Distributed State Estimation Method Research Articles

Distributed state estimation for leak detection in water supply networks

In this paper, we focus on observer-based approaches of leak detection and isolation in pipeline networks, which has the potential to be extended to large-scale water supply network systems, while in previous studies only single pipeline scenario is considered. Due to several disadvantages of implementing centralized state estimation for large-scale systems, the distributed Kalman filter algorithm has been applied in this paper. The observers are designed on the basis of a set of nonlinear fluid models of pipelines, pumps and other hydraulic accessories, with uncertainties in leak position and magnitude. The approach assumes only flow and pressure measurements at the ends of each duct. Simulation results with a water transmission line are presented to assess the efficiency of the proposed distributed state estimation method while comparing with its centralized counterpart.

Toward Data Integrity Attacks Against Distributed Dynamic State Estimation in Smart Grid

With the continuous expansion of the power grid nodes scale, traditional centralized state estimation method shows certain limitations in estimation efficiency and accuracy. Recently, some power grids adopt a distributed state estimation method, in which each partition independently estimates the partial state information by partitioning the entire power system. However, the deviation of the state estimation in certain partition will result in the deviation of the estimation results in the entire power grid system. In this paper, we propose the attack strategy against the distributed state estimation in smart grids from two perspectives, i.e. the attack against local physical measurement value of the power system partition and the attack against the measurement value of coordination center. Moreover, the theoretical analysis of the state estimation deviation caused by the proposed data integrity attack and the propagation processes of proposed attack vectors in measurement calculations are formalized. The effectiveness of the proposed attack strategy is verified in the IEEE-30 bus and IEEE-118 bus systems. Simulation results show that attacking against a certain partition of a distributed system can indirectly affect the state estimation results of other partitions and attacking against the measurement value of coordination center can directly threaten the state estimation results of the entire power grid. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper proposes two attack strategies against the distributed state estimation of power grid from two perspectives, i.e. the attack against local physical measurement value of the power system partition and the attack against the measurement value of coordination center. Most of the previous works fail to formalize the state estimation deviation of both partial and entire state estimation results of power grid after the attacker launches the attack against the distributed state estimation. We formalize the state estimation deviation caused by the proposed data integrity attack and the propagation processes of proposed attack vectors in measurement calculations. The effectiveness of the proposed attack strategy against the state estimation of power grid is verified in the IEEE-30 bus and IEEE-118 bus systems. Simulation results show that attacking against a certain partition of power grid can indirectly cause the deviation in the state estimation results of entire power grid and attacking against the measurement value of the coordination center can directly threaten the state estimation results of the entire power grid. In conclusion, the proposed attack strategies are helpful for the research community to design detection strategies in a targeted manner and can be conveniently applied to the real-world security management system of smart grid.

Distributed security state estimation-based carbon emissions and economic cost analysis for cyber–physical power systems under hybrid attacks

Sustainable cyber–physical power systems (CPPSs) significantly reduce carbon emissions due to climate change. However, when the data exchange in CPPSs suffers from hybrid attacks, the distributed state estimation and optimal power flow (OPF) analysis will inevitably be compromised, leading to inadequate or faulty scheduling of clean energy and thermal power generations and further affecting the total carbon emissions and economic cost. To address these problems, this paper proposes a novel consensus-based distributed security state estimation (DSSE) method for CPPSs, which is used to analyze the impact of hybrid attacks on carbon emissions and economic cost. Firstly, the incomplete and non-authentic data features caused by hybrid attacks are described, and their influence on distributed state estimation model is analyzed. A new residual-based attack detection method is then constructed in each subregion, where secure and non-secure sets are employed to describe whether the subregion is attacked and the compensation mechanism is designed for the non-secure set. Secondly, considering data compensation, distributed state estimation model is reconstructed, and a distributed security state estimation method under hybrid attacks is proposed while its convergence condition is derived. Thirdly, the impacts of hybrid attacks on carbon emissions and economic costs are analyzed based on the proposed DSSE method. Finally, experimental results confirm the validity of the theoretic analysis.

A distributed multi-area power system state estimation method based on generalized loss function

For power system state estimation, the measurement noise is usually assumed to follow the Gaussian distribution, and the widely used estimator is the weighted least squares (WLS). However, the Gaussian distribution assumption is not always true, and the performance of WLS becomes bad when the measurement noise is non-Gaussian. In this paper, a new distributed state estimation (SE) method is proposed for multi-area power systems. The proposed distributed method is based on the generalized loss function so that it can reduce the influence of non-Gaussian noise and bad data. Further, thanks to the matrix-splitting technology, the proposed distributed method can be implemented in a distributed way so that the computation time in each local area can be reduced. The simulation results carried out in the IEEE 30-bus and 118-bus systems verify the robustness and effectiveness of the proposed distributed SE method.

An Agent-Based Distributed State Estimation Approach for Interconnected Power Systems

Phasor measurement units (PMUs) are becoming more popular in power systems and most of the distributed state estimation methods are based on the Gaussian measurement noise assumption. However, the PMU measurement noise has been demonstrated to be non-Gaussian. This article presents a distributed multiarea state estimation approach based on the quadratic and exponential functions for power systems to deal with the non-Gaussian measurement noise efficiently. The matrix splitting technique is utilized to implement a robust estimator in a fully distributed scheme. Based on the local measurements and the limited information exchanged between neighboring areas, each local area only estimates its local states and the computation time needed is further reduced. The effective and robust performance of the proposed distributed multiarea state estimation approach is demonstrated using the IEEE 30-, 118-, and 300-bus systems.

Distributed state estimation method of distribution networks based on LSTM

In this paper, long-short-term memory (LSTM) is introduced into the distributed state estimation (DSE) method, and the state prediction value obtained by LSTM is used as the new measurement in each sub-area. The state prediction value obtained by LSTM is used as a sign to judge whether the measurement in each sub-area at the current time is abnormal, which avoids unnecessary bad data detection when the measurement is normal. Through the simulation of IEEE33 bus distribution network system, it is verified that the proposed method can effectively identify bad data and has high computational efficiency.

A novel hybrid consensus-based variational Bayesian filter with position uncertainty in multi-agent system

Most existing distributed state estimation approaches assume that the position of agent in multi-agent system (MAS) is precisely known. However, in target tracking applications, the position of agent is noisy, which makes traditional distributed state estimation methods suffer from accuracy reduction. This paper focuses on developing a novel hybrid consensus-based variational Bayesian filter (HCVB) for target tracking with position uncertainty in nonlinear MAS. To improve the nonlinear approximation accuracy, high-degree cubature information filter framework is used. To cope with agent position uncertainty, the measurement update is derived by using variational Bayesian (VB) method to approximate the joint posterior distribution of the target state and agent position, which can estimate the state and agent position jointly. To decrease the required consensus iterations, a hybrid consensus method is proposed, which can achieve global consistency of all agents with a few consensus iterations. Simulations on UAV tracking in MAS verify the superiority of the proposed method.

Distributed state estimation method based on WLS-AKF hybrid algorithm for active distribution networks

Given the difficulty of traditional state estimation methods in meeting the computational efficiency and accuracy requirements of active distribution networks, we propose a distributed state estimation (DSE) method for active distribution networks based on the weighted least squares-adaptive Kalman filter (WLS-AKF) hybrid algorithm. A multi-criteria partition model of an active distribution network that is suitable for DSE has been established. The model comprehensively considers the impact of partitioning results on DSE calculation accuracy and efficiency from the three perspectives of structure, measurement, and performance and solves the model using an improved genetic algorithm. A partition decoupling method is proposed herein, which completely decouples the sub-regions without requiring the measurement configuration of the sub-region boundary nodes and effectively reduces the DSE calculation scale. Furthermore, the paper proposes a DSE algorithm based on WLS-AKF that uses AKF to provide accurate pseudo-measurement of boundary nodes for WLS, which improves the calculation efficiency while ensuring the DSE calculation accuracy. The proposed method is analyzed and verified using the improved IEEE118 node system. The results show that the proposed method has high computational accuracy and efficiency, and can obtain high-precision estimation results in the case of missing data.

Distributed state estimation and fault diagnosis using reduced sensitivity to neighbor estimates with application to building control

This paper proposes solutions that reduce the inaccuracy of distributed state estimation and consequent performance deterioration of distributed model predictive control caused by faults and inaccurate models. A distributed state estimation method for large-scale systems is introduced. A local state estimation approach considers the uncertainty of neighbor estimates, which can improve the state estimation accuracy, whereas it keeps a low network communication burden. The method also incorporates the uncertainty of model parameters which improves the performance when using simplified models. The proposed method is extended with multiple models and estimates the probability of nominal and fault behavior models, which creates a distributed fault detection and diagnosis method. An example with application to the building heating control demonstrates that the proposed algorithm provides accurate state estimates to a controller and detects local or global faults while using simplified models.

Distributed State Estimation in Digital Distribution Networks Based on Proximal Atomic Coordination

With the emerging digitalization technologies represented by edge computing, distribution networks are gradually transforming into digital distribution networks (DDNs). The realization of edge computing drives the distributed operation of DDNs, where multiple areas exchange boundary information through edge computing devices. Benefitting from the data acquisition and computing capacity of edge computing devices, it is feasible to perform accurate and real-time state estimation on the edge side. Aiming at the state perception with edge computing devices in DDNs, this paper proposes a distributed state estimation (DSE) method based on the proximal atomic coordination (PAC) algorithm. Firstly, based on convex relaxation optimization, the state estimation model is converted into a positive semidefinite programming model to solve the nonconvexity caused by nonlinear measurements, which ensures the accuracy and convergence of state estimation. Then, a DSE method based on the PAC algorithm is proposed to exchange information of each area, which reduces the computation time and realizes the efficient state estimation on the edge side. The model and the effectiveness of the proposed method are numerically demonstrated on the modified PG&#x0026;E 69-node system and the test case from a practical pilot in Guangzhou, China.

Adaptive Event-Triggered Quantized Communication-Based Distributed Estimation Over Sensor Networks With Semi-Markovian Switching Topologies

This paper presents a distributed state estimation method for nonlinear systems over sensor networks with Semi-Markovian switching topologies (S-MSTs). An adaptive event-triggered quantization scheme (AETQS) is developed to reduce the communication and computation burden for bandwidth-constrained sensor networks, where the quantified measurement data is determined by the specific event triggering condition. The filtering network topology evolves over time, which is assumed to be governed by a Semi-Markov chain. Based on the Semi-Markov kernel theory and Lyapunov stability theory, sufficient conditions are obtained to guarantee that the error dynamics has <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\sigma$</tex-math></inline-formula> -error mean square stability and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${H_\infty }$</tex-math></inline-formula> performance, which is given in the form of linear matrix inequalities. Then, the optimal disturbance attenuation level, initial triggering thresholds, and elapsed-time-dependent distributed filter gains can be determined by addressing a convex optimization problem. Finally, two numerical examples are presented to verify the effectiveness of the proposed approach.

Consensus-Based Distributed Target Tracking with False Data Injection Attacks over Radar Network

For target tracking in radar network, any anomaly in a part of the system can quickly spread over the network and lead to tracking failures. False data injection (FDI) attacks can damage the state estimation mechanism by modifying the radar measurements with unknown and time-varying attack variables, therefore making traditional filters inapplicable. To tackle this problem, we propose a novel consensus-based distributed state estimation (DSE) method for target tracking with FDI attacks, which is effective even when all radars are under FDI attacks. First, a real-time residual-based detector is introduced to the DSE framework, which can effectively detect FDI attacks by analyzing the statistical properties of the residual. Secondly, a simple yet effective attack parameter estimation method is proposed to provide attack parameter estimation based on a pseudo-measurement equation, which has the advantage of decoupled estimation of state and attack parameters compared with augmented state filters. Finally, for timely attack mitigation and global consistency achievement, a novel hybrid consensus method is proposed which can compensate for the estimation error caused by FDI attacks and provide estimation accuracy improvement. The simulation results show that the proposed solution is effective and superior to the traditional DSE method for target tracking in the presence of FDI attacks.

Distributed State Estimation under Heterogeneous Time-Varying Communication Delays

In this paper we study the distributed leader state estimation problem in leader-follower multi-agent systems over a deterministic network and under time-varying communication delays. In this work we propose a distributed estimation technique that allows the follower agents to collectively reconstruct the leader agent states by communicating their estimates with neighboring agents. Additionally, we assume that the communications between the leader and followers are subject to heterogeneous time-varying delays. By using the low gain methodology, sufficient stability conditions of the estimation error dynamics in the presence of network latency are derived, including an upper bound for the delay magnitude. Lastly, the proposed distributed state estimation method is applied to develop a solution to the leader tracking problem in leader-follower multi-agent systems. An illustrative example is also presented to verify the effectiveness of our theoretical results.

A Distributed Maximum-Likelihood-Based State Estimation Approach for Power Systems

The distribution of measurement noise is commonly considered as an assumed Gaussian model in power systems, but this assumption is not always true in reality. This article introduces a distributed maximum-likelihood-based state estimation approach for multiarea power systems using the student's t-distribution measurement noise model. The t-distribution has the property of “thick tail” to better model the occurrence of outliers and is fairly flexible to model different noise statistics. The finite-time average consensus algorithm is utilized in conjunction with an influence function to realize the proposed distributed approach within a totally distributed framework. Based on the local measurement residuals and the limited information exchanged with neighboring areas, each local area can obtain the global optimum system-wide robust state estimates, while the existing distributed state estimation methods can only get local estimates. Moreover, the communication scheme is more flexible and can be totally different from the transmission lines between local areas. Simulations tested on the IEEE 14-bus and 118-bus systems verify the effectiveness of the proposed distributed approach.

An operating state estimation model for integrated energy systems based on distributed solution

In view of the disadvantages of the traditional energy supply systems, such as separate planning, separate design, independent operating mode, and the increasingly prominent nonlinear coupling between various sub-systems, the production, transmission, storage and consumption of multiple energy sources are coordinated and optimized by the integrated energy system, which improves energy and infrastructure utilization, promotes renewable energy consumption, and ensures reliability of energy supply. In this paper, the mathematical model of the electricity-gas interconnected integrated energy system and its state estimation method are studied. First, considering the nonlinearity between measurement equations and state variables, a performance simulation model is proposed. Then, the state consistency equations and constraints of the coupling nodes for multiple energy subsystems are established, and constraints are relaxed into the objective function to decouple the integrated energy system. Finally, a distributed state estimation framework is formed by combining the synchronous alternating direction multiplier method to achieve an efficient estimation of the state of the integrated energy system. A simulation model of an electricity-gas interconnected integrated energy system verifies the efficiency and accuracy of the state estimation method proposed in this paper. The results show that the average relative errors of voltage amplitude and node pressure estimated by the proposed distributed state estimation method are only 0.0132% and 0.0864%, much lower than the estimation error by using the Lagrangian relaxation method. Besides, compared with the centralized estimation method, the proposed distributed method saves 5.42 s of computation time. The proposed method is more accurate and efficient in energy allocation and utilization.

Distributed data‐driven observer for linear time invariant systems

SummaryThis paper is concerned with distributed data‐driven observer design problem. The existing data‐driven observers rely on a common assumption that all the information about the system, and the calculations based upon this information are centralized. Therefore the resulting algorithms cannot be applied to the distributed systems in which each local observer receives only a part of the output signal. On the other hand, traditional model‐based distributed state estimation methods generally assume that the processes are decomposed according to the known process models, while in data‐driven approaches there is no such information available. The main goal of this paper is to extend the centralized data‐driven observer design approach to the distributed framework. The stability of the proposed data‐driven distributed observer is also proved analytically. A quadruple‐tank process is simulated to demonstrate the performance of the proposed scheme.

Fully Distributed State Estimation for Power System with Information Propagation Algorithm

In this paper, a new fully distributed state estimation (DSE) based on weighted least square (WLS) method and graph theory is proposed for power system. The proposed method is fully distributed so that the centralized facilities, e.g., supervisory control and data acquisition (SCADA) and centralized estimators, are not required. Also, different from the existing DSE methods, the proposed method is a bus-level DSE method, in which the power system is not required to be partitioned into several areas. In order to realize the proposed fully distributed DSE method, a novel information propagation algorithm is developed in this paper. This algorithm has great potential in future applications since it is useful to broadcast the local information of the nodes to the entire system in a fully distributed network. The proposed DSE method is compared with the conventional centralized state estimation method and existing multi-area DSE method in different models in this paper. The results show that the proposed method has better performance than the traditional methods.

Secure Distributed State Estimation for Networked Microgrids

Distributed state estimation (DSE) allows networked microgrids to achieve global state awareness with conservation of local information privacy by peer-to-peer message exchange implemented with Internet of Things protocols over heterogeneous communications. This paper presents a secure DSE (SDSE) method for networked microgrids to enhance system resiliency by addressing false data injection threat in distributed microgrid agent nodes. The designated SDSE applies a trust-based diffusion algorithm using adaptive combination policy, which allows agents to adapt their combination coefficients to exclude misbehaving nodes from the network. The results demonstrate that proposed SDSE algorithm addresses emerging data integrity and security problems in critical energy delivery infrastructure and SCADA environment.

ADMM-Based Distributed State Estimation of Smart Grid Under Data Deception and Denial of Service Attacks

Smart grid (SG) represents a large-scale network system with the tight integration of a physical power network and an information network, which makes it more vulnerable to hybrid cyber attacks against different regional subsystems. First, an alternating direction method of multipliers-based distributed state estimation method is developed to overcome the limitation of conventional state estimation and performance analysis of SG against a single type of cyber attacks. Regional subsystems are partitioned via the ${K}$ -means method. Second, a novel distributed state estimation method integrated with the characteristics of data deception attacks and denial of service (DoS) attacks is proposed to account for the simultaneous presence of different cyber attacks on individual regional subsystems. Third, the convergence of a distributed state estimation algorithm under hybrid cyber attacks is proved theoretically. Furthermore, the relationships between the convergence and algorithm parameters as well as the occurring probability of DoS attacks are established. Finally, the simulations on a modified IEEE 118-bus system are given to demonstrate the feasibility and effectiveness of the proposed method.

Adaptive Consensus-Based Unscented Information Filter for Tracking Target with Maneuver and Colored Noise.

Distributed state estimation plays a key role in space situation awareness via a sensor network. This paper proposes two adaptive consensus-based unscented information filters for tracking target with maneuver and colored measurement noise. The proposed filters can fulfill the distributed estimation for non-linear systems with the aid of a consensus strategy, and can reduce the impact of colored measurement noise by employing the state augmentation and measurement differencing methods. In addition, a fading factor that shrinks the predicted information state and information matrix can suppress the impact of dynamical model error induced by target maneuvers. The performances of the proposed algorithms are investigated by considering a target tracking problem using a space-based radar network. This shows that the proposed algorithms outperform the traditional consensus-based distributed state estimation method in aspects of tracking stability and accuracy.