Estimating the system state is a non-trivial task given a large set of measurements, fuelling the ongoing research attempts to find efficient, scalable and fast state estimation (SE) algorithms. The centralised SE becomes impractical for large-scale systems, particularly if the measurements are spatially distributed across wide geographical areas. Dividing the large-scale systems into clusters (i.e., subsystems) and distributing the computation across clusters, solves the constraints of a centralised based approach. In such scenarios, using distributed SE methods brings many advantages over the centralised approaches. In this paper, we propose a novel distributed method to solve the linear SE model by combining local solutions obtained by applying weighted least-squares (WLS) of the given subsystems with the Gaussian belief propagation (GBP) algorithm. The proposed method is based on the factor graph operating without a central coordinator, where subsystems exchange only “beliefs”, thus preserving the privacy of the measurement data and state variables. Further, we propose an approach to speed-up evaluation of the local solutions upon arrival of new information to the subsystem. Finally, the proposed algorithm reaches the accuracy of the centralised WLS solution in a few iterations and outperforms the vanilla GBP algorithm with respect to its convergence properties.

The state estimation algorithm estimates the values of the state variables based on the measurement model described as the system of equations. Prior to applying the state estimation algorithm, the existence and uniqueness of the solution of the underlying system of equations is determined through the observability analysis. If a unique solution does not exist, the observability analysis defines observable islands and further defines an additional set of equations (measurements) needed to determine a unique solution. For the first time, we utilise factor graphs and Gaussian belief propagation algorithm to define a novel observability analysis approach. The observable islands and placement of measurements to restore observability are identified by following the evolution of variances across the iterations of the Gaussian belief propagation algorithm over the factor graph. Due to sparsity of the underlying power network, the resulting method has the linear computational complexity (assuming a constant number of iterations) making it particularly suitable for solving large-scale systems. The method can be flexibly matched to distributed computational resources, allowing for determination of observable islands and observability restoration in a distributed fashion. Finally, we discuss performances of the proposed observability analysis using power systems whose size ranges between 1354 and 70 000 buses.

We propose a linear state estimation (SE) model with complex coefficients and variables suitable for processing large-scale data in electric power systems observable by phasor measurement units. The presented model is based on factor graphs and solved using the belief propagation (BP) algorithm. The proposed algorithm is placed in the non-overlapping multi-area SE scenario without a central coordinator. The communication between areas is asynchronous, where neighboring areas exchange only “beliefs” about specific state variables. Presented architecture directly exploits system sparsity, can be flexibly paralellized and results in substantially lower computational complexity compared to traditional SE solutions. Finally, we discuss performances of the BP-based SE algorithm using power systems with 118, 1354 and 9241 buses.

Lighting systems based on light-emitting diodes (LEDs) possess many benefits over their incandescent counterparts including longer lifespans, lower energy costs, better quality of light and no toxic elements, all without sacrificing consumer satisfaction. Their lifespan is not affected by switching frequency allowing for better illumination control and system efficiency. In this paper, we present a fully distributed energy-saving illumination dimming control strategy for the system of a lighting network which consists of a group of LEDs and user-associated devices. In order to solve the optimization problem, we are using a distributed approach that utilizes factor graphs and the belief propagation algorithm. Using probabilistic graphical models to represent and solve the system model provides for a natural description of the problem structure, where user devices and LED controllers exchange data via line-of-sight communication.

We present a detailed study on application of factor graphs and the belief propagation (BP) algorithm to the power system state estimation (SE) problem. We start from the BP solution for the linear DC model, for which we provide a detailed convergence analysis. Using BP-based DC model we propose a fast real-time state estimator for the power system SE. The proposed estimator is easy to distribute and parallelize, thus alleviating computational limitations and allowing for processing measurements in real time. The presented algorithm may run as a continuous process. Using insights from the DC model, we use two different approaches to derive the BP algorithm for the non-linear model. The first method directly applies BP methodology, however, providing only approximate BP solution for the non-linear model. In the second approach, we make a key further step by providing the solution in which the BP is applied sequentially over the non-linear model, akin to what is done by the Gauss-Newton method. The resulting iterative Gauss-Newton belief propagation (GN-BP) algorithm can be interpreted as a distributed Gauss-Newton method with the same accuracy as the centralized SE.

Distributed energy trading among energy prosumers (i.e., energy producers that also consume energy) is expected to bring significant cost benefits for the participating actors. In terms of the system architecture, physical grouping into microgrids (MG) can be further enhanced by communication infrastructure that provides support for flexible organization of prosumers into virtual MGs. However, how to manage prosumers using communication infrastructure is not widely investigated. In this paper, we propose a virtual MG architecture induced by communication constraints and consider its impact on total costs of energy trading. More precisely, we refine the distributed energy trading model considered in the recent literature with additional communication constraints and investigate impact of the resulting virtualized MG architecture on the overall energy trading costs. We show by simulations that there indeed exists an optimal energy trading architecture that achieves minimum possible energy trading cost, for any given model parameters.

Machine-type communications and large-scale information processing architectures are among key (r)evolutionary enhancements of emerging fifth-generation (5G) mobile cellular networks. Massive data acquisition and processing will make 5G network an ideal platform for large-scale system monitoring and control with applications in future smart infrastructures. In this work, we investigate a capability of such a 5G network architecture to provide the state estimate of an underlying linear system from the input obtained via large-scale deployment of measurement devices. Assuming that the measurements are communicated via densely deployed cloud radio access network (C-RAN), we formulate and solve the problem of estimating the system state from the set of signals collected at C-RAN base stations. Our solution, based on the Gaussian Belief-Propagation (GBP) framework, allows for large-scale and distributed deployment within the emerging 5G information processing architectures. The presented numerical study demonstrates the accuracy, convergence behavior and scalability of the proposed GBP-based solution to the large-scale state estimation problem.

We propose a fast real-time state estimator based on the belief propagation algorithm for the power system state estimation. The proposed estimator is easy to distribute and parallelize, thus alleviating computational limitations and allowing for processing measurements in real time. The presented algorithm may run as a continuous process, with each new measurement being seamlessly processed by the distributed state estimator. In contrast to the matrix-based state estimation methods, the belief propagation approach is robust to ill-conditioned scenarios caused by significant differences between measurement variances, thus resulting in a solution that eliminates observability analysis. Using the DC model, we numerically demonstrate the performance of the state estimator in a realistic real-time system model with asynchronous measurements. We note that the extension to the AC state estimation is possible within the same framework.

With the transition toward 5G, mobile cellular networks are evolving into a powerful platform for ubiquitous large-scale information acquisition, communication, storage, and processing. 5G will provide suitable services for mission-critical and real-time applications such as the ones envisioned in future smart grids. In this work, we show how the emerging 5G mobile cellular network, with its evolution of machine-type communications and the concept of mobile edge computing, provides an adequate environment for distributed monitoring and control tasks in smart grids. In particular, we present in detail how smart grids could benefit from advanced distributed state estimation methods placed within the 5G environment. We present an overview of emerging distributed state estimation solutions, focusing on those based on distributed optimization and probabilistic graphical models, and investigate their integration as part of the future 5G smart grid services.

We present a detailed study on application of factor graphs and the belief propagation (BP) algorithm to the power system state estimation (SE) problem. We start from the BP solution for the linear DC model, for which we provide a detailed convergence analysis. Using insights from the DC model, we use two different approaches to derive the BP algorithm for the non-linear AC model. The first method directly applies BP methodology, however, providing only approximate BP solution for the AC model. In the second approach, we make a key further step by providing the solution in which the BP is applied sequentially over the AC model, akin to what is done by the Gauss-Newton method. The resulting BP-based Gauss-Newton algorithm has the interpretation of a fully distributed Gauss-Newton method with the same accuracy as the centralized SE, preserving a number of advantages of the BP framework. The paper provides extensive numerical study of the proposed algorithms, provides details on their convergence properties, and gives a number of useful insights for their implementation.

We present a novel distributed Gauss–Newton method for the non-linear state estimation (SE) model based on a probabilistic inference method called belief propagation (BP). The main novelty of our work comes from applying BP sequentially over a sequence of linear approximations of the SE model, akin to what is done by the Gauss–Newton method. The resulting iterative Gauss–Newton belief propagation (GN-BP) algorithm can be interpreted as a distributed Gauss–Newton method with the same accuracy as the centralized SE, however, introducing a number of advantages of the BP framework. The paper provides extensive numerical study of the GN-BP algorithm, provides details on its convergence behavior, and gives a number of useful insights for its implementation.