State Estimation Solution Research Articles

A parallel approach for ultra-fast state estimation in large power system using graph partitioning theory

This paper introduces a novel approach for multi-area state estimation in large transmission networks through the application of graph partitioning theory. By harnessing the eigenvalues and eigenvectors of the Laplacian matrix, a large-scale transmission network is partitioned into manageable sections. Within these partitions, state estimation processes run in parallel, markedly improving efficiency compared to conventional methods. Linear state estimation is employed within each area, expediting computations and making it adaptable to large-scale networks, which traditionally pose computational challenges. The method's efficacy is demonstrated through comprehensive validation, commencing with small networks and extending to real-world applications on the IEEE 118-bus test system and the 9241-bus European high-voltage transmission network. In comparison to the integrated network method, our approach has achieved state estimation answers with reduced computation time. The partitioning of the integrated network into multi areas has effectively mitigated computational loads, showcasing its potential for enhancing operational efficiency and reliability in complex power transmission systems. This approach not only offers a robust solution for state estimation but also represents a significant stride toward advancing the field of state estimation, promising to bolster the stability and performance of modern power grids.

Decentralized Moving Horizon Estimation for Large-Scale Networks of Interconnected Unconstrained Linear Systems

This paper addresses the problem of designing a decentralized state estimation solution for a large-scale network of interconnected unconstrained linear time invariant (LTI) systems. The problem is tackled in a novel moving horizon estimation (MHE) framework, while taking into account the limited communication capabilities and the restricted computational power and memory, which are distributed across the network. The proposed design is motivated by the fact that, in a decentralized setting, a Luenberguer-based framework is unable to leverage the full potential of the available local information. A method is derived to solve a relaxed version of the resulting optimization problem. It can be synthesized offline and its stability can be assessed prior to deployment. It is shown that the proposed approach allows for significant improvement on the performance of recent Luenberger-based filters. Furthermore, we show that a state-of-the-art distributed MHE solution with comparable requirements underperforms in comparison to the proposed solution.

A Distributed Robust System-Wide State Estimation Method for Power Systems Based on Maximum Correntropy

The distribution of measurement noise applied in practical power system state estimation (PSSE) can deviate from the assumed Gaussian model and the performance of an estimator becomes bad if the Gaussian model is still used. This paper proposes a new distributed robust PSSE method for multi-area power systems. The non-Gaussian model is utilized to fit the measurement noise distribution to reach high model accuracy. The proposed distributed method is derived based on the maximum correntropy criterion to further reduce the impact of non-Gaussian measurement noise and outliers. The influence function combined with the finite-time average consensus algorithm is used to implement the proposed distributed robust method in a fully distributed manner. Simulations conducted on the IEEE 30-bus, 118-bus and 300-bus systems and the Polish 2383-bus system demonstrate the robustness and effectiveness of the proposed distributed method. Each local area can get the system-wide robust state estimation solution by only using local information and small amounts of data from neighboring areas. Our proposed distributed robust method has at least twelve percent improvement in reducing the mean squared error under Gaussian-Uniform noise. It is verified the communication network applied for the proposed method is fairly flexible while the existing distributed approaches use a fixed communication network when the power systems are partitioned. The simulation results also verify the robustness of the proposed method to bad data and communication failure.

IEC 61850-9-2 based module for state estimation in co-simulated power grids

<p><span lang="EN-US">This paper presents a research context on the virtualization of phasor measurement units (PMUs) and real-time power grids simulation with state estimation. In this research, real-time simulation is introduced to use powerful features for validating state estimation solutions with PMUs. Virtual and online measurement equipment are reviewed in this manuscript to develop an innovative integration of the OpenPMU incorporated with a real-time simulation power grid and additional virtualized PMUs. The implementation of the platform has useful features within the infrastructure that allows the user to reproduce a detailed modeled power grid with simulation software. The use of real-time simulation tools brings several possibilities for improving testing and prototype assessment with higher precision in different applications. In this case, 2 tests power systems are evaluated by realistic integration of IEC61850-9-2 data utilization to observe the performance of a customized state estimation approach. The study implements a versatile methodology for commissioning OpenPMU devices, interacting simultaneously with additional virtual PMUs within the same simulation through sampled values (SV) to validate the measurement frames and assess the estimation with the generated data. Finally, the proposed work identifies the potential of virtualizing PMUs and the features of the OpenPMU applied to state estimation in conjunction with real-time simulation data.</span></p>

Graph neural networks on factor graphs for robust, fast, and scalable linear state estimation with PMUs

As phasor measurement units (PMUs) become more widely used in transmission power systems, a fast state estimation (SE) algorithm that can take advantage of their high sample rates is needed. To accomplish this, we present a method that uses graph neural networks (GNNs) to learn complex bus voltage estimates from PMU voltage and current measurements. We propose an original implementation of GNNs over the power system’s factor graph to simplify the integration of various types and quantities of measurements on power system buses and branches. Furthermore, we augment the factor graph to improve the robustness of GNN predictions. This model is highly efficient and scalable, as its computational complexity is linear with respect to the number of nodes in the power system. Training and test examples were generated by randomly sampling sets of power system measurements and annotated with the exact solutions of linear SE with PMUs. The numerical results demonstrate that the GNN model provides an accurate approximation of the SE solutions. Furthermore, errors caused by PMU malfunctions or communication failures that would normally make the SE problem unobservable have a local effect and do not deteriorate the results in the rest of the power system.

Hierarchical mixture of experts for autonomous unmanned aerial vehicles utilizing thrust models and acoustics

Accurate position, velocity, attitude, and angular velocity state estimation is crucial for unmanned aerial vehicles, especially in enabling them with autonomous capabilities. It is necessary to adequately model and account for all the environmental and dynamic flight parameters. A hierarchical mixture of experts (HME) framework has been viable in improving state estimation accuracy in interplanetary orbit determination problems, and this paper proposes an extension for quadcopters. It is shown that the state and motor angular velocity estimation accuracy can be significantly improved by processing different thrust models, and acoustic parameters have an important, previously unreported, role in this improvement. Higher motor angular velocities produce higher noise levels, and thus, the relationships of the onboard acoustic measurements to the vehicle state parameters play an essential part in estimation. The motor angular velocities’ estimations depend on the extended Kalman filter solutions or an acoustic curve fit. The experts in the HME framework utilize the state estimation solutions from the extended Kalman filters and the motor angular velocity estimations to compare against the telemetry data as truth. The overall HME solution is compared against a non-acoustic static thrust model. Illustrative examples and analysis presented in this paper reveal that the proposed estimation solutions can also apply to other flight vehicles for onboard real-time implementation to leverage autonomy.

The Simple Solution for Nonlinear State Estimation of Ill-Conditioned Systems: The Normalized Unscented Kalman Filter

An easy-to-implement method for nonlinear state estimation for ill-conditioned systems is proposed. By propagating standard deviations and correlations instead of the covariance in the unscented Kalman filter (UKF), the condition numbers of relevant matrices are reduced. The reduction in the condition number is related to the scaling of the problem. Hence, what we propose is a normalization method that acts as an “auto-scaler”. Compared to other methods in state estimation for ill-conditioned systems, our proposed method factors the covariance matrix into physically meaningful statistics which can be used to check for filter divergence online. The method is compared to a standard UKF in a case study and shows a significant reduction in the condition number.

A Backward–Forward Sweep Algorithm for Distribution System State Estimation

Grid monitoring is today essential to provide situational awareness and to enable the smart management of distribution networks. Due to the diverse characteristics of the distribution grids, different monitoring approaches may be required, or more convenient, in each distribution system scenario. This paper presents a novel state estimation solution based on the Backward-Forward Sweep method, which is tailored to the monitoring of radially operated distribution grids. Differently from the standard Backward-Forward Sweep algorithm used for power flow analysis, the designed algorithm allows integrating redundant measurements, including power and current measurements in the branches as well as multiple voltage measurements, as needed for state estimation purposes. The proposed formulation achieves the same accuracy performance of classical Weighted Least Squares estimators, while offering the typical benefits of the Backward-Forward Sweep approach: simplicity, robust convergence, low computational burden and no risk of ill-conditioning issues. The paper presents the design of the Backward-Forward Sweep estimator and validates the proposed formulation via tests performed on the three-phase unbalanced IEEE 123-bus grid.

Enhancing topology error detection via multiple measurement scans

In today’s energy management systems, the network model being fed into state estimation (SE) is assumed to be free of topology errors. In this conventional approach, bus-branch (BB) models are created as electrical equivalents of the actual network. If any topology error goes undetected while forming BB models, the subsequent SE solution will be either biased or divergent. To deal with topology errors, in this paper, a topology tracking method, using the detailed node-breaker (NB) models, is formulated. In large systems, it is computationally intensive to run SE and the following bad data tests. Therefore, SE analysis is carried out every few minutes, which is less frequent than the measurement updates (every few seconds). Since contingencies develop quickly (less than a second), the switching device flows in a few substations can change significantly from one measurement scan to the next. To identify the substation most impacted by the event, an efficient SE procedure based on the Lasso (least absolute shrinkage and selection operator) method is developed. Then, the correct topology is obtained by running a localized SE centered around the identified substation. The efficacy of the proposed approach is demonstrated both in a small 13-bus and a large 300-bus IEEE test cases.

A General Regularized Distributed Solution for System State Estimation From Relative Measurements

This work presents a novel general regularized distributed solution for the state estimation problem in networked systems. Resting on the graph-based representation of sensor networks and adopting a multivariate least-squares approach, the designed solution exploits the set of the available inter-sensor relative measurements and leverages a general regularization framework, whose parameter selection is shown to control the estimation procedure convergence performance. As confirmed by the numerical results, this new estimation scheme allows (i) the extension of other approaches investigated in the literature and (ii) the convergence optimization in correspondence to any (undirected) graph modeling the given sensor network.

Image Processing Based Approach for False Data Injection Attacks Detection in Power Systems

With more sensors being installed by utilities for accurate control of power grids, there is a growing risk of vulnerability to sophisticated data integrity attacks such as false data injection (FDI), circumventing current bad data detection schemes resulting in inaccurate state estimation solutions. While diverse automated detectors to battle FDI have been grown, such methodologies underestimate the strong analytical abilities of humans. This is while most proposed automated methods need observant human control. Although automated methods provide opportunities to improve scalability, humans can cope with exceptions and new attack trends. In this paper, to address the ever-increasing cyber-attack challenge in power systems, a visualization based attack detection framework using deep learning techniques is developed to provide human security researchers with improved techniques to uncover trends, identify outliers, recognize correlations, and communicate their results. Specifically, we first encode multivariate systems state time-series data into 2D colored images and then utilize a carefully designed deep convolutional neural network (CNN) classifier. The proposed method is developed to allow network operators to immediately capture and visually understand the statistical features of a network attack at a glance. The proposed method has been evaluated on the IEEE 14-bus and IEEE 118-bus systems. Our experiments show that the proposed framework accomplishes high classification accuracy.

Discrete-time distributed Kalman filter design for networks of interconnected systems with linear time-varying dynamics

This paper addresses the problem of designing distributed state estimation solutions for a network of interconnected systems modelled by linear time-varying (LTV) dynamics in a discrete-time framework. The problem is formulated as a classical optimal estimation problem, for the global system, subject to a given sparsity constraint on the filter gain, which reflects the distributed nature of the network. Two methods are presented, both of them able to compute a sequence of well-performing stabilising gains. Moreover, both methods are validated by resorting to simulations of: (i) a randomly generated synthetic LTV system; and (ii) a large-scale nonlinear network of interconnected tanks. One of the proposed methods relies on a computationally efficient solution, thus it is computed very rapidly. The other achieves better performance, but it is computationally more expensive and requires that a window of the future dynamics of the system is known. When implemented to a nonlinear network, approximated by an LTV system, the proposed methods are able to compute well-performing gains that stabilise the estimation error dynamics. Both algorithms are scalable, being adequate for implementation in large-scale networks.

A multi-model ensemble digital twin solution for real-time unsteady flow state estimation of a pumping station

This paper proposes a digital twin solution for unsteady flow state estimation in a pumping station. Digital twin is expected to accurately estimate the real-time hydraulic parameters of blind spots of the pumping station system even under some adverse conditions including the interference of observation noise and model parameters drift. To solve these challenges, a digital twin framework integrating the model-driven method, control theory and data-driven method is presented. In this framework, an unsteady flow state estimation method combining frequency domain analysis and generalized predictive control theory is developed for the first time, which is superior to traditional time-domain numerical discrete methods in terms of computational efficiency and anti-noise interference. In the model parameter calibration process, the novelty concerns modeling of the optimization problem considering the dynamic operation control of the station and unsteady flow of pipelines. And this process is accomplished through the comprehensive application of the model-free adaptive control algorithm, the transient flow model and the particle swarm optimization algorithm. This work is applied to a pumping station in a product pipeline to verify its effectiveness in estimating the transient flow state of data blind spots and map the dynamic operation behavior under the interference of colored noise and parameter drift.

GPU-based matrix structure driven state estimation for large-scale power systems

The rapid development of the power grid brings more computational burden to the online state monitoring of the power system. State estimation (SE), the key fundamental part as well as the cornerstone of other applications, requires urgent improvement in its computing efficiency. Recently, the graphics processing unit (GPU) provides potentials for computationally intensive tasks. This paper proposes a GPU-based matrix structure driven (MSD) strategy for the Weighted Least Squares (WLS) state estimator. In this scheme, structures of all the sparse matrices are determined on CPU in advance and numerical calculations are completed during each iteration, with carefully-tuned kernels on GPU. Besides, a novel parallel algorithm is designed to tackle the sparse matrix–matrix multiplication (SPMM) problem, where shared memory is exploited to a great extent for performance improvement. Case studies verify the superiority of the framework and results show that the proposed MSD-SE solution is 4.97 times faster than the CPU-based SE solution on a 27723-bus system.

Cyber Attack Detection Based on Wavelet Singular Entropy in AC Smart Islands: False Data Injection Attack

Since Smart-Islands (SIs) with advanced cyber-infrastructure are incredibly vulnerable to cyber-attacks, increasing attention needs to be applied to their cyber-security. False data injection attacks (FDIAs) by manipulating measurements may cause wrong state estimation (SE) solutions or interfere with the central control system performance. There is a possibility that conventional attack detection methods do not detect many cyber-attacks; hence, system operation can interfere. Research works are more focused on detecting cyber-attacks that target DC-SE; however, due to more widely uses of AC SIs, investigation on cyber-attack detection in AC systems is more crucial. In these regards, a new mechanism to detect injection of any false data in AC-SE based on signal processing technique is proposed in this paper. Malicious data injection in the state vectors may cause deviation of their temporal and spatial data correlations from their ordinary operation. The suggested detection method is based on analyzing temporally consecutive system states via wavelet singular entropy (WSE). In this method, to adjust singular value matrices and wavelet transforms' detailed coefficients, switching surface based on sliding mode controller are decomposed; then, by applying the stochastic process, expected entropy values are calculated. Indices are characterized based on the WSE in switching level of current and voltage for cyber-attack detection. The proposed detection method is applied to different case studies to detect cyber-attacks with various types of false data injection, such as amplitude, and vector deviation signals. The simulation results confirm the high-performance capability of the proposed FDIA detection method. This detection method's significant characteristic is its ability in fast detection (10 ms from the attack initiation); besides, this technique can achieve an accuracy rate of over 96.5%.

Dynamic Process Operation Under Demand Response – A Review of Methods and Tools

AbstractParticipating in electricity markets through demand response causes new requirements for optimizing process control of chemical plants. The last ten years have brought great advances in the formulation and solution of economic nonlinear model predictive control and state estimation to support operation of processes under dynamic constraints. However, gaps remain regarding the availabilities of suitable plant models capable of describing processes active in demand response as well as of robust schemes for state estimation and economic nonlinear model predictive control in commercial tools.

A Nonlinear Double Model for Multisensor-Integrated Navigation Using the Federated EKF Algorithm for Small UAVs.

Aimed at improving upon the disadvantages of the single centralized Kalman filter for integrated navigation, including its fragile robustness and low solution accuracy, a nonlinear double model based on the improved decentralized federated extended Kalman filter (EKF) for integrated navigation is proposed. The multisensor error model is established and simplified in this paper according to the near-ground short distance navigation applications of small unmanned aerial vehicles (UAVs). In order to overcome the centralized Kalman filter that is used in the linear Gaussian system, the improved federated EKF is designed for multisensor-integrated navigation. Subsequently, because of the navigation requirements of UAVs, especially for the attitude solution accuracy, this paper presents a nonlinear double model that consists of the nonlinear attitude heading reference system (AHRS) model and nonlinear strapdown inertial navigation system (SINS)/GPS-integrated navigation model. Moreover, the common state parameters of the nonlinear double model are optimized by the federated filter to obtain a better attitude. The proposed algorithm is compared with multisensor complementary filtering (MSCF) and multisensor EKF (MSEKF) using collected flight sensors data. The simulation and experimental tests demonstrate that the proposed algorithm has a good robustness and state estimation solution accuracy.

Hybrid data‐driven physics model‐based framework for enhanced cyber‐physical smart grid security

This paper presents a hybrid data-driven physics model-based framework for real time monitoring in smart grids. As the power grid transitions to the use of smart grid technology, it's real time monitoring becomes more vulnerable to cyber attacks like false data injections (FDI). Although smart grids cyber-physical security has an extensive scope, this paper focuses on FDI attacks, which are modeled as bad data. State of the art strategies for FDI detection in real time monitoring rely on physics model-based weighted least squares state estimation solution and statistical tests. This strategy is inherently vulnerable by the linear approximation and the companion statistical modeling error, which means it can be exploited by a coordinated FDI attack. In order to enhance the robustness of FDI detection, this paper presents a framework which explores the use of data-driven anomaly detection methods in conjunction with physics model-based bad data detection via data fusion. Multiple anomaly detection methods working at both the system level and distributed local detection level are fused. The fusion takes into consideration the confidence of the various anomaly detection methods to provide the best overall detection results. Validation considers tests on the IEEE 118 bus system.

Fast Nonconvex SDP Solvers for Large-Scale Power System State Estimation

Fast power system state estimation (SE) solution is of paramount importance for achieving real-time decision making in power grid operations. Semidefinite programming (SDP) reformulation has been shown effective to obtain the global optimum for the nonlinear SE problem, while suffering from high computational complexity. Thus, we leverage the recent advances in nonconvex SDP approach that allows for the simple first-order gradient-descent (GD) updates. Using the power system model, we can verify that the SE objective function enjoys nice properties (strongly convex, smoothness) which in turn guarantee a linear convergence rate of the proposed GD-based SE method. To further accelerate the convergence speed, we consider the accelerated gradient descent (AGD) extension, as well as their robust versions under outlier data and a hybrid GD-based SE approach with additional synchrophasor measurements. Numerical tests on the IEEE 118-bus, 300-bus and the synthetic ACTIVSg2000-bus systems have demonstrated that FGD-SE and AGD-SE, can approach the near-optimal performance of the SDP-SE solution at significantly improved computational efficiency, especially so for AGD-SE.

Avoiding Divergence in Multi-Area State Estimation

This paper is concerned about the divergence of state estimation solution for multi-area power grids. Such cases typically occur due to a single anomaly in the measurement set or network model, yet will cause failure of the state estimator to provide the solution for the entire system. The objective of our study is to develop an approach that will allow detection, identification, and isolation of the anomaly during the state estimation solution so that a large percentage of the system states can still be estimated, while isolating the anomaly that is causing the divergence of the estimator. The proposed approach is described in detail and its effective utilization for a very large utility system is illustrated by simulations.