arXiv subjects

Mirsad Cosovic

Publications and source records attributed to Mirsad Cosovic.

At least 19 recordsLinked to original sources

arXiv2026

Vectorized Gaussian Belief Propagation for Near Real-Time Fully-Distributed PMU-Based State Estimation

Electric power systems require accurate, scalable, distributed, and near real-time state estimation (SE) to support reliable monitoring and control under increasingly complex operating conditions. Limited monitoring capabilities can lead to inefficient operation and, in extreme cases, large-scale disturbances such as blackouts. To address these challenges, this paper proposes a vectorized Gaussian belief propagation (GBP) framework for phasor measurement unit-based SE, formulated over factor graphs and specifically designed to support distributed and near real-time monitoring. The proposed framework includes multivariate and fusion-based GBP formulations. The multivariate formulation jointly models related state variables and their measurement relationships, while the fusion-based formulation reduces factor graph complexity by combining multiple measurements associated with the same set of variables, resulting in a structure that more closely reflects the underlying electrical coupling of the power system. The resulting algorithms operate in a fully distributed manner at the bus level and achieve fast convergence and high estimation accuracy, often within a few iterations, as demonstrated by numerical results on systems ranging from 60 to 13659 buses, where the fusion-based formulation achieves single-digit millisecond iteration times on the largest test case.

cs.IT↗

arXiv2025

JuliaGrid: An Open-Source Julia-Based Framework for Power System State Estimation

Modern electric power systems have an increasingly complex structure due to rise in power demand and integration of diverse energy sources. Monitoring these large-scale systems, which relies on efficient state estimation, represents a challenging computational task and requires efficient simulation tools for power system steady-state analyses. Motivated by this observation, we propose JuliaGrid, an open-source framework written in the Julia programming language, designed for high performance execution across multiple platforms. The framework implements observability analysis, weighted least-squares and least-absolute value estimators, bad data analysis, and various algorithms related to phasor measurements. To complete power system analysis, the framework includes power flow and optimal power flow, enabling measurement generation for the state estimation routines. Leveraging computationally efficient algorithms, JuliaGrid solves large-scale systems across all methods, offering competitive performance compared to other open-source tools. It is specifically designed for quasi-steady-state analysis, with automatic detection and reuse of computed data to boost performance. These capabilities are validated on systems with 10000, 20000 and 70000 buses.

cs.SE↗

arXiv2024

Identification of Black-Box Inverter-Based Resource Control Using Hammerstein-Wiener Models

The development of more complex inverter-based resources (IBRs) control is becoming essential as a result of the growing share of renewable energy sources in power systems. Given the diverse range of control schemes, grid operators are typically provided with black-box models of IBRs from various equipment manufacturers. As such, they are integrated into simulation models of the entire power system for analysis, and due to their nature, they can only be simulated in the time domain. Other system analysis approaches, like eigenvalue analysis, cannot be applied, making the comprehensive analysis of defined systems more challenging. This work introduces an approach for identification of three-phase IBR models for grid-forming and grid-following inverters using Hammerstein-Wiener models. To this end, we define a simulation framework for the identification process, and select suitable evaluation metrics for the results. Finally, we evaluate the approach on generic grid-forming and grid-following inverter models showing good identification results.

eess.SY↗

arXiv2023

Graph Neural Networks on Factor Graphs for Robust, Fast, and Scalable Linear State Estimation with PMUs

As phasor measurement units (PMUs) become more widely used in transmission power systems, a fast state estimation (SE) algorithm that can take advantage of their high sample rates is needed. To accomplish this, we present a method that uses graph neural networks (GNNs) to learn complex bus voltage estimates from PMU voltage and current measurements. We propose an original implementation of GNNs over the power system's factor graph to simplify the integration of various types and quantities of measurements on power system buses and branches. Furthermore, we augment the factor graph to improve the robustness of GNN predictions. This model is highly efficient and scalable, as its computational complexity is linear with respect to the number of nodes in the power system. Training and test examples were generated by randomly sampling sets of power system measurements and annotated with the exact solutions of linear SE with PMUs. The numerical results demonstrate that the GNN model provides an accurate approximation of the SE solutions. Furthermore, errors caused by PMU malfunctions or communication failures that would normally make the SE problem unobservable have a local effect and do not deteriorate the results in the rest of the power system.

cs.LG↗

arXiv2023

Scalability and Sample Efficiency Analysis of Graph Neural Networks for Power System State Estimation

Data-driven state estimation (SE) is becoming increasingly important in modern power systems, as it allows for more efficient analysis of system behaviour using real-time measurement data. This paper thoroughly evaluates a phasor measurement unit-only state estimator based on graph neural networks (GNNs) applied over factor graphs. To assess the sample efficiency of the GNN model, we perform multiple training experiments on various training set sizes. Additionally, to evaluate the scalability of the GNN model, we conduct experiments on power systems of various sizes. Our results show that the GNN-based state estimator exhibits high accuracy and efficient use of data. Additionally, it demonstrated scalability in terms of both memory usage and inference time, making it a promising solution for data-driven SE in modern power systems.

cs.LG↗

arXiv2022

Distributed Inference over Linear Models using Alternating Gaussian Belief Propagation

We consider the problem of maximum likelihood estimation in linear models represented by factor graphs and solved via the Gaussian belief propagation algorithm. Motivated by massive internet of things (IoT) networks and edge computing, we set the above problem in a clustered scenario, where the factor graph is divided into clusters and assigned for processing in a distributed fashion across a number of edge computing nodes. For these scenarios, we show that an alternating Gaussian belief propagation (AGBP) algorithm that alternates between inter- and intra-cluster iterations, demonstrates superior performance in terms of convergence properties compared to the existing solutions in the literature. We present a comprehensive framework and introduce appropriate metrics to analyse AGBP algorithm across a wide range of linear models characterised by symmetric and non-symmetric, square, and rectangular matrices. We extend the analysis to the case of dynamic linear models by introducing dynamic arrival of new data over time. Using a combination of analytical and extensive numerical results, we show the efficiency and scalability of AGBP algorithm, making it a suitable solution for large-scale inference in massive IoT networks.

cs.IT↗

arXiv2022

Distributed Nonlinear State Estimation in Electric Power Systems using Graph Neural Networks

Nonlinear state estimation (SE), with the goal of estimating complex bus voltages based on all types of measurements available in the power system, is usually solved using the iterative Gauss-Newton method. The nonlinear SE presents some difficulties when considering inputs from both phasor measurement units and supervisory control and data acquisition system. These include numerical instabilities, convergence time depending on the starting point of the iterative method, and the quadratic computational complexity of a single iteration regarding the number of state variables. This paper introduces an original graph neural network based SE implementation over the augmented factor graph of the nonlinear power system SE, capable of incorporating measurements on both branches and buses, as well as both phasor and legacy measurements. The proposed regression model has linear computational complexity during the inference time once trained, with a possibility of distributed implementation. Since the method is noniterative and non-matrix-based, it is resilient to the problems that the Gauss-Newton solver is prone to. Aside from prediction accuracy on the test set, the proposed model demonstrates robustness when simulating cyber attacks and unobservable scenarios due to communication irregularities. In those cases, prediction errors are sustained locally, with no effect on the rest of the power system's results.

cs.LG↗

arXiv2022

Near Real-Time Distributed State Estimation via AI/ML-Empowered 5G Networks

Fifth-Generation (5G) networks have a potential to accelerate power system transition to a flexible, softwarized, data-driven, and intelligent grid. With their evolving support for Machine Learning (ML)/Artificial Intelligence (AI) functions, 5G networks are expected to enable novel data-centric Smart Grid (SG) services. In this paper, we explore how data-driven SG services could be integrated with ML/AI-enabled 5G networks in a symbiotic relationship. We focus on the State Estimation (SE) function as a key element of the energy management system and focus on two main questions. Firstly, in a tutorial fashion, we present an overview on how distributed SE can be integrated with the elements of the 5G core network and radio access network architecture. Secondly, we present and compare two powerful distributed SE methods based on: i) graphical models and belief propagation, and ii) graph neural networks. We discuss their performance and capability to support a near real-time distributed SE via 5G network, taking into account communication delays.

cs.LG↗

arXiv2022

Robust and Fast Data-Driven Power System State Estimator Using Graph Neural Networks

The power system state estimation (SE) algorithm estimates the complex bus voltages based on the available set of measurements. Because phasor measurement units (PMUs) are becoming more widely employed in transmission power systems, a fast SE solver capable of exploiting PMUs' high sample rates is required. To accomplish this, we present a method for training a model based on graph neural networks (GNNs) to learn estimates from PMU voltage and current measurements, which, once it is trained, has a linear computational complexity with respect to the number of nodes in the power system. We propose an original GNN implementation over the power system's factor graph to simplify the incorporation of various types and numbers of measurements both on power system buses and branches. Furthermore, we augment the factor graph to improve the robustness of GNN predictions. Training and test examples were generated by randomly sampling sets of power system measurements and annotated with the exact solutions of linear SE with PMUs. The numerical results demonstrate that the GNN model provides an accurate approximation of the SE solutions. Additionally, errors caused by PMU malfunctions or the communication failures that make the SE problem unobservable have a local effect and do not deteriorate the results in the rest of the power system.

cs.LG↗

arXiv2022

Realistic Video Sequences for Subjective QoE Analysis

Multimedia streaming over the Internet (live and on demand) is the cornerstone of modern Internet carrying more than 60% of all traffic. With such high demand, delivering outstanding user experience is a crucial and challenging task. To evaluate user QoE many researchers deploy subjective quality assessments where participants watch and rate videos artificially infused with various temporal and spatial impairments. To aid current efforts in bridging the gap between the mapping of objective video QoE metrics to user experience, we developed DashReStreamer, an open-source framework for re-creating adaptively streamed video in real networks. DashReStreamer utilises a log created by a HAS algorithm run in an uncontrolled environment (i.e., wired or wireless networks), encoding visual changes and stall events in one video file. These videos are applicable for subjective QoE evaluation mimicking realistic network conditions. To supplement DashReStreamer, we re-create 234 realistic video clips, based on video logs collected from real mobile and wireless networks. In addition our dataset contains both video logs with all decisions made by the HASalgorithm and network bandwidth profile illustrating throughput distribution. We believe this dataset and framework will permit other researchers in their pursuit for the final frontier in understanding the impact of video QoE dynamics.

cs.MM↗

arXiv2022

State Estimation in Electric Power Systems Leveraging Graph Neural Networks

The goal of the state estimation (SE) algorithm is to estimate complex bus voltages as state variables based on the available set of measurements in the power system. Because phasor measurement units (PMUs) are increasingly being used in transmission power systems, there is a need for a fast SE solver that can take advantage of high sampling rates of PMUs. This paper proposes training a graph neural network (GNN) to learn the estimates given the PMU voltage and current measurements as inputs, with the intent of obtaining fast and accurate predictions during the evaluation phase. GNN is trained using synthetic datasets, created by randomly sampling sets of measurements in the power system and labelling them with a solution obtained using a linear SE with PMUs solver. The presented results display the accuracy of GNN predictions in various test scenarios and tackle the sensitivity of the predictions to the missing input data.

cs.LG↗

arXiv2019

Observability Analysis for Large-Scale Power Systems Using Factor Graphs

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 70000 buses.

cs.IT↗

arXiv2018

Design and Analysis of Distributed State Estimation Algorithms Based on Belief Propagation and Applications in Smart Grids

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.

cs.IT↗

arXiv2018

Distributed Gauss-Newton Method for State Estimation Using Belief Propagation

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.

cs.IT↗

arXiv2018

Linear State Estimation via 5G C-RAN Cellular Networks using Gaussian Belief Propagation

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 transportation, connected industry, power grids, etc. 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.

cs.IT↗

arXiv2017

Fast Real-Time DC State Estimation in Electric Power Systems Using Belief Propagation

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.

cs.IT↗

arXiv2017

5G Mobile Cellular Networks: Enabling Distributed State Estimation for Smart Grids

With transition towards 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 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 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.

cs.IT↗

arXiv2016

Distributed Gauss-Newton Method for AC State Estimation: A Belief Propagation Approach

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.

cs.IT↗