Constrained Power System State Estimation

Decoupled State-Estimation in Energy Control Centres

The weighted least absolute value minimization method is used to solve the power system state estimation problem. The problem can be shown to be equivalent to a linear programming program and hence can be solved using the well-known Simplex method. However, a direct adaptation of the Simplex method results in an inefficient code. A fast algorithm originally suggested by I. Barrodale and F.D.K. Roberts (1973) is further improved and applied to the power system state estimation problem. The use of the algorithm resulted in considerable savings in computation times, as demonstrated by the numerical examples given for various test systems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

One of the major questions in high-density transcranial electrical stimulation (TES) is: given a region of interest (ROI) and electric current limits for safety, how much current should be delivered by each electrode for optimal targeting of the ROI? Several solutions, apparently unrelated, have been independently proposed depending on how “optimality” is defined and on how this optimization problem is stated mathematically. The least squares (LS), weighted LS (WLS), or reciprocity-based approaches are the simplest ones and have closed-form solutions. An extended optimization problem can be stated as follows: maximize the directional intensity at the ROI, limit the electric fields at the non-ROI, and constrain total injected current and current per electrode for safety. This problem requires iterative convex or linear optimization solvers. We theoretically prove in this work that the LS, WLS and reciprocity-based closed-form solutions are specific solutions to the extended directional maximization optimization problem. Moreover, the LS/WLS and reciprocity-based solutions are the two extreme cases of the intensity-focality trade-off, emerging under variation of a unique parameter of the extended directional maximization problem, the imposed constraint to the electric fields at the non-ROI. We validate and illustrate these findings with simulations on an atlas head model. The unified approach we present here allows a better understanding of the nature of the TES optimization problem and helps in the development of advanced and more effective targeting strategies.

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 weighted least absolute value minimization method is used to solve the power system state estimation problem (PSSEP). In this paper, a fast algorithm originally suggested by Barrodale and Roberts is further improved and applied to the PSSEP. The use of the developed algorithm resulted in considerable savings in computation times as demonstrated by the numerical examples given for various test systems

Nowadays the operation of electric power systems (EPS) requires that measures against cyber attacks be taken not only to protect the process equipment but also to upgrade the software involved in the power system control. State estimation (SE) is the most important function providing the EPS monitoring and control with reliable quality information. A state estimation tool acts as a barrier to the corruption of data on current operating conditions of the EPS in the control problem, including the data corruption caused by cyber attacks (CA) on data collection and processing systems. The paper presents a new decomposition approach to solve the SE problem under cyber attack: the calculation network is divided into areas that have a SCADA server and a Wide Area Measurement System (WAMS) concentrator at the center of every area. To detect the CA event and its localization, we propose to use a combination of a-priori and a-posteriori bad data detection (BDD).

Pattern analysis in power system state estimation

In allusion to the defect that conventional weight least squares (WLS), when applied to the power system state estimation, generally takes the same weight. It causes large state estimation error. A state estimation method combining optimal weight setting with weighted least squares is proposed. On the basis of weighted least squares state estimation models, through the theoretical analysis of different kinds of voltage measurements, power injection measurements and power flow measurements data, which impact differently on the results, different weights are set corresponding to their measurement sensitivity in order to reduce the estimation errors. Finally, the algorithm is tested on IEEE14 bus system by MATLAB. Compared with the traditional weighted least squares, this method is similar with regard to iteration time. However, the voltage and phase angle state estimation accuracy can be improved by about 0.16 and 4.66 percentage points. Therefore, the algorithm has certain advantages and application value.

Visible light positioning (VLP) has drawn great attention in the field of indoor positioning as light communication has been popularized in low-cost Internet-of-Things (IOT) devices. In this paper, we investigate the VLP problem using the received signal strength (RSS) and by only considering the line-of-slight (LOS) propagation. The RSS-based VLP problem is highly nonlinear, and its solutions may be trapped in local optima without a good initial guess. To circumvent this difficulty, we propose closed-form solutions of the VLP problem considering a known or unknown user orientation. By applying the weighted least squares (WLS) method, the closed-form solutions are divided into two stages. In the stage-one WLS solution, the nonlinear VLP problem is transformed into a pseudo-linear form by introducing some auxiliary variables, which are considered to be independent of each other. The estimates of the stage-one WLS solution are further refined in the stage-two WLS solution by exploiting the constrained relationships among these defined variables. The simulation results show that the stage-two WLS solution provides good estimates for the user position and orientation. The proposed stage-two WLS solution outperforms the existing methods especially at a high signal-to-noise ratio (SNR).

Asymptotically efficient GNSS trilateration

Measurements from the electrical network are generally transmitted towards the control centres using special communication links. These measurements allow determining the state of the network in real time. However, these measurements often contain uncertainties due to the meter and communication errors, incomplete metering or unavailability of some of these measurements, etc. This paper presents the application of the Particle Swarm Optimization (PSO) algorithm in minimizing the raw measurement errors in order to identify or estimate the optimal operating state of the power system. Two different objective function formulations are assessed by PSO. The first formulation is the Weighted Least Square (WLS) and the second one is the Iteratively Reweighted Least Squares (IRLS) implementation of the Weighted Least Absolute Value (WLAV). Both solutions are compared with a Newton-Raphson (NR) power flow solution using an IEEE 6-bus test system.

State estimation is an essential part of every energy control management system. Accurate estimation of state or operating state is essential for security control and monitoring of power systems. Power system state estimation is a procedure to estimate true state from the inexact state of a power system. The conventional state estimator provides estimates of the power system states, i.e., bus voltages and angles which is obtained. State estimation is a computational technique for electrical power system. It empowers the calculation of the power flows of the electrical power system which are not observed or not directly measured. State estimation is a computer program that detects, isolate and eliminate the incorrect or bad measurement data and estimates the accurate state. The magnitudes of bus voltage and phase angle are the states variables for an electrical power system. This paper outlines Weighted Least Square (WLS) estimation techniques and simulated estimation for standard IEEE systems.

It has been demonstrated by several authors that the well-known weighted least squares (WLS) approximation can be equiripple if a suitable weighting function is applied. In the pre- sent paper, the WLS algorithm is generalized to SAW filter syn- thesis with prescribed magnitude and phase specifications. Several weighting techniques producing quasi-equiripple designs are pre- sented. The frequency sampling technique is used for SAW filter frequency response approximation to reduce the number of the optimized variables. The WLS algorithm rapidly converges both for linear and non-linear phase SAW filters. Typically, no more than 5-10 iterations are required to obtain the WLS solution to accuracy better than 0.5-1 dB in the stopband when compared with the optimum Chebyshev approximation. Moreover, it is shown that the WLS technique can be effectively applied for sec- ond-order effect compensation.

Noise resilient solution and its analysis for multistatic localization using differential arrival times

This thesis implements a state-of-the-art solution separation advanced RAIM (ARAIM) algorithm as it is written as reported in the literature. Specifically, a GNSS fault detection and exclusion algorithm for a multi-constellation GNSS was implemented in software and tested against simulated data. RAIM algorithms have been created in many forms over the last couple of decades and are still in development today. The position solution results produced by this ARAIM algorithm were compared to that of a snapshot weighted least squares (WLS) solution in which failed satellites are removed before processing and an WLS solution with no corrections applied. In addition, the difference in position solution between ARAIM and the simulation truth was compared to the ARAIM reported horizontal and vertical protection limits, as well as, the position performance criteria. This thesis also investigates the performance of the exclusion method and how it affects the performance of the overall ARAIM algorithm. The algorithm implemented and tested in this thesis will be used as a basis of comparison for on-going research into robust GNSS processing techniques.