Power System Static State Estimation Research Articles

Guest Editorial: Situational awareness of integrated energy systems

Guest Editorial: Situational awareness of integrated energy systems

Lp Quasi Norm State Estimator for Power Systems

This paper proposes an L<inf>p</inf> (0&#x003C;p&#x003C;1) quasi norm state estimator for power system static state estimation. Compared with the existing L, and L<inf>2</inf> norm estimators, the proposed estimator can suppress the bad data more effectively. The robustness of the proposed estimator is discussed, and an analysis shows that its ability to suppress bad data increases as <tex>$p$</tex> decreases. Moreover, an algorithm is suggested to solve the non-convex state estimation problem. By introducing a relaxation factor in the mathematical model of the proposed estimator, the algorithm can prevent the solution from converging to a local optimum as much as possible. Finally, simulations on a 3-bus DC system, the IEEE 14-bus and IEEE 300-bus systems as well as a 1204-bus provincial system verify the high computation efficiency and robustness of the proposed estimator.

LTS-Based Robust Hybrid SE Integrating Correlation

The paper introduces a robust approach for hybrid power system static state estimation (SE) utilizing phasor measurement units (PMUs). The proposed PMU-based SE exploits the time and space correlation in the PMU measurements in order to provide rejection of bad measurements and improve the SE cyber security and accuracy. The SE robustness is introduced in two steps. The first step is to robustly fit multichannel or vector autoregressive models to adjacent PMUs. The second step replaces the classical weighted least squares algorithm with a robust regression estimator. The robustness is introduced by exploiting the least trimmed squares estimator. The effectiveness of the proposed robust PMU-based SE is assessed based on Monte Carlo simulations and compared with other existing robust SE methods. A theoretical analysis is provided to explain the improvement by higher PMU sampling rates and longer periods of SE.

Power system static state estimation using a least winsorized square robust estimator

State estimation is the heart of the energy management system, primarily used for control and monitoring of electrical power systems. Commonly used conventional weighted least square estimator is not reliable, particularly in the presence of bad data. Subsequently, bad data processing techniques have been developed to detect, identify, and eliminate the bad data present in the measurement set. In the present paper, a robust least winsorized square (LWS) estimator is proposed for the power system static state estimation. One of the main advantages of this estimator is that it has an inbuilt outlier rejection property and is less sensitive to bad data (outliers) measurements. The power system state estimation problem has been solved as an optimisation problem using the jDE-self adaptive differential evolution algorithm. The proposed approach has been implemented and tested on standard IEEE test systems. The effectiveness of the LWS estimator has been demonstrated under different operating conditions, namely, normal operating condition, bad data condition, different operating points, different measurement condition, under the ill-conditioned system, and the presence of false data injection. The performance of the proposed approach has been compared with the conventional and the evolutionary based state estimation techniques. Based on the various performance indices, the results thus obtained show that the proposed technique has better accuracy, robustness, and reliability compared to the results obtained using conventional and evolutionary based state estimation techniques.

PMU Based State Estimation by Integrating Correlation

In this paper, a novel approach for hybrid power system static state estimation (SE) in the presence of phasor measurement units (PMUs) is presented. The proposed PMU-based SE takes into account existing time correlation in the PMU measurements. The PMU time series of measurements are modeled by short memory autoregressive (AR) models over short time periods. The correlation existing between PMU measurements at different buses is included using vector or multichannel AR models. The effectiveness and improved performance of the proposed PMU-based SE is demonstrated through a comparison analysis with practical hybrid SE methods. A theoretical analysis highlights the improvement over long execution periods of SE and high PMU sampling rates. Finally, a practical comparison is carried out on results from simulated Monte Carlo runs on the IEEE 14- and 118-bus test beds.

A recursive measurement error estimation identification method for bad data analysis in power system state estimation

A recursive measurement error estimation identification algorithm is proposed for identifying multiple interacting bad data in power system static state estimation. A set of linearized formulae are developed and used to recursively calculate normalized residuals and normalized measurement error estimates upon which the bad data identification method is based. Sparse vector and partial factor modification techniques are used in the recursive identification calculations. Neither the submatrix of the residual sensitivity matrix, W/sub ss/, nor state reestimation is needed in the whole identification process. Digital tests on various power systems, including a 171 bus real system, are done to show the validity and efficiency of the proposed bad data identification method. >

A blocked sparse matrix formulation for the solution of equality-constrained state estimation

A block-partitioned (blocked) sparse formulation for the solution of equality-constrained power system static-state estimation is presented. The blocked structure is formed based on a new formulation of Hachtel's augmented matrix method, which preserves several desired features of the conventional normal equations with equality constraints approach. The proposed formulation treats the constraints by the method of Lagrange multipliers, but allows triangular factorization to proceed in a positive-definite manner. A mixed-size blocked structure is proposed for the internal solution, while a formulation composed exclusively of (2*2) blocks is proposed for the external solution. The method is well suited to the implementation of regulation schemes and limit enforcement, necessary in the state-emission-based external solution. The pairing of equations with state variables in the observable state-estimation solution is tightly linked to the results of a topological observability algorithm.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A bad data identification method for linear programming state estimation

The author presents a bad-data identification procedure for linear programming (LP) power system static state estimation. LP state estimators minimize the weighted sum of the absolute values of the measurement residuals. The proposed procedure first detects the bad data using the measurement residuals of those measurements rejected by the LP estimator. Then the bad measurement is identified and eliminated by estimating the measurement errors of the zero residual measurements. The residuals obtained from this second estimation step are made use of for this purpose. In order to minimize the computational burden during the elimination cycles, a fast way of eliminating measurements through weight changing is also presented. The performance of the proposed procedure is tested and the results are presented, using AEP's 14, 30, 57 and 118. >

A new method for solving equality-constrained power system static-state estimation

An algorithm for solving equality-constrained power system static-state estimation problems is presented. The method employs a transformation of variables that makes it possible to treat the constraints in a direct fashion, without the need to compute the Lagrange multipliers. The method appears to have good numerical properties, due to the fact that the transformation employed enhances the numerical conditioning of the equations. The algorithm is shown to perform successfully on several examples of realistic size. Normalized residuals can be computed in an efficient manner with the new algorithm. >

Decoupled State-Estimation in Energy Control Centres

Abstract STATE-ESTIMATION (SE) is the process of assigning a value to an unknown system state-variable based on measurements from that system according to some criteria. Usually, the process involves imperfect measurements inherent in the process and therefore estimating the system state is based on a statistical criteria that estimates the true value of the state-variable so as to minimize or maximize the selected criteria. A commonly used and familiar criteria is that of minimizing the sum of squares of the differences between the estimated and ‘true’ (i.e. measured) values. Power System Static State-Estimation (PSSE) is a proven technique for providing modern energy control centres with reliable real-time data bases for security monitoring and on-line control. The state-estimation processes real-time raw measurements to obtain optimal estimates of voltage magnitudes and angles at all buses, which determines the static state of the Power System (PS). The estimation problem of PSSE is usually formulated as a nonlinear least-square problem. Among state estimators based on the normal equations approach, the weighted least square (WLS) estimator provides reliable estimates but is slow, mainly due to its requirement for updating and factorization of the full-matrix in every iteration. The decoupled state-estimator requires less computation time per iteration and less storage requirement than WLS. The concept of p- δ, Q-V decoupling technique as applied in load flow studies is extended to state estimation technique also which reduces the storage requirement and also the time for convergence. The most common approach to the SE problem is to formulate it as a nonlinear problem usually solved by an iterative procedure based on successive linearization; in each iteration one has to solve a linear least-squares problem. Associated with WLS estimation is a set of redundant equations are to be solved to yield the solution. These equations are ‘Normal Equations’ and are solved using Cholesky factorization. The normal equations are very satisfactory with respect to preserving sparsity, but they may give rise to numerical ill-conditioning. Methods using orthogonal transformations, such as those of Householder have far better stability properties. The Method of Data Equations which uses the Householder orthogonal transformation is more efficient than the conventional method of normal equations. Also, it is less prone to computer round-off errors and is more numerically stable. The standard approach to the solution of the WLS state estimation in power system is the iterative normal equations method. Occassional ill-conditioning has been experienced with this method. Alternative approaches to state-estimation are based on ‘orthogonal transformation’. These methods have improved numerical behaviour, but generally their sparsity suffers when the measurement redundancy is high. In this paper the decoupled estimator based on transformation method is presented using different algorithms and the results agree with the method of normal equations. Measurements are transformed into new ‘measurements’ that are functions of the states and of the original measurements. In PSSE redundancy rate is an important aspect. Estimator obtained from various redundancy rates, by considering active and reactive redundancy seperately obtained by uniformly distributing the measurements over the system is presented. Line flows and bus injection measurements required for stateestimation studies, have been obtained from load-flow computations. Error (noise) terms (σ = 0.01 and 0.001) are added to these measurements. The error vector being simulated using a random number generator. Convergence tolerance of 0.001 PU and 0.001 are used for V and δ, respectively. Results obtained for various combinations of measurements; and with different order of processing these measurements have been presented. Measurements are classified as. Type 1, 2 : Power injections. Type 3, 4 : Power flows. Type 5 : Voltage magnitudes. Different cases analysed are. i) Case 1 : 1, 2, 3, 4 & 5 Type measurements. ii) Case 2 : 1, 3, 4 and 5 Type measurements. iii) Case 3 : 1, 2, 3 and 4 Type measurements. iv) Case 4 : 3 and 5 Type measurements. It is important that at least few voltage measurements (NBUS/ 10 to NBUS/5) must be included while estimating the states. When line-flows only are used as measurements, solution takes large number of iterations to converge. Comparative results obtained from ‘method of Normal equations’ and ‘Data equations’ have been presented. Illustrative examples considered are IEEE-14 bus system and 5-bus sytem.

Power system static state estimation based upon nodal voltages

Static state estimation of a power system based upon measurement of nodal voltages is presented in this paper. Nodal voltages are calculated from a true state by load flow calculation and corrupted deliberately to simulate errors introduced by the telemetry system equipments. These are used as data to state estimation program. The problem of any communication link failure is treated by considering the previous estimation data (bus voltages) of the bus whose communication link has failed in the last estimation. Accuracy of the results from state estimation program are checked by comparison with true state.

Reliable Bad Data Processing for Real-Time State Estimation

The weighted least squares performance index test (J(x) test) conventionally used in power system static state estimation has poor reliability for detecting the presence of measurement errors in the range 3 to 20 standard deviations. This paper describes a very simple alternative method, with considerably improved bad data detection properties, based on evaluating the coherency between the measurement with the largest normalized residual and the remainder of the measurement system. In fact, the detection and identification phases of bad data processing become combined. Inanexistent state estimator using normalized residuals, the cost of implementation of the new method is negligible. The new method has been tested extensively on several power systems, and compared with the J(x) test.