AB 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 BPbased 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, with each new measurement being seamlessly processed by the distributed state estimator. In contrast to the matrixbased SE methods, the BP approach is robust to illconditioned 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 non-linear SE is possible within the same framework. 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 GaussNewton method with the same accuracy as the centralized SE, however, introducing a number of advantages of the BP framework. The thesis 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. Finally, we define the bad data test based on the BP algorithm for the non-linear model. The presented model establishes local criteria to detect and identify bad data measurements. We numerically demonstrate that the BP-based bad data test significantly improves the bad data detection over the largest normalized residual test. Accepted by Scientific Board on ASB 2018/09/27 Defended on DE Defend Board DB Advisor: Dr Dejan Vukobratović, Associate Professor Department of Power, Electronics and Communication Engineering, University of Novi Sad, Serbia. Thesis Committee Members: Dr Andrija Sarić, Full Professor Department of Power, Electronics and Communication Engineering, University of Novi Sad, Serbia. Dr Petar Popovski, Full Professor Department of Electronic Systems, Aalborg University, Denmark. Dr Čedomir Stefanović, Associate Professor Department of Electronic Systems, Aalborg University Copenhagen, Denmark. Dr Izudin Džafić, Full Professor, Department of Electrical Engineering, International University of Sarajevo, Bosnia and Herzegovina. Dr Dušan Jakovetić, Assistant Professor Department of Mathematics and Informatics, University of Novi Sad, Serbia. Distributed State Estimation in Power Systems using Probabilistic Graphical Models by Mirsad Ćosović Mr.-Ing. Power Electrical Engineering, University of Sarajevo, Bosnia and Herzegovina, 2013. Dipl.-Ing. Power Electrical Engineering, University of Sarajevo, Bosnia and Herzegovina, 2009.

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.

This paper explores a belief propagation algorithm approach, for state estimation of thermal states of aggregated populations of thermostatically controlled loads to provide balancing services in power systems. Balancing services such as frequency control require high accuracy and thus estimation is crucial, especially when sensing and communication in real time is not available or partially. We use Markov chain models to describe the thermal states of aggregated thermostatically controlled loads populations and belief propagation for state estimation. Kalman filter, which has been used in similar studies, is known to be an instance of belief propagation framework. This fact motivates us to introduce belief propagation in this framework, and demonstrate that it provides the same results as Kalman filter. Moreover, belief propagation algorithm is fully decentralized, offering higher flexibility of system modeling using factor graphs. Besides demand response, belief propagation can be applied for different purposes in power systems, either in fully distributed or in mixed systems, and is easily integrated with Kalman filter or similar probabilistic frameworks.

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.

We present a detailed study of the applications of factor graphs and the belief propagation (BP) algorithm to the state estimation (SE) problem. Our methodology starts with the BP solution for the linearized DC model, and use insights obtained therein to derive the BP algorithm for the non-linear AC model. Then, we make a key further step, where we present 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 brought in by the BP framework. The BP-based algorithms presented in this paper are fully distributed, however, they can be easily extended to the case of multi-area SE. Finally, the paper provides extensive numerical study of the proposed algorithms and gives a number of useful insights for their implementation.

The European Marie Curie Project ADVANTAGE (Advanced Communications and Information processing in smart grid systems) was launched in 2014. It represents a major inter-disciplinary research project into the topic of Smart Grid technology. A key aspect of the project is to bring together and train 13 early stage researchers from the traditionally separate fields of power systems and communications engineering research. This chapter describes some of the initial research results that have arisen from the project and to highlight some of the key advances and developments that are being studied in the project. The major research focus of the ADVANTAGE project is on advancing technologies for the smart grid, providing architectural solutions and developing innovative information and communications technology (ICT) solutions to support its operation.

In this paper, we model an extended DC state estimation (SE) in an electric power system as a factor graph (FG) and solve it using belief propagation (BP) algorithm. The DC model comprises bus voltage angles as state variables, while the extended DC model includes bus voltage angles and bus voltage magnitudes as state variables. By applying BP to solve the SE problem in the extended DC model, we obtain a Gaussian BP scenario for which we derive closed-form expressions for BP messages exchanged along the FG. The performance of the BP algorithm is demonstrated for the IEEE 14 bus test case. Finally, the application of BP algorithm on the extended DC scenario provides significant insights into a fundamental structure of BP equations in more complex models such as the AC model - the topic we will investigate in our follow up work. As a side-goal of this paper, we aim at thorough and detailed presentation on applying BP on the SE problem in order to make the powerful BP algorithm more accessible and applicable within the power-engineering community.

In this paper, we propose a solution to an AC state estimation problem in electric power systems using a fully distributed Gauss-Newton method. The proposed method is placed within the context of factor graphs and belief propagation algorithms and closed-form expressions for belief propagation messages exchanged along the factor graph are derived. The obtained algorithm provides the same solution as the conventional weighted least-squares state estimation. Using a simple example, we provide a step-by-step presentation of the proposed algorithm. Finally, we discuss the convergence behaviour using the IEEE 14 bus test case.

The design method of initial topology of interior permanent magnet synchronous machine (IPMSM) for hybrid electric vehicle (HEV) propulsion is described in this paper. Design constraints are selected on the basis of limitations imposed by machine's manufacturer and application (e.g. maximum copper slot fill factor, air gap length, permanent magnet material, limited space available in drive trains, etc.). Design variables are rotor radius, stator slot width and number of turns per phase winding. Parametric analysis is performed for various machine topologies. The cost function, which connects the distribution of operating points of HEV and the efficiency maps of various topologies of an electrical machine, is defined. Obtained parametric results are compared to find the result leading to the extreme value of the cost function. The initial design of IPMSM that corresponds to this result is considered as the best initial design.

This paper describes fast analytical model for computation of the switched reluctance machine's (SRM) nonlinear magnetization characteristic and torque lookup table. The flux-tube and the gage-curve methods are used to develop this fast analytical model. Presented model is used for computation of the magnetization characteristic and torque lookup table of three and four-phase SRMs. The simulation results obtained using proposed analytical model are compared to the results of magnetostatic finite-element analysis (FEA) for a three-phase 12/8 SRM. Experimental verification of the analytical model is also presented for the same 12/8 SRM prototype.