The estimator is applied to a 250 MW, double-flow, single reheat steam turbine which has seven feedwater heaters. Tests results show that the estimator performs well under a wide range of measurement errors and measurement redundancy ratios. A sample of estimated results for rated loading condition are presented. In the appendix, the turbine modelling procedure is discussed.

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.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Power system observability and related functions Derivation of appropriate strategies and algorithms

Observability analysis deals with the adequacy of the available measurement configuration for state estimation purposes. This paper considers methods to explore observability and to face unobservable situations. More explicity, first, the problem of unobservable networks is examined; strategies currently used are discussed and a more general method is proposed, to build a complete and reliable database. Second, topological concepts derived from observability are used to enhance the reliability of the bad data analysis under stringent identification conditions. Third, a concrete algorithm for observability analysis is proposed.