Adaptive State Estimation for Power Systems Measured by PMUs With Unknown and Time-Varying Error Statistics

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.

This paper presents a new power system state estimation method based on pseudo-measurements. The conventional and synchronizing phasor measurements are employed to calculate the pseudo-measurements of voltage and current phasors. Using pseudo-measurement, the measurement matrix which describes relations between measurements and state variables contains only 0 or 1. In this work, the state estimation problem is formulated based on the weighted least absolute value (WLAV) criteria. The solutions are obtained by an interior point method considering equality and inequality constraints. Comparisons with the conventional hybrid method are also performed on the IEEE 14-bus system in the presence of bad data. Results indicate that the proposed method can provide accurate solutions but with smaller computation time.

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.

<p>The realization of advanced electrical grid functionalities, e.g., phasor measurement unit (PMU) information acquisition in wide-area monitoring systems (WAMS), requires a scalable and reliable underlying communication technology. Cellular networks, e.g., LTE/LTE-A systems, appear as a promising option to facilitate the smart grid evolution. However, the effect of LTE communication constraints on power system state estimation (SE) has not been thoroughly addressed in the literature. In this paper, we investigate the impact of the LTE random access channel (RACH) reliability on the transmitted PMU measurements and, consequently, on the SE accuracy. In particular, we assess the SE performance based on the achieved reliability per PMU attained with i) increasing number of contending devices in the system, i.e., smart meters and PMUs, and ii) varying cell coverage range. Numerical results demonstrate that, under different network and traffic configurations, SE accuracy can be significantly affected by the RACH reliability levels. Useful insights can thus be drawn for a reliability-aware design of a power system state estimator in LTE-based WAMS.</p>

Accurate state estimation is essential for correct supervision of power grids. With the existence of cyber-attacks, state estimation may become inaccurate, which can eventually lead to wrong supervisory decision making. To detect cyber-attacks in power grids equipped with phasor measurement units (PMUs), a new intrusion detection system based on clustering approach, called PMU Intrusion Detection System (PMUIDS), is proposed in this article. After solving the optimal PMU placement in <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> -1 contingency, several static state estimations are obtained by removing the measurements of one PMU in each time. The resulting state vectors are clustered in two steps: First, subtractive clustering is employed to obtain the number of clusters, which determines the number of integrity attacks; and second, fuzzy C-means clustering assigns the state vectors to the corresponding clusters, which determines the attacked PMUs. In addition, two theorems are proved, which indicate that the attacker cannot coordinate successful stealth attacks in cases that by removing attacked PMUs from state estimation, the power system still remains full observable. Furthermore, in the case of possible stealth attacks, the attacker cannot falsify the estimation of any arbitrary state variable. The hardware-in-the-loop results on a sample power system show that the proposed approach can detect integrity attacks, determine the number of attacks, obtain the correct state vector, and localize the attacks, even in case of multiple simultaneous attacks.

This paper presents a privacy preserving approach to decentralized state estimation in multi-area power systems. By formulating state estimation as a model-distributed regularized least-squares (MDRLS) problem, we ensure that the state variables and system matrix of each area are hidden from all other areas in order to protect privacy and sensitive information. We present a scheme that solves the primal MDRLS problem using the alternating direction method of multipliers, and a second method that solves the dual problem using a distributed form of the coordinate descent algorithm. Only information related to current measurements on tie-lines linking neighboring areas is exchanged between those areas. The proposed schemes enable the local state estimator in each area to estimate the voltage magnitude and phase angle of each bus in its own control area from phasor measurement units (PMU) without the need for full local PMU-observability. The novelty of the proposed methods is in that they employ the inherently hierarchical architecture of the wide-area monitoring system to perform decentralized state estimation. Our simulation results show that the estimation error of both methods converges to that of the centralized approach.

The accurate real-time state estimation is needed to perform real-time monitoring and control. However, the current power system uses SCADA technology as a tool for monitoring and control. SCADA existing measurement device has a few disadvantages: low accuracy, low sampling rate in measuring the measurements data, and asynchronous measurements between instrument. Due to those disadvantages, state estimation resulted has low accuracy, and not in real-time. These disadvantages can be minimized by installing several phasor measurement unit (PMU). IEEE-30 bus test system is applied to simulate the proposed technique. The result shows, the required PMU should be installed in power system that already has 116 conventional SCADA measurements is 6. The location of these PMUs are in buses 2, 10, 12, 15, 25, and 27. That result is achieved in 320 iteration of genetic algorithm (GA). In this paper, mean absolute error (MAE) is used to asses the state estimation accuracy. The value of $\overline {MAE} $ system with PMU is 7.20718X10−6. While, the value of $\overline {MAE} $ system without PMU is 0.110162054.

In this paper, we model the generalized power system state estimation problem as a hybrid estimation problem in which the network configuration and voltage phasor states are treated as discrete and continuous states, respectively. We propose the Multiple model Adaptive Power system State Estimator (MAPSE), which implements a multiple model adaptive estimator with a bank of Unscented Kalman Filters (UKFs) to provide a running estimate of the voltage phasor states and a probability distribution for the candidate network configurations. The MAPSE updates the network configuration probability distribution by applying a Bayesian recursion to the measurement residuals from each of the UKFs at each timestep. Simulation on a modified version of the 33 node distribution network demonstrates successful network configuration detection and accurate voltage phasor state estimation.

Dynamic state estimation of a power system provides essential information about its inherent dynamic change. Nonlinear Kalman filters (NKFs) have been identified as potential versatile tools in performing state estimations. One key challenge of using NKFs lies in the fact that the available observations are inaccurate due to the presence of non-Gaussian noise that degrades the filtering precision and robustness. Some robust NKFs are developed to correct the state estimation via using robust optimality criteria or approximating the posterior density. Considering that the essence in these robust NKFs is to weight the error covariance and noise variance, we propose a novel method that can directly act on measurement to weight error covariance and noise variance. The novel method is based on a square root unscented Kalman filter that can enhance the numerical stability. Then, a weighting factor is applied to the measurement model for alleviating the effect of abnormal measurement errors. The weighting factor is derived from consideration of an anisotropy covariance function and an upper envelope of the traditional &#x201C;sinc&#x201D; function for suppressing large measurement errors and retaining the information of very large errors. We call the new filter the square root unscented Kalman filter with modified measurement (SRUKF-MM). The proposed SRUKF-MM is applied to state estimation of the Western System Coordinating Council (WSCC) 3-machine system and the Northeastern Power Coordinating Council (NPCC) 48-machine system in a non-Gaussian noise environment. Simulation results show that the proposed method achieves significantly improved filtering performance compared to other related NKFs.

Maintaining reliability during power system operation relies heavily on the operator’s knowledge of the system and its current state. With the increasing complexity of power systems, full system monitoring is needed. Due to the costs to install and maintain measurement devices, a cost-effective optimal placement is normally employed, and as such, state estimation is used to complete the picture. However, in order to provide accurate state estimates in the current power system climate, the models must be fully expanded to include probabilistic uncertainties and non-linear assets. Recognizing its analogous relationship with state estimation, machine learning and its ability to summarily model unseen and complex relationships between input data is used. Thus, a power system state estimator was developed using modified long short-term (LSTM) neural networks to provide quicker and more accurate state estimates over the conventional weighted least squares-based state estimator (WLS-SE). The networks are then subject to standard polynomial scheduled weight pruning to further optimize the size and memory consumption of the neural networks. The state estimators were tested on a hybrid AC/DC distribution system composed of the IEEE 34-bus AC test system and a 9-bus DC microgrid. The conventional WLS-SE has achieved a root mean square error (RMSE) of 0.0151 p.u. for voltage magnitude estimates, while the LSTM’s were able to achieve RMSE’s between 0.0019 p.u. and 0.0087 p.u., with the latter having 75% weight sparsity, estimates about ten times faster, and half of its full memory requirement occupied.

State estimation is the core operation performed within the energy management system (EMS) of smart grid. Hence, the reliability and integrity of a smart grid relies heavily on the performance of sensor measurement dependent state estimation process. The increasing penetration of cyber control into the smart grid operations has raised severe concern for executing a secured state estimation process. The limitation with regard to monitoring large number of sensors allows an intruder to manipulate sensor information, as one of the soft targets for disrupting power system operations. Phasor measurement unit (PMU) can be adopted as an alternative to immunize the state estimation from corrupted conventional sensor measurements. However, the high installation cost of PMUs restricts its installation throughout the network. In this paper a graphical approach is proposed to identify minimum PMU placement locations, so as to detect any intrusion of malicious activity within the smart grid. The high speed synchronized PMU information ensures processing of secured set of sensor measurements to the control center. The results of PMU information based linear state estimation is compared with the conventional non-linear state estimation to detect any attack within the system. The effectiveness of the proposed scheme has been validated on IEEE 14 bus test system.

This paper considers robust allocation of additional phasor measurement units (PMUs) into a PMU network in order to meet a data availability profile in the face of random communication interruptions and transmission line faults. Synchrophasor availability (SA) at a bus is the fraction of time the time-synchronized current/voltage phasors are correctly present for real-time usage. An algorithm that achieves the above objectives is developed. The algorithm switches between a placement step solved via integer programming and an SA evaluation step that uses a bus-centric stochastic model to efficiently determine the need for another placement step with a tightened constraint. The algorithm is shown to subsume the phasor observability and is equally applicable PMU network upgrade and creation. Scalability and computational efficiency of the algorithm are analyzed. The results of tests of the algorithm applied to the IEEE 118-bus system are reported, which are performed under a variety of availability specifications and random event arrival rates associated with communication interruptions, equipment faults, and their removals. Superior accuracy and fault tolerance in state estimation are achieved by PMU networks meeting more stringent SA.

State estimation in today's power systems is one of the effective tools for control and monitoring which is of great importance. In state estimation context, measurement and observability of the power system is important. One of the effective and accurate tools for parameter measurement is the phasor measurement unit (PMU). This type of measurement device has an advanced communication system with fast sampling rate. PMUs are costly; thus, optimal location is performed with minimum number of such measurements in the power system. Indeed, optimal number of such devices should satisfy observability of the system also. In this paper, a new method is proposed based on connection matrix of the power system for locating PMUs. Advantage of this method is its simple implementation on small and medium networks which follows a simple and clear algorithm. In this paper, the proposed method is tested on IEEE standard 18, 24 and 30 bus power systems and the results validate this method.

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.

This paper discusses an optimal joint placement problem of phasor measurement units (PMUs) and flow measurement devices for ensuring topological observability of power systems under N-2 transmission contingencies. Previous relevant studies focus on topological observability with the least-cost deployment of PMUs and flow measurement devices. In comparison, besides minimizing the total investment cost of PMUs and flow measurements, the proposed optimal location-based joint placement model also optimizes their locations for avoiding PMUs on radial nodes and encouraging flow measurements incident to nodes that are adjacent to PMU installed buses. The proposed model can be equivalently formulated as a mixed-integer linear programming (MILP) problem and solved via a decomposition based algorithm. Effectiveness of the proposed model is verified via a 14-bus IEEE power system. Numerical results show that, compared to traditional optimal joint placement models, optimal locations obtained by the proposed approach lead to noticeable improvements in state estimation accuracy when time skew errors are considered.