Considering that the increasing scale of power systems may lead to high measurement transmitted load and the large amount of measurements also includes many bad data and outliers, a novel distributed multi-agent fusion state estimation (DMFSE) method leveraging the finite-time average consensus algorithm and influence function is proposed for large-scale power systems in this paper. Large-scale power systems are partitioned into multiple subareas, where each subarea deploys a local estimator. Measurements from each subarea are sent directly to their respective local estimator rather than to the central estimator, which reduces the burden of extensive data transmission. The finite-time average consensus algorithm and the influence function are combined together so as to make each local estimator obtain the global state estimation results. The optimization function for the proposed DMFSE method is derived from the generalized correntropy loss function, aiming to mitigate issues arising from bad data and outliers. The simulation results obtained from the IEEE 30-bus, 118-bus and 300-bus systems demonstrate the superior performances of the proposed DMFSE method.

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.

The complexity of a large-scale integrated energy system imposes huge computational burden. Besides, centralised state estimation is not suitable for fast and coordinated optimal management of multi-flow coupled systems and efficient energy utilisation. Furthermore, existing distributed state estimations are dealing with the established static system in the form of partitions. Considering the current method of modelling nonlinear fluids, the final impact on the performance of multiple assessments is non-convex for different partitioning approaches. This paper proposes a multi-objective distributed state estimation design approach for an integrated energy system based on non-dominated sorting genetic algorithm-II and unscented Kalman filter. The integrated energy system model contains the electric-gas-thermal system and various coupled units. By comparing and evaluating the estimation accuracy, calculation time and economic indicators of the system with different partitions of the system load, the optimal Pareto solution set are obtained from the multiobjective optimisation, which then guides the construction layout to satisfy different application requirements. In situations where the specific requirements are not clear, this paper gives the operator an objective method recommendation with the help of the entropy weight and Topsis synthesis assessment method. The validity of the method is verified by several case studies, and the method not only assists the estimation of the existing integrated energy system, but it also offers engineering significance in guiding the construction of the future integrated energy system.

The accurate estimation of power system states is crucial for effective monitoring and control. However, the performance of conventional state estimators, which assume Gaussian measurement noise and do not account for denial-of-service attacks, can deteriorate significantly in real power systems. To address these issues, this paper proposes a novel robust state estimation method based on the quadratic function (QF) and the generalized correntropy loss function (GCL). The proposed QF-GCL state estimation method can effectively deal with non-Gaussian measurement noise and denial-of-service attacks. To enhance the computational efficiency, an influence function based solving method is developed. To determine the optimal parameters for the proposed QF-GCL state estimation method, a new state estimation error covariance equation is further derived. Simulations are performed on the IEEE 30-bus, 118-bus and 300-bus systems, to demonstrate the accurate and robust performance of the proposed QF-GCL robust state estimation method.

Partially observable Markov decision processes (POMDPs) is a well-developed framework for sequential decision-making under uncertainty and partial information. This article considers the (inverse) structural estimation of the primitives of a POMDP based upon data in the form of sequences of observables and implemented actions. We analyze the structural properties of an entropy regularized POMDP and specify conditions under which the model is identifiable without knowledge of the state dynamics. We consider a soft policy gradient algorithm to compute a maximum likelihood estimator, and illustrate the approach with an equipment replacement problem.

Uncertainties such as abnormal system inputs, strong model nonlinearities, outliers and impulsive noise unavoidably exist in the power system dynamic state estimation (SE) (DSE). The existing Kalman filter-based DSE methods cannot deal with the uncertainties well and can be improved further. In this paper, a robust DSE method based on the maximum correlation entropy (MCE), quadratic function (QF) and the cubature Kalman filter is proposed to reduce the effects caused by the uncertainties. The MCE-QF based estimator is robust and can alleviate the influence of uncertainties. A new SE error covariance is derived by using the robust statistical tool, influence function. The robustness and estimation precision of the proposed DSE method is demonstrated by conducting simulations on a synchronous generator under different cases.

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.

This paper proposes a new method for the placement of the important synchrophasor sensors, the distribution-level phasor measurement units (DPMUs). A new objective function is developed to achieve minimization of distribution system state estimation errors where the limited number of DPMUs, the zero injection buses, the limited DPMU channels and the supervisory control and data acquisition measurements are taken into account. The A-optimal experimental design criterion is used to formulate the proposed objective function and constraints. The state estimates are obtained by using the maximum likelihood estimator where both Gaussian and non-Gaussian measurement noise scenarios are studied. The performance of the proposed method is demonstrated by simulations on IEEE 34-bus and 123-bus distribution systems.

In realistic power system state estimation, the distribution of measurement noise is usually assumed to be Gaussian while many researcher have verified that it can be non-Gaussian. In this paper, a new robust state estimator based on exponential absolute value function is proposed to address the non-Gaussian measurement noise and outliers. The influence function, a robust statistics tool, is used to obtain the state estimates to reduce its computational burden. A state estimation mean squared error formula of the proposed robust estimator is derived which can be used as a reference in the wide area monitoring system design or upgrade. Simulation results obtained from the IEEE 30-bus, 118-bus and 300-bus systems verify the effectiveness and robustness of the proposed robust estimator.

In this paper, a recursive t-distribution noise model based maximum likelihood estimation algorithm for discrete-time dynamic state estimation is proposed. The proposed estimator is robust to outliers because the "thick tail" of the t-distribution reduces the effect of large errors in the likelihood function. A computationally efficient recursive algorithm is derived using the influence function. As the t-distribution reduces to the Gaussian distribution when its degree of freedom tends to infinity, the proposed estimator reduces to the Kalman filter. The mean squared error is used to evaluate the performance of the proposed estimator. Compared with the Kalman filter, the proposed estimator is more robust to outliers in the process and measurement noise. Simulations show that for the particle filter to give a better mean squared error, its computational time is two orders of magnitude slower than the proposed estimator.

In practical power system applications, the distribution of the measurement noise is sometimes unknown and deviates from the assumed Gaussian noise model due to measurement outliers. In such cases, the performances of the state estimators based on Gaussian noise assumption may deteriorate significantly. In this article, we propose a fully distributed and robust power system state estimation approach based on the t-distribution noise model and the maximum likelihood criterion. The t-distribution is used to model Gaussian and non-Gaussian statistics in the field of robust statistics. The matrix-splitting techniques are employed to carry out the extensive matrix inversion of the gain matrix in a distributed way to achieve efficient computation. In the proposed distributed estimation framework, each local control area only requires limited data exchange with its neighboring areas. Simulations on the IEEE 14-bus, 118-bus and 300-bus systems are used to verify the effectiveness and robustness of the proposed distributed state estimation algorithm.

This paper investigates how to add a limited number of Phasor Measurement Units (PMUs) to the existing monitoring system so as to improve the estimation accuracy further. The existing methods are usually based on Gaussian noise assumption and the weighted least squares (WLS) estimator is taken into account. However, the Gaussian noise assumption is not always true in reality and the WLS is non-robust in this case. This paper proposes a new optimal PMU placement approach where the distribution of measurement noise can be non-Gaussian or Gaussian and many robust estimators such as the maximum likelihood estimator, Multiple-Segment, Quadratic-Linear, Square-Root and Schweppe-Huber Generalized-M estimator are considered. Based on the new Gain matrix obtained from the influence function approximation, the D-optimal and E-optimal experiment criterions are exploited in the optimal PMU placement problem. A convex relaxation in conjunction with an optimization improvement method based on the Fedorov exchange algorithm is utilized to solve the optimizing problem. Simulations on the IEEE 57-bus system and the Polish 2383-bus system are carried out to evaluate the effective performance of the proposed approach.

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.

Uncertainties of renewable energy sources (RES) power generation and load demand have detrimental effects on the microgrid operation. In this paper, a robust optimization approach based on modified grey wolf optimizer is proposed to determine the optimal energy management for a typical micro-grid with regard to uncertainties. Furthermore, the influence of uncertainty budget for RES power generation and load demand on operation cost and pollutant gas emissions are studied. Simulation results show a good reduction both in operation cost and pollution emissions as well verify the effectiveness of our proposed approach.

In power system state estimation, the robust least absolute value robust dynamic estimator is well known. However, the covariance of the state estimation error cannot be obtained easily. In this article, an analytical equation is derived using influence function approximation to analyze the covariance of the robust least absolute value dynamic state estimator. The equation gives insights into the precision of the estimation and can be used to express the variances of the state estimates as functions of measurement noise variances, enabling the selection of sensors for specified estimator precision. Simulations on the IEEE 14-bus, 30-bus, and 118-bus systems are given to illustrate the usefulness of the equation. Monte Carlo experiments can also be used to determine the covariance, but many data points are needed and hence many runs are required to achieve convergence. Our result shows that to obtain the covariance of the state estimation error, the analytical equation proposed in this article is four orders of magnitude faster than a 10 000-run Monte Carlo experiment on both the IEEE 14-bus and 30-bus systems.

Energy management plays an important role in the efficient and reliable operation of microgrid with various distributed energy resources. In this paper, the energy management of an isolated microgrid involving two batteries and other distributed energy resources such as photovoltaic, wind turbine and diesel generator is presented. For obtaining a better energy management, a modified grey wolf optimizer is proposed to determine the optimal power schedule plan of a microgrid. Moreover, different charging and discharging priorities of the two batteries result in operation cost and the equivalent pollutant gas emissions are investigated so as to obtain a more economic operation strategy. Simulation results show a good reduction in operation cost and pollution emissions as well verify the effectiveness of our proposed approach.

In this paper, we propose an optimal robust state estimator using maximum likelihood optimization with the t-distribution noise model. In robust statistics literature, the t-distribution is used to model Gaussian and non-Gaussian statistics. The influence function, an analytical tool in robust statistics, is employed to obtain the solution to the resulting maximum likelihood estimation optimization problem, so that the proposed estimator can be implemented within the framework of traditional robust estimators. Numerical results obtained from simulations of the IEEE 14-bus system, IEEE 118-bus system, and experiment on a micro-grid demonstrated the effectiveness and robustness of the proposed estimator. The proposed estimator could suppress the influence of outliers with smaller average mean-squared errors (AMSE) than the traditional robust estimators, such as quadratic-linear, square-root, Schweppe-Huber generalized-M, multiple-segment, and least absolute value estimators. A new approximate AMSE formula is also derived for the proposed estimator to predict and evaluate its precision.

In this paper, we proposed to evaluate the optimal phasor measurement unit (PMU) placement based on the sum of variance (SV) of the robust estimators. Variance is traditionally used as a measure of the quality of estimates. In this paper, after satisfying the requirements of the minimum number of PMUs, maximum measurement redundancy, and observability, the placements obtained are further distinguished on the basis of the variance of the estimated states. Both the weighted least squares (WLS) and robust estimators are considered. Examples on the IEEE 30-bus system using least absolute value (LAV) estimation are given. The covariance of the state estimates from the WLS can be calculated using the existing formulas. However, there is no equivalent formula for the robust LAV estimator. A formula is derived in this paper using influence function to approximately calculate the covariance matrix of the state estimates from the robust LAV estimator. The optimum placement, i.e., the placement with the smallest SV, can be selected.

Integer linear programming (ILP) has been widely applied to solve the optimal phasor measurement unit (PMU) placement (OPP) problem for its computational efficiency. Using ILP, a placement with minimum number of Phasor Measurement Units (PMUs) and maximum measurement redundancy can be obtained while ensuring system observability. Author response: please delete this above sentence. However, the existing ILP-based OPP methods does not guarantee full coverage of solutions to the optimization problem, which may sequentially results in suboptimal supervision of the system. In this paper, a hybrid ILP-based method is proposed to cover all solutions to the OPP problem without any omission. Comparing with the existing exhaustive searching methods, the proposed method is more computationally efficient, which makes finding all solutions in a large system a more feasible problem.

An analytical equation is derived using influence function approximation to calculate the variance of the state estimate for traditional robust state estimators such as the Quadratic-Constant, Quadratic-Linear, Square-Root, Schweppe-Huber Generalized-M and Multiple-Segment estimator. The equation gives insights into the precision of the estimation. Using the equation, the variance of a state estimate can be expressed as a function of measurement noise variances enabling the selection of sensors for a specified estimator precision. It can also be used to search for the optimum estimator parameters to give the minimum sum of variances. The well-known Weighted-Least-Squares variance formula is a special case of the equation and simulations on the IEEE 14-bus system are given to show the usefulness of the equation.