State Estimation Approach Research Articles

Data-driven dynamic state estimation in power systems via sparse regression unscented Kalman filter

This paper proposes a novel data-driven modeling and dynamic state-estimation approach for nonlinear power and energy systems, highlighting the critical role of a known dynamic model for accurate state estimation in the face of uncertainty and complex models. The proposed framework consists of a two-phase approach: data-driven model identification and state-estimation. During the model identification phase, which spans a relatively short time interval, state feedback is collected to identify the dynamics of the nonlinear systems in the power grid using a novel density-guided sparse identification algorithm. Unlike conventional sparse regression, which relies on a large library of linear and nonlinear functions to fit data, our proposed algorithm iteratively updates a relatively small initial library by adding higher-order nonlinear functions if the coefficients of the current functions are dense. Following the identification of the model’s dynamics, the estimation phase addresses the challenge of incomplete state measurements. By implementing an unscented Kalman filter, the state variables of the system are dynamically estimated by measuring the noisy output. Finally, simulation results on an IEEE 30-bus system are presented to illustrate the effectiveness of the density-guided sparse regression unscented Kalman filter compared to a physics-based unscented Kalman filter with model uncertainty. This study contributes to the fields of data-driven modeling techniques, machine learning for power systems, and computational intelligence in smart grids. It emphasizes the use of advanced sparse regression and unscented Kalman filter methods for state estimation, enhancing the robustness and accuracy of monitoring and control in electrical and energy systems.

Three-Dimensional CKANs: UUV Noncooperative Target State Estimation Approach Based on 3D Convolutional Kolmogorov–Arnold Networks

Accurate and stable estimation of the position and trajectory of noncooperative targets is crucial for the safe navigation and operation of sonar-equipped underwater unmanned vehicles (UUVs). However, the uncertainty associated with sonar observations and the unpredictability of noncooperative target movements often undermine the stability of traditional Bayesian methods. This paper presents an innovative approach for noncooperative target state estimation utilizing 3D Convolutional Kolmogorov–Arnold Networks (3DCKANs). By establishing a non-Markovian model that characterizes state estimation of UUV noncooperative targets under uncertain observations, we leverage historical data to construct 3D Convolutional Kolmogorov–Arnold Networks. This network learns the patterns of sonar observations and target state transitions from a substantial offline dataset, allowing it to approximate the posterior probability distribution derived from past observations effectively. Additionally, a sliding window technique is integrated into the convolutional neural network to enhance the estimator’s fault tolerance with respect to observation data in both temporal and spatial dimensions, particularly when posterior probabilities are unknown. The incorporation of the Kolmogorov–Arnold representation within the convolutional layers enhances the network’s capacity for nonlinear expression and adaptability in processing spatial information. Finally, we present statistical experiments and simulation cases to validate the accuracy and stability of the proposed method.

Joint detection and localization of False Data Injection Attacks in smart grids: An enhanced state estimation approach

The transition to smart grids introduces significant cybersecurity vulnerabilities, particularly with the rise of False Data Injection Attacks (FDIAs). These attacks allow malicious actors to manipulate sensor data, alter the internal state of the grid, and bypass traditional Bad Data Detection (BDD) systems. FDIAs pose a serious threat to grid security, potentially leading to incorrect state estimation and destabilization of the power system, which could result in system outages and economic losses. To address this challenge, this paper proposes a novel detection and localization method. First, false data and measurement errors are modeled as non-Gaussian noise. Recognizing the limitations of the traditional Extended Kalman Filter (EKF) under non-Gaussian conditions, the Maximum Correntropy Criterion (MCC) is integrated into the EKF to improve the robustness of state estimation. Additionally, the Maximum Correntropy Criterion Extended Kalman Filter (MCCEKF) is combined with Weighted Least Squares (WLS), and cosine similarity is introduced to quantify the differences between these two estimators for FDIA detection. A partition approach is then used to construct a logical localization matrix, with cosine similarity detection applied in each section to generate a detection matrix. By performing a logical AND operation on these matrices, the attacked bus is identified. Simulations on IEEE-14-bus and IEEE-30-bus systems validate the proposed approach, demonstrating its effectiveness in reliably detecting and localizing FDIAs in smart grids.

Model-free distributed state estimation with local measurements.

In this paper, the state estimation problem of physical plants with unknown system dynamic is revisited from the perspective of limited output information measurement, which corresponds to those with characteristics of high-dimensional, wide-area coverage and scatter. Given this fact, a network of sensors are used to carry out the measurement with each one accessing only partial outputs of the targeted systems and a novel model-free state estimation approach, named distributed stochastic variational inference state estimation, is proposed. The key idea of this method is to compensate for the impacts of local output measurements by adding nearest-neighbor rule-based information interaction among estimators to complete the state estimation. It finds from the numerical experiments that the proposed method has clear advantages in both estimation accuracy and speed, and it also provides guidance on how to improve the efficiency of state estimation under local measurements.

Adaptive polynomial Kalman filter for nonlinear state estimation in modified AR time series with fixed coefficients

AbstractThis article presents a novel approach for adaptive nonlinear state estimation in a modified autoregressive time series with fixed coefficients, leveraging an adaptive polynomial Kalman filter (APKF). The proposed APKF dynamically adjusts the evolving system dynamics by selecting an appropriate autoregressive time‐series model corresponding to the optimal polynomial order, based on the minimum residual error. This dynamic selection enhances the robustness of the state estimation process, ensuring accurate predictions, even in the presence of varying system complexities and noise. The proposed methodology involves predicting the next state using polynomial extrapolation. Extensive simulations were conducted to validate the performance of the APKF, demonstrating its superiority in accurately estimating the true system state compared with traditional Kalman filtering methods. The root‐mean‐square error was evaluated for various combinations of standard deviations of sensor noise and process noise for different sample sizes. On average, the root‐mean‐square error value, which represents the disparity between the true sensor reading and estimate derived from the adaptive Kalman filter, was 35.31% more accurate than that of the traditional Kalman filter. The comparative analysis highlights the efficacy of the APKF, showing significant improvements in state estimation accuracy and noise resilience.

Distribution System State Estimation Based on Power Flow-Guided GraphSAGE

Acquiring real-time status information of the distribution system forms the foundation for optimizing the management of power system operations. However, missing measurements, bad data, and inaccurate system models present a formidable challenge for distribution system state estimation (DSSE) in practical applications. This paper proposes a physics-informed graphical learning state estimation approach, to address these limitations by integrating power flow equations and GraphSAGE. The generalization ability of GraphSAGE for unknown nodes is used to perform inductive learning of measurement information. For unseen measurement points in the training set, the simulation proves that the proposed approach can still satisfactorily predict the state quantity. The training process is guided by power flow equations to ensure it has physical significance. Additionally, the possibility of applying the proposed approach to an actual distribution area is explored. Equivalent preprocessing of the three-phase voltage measurement data of the actual distribution area is conducted to improve the estimation accuracy of the transformer measurement points and simplify the computation required for state estimation.

Event-triggered fixed-time distributed observers for general linear systems

This paper delves into the implementation of a distributed fixed-time state estimation approach for linear systems, utilizing an event-triggered strategy. Particularly, the output data from the linear systems are strategically distributed across various observers. A novel fixed-time distributed observer is proposed to reconstruct full states of the linear system cooperatively with the observer error converges to zero within fixed time. Based on the event-triggered strategy, the communication times among observers are reduced by intermittent communication. Simultaneously, Zeno-behavior is ruled out completely. Finally, the proposed results are verified by a simulation example.

Physics and data‐driven approach for online joint state and parameter estimation of electricity and steam networks

Physics and data‐driven approach for online joint state and parameter estimation of electricity and steam networks

A least-squares identification method for vehicle cornering stiffness identification from common vehicle sensor data

In this study, we present a robust framework for vehicle tire cornering stiffness identification, leveraging commonly available lateral acceleration and yaw rate measurements. In contrast to most of the state-of-the-art approaches, our methodology does not rely on (augmented) state estimation, but on batch least-squares optimisation of larger time windows. This batch-approach has as a major benefit that many of the observability issues which are encountered in estimation-based methods are completely eliminated. By immediately exploiting the measurement equations, rather than comparing dynamic simulation responses, we obtain a very efficient and sparse formulation which enables online processing. The methodology was validated on (openly available) datasets from two different vehicles – a Ferrari 250LM and Range Rover Evoque, delivering consistent and accurate results for both vehicles. This work shows that batch optimisation can be a very promising alternative for the more common state-estimation approaches for extracting reliable vehicle cornering stiffnesses in various driving scenarios with a much more straightforward tuning.

A data-driven optimization-based approach for freeway traffic state estimation based on heterogeneous sensor data fusion

Accurate estimation of freeway traffic states is crucial for designing effective traffic management and operational strategies. The integration of various sensor data, such as data from the Electronic Toll Collection (ETC) system and traffic detectors, can significantly enhance the granularity and coverage of traffic state estimation. This study introduces a data-driven optimization-based approach for estimating freeway traffic states, leveraging the fusion of ETC data with detector data. This methodology capitalizes on the broad coverage provided by ETC data and the fine granularity offered by detector data. The probabilistic interdependence between the traffic state of a segment and its upstream and downstream counterparts is captured from real-world traffic state data. Two optimization models, based on the maximum likelihood and maximin likelihood principles, are developed to accurately depict the distribution patterns of freeway traffic states. To address the computational challenges of large-scale scenarios, the study proposes both a decomposition algorithm and a heuristic algorithm. A case study utilizing real-world data from the G92 freeway in Zhejiang, China, is conducted. The findings indicate that the two optimization models exhibit commendable accuracy, with mean absolute percentage errors of 0.9% and 2.3% during peak hours, and 0.9% and 1.4% during off-peak hours, respectively.

A Kalman filter approach for state estimation in weakly monitored active distribution networks

Distribution networks are becoming active to improve security of operation under high net load volatility. Yet, the deployment of active devices creates new challenges to the operation of the weakly monitored distribution networks. One such challenge is to improve state estimation accuracy. This paper proposes to improve the estimation process of active distribution networks by embedding the active devices dynamics into the state dynamic equations, instead of translating them into the static measurement models. This is carried out with the Kalman filter (KF) by making use of the dynamic models and the static measurement models we have proposed earlier for active distribution networks. The paper provides the main steps to implement the estimation framework and illustrates its advantages under slow-responsive distribution network interactions. Results obtained show that the proposed KF approach has better performance than the static counterparts for networks subjected to multiple control decisions — the case where the relevance information on dynamics surpasses the relevance of setpoint information on static models alone.

Influence of usage and model inaccuracies on the performance of smart hot water heaters: lessons learned from a demand response field test

Domestic hot water heaters are considered to be easily integrated as flexible loads for demand response. While literature grows on reproducible simulation and lab tests, real-world implementation in field tests considering state estimation and demand prediction-based model predictive control approaches is rare. This work reports the findings of a field test with 16 autonomous smart domestic hot water heaters. The heaters were equipped with a retrofittable sensor/actuator setup and a real-time price-driven model predictive control unit, which covers state estimation, demand prediction, and optimization of switching times. With the introduction of generic performance indicators (specific costs and thermal efficiency), the results achieved in the field are compared by simulations to standard control modes (instantaneous heating, hysteresis, night-only switching). To evaluate how model predictive control performance depends on the user demand prediction and state estimation accuracy, simulations assuming perfect predictions and state estimations are conducted based on the data measured in the field. Results prove the feasible benefit of RTP-based model predictive control in the field compared to a hysteresis-based standard control regarding cost reduction and efficiency increase but show a strong dependency on the degree of utilization.

SAFENESS: A Semi-Supervised Transfer Learning Approach for Sea State Estimation Using Ship Motion Data

SAFENESS: A Semi-Supervised Transfer Learning Approach for Sea State Estimation Using Ship Motion Data

An Improved FDIA Approach for PMU-Assisted Linear Power System State Estimation

An Improved FDIA Approach for PMU-Assisted Linear Power System State Estimation

On the update of algebraic states during state estimation of differential–algebraic equation (DAE) systems

This manuscript presents a discussion on the algebraic state update step performed during recursive filtering of the differential–algebraic equation (DAE) systems. Existing DAE state estimation approaches follow a two-step state update procedure at each sampling instant. In particular, they first estimate the differential states using the Kalman update, and then update algebraic states by explicitly solving the algebraic equations. Specifically, for the case of DAE systems involving linear algebraic equations though the differential equations are nonlinear, we show that when appropriately initialized, this two-step state update procedure is not needed. It can instead be replaced with a one-step state update procedure that computes the differential and algebraic state estimates simultaneously through the Kalman update. The satisfaction of algebraic equations is guaranteed by this one-step update without it being explicitly enforced. Towards this end, we show that the error covariance matrix of augmented states, when properly initialized, satisfies a null-space property after prediction and update step at each sampling instant. This property ensures that the state estimates obtained using the proposed one-step update approach, satisfy the algebraic equations. This holds for both analytical linearization based extended Kalman filtering and statistical linearization based sigma-point filtering approaches. We also propose a heuristic-based update procedure for state estimation of DAE systems that involve nonlinear algebraic equations. This procedure draws out inferences from the case of DAE systems involving linear algebraic equations and is based on the analysis of algebraic equations residuals obtained from the updated differential and algebraic state estimates with a one-step state update. The efficacy of the proposed state update procedures is demonstrated by performing simulation studies on a benchmark drum boiler system case study. Results demonstrate that the proposed update procedures satisfactorily estimate the differential and algebraic states of a DAE system when compared to the traditional two-step update procedure.

A new robust dynamic state estimation approach for power systems with non-Gaussian noise

The Gaussian noise distribution is typically used in dynamic state estimation (DSE) but it is not always true in practice because of abnormal system inputs, impulsive noise and measurement outliers. In this paper, a new robust DSE approach based on a new robust Lp norm based estimator and the cubature Kalman filter (CKF) is developed for power systems with non-Gaussian noise statistics. The Lp norm based estimator is derived from the Lp norm formula and the quadratic formula in order to alleviate the impacts from bad data and outliers. The proposed Lp-CKF DSE approach exhibits good accuracy because a new estimation error covariance is obtained by using the influence function. The robustness of the proposed Lp-CKF DSE approach is verified by performing simulations on a generator in the IEEE 39-bus system.

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.

A Flow Graph–Based Scalable Critical Branch Identification Approach for AC State Estimation Under Load Redistribution Attacks

A Flow Graph–Based Scalable Critical Branch Identification Approach for AC State Estimation Under Load Redistribution Attacks

Online State Estimation for Supervisor Synthesis in Discrete-Event Systems With Communication Delays and Losses

In the context of networked discrete-event systems (DESs), communication delays and losses exist between the plant and the supervisor for observation and between the supervisor and the actuator for control. In this paper, we first introduce a new framework for supervisory control of networked DESs. Under the introduced framework, we address the state estimation problem for supervisor synthesis of networked DESs with both communication delays and losses. The estimation algorithm considers the effect of the controls imposed on the system. Additionally, the estimation algorithm is based on the control decisions available up to the moment, and all the future control decisions are assumed to be unknowable. Two notions, called “observation channel configuration” for tracking observation delays and losses and “control channel configuration” for tracking control delays and losses, are defined. Then, we introduce an online approach for state estimation of the controlled system. Compared with the existing approach, the proposed approach under the introduced framework can estimate the states of the controlled system more accurately. As an application of the proposed approach, we finally show that the existing methods can be applied to synthesize maximally permissible and safe networked supervisors.

Power System Frequency Dynamics Modeling, State Estimation, and Control using Neural Ordinary Differential Equations (NODEs) and Soft Actor-Critic (SAC) Machine Learning Approaches

With the global energy transition of the electric power system, grid control, supervision, and protection is becoming more challenging. With the increasing integration of renewable energy sources (RES), the system dynamics are changing, causing traditional power system dynamic modeling with swing equation-based modeling approaches to fail. Additionally, the converter-dominated power grid is decreasing the system inertia, making the power system more fragile to the frequency swings. This paper first investigates and compares the application of a model-based Kalman filter state estimation approach with (i) a model-free machine learning approach --- neural ordinary differential equations (NODEs) --- and (ii) a data-driven system identification (SysId) approach to model and infer critical state values of the power system frequency dynamics. Then a model predictive control (MPC) framework is compared to a model-free Soft Actor-Critic (SAC) reinforcement learning (RL) control algorithm in providing efficient fast frequency response (FFR) to the power system frequency dynamics. The approaches are compared in terms of their performance goals as well as their per-timestep computational efficiency. The comparative study for state estimation shows that for the model-free requirement, both NODEs and SysId can provide accurate state estimates; however, with increasing model complexity, NODEs can be a better choice for model identification. Similarly, the results from the FFR comparative study show that the SAC RL-based FFR, once trained, outperforms MPC with better control signals and faster computation time, making the SAC RL-based FFR better option for providing FFR to the power system.