Synchrophasor-Based Linear State Estimation Techniques and Applications

Decoupled State-Estimation in Energy Control Centres

This paper presents a review on major blackouts occurred in power grid across the world and importance for the need of state estimation (SE) solution. This work introduces the applications of phasor measurement units (PMU) to reduce the occurrence of blackouts in power system. The blackouts in power system can occur due to overload, light load conditions, heavy storms or due to line outages. The cascade failure due to line outages, i.e., measured as N-1 outages can lead to power system blackout. The necessity of power system state estimation (PSSE) solution for protection in view of blackouts is discussed in this paper. A Generalized Linear State Estimation (GLSE) method is proposed to obtain robust and accurate states of power system network. A matrix integrating phasor and conventional measurements are formulated to obtain accurate states. IEEE transmission bus network such as 14-bus network is considered as test case for proposed GLSE programming in MATLAB. The accurate states are computed and compared with standard weighted least squares (WLS) method to show its effectiveness.

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.

Power system state estimation is heavily subjected to measurement error, which comes from the noise of measuring instruments, communication noise, and some unclear randomness. Traditional weighted least square (WLS), as the most universal state estimation method, attempts to minimize the residual between measurements and the estimation of measured variables, but it is unable to handle the measurement error. To solve this problem, based on random matrix theory, this paper proposes a data-driven approach to clean measurement error in matrix-level. Our method significantly reduces the negative effect of measurement error, and conducts a two-stage state estimation scheme combined with WLS. In this method, a Hermitian matrix is constructed to establish an invertible relationship between the eigenvalues of measurements and their covariance matrix. Random matrix tools, combined with an optimization scheme, are used to clean measurement error by shrinking the eigenvalues of the covariance matrix. With great robustness and generality, our approach is particularly suitable for large interconnected power grids. Our method has been numerically evaluated using different testing systems, multiple models of measured noise and matrix size ratios.

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.

Power system state estimation is classically formulated as a weighted least squares (WLS) optimization problem over the real domain, with the state variables being the voltage magnitudes and angles or the voltage real and imaginary parts. Although the voltages in ac networks are complex variables, a solution in the complex domain has not been previously reported; this is because a real function of complex variables is nonanalytic in its arguments, i.e., the Taylor series expansion in its arguments alone does not exist. By making use of the Wirtinger calculus, this paper presents a new implementation of the WLS state estimation problem in complex variables. The partial derivatives employed in the method give rise to a structure that is very simple to implement. The method can straightforwardly handle both legacy and phasor measurements; particularly, the processing of phasor current measurements does not require any special provisions, unlike previously reported hybrid state estimator implementations over the real domain. Numerical results are reported on networks with up to 9241 nodes, and they demonstrate that the accuracy of the complex variable implementation is competitive with that of the real variable constrained hybrid state estimator, while being significantly faster.

This chapter deals with the power flow problem. The power flow algorithms include the Newton-Raphson method in both polar and rectangular forms, the Gauss-Seidel method, the DC power flow method, and all kinds of decoupled power flow methods such as fast decoupled power flow, simplified BX and XB methods, as well as decoupled power flow without major approximation. Power system state estimation derives a real-time model through the received data from a redundant measurement set. Different kinds of methods about state estimation are introduced in the chapter. Among them, the weighted least squares (WLS) state estimation methods are widely used. There are three most commonly used measurement types in power system state estimation. They are the bus power injections, the line power flows, and the bus voltage magnitudes.

State estimation is often a challenging task in distribution systems due to deploying a limited number of measurement devices. Moreover, the integration of precise distribution-level phasor measurement unites, a.k.a micro-PMUs, along with inaccurate pseudo-measurements in state estimation introduces another challenge. These issues might decrease the efficiency of traditional standard weighted least squares (WLS) for distribution system state estimation. This paper proposes a novel linear distribution system state estimation based on limited number of synchrophasor measurements and pseudo-measurements. To involve pseudo-measurements into the linear state estimation, Taylor's approximation is adopted to reformulate pseudo-measurement functions in a linear form. The results obtained via numerical simulations demonstrate that the proposed linear state estimation method performs as good as the standard nonlinear WLS estimator. Moreover, the sensitivity analyses results show that our method has a better performance compared to WLS once a limited number of highly precise micro-PMUs are accompanied with inaccurate pseudo-measurements in state estimation.

State estimation in power systems is utilized to provide an ongoing data set for controlling and observing power systems' performance. There are a few traditional methods like Weighted Least Square (WLS), Weighted Least Average Value (WLAV), and settled utilizing iterative techniques, for example, Gauss-Newton methods. However, these techniques are sensitive to the operating conditions of power systems and uncertainties associated with Renewable Energy Systems (RESs). These techniques yield poor results in the presence of missing data arising out of unreliable communication networks and false data injection, as in the case of a cyber-attack. This paper proposes Bi-directional LSTM (BiLSTM) based Machine Learning method to forecast the state values of power systems. The BiLSTM model utilizes forward and backward layers, having bidirectional memory, making it capable of estimating both past and future hidden layers data. This paper investigates the performance of the proposed method studied on different test system datasets. The efficacy of the proposed method is investigated by comparing the obtained results with other Machine Learning techniques results in the literature. Further, the BiLSTM model's robustness for state estimation is analyzed in the presence of Gaussian noise and missing data points.

State estimation of power systems containing facts controllers

This chapter addresses the problem of time-varying nonlinear modeling and monitoring of a continuously stirred tank reactor (CSTR) process using state estimation techniques. These techniques include the extended Kalman filter (EKF), particle filter (PF), and the more recently the variational Bayesian filter (VBF). The objectives of this chapter are threefold. The first objective is to use the variational Bayesian filter with better proposal distribution for nonlinear states and parameters estimation. The second objective is to extend the state and parameter estimation techniques to better handle nonlinear and non-Gaussian processes without a priori state information, by utilizing a time-varying assumption of statistical parameters. The third objective is to apply the state estimation techniques EKF, PF and VBF for time-varying nonlinear modeling and monitoring of CSTR process. The estimation performance is evaluated on a synthetic example in terms of estimation accuracy, root mean square error and execution times.

Objective: State estimation is used as a necessary tool for online monitoring, analysis and control of power systems. The main objective of this paper is to deal with static state estimation using the snap shot data and dynamic state estimation which accounts for the time varying behaviour of power system states in to consideration. Methods/Analysis: Effects of inclusion of PMU measurements along with the available metered data have been explored using the weighted least square state estimation technique in this paper. A comparative analysis of static state estimation with and without bad data has been carried out and the bad data has been identified and eliminated by using largest normalized residue test. Findings: To investigate the time varying nature of the system states linear state estimator with second order approximation and kalman filter techniques has been proposed in this paper. Case studies are conducted on IEEE 14 bus test system and the test results obtained from non linear, linear first order, second order and kalman filter techniques have been compared. Application/Improvements: Correction of state variables are obtained using linear state estimation with first order and second order approximation and kalman filter techniques has been compared to get the better state estimation algorithm.

This paper deals with a simple technique for measurement placement method of power system state estimation. The minimum condition number of the measurement matrix is used as the criteria in conjunction with sequential elimination to generalize the measurement placement. The singular value decomposition (SVD) approach will be used to solve the state estimation. The simulation study is performed on the IEEE 14-bus test system by linear weighted least square (WLS). It is found that, this algorithm can give a solution of measurement placement of injection current and voltage that make the power system observable.

Hybrid measurement of the phasor measurement units (PMU) and the supervisory control and data acquisition (SCADA) system is used for state estimation of power transmission system when PMU deployment can not cover all buses. The traditional iterative solution process of state estimation is low efficient and may cause truncation error. A fast state estimation method based on pseudo-measurement modeling of extreme learning machine (ELM) for power transmission system state estimation is proposed. The injected powers measured by SCADA are used as input, the real and imaginary parts of bus voltages are used as output. The pseudo-measurement value model and pseudo-measurement error model are trained using historical data. In the new time, the pseudo-measurements obtained from the trained model are combined with the PMU measurements for fast linear state estimation. The final state estimation results can be obtained quickly. Simulation results of IEEE 14 system show that the proposed method not only improves the accuracy of state estimation, but also greatly reduces the calculation time. It can provide basic information for other applications in EMS accurately and quickly.

Power system state estimation is one of the most important functions of power system control centers. In recent years, the complexity of power system state estimation has significantly increased due to the growing number of distributed, including renewable energy sources, electric vehicles, the demand response technologies, and the increased risk of cyber-attacks. Under these conditions, state estimation methods, which consider information about the time-correlation of the power system states have a great potential. The correlation is described by a transition model. The well-known state estimation methods usually use one single model. However, in case of stochastic behavior of the load and generation, it is impossible to assert the adequacy of the chosen model over the entire observation interval. Therefore, the paper proposes a multi-model forecasting power system state estimation method, which has lower errors in comparison with a single-model assessment at the moments of the lowest accuracy of the latter. Multi-model parameter estimation is used based on three procedures of the single-model Kalman filtering estimation and various transition models based on autoregressive and vector autoregressive analyzes, as well as Holt's exponential smoothing. Uniting the single-model estimation has been carried out according to the criterion of the minimum of variance of the resulting estimate. An algorithm of multi-model power system state estimation has been developed. Its version has been analyzed using a three-model forecasting-aided estimation using linear transition models. The state of the IEEE 30-bus test power system has been assessed by the means of simulation modeling. The maximum accuracy increase of the multi-model estimation in comparison with the single model is set up. 26,1 % is for autoregressive analysis; 16,9 % is for vector regression analysis and 37,7 % is for Holt’s exponential smoothing. The proposed method of multi-model state estimation has higher robustness and accuracy at the moments of the lowest accuracy of single-model estimation. It is advisable to use the method to solve control tasks of power systems with rapidly changing dynamic modes.