ADMM-based Distributed State Estimation for Integrated Energy System

In order to have an accurate knowledge of system-wide operation states,it is necessary to perform state estimation for the integrated energy system(IES)as the basis of energy man-agement and control.Centralized state estimation is practically infeasible for IES due to the unreliability of communication,the barrier on privacy,and the large scale of integrated systems.This paper proposes a distributed state estimation algorithm based on the alternating direction method of multipliers(ADMM)for IES containing electricity,heat,and natural gas.Various coupling units are taken into full consideration in modeling of IES state estimation to reflect the harmonization of multi energy.On the basis of bilinear measurement model,the state estimation considering nonlinear measurements can be replaced by an equivalent three-stage problem containing two linear state estimations and an intermediate transformation to avoid non-convex optimization.The three-stage procedure for IES state estimation can be further decoupled over three sub-systems with coordination on coupling units,yielding a fully distributed scheme based on ADMM.A modified ADMM with the self-adjusting penalty parameter is also adopted to enhance the convergence.Simulation results demonstrate the validity and superiority of the proposed algorithm.

Performance Comparison of Distributed State Estimation Algorithms for Power Systems

A newly proposed distributed dynamic state estimation algorithm based on the maximum a posteriori(MAP) technique is generalised and studied for power systems. The system model involves linear time-varying load dynamics and nonlinear measurements. The main contribution of this paper is to compare the performance and feasibility of this distributed algorithm with several existing distributed state estimation algorithms in the literature. Simulations are tested on the IEEE 39-bus and 118-bus systems under various operating conditions. The results show that this distributed algorithm performs better than distributed quasi-steady state estimation algorithms which do not use the load dynamic model. The results also show that the performance of this distributed method is very close to that by the centralized state estimation method. The merits of this algorithm over the centralized method lie in its low computational complexity and low communication load. Hence, the analysis supports the efficiency and benefits of the distributed algorithm in applications to large-scale power systems.

Optimal Network Partition and Edge Server Placement for Distributed State Estimation

This paper investigates network partition and edge server placement problem to exploit the benefit of edge computing for distributed state estimation.A constrained many-objective optimization problem is formulated to minimize the cost of edge server deployment,operation,and maintenance,avoid the difference in the partition sizes,reduce the level of coupling between connected partitions,and maximize the inner cohesion of each partition.Capacities of edge server are constrained against underload and overload.To efficiently solve the problem,an improved non-dominated sorting genetic algorithm III(NSGA-III)is developed,with a specifically designed directed mutation operator based on topological characteristics of the partitions to accelerate convergence.Case study validates that the proposed formulations effectively characterize the practical concerns and reveal their trade-offs,and the improved algorithm outperforms existing representative ones for large-scale networks in converging to a near-optimal solution.The optimized result contributes significantly to real-time distributed state estimation.

Distributed Secure State Estimation of Multi-Agent Systems Under Homologous Sensor Attacks

This paper addresses the problem of distributed secure state estimation for multi-agent systems under homologous sensor attacks.Two types of secure Luenberger-like distributed observers are proposed to estimate the system state and attack signal simultaneously.Specifically,the proposed two observers are applicable to deal with the cases in the presence and absence of time delays during network communication.It is also shown that the proposed observers can ensure the attack estimations from different agents asymptotically converge to the same value.Sufficient conditions for guaranteeing the asymptotic convergence of the estimation errors are derived.Simulation examples are finally provided to demonstrate the effectiveness of the proposed results.

Multi-area distributed three-phase state estimation for unbalanced active distribution networks

This paper proposes a new multi-area framework for unbalanced active distribution network(ADN) state estimation. Firstly, an innovative three-phase distributed generator(DG) model is presented to take the asymmetric characteristics of DG three-phase outputs into consideration. Then a feasible method to set pseudo-measurements for unmonitored DGs is introduced. The states of DGs,together with the states of alternating current(AC) buses in ADNs, were estimated by using the weighted least squares(WLS) method. After that, the ADN was divided into several independent subareas. Based on the augmented Lagrangian method, this work proposes a fully distributed three-phase state estimator for the multi-area ADN.Finally, from the simulation results on the modified IEEE123-bus system, the effectiveness and applicability of the proposed methodology have been investigated and discussed.

A distributed approach for lidar-based relative state estimation of multi-UAV in GPS-denied environments

In this paper,we present a distributed framework for the lidar-based relative state estimator which achieves highly accurate,real-time trajectory estimation of multiple Unmanned Aerial Vehicles(UAVs)in GPS-denied environments.The system builds atop a factor graph,and only on-board sensors and computing power are utilized.Benefiting from the keyframe strategy,each UAV performs relative state estimation individually and broadcasts very partial information without exchanging raw data.The complete system runs in real-time and is evaluated with three experiments in different environments.Experimental results show that the proposed distributed approach offers comparable performance with a centralized method in terms of accuracy and real-time performance.The flight test demonstrates that the proposed relative state estimation framework is able to be used for aggressive flights over 5 m/s.

Analytical Verification of Performance of Deep Neural Network Based Time-synchronized Distribution System State Estimation

Recently,we demonstrated the success of a time-synchronized state estimator using deep neural networks(DNNs)for real-time unobservable distribution systems.In this paper,we provide analytical bounds on the performance of the state estimator as a function of perturbations in the input measurements.It has already been shown that evaluating performance based only on the test dataset might not effectively indicate the ability of a trained DNN to handle input perturbations.As such,we analytically verify the robustness and trustworthiness of DNNs to input perturbations by treating them as mixed-integer linear programming(MILP)problems.The ability of batch normalization in addressing the scalability limitations of the MILP formulation is also highlighted.The framework is validated by performing time-synchronized distribution system state estimation for a modified IEEE 34-node system and a real-world large distribution system,both of which are incompletely observed by micro-phasor measurement units.

Cyber-attack Detection Strategy Based on Distribution System State Estimation

Cyber-attacks that tamper with measurement information threaten the security of state estimation for the current distribution system.This paper proposes a cyber-attack detection strategy based on distribution system state estimation(DSSE).The uncertainty of the distribution network is represented by the interval of each state variable.A three-phase interval DSSE model is proposed to construct the interval of each state variable.An improved iterative algorithm(IIA)is developed to solve the interval DSSE model and to obtain the lower and upper bounds of the interval.A cyber-attack is detected when the value of the state variable estimated by the traditional DSSE is out of the corresponding interval determined by the interval DSSE.To validate the proposed cyber-attack detection strategy,the basic principle of the cyber-attack is studied,and its general model is formulated.The proposed cyber-attack model and detection strategy are conducted on the IEEE 33-bus and 123-bus systems.Comparative experiments of the proposed IIA,Monte Carlo simulation algorithm,and interval Gauss elimination algorithm prove the validation of the proposed method.

Measurement Sensitivity and Estimation Error in Distribution System State Estimation using Augmented Complex Kalman Filter

Distribution state estimation(DSE)is an essential part of an active distribution network with high level of distributed energy resources.The challenges of accurate DSE with limited measurement data is a well-known problem.In practice,the operation and usability of DSE depend on not only the estimation accuracy but also the ability to predict error variance.This paper investigates the application of error covariance in DSE by using the augmented complex Kalman filter(ACKF).The Kalman filter method inherently provides state error covariance prediction.It can be utilized to accurately infer the error covariance of other parameters and provide a method to determine optimal measurement locations based on the sensitivity of error covariance to measurement noise covariance.This paper also proposes a generalized formulation of ACKF to allow scalar measurements to be incorporated into the complex-valued estimator.The proposed method is simulated by using modified IEEE 34-bus and IEEE 123-bus test feeders,and randomly generates the load data of complex-valued Wiener process.The ACKF method is compared with an equivalent formulation using the traditional weighted least squares(WLS)method and iterated extended Kalman filter(IEKF)method,which shows improved accuracy and computation performance.

Outlier Reconstruction Based Distribution System State Estimation Using Equivalent Model of Long Short-term Memory and Metropolis-Hastings Sampling

The accuracy of distribution system state estimation(DDSE)is reduced when phasor measurement unit(PMU)measurements contain outliers because of cyber attacks or global positioning system spoofing attacks.Therefore,to enhance the robustness of DDSE to measurement outliers,approximate the target distribution of Metropolis-Hastings(MH)sampling,and judge the prediction of the long short-term memory(LSTM)network,this paper proposes an outlier reconstruction based state estimation method using the equivalent model of the LSTM network and MH sampling(E-LM model),motivated by the characteristics of the chronological correlations of PMU measurements.First,the target distribution of outlier reconstruction is derived using a kernel density estimation function.Subsequently,the reasons and advantages of the E-LM model are explained and analyzed from a mathematical point of view.The proposed LSTM-based MH sampling can approximate the target distribution of MH sampling to decrease the number of the futile iterations.Moreover,the proposed MH-based forecasting of the LSTM can judge each LSTM prediction,which is independent of its true value.Finally,simulations are conducted to evaluate the performance of the E-LM model by integrating the LSTM network and the MH sampling into the outlier reconstruction based DDSE.

Optimal Micro-PMU Placement for Improving State Estimation Accuracy via Mixed-integer Semidefinite Programming

Micro-phasor measurement units(μPMUs)with a micro-second resolution and milli-degree accuracy capability are expected to play an important role in improving the state estimation accuracy in the distribution network with increasing penetration of distributed generations.Therefore,this paper investigates the problem of how to place a limited number ofμPMUs to improve the state estimation accuracy.Combined with pseudo-measurements and supervisory control and data acquisition(SCADA)measurements,an optimalμPMU placement model is proposed based on a two-step state estimation method.The E-optimal experimental criterion is utilized to measure the state estimation accuracy.The nonlinear optimization problem is transformed into a mixed-integer semidefinite programming(MISDP)problem,whose optimal solution can be obtained by using the improved Benders decomposition method.Simulations on several systems are carried out to evaluate the effective performance of the proposed model.

A Value-at-Risk Based Approach for PMU Placement in Distribution Systems

With the application of phasor measurement units(PMU)in the distribution system,it is expected that the performance of the distribution system state estimation can be improved obviously with the PMU measurements into consideration.How to appropriately place the PMUs in the distribution is therefore become an important issue due to the economical consideration.According to the concept of efficient frontier,a value-at-risk based approach is proposed to make optimal placement of PMU taking account of the uncertainty of measure errors,statistical characteristics of the pseudo measurements,and reliability of the measurement instrument.The reasonability and feasibility of the proposed model is illustrated with 12-node system and IEEE-33 node system.Simulation results indicated that uncertainties of measurement error and instrument fault result in more PMU to be installed,and measurement uncertainty is the main affect factor unless the fault rate of PMU is quite high.

Event-based Control and Filtering of Networked Systems:A Survey

In recent years, theoretical and practical research on event-based communication strategies has gained considerable research attention due primarily to their irreplaceable superiority in resource-constrained systems（especially networked systems）. For networked systems, event-based transmission scheme is capable of improving the efficiency in resource utilization and prolonging the lifetime of the network components compared with the widely adopted periodic transmission scheme. As such, it would be interesting to 1） examining how the event-triggering mechanisms affect the control or filtering performance for networked systems, and 2） developing some suitable approaches for the controller and filter design problems. In this paper, a bibliographical review is presented on event-based control and filtering problems for various networked systems. First, the event-driven communication scheme is introduced in detail according to its engineering background, characteristic, and representative research frameworks. Then, different event-based control and filtering（or state estimation） problems are categorized and then discussed. Finally, we conclude the paper by outlining future research challenges for event-based networked systems.