State of the Art Monte Carlo Method Applied to Power System Analysis with Distributed Generation

Abud, Tiago P.; Augusto, André Guimarães; Fortes, Márcio Zamboti; Maciel, Renan Silva; Borba, Bruno Soares Moreira César

doi:10.3390/en16010394

Cited by 18 publications

(7 citation statements)

References 111 publications

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“…The stochastic algorithms are employed numerical and analytical strategies as discussed in [56]. In numerical approaches, the MC simulation algorithms such as sequential and non-sequential MC are applied which are elaborated adequately in [138]. The analytical strategies attaint the PDF or PMF of the output variables as a relationship of the PDF or PMF of their input variables by linearization-based and approximation-based approaches [10].…”

Section: B Stochastic Approachesmentioning

confidence: 99%

A Comprehensive Review on Recent Developments of Hosting Capacity Estimation and Optimization for Active Distribution Networks

Mousa,

Mahmoud,

Lehtonen

2024

IEEE Access

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Recently, several types of distributed energy resources (DERs) have been developed to reduce the environmental impact and support the global demand for electrical energy. However, the continuous penetration of the DERs into modern power systems (MPSs) may cause several adverse impacts in terms of operation performance indices (PIs) and power quality issues, especially in low-voltage distribution systems (LVDSs). To cope with these serious impacts and achieve optimal control, the hosting capacity (HC) of DERs must be accurately estimated and optimally optimized. However, it requires an extensive communication infrastructure, which is hardly offered without clear financial benefits. In this regard, this article investigates the historical developments of HC definitions as well as the recent developments in terms of operational performance indices, and estimation methods for active distribution networks (ADNs) with the highpenetration level existence of the DERs, energy storage systems (ESSs), electric vehicle (EV) charging systems, sector coupling, hydrogen technologies, and multi-carrier energy systems (MESs) to deal with electrical, thermal, and cooling demands. In this regard, this review article is intended to exhibit an appropriate reference for comprehensive research trends in HC estimation and optimization based on ADNs. Additionally, it involves and covers most current research HC topics in detail compared to other published review articles. Moreover, the authors deliberate the recent approaches for evaluating and improving the HC, especially concerning data-driven methods, with the aid of various software for simulating real systems. Moreover, modern research trends and main factors of MPS operations are deliberated with current energy market developments. Also, prominent challenges, current status, and future aspects are discussed.

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Section: B Stochastic Approachesmentioning

confidence: 99%

A Comprehensive Review on Recent Developments of Hosting Capacity Estimation and Optimization for Active Distribution Networks

Mousa,

Mahmoud,

Lehtonen

2024

IEEE Access

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“…Monte Carlo (MC) algorithms [33][34][35] for LAPs leverage probabilistic sampling techniques to address challenges associated with large-scale linear systems. These algorithms are particularly useful when traditional methods become computationally expensive or impractical.…”

Section: Introductionmentioning

confidence: 99%

Cutting-Edge Monte Carlo Framework: Novel “Walk on Equations” Algorithm for Linear Algebraic Systems

Todorov,

Dimov

2024

Axioms

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In this paper, we introduce the “Walk on Equations” (WE) Monte Carlo algorithm, a novel approach for solving linear algebraic systems. This algorithm shares similarities with the recently developed WE MC method by Ivan Dimov, Sylvain Maire, and Jean Michel Sellier. This method is particularly effective for large matrices, both real- and complex-valued, and shows significant improvements over traditional methods. Our comprehensive comparison with the Gauss–Seidel method highlights the WE algorithm’s superior performance, especially in reducing relative errors within fewer iterations. We also introduce a unique dominancy number, which plays a crucial role in the algorithm’s efficiency. A pivotal outcome of our research is the convergence theorem we established for the WE algorithm, demonstrating its optimized performance through a balanced iteration matrix. Furthermore, we incorporated a sequential Monte Carlo method, enhancing the algorithm’s efficacy. The most-notable application of our algorithm is in solving a large system derived from a finite-element approximation in constructive mechanics, specifically for a beam structure problem. Our findings reveal that the proposed WE Monte Carlo algorithm, especially when combined with sequential MC, converges significantly faster than well-known deterministic iterative methods such as the Jacobi method. This enhanced convergence is more pronounced in larger matrices. Additionally, our comparative analysis with the preconditioned conjugate gradient (PCG) method shows that the WE MC method can outperform traditional methods for certain matrices. The introduction of a new random variable as an unbiased estimator of the solution vector and the analysis of the relative stochastic error structure further illustrate the potential of our novel algorithm in computational mathematics.

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“…The aim of the article is to study an approach to fault recognition on power lines with branches by simultaneously analyzing several information features and applying such machine learning methods as the following: decision tree, random forest, and gradient boosting. Simulation and the Monte Carlo method are at the heart of obtaining training samples [17].…”

Section: Introductionmentioning

confidence: 99%

Decision Tree Models and Machine Learning Algorithms in the Fault Recognition on Power Lines with Branches

et al. 2023

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The complication of the structure, topology and composition of the future electrical networks is characterized by difficult-to-recognize circuit-mode situations and requires modern methods for analyzing information parameters. The growing trend of digitizing signals in substations and the use of the IEC 61850 standard results in a huge amount of new data available at the nodes of the electrical network. The development and analysis of new methods for detecting and recognizing the modes of electrical networks (normal and emergency) are topical research issues. The article explores a new approach to recognizing a faulted section of an electrical network with branches by concurrently analyzing several information features and applying machine learning methods: decision tree, random forest, and gradient boosting. The application of this approach for decision-making by relay protection has not been previously implemented. Simulation modeling and the Monte Carlo method are at the heart of obtaining training samples. The results of testing the studied methods under review showed the required flexibility, the ability to use a large number of information parameters, as well as the best results of fault recognition in comparison with the distance protection relay.

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State of the Art Monte Carlo Method Applied to Power System Analysis with Distributed Generation

Cited by 18 publications

References 111 publications

A Comprehensive Review on Recent Developments of Hosting Capacity Estimation and Optimization for Active Distribution Networks

A Comprehensive Review on Recent Developments of Hosting Capacity Estimation and Optimization for Active Distribution Networks

Cutting-Edge Monte Carlo Framework: Novel “Walk on Equations” Algorithm for Linear Algebraic Systems

Decision Tree Models and Machine Learning Algorithms in the Fault Recognition on Power Lines with Branches

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