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Mathematics
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Mathematical Methods applied in Power Systems
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Mathematical Methods applied in Power Systems

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Computational and Applied Mathematics".

Deadline for manuscript submissions: closed (30 June 2020) | Viewed by 17150

Special Issue Editor

Prof. Dr. Gheorghe Grigoras

E-Mail Website
Guest Editor
Department of Power Engineering, “Gheorghe Asachi” Technical University of Iasi, 700050 Iasi, Romania
Interests: smart grids; applications of artificial intelligence in analysis; operation; control and management; optimization techniques; energy efficiency
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The latest research directions in the Power Engineering field were motivated by the current technological developments and the gradual implementation of the “Smart Grids” concept. The planning and operation of modern power systems requires an efficient management of large databases, essential in the decision-making process, which enables obtaining the best solutions. In this context, it is necessary to improve the routine calculations, with emphasis on data classification and the implementation of complex tasks (selective analysis, multiobjective optimization, optimal online control, etc.). Thus, the practical problems related to the optimal planning and operation of power systems can be solved combining classical algorithms with the facilities offered by Artificial Intelligence algorithms. These approaches are used in all stages of the decision-making process, but especially for overcoming difficulties in multiobjective modeling, handling of constraints, and uncertainty considerations (load estimation, costs, electricity demands, etc.).

This Special Issue, entitled “Mathematical Methods applied in Power Systems”, was proposed to highlight the innovative solutions obtained using the latest models and techniques developed in the planning and operation of modern power systems. The topics of interest for publication include but are not limited to:

  • Modelling and simulation
  • Computational techniques 
  • Performance analysis and forecasting 
  • Optimization and operational research
  • Data mining and soft computing
  • Statistics
  • Evolutionary computation
  • Fuzzy logic
  • Expert systems

Prof. Dr. Grigoras Gheorghe
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (6 papers)

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Research

21 pages, 6691 KiB  
Article
Improved Performance of M-Class PMUs Based on a Magnitude Compensation Model for Wide Frequency Deviations
by Jose Roberto Razo-Hernandez, Ismael Urbina-Salas, Guillermo Tapia-Tinoco, Juan Pablo Amezquita-Sanchez, Martin Valtierra-Rodriguez and David Granados-Lieberman
Mathematics 2020, 8(8), 1361; https://doi.org/10.3390/math8081361 - 14 Aug 2020
Cited by 3 | Viewed by 2099
Abstract
Phasor measurement units (PMUs) are important elements in power systems to monitor and know the real network condition. In order to regulate the performance of PMUs, the IEEE Std. C37.118.1 stablishes two classes—P and M, where the phasor estimation is carried out using [...] Read more.
Phasor measurement units (PMUs) are important elements in power systems to monitor and know the real network condition. In order to regulate the performance of PMUs, the IEEE Std. C37.118.1 stablishes two classes—P and M, where the phasor estimation is carried out using a quadrature oscillator and a low-pass (LP) filter for modulation and demodulation, respectively. The LP filter plays the most important role since it determines the accuracy, response time and rejection capability of both harmonics and aliased signals. In this regard and by considering that the M-class filters are used for more accurate measurements, the IEEE Std. presents different M-class filters for different reporting rates (when a result is given). However, they can degrade their performance under frequency deviations if the LP frequency response is not properly considered. In this work, a unified model for magnitude compensation under frequency deviations for all the M-class filters is proposed, providing the necessary values of compensation to improve their performance. The model considers the magnitude response of the M-class filters for different reporting rates, a normalized frequency range based on frequency dilation and a fitted two-variable function. The effectiveness of the proposal is verified using both static and dynamic conditions for frequency deviations. Besides that, a real-time simulator to generate test signals is also used to validate the proposed methodology. Full article
(This article belongs to the Special Issue Mathematical Methods applied in Power Systems)
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32 pages, 7144 KiB  
Article
A Robust Electric Spring Model and Modified Backward Forward Solution Method for Microgrids with Distributed Generation
by Guillermo Tapia-Tinoco, David Granados-Lieberman, David A. Rodriguez-Alejandro, Martin Valtierra-Rodriguez and Arturo Garcia-Perez
Mathematics 2020, 8(8), 1326; https://doi.org/10.3390/math8081326 - 10 Aug 2020
Cited by 1 | Viewed by 2242
Abstract
The electric spring (ES) is a contemporary device that has emerged as a viable alternative for solving problems associated with voltage and power stability in distributed generation-based smart grids (SG). In order to study the integration of ESs into the electrical network, the [...] Read more.
The electric spring (ES) is a contemporary device that has emerged as a viable alternative for solving problems associated with voltage and power stability in distributed generation-based smart grids (SG). In order to study the integration of ESs into the electrical network, the steady-state simulation models have been developed as an essential tool. Typically, these models require an equivalent electrical circuit of the in-test networks, which implies adding restrictions for its implementation in simulation software. These restrictions generate simplified models, limiting their application to specific scenarios, which, in some cases, do not fully apply to the needs of modern power systems. Therefore, a robust steady-state model for the ES is proposed in this work to adequately represent the power exchange of multiples ESs in radial micro-grids (µGs) and renewable energy sources regardless of their physical location and without the need of additional restrictions. For solving and controlling the model simulation, a modified backward–forward sweep method (MBFSM) is implemented. In contrast, the voltage control determines the operating conditions of the ESs from the steady-state solution and the reference voltages established for each ES. The model and algorithms of the solution and the control are validated with dynamic simulations. For the quasi-stationary case with distributed renewable generation, the results show an improvement higher than 95% when the ESs are installed. On the other hand, the MBFSM reduces the number of iterations by 34% on average compared to the BFSM. Full article
(This article belongs to the Special Issue Mathematical Methods applied in Power Systems)
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24 pages, 2324 KiB  
Article
A Novel Algorithm with Multiple Consumer Demand Response Priorities in Residential Unbalanced LV Electricity Distribution Networks
by Ovidiu Ivanov, Samiran Chattopadhyay, Soumya Banerjee, Bogdan-Constantin Neagu, Gheorghe Grigoras and Mihai Gavrilas
Mathematics 2020, 8(8), 1220; https://doi.org/10.3390/math8081220 - 24 Jul 2020
Cited by 3 | Viewed by 1824
Abstract
Demand Side Management (DSM) is becoming necessary in residential electricity distribution networks where local electricity trading is implemented. Amongst the DSM tools, Demand Response (DR) is used to engage the consumers in the market by voluntary disconnection of high consumption receptors at peak [...] Read more.
Demand Side Management (DSM) is becoming necessary in residential electricity distribution networks where local electricity trading is implemented. Amongst the DSM tools, Demand Response (DR) is used to engage the consumers in the market by voluntary disconnection of high consumption receptors at peak demand hours. As a part of the transition to Smart Grids, there is a high interest in DR applications for residential consumers connected in intelligent grids which allow remote controlling of receptors by electricity distribution system operators and Home Energy Management Systems (HEMS) at consumer homes. This paper proposes a novel algorithm for multi-objective DR optimization in low voltage distribution networks with unbalanced loads, that takes into account individual consumer comfort settings and several technical objectives for the network operator. Phase load balancing, two approaches for minimum comfort disturbance of consumers and two alternatives for network loss reduction are proposed as objectives for DR. An original and faster method of replacing load flow calculations in the evaluation of the feasible solutions is proposed. A case study demonstrates the capabilities of the algorithm. Full article
(This article belongs to the Special Issue Mathematical Methods applied in Power Systems)
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29 pages, 5741 KiB  
Article
Optimal Phase Load Balancing in Low Voltage Distribution Networks Using a Smart Meter Data-Based Algorithm
by Gheorghe Grigoraș, Bogdan-Constantin Neagu, Mihai Gavrilaș, Ion Triștiu and Constantin Bulac
Mathematics 2020, 8(4), 549; https://doi.org/10.3390/math8040549 - 08 Apr 2020
Cited by 20 | Viewed by 3501
Abstract
In the electric distribution systems, the “Smart Grid” concept is implemented to encourage energy savings and integration of the innovative technologies, helping the distribution network operators (DNOs) in choosing the investment plans which lead to the optimal operation of the networks and increasing [...] Read more.
In the electric distribution systems, the “Smart Grid” concept is implemented to encourage energy savings and integration of the innovative technologies, helping the distribution network operators (DNOs) in choosing the investment plans which lead to the optimal operation of the networks and increasing the energy efficiency. In this context, a new phase load balancing algorithm was proposed to be implemented in the low voltage distribution networks with hybrid structures of the consumption points (switchable and non-switchable consumers). It can work in both operation modes (real-time and off-line), uploading information from different databases of the DNO which contain: The consumers’ characteristics, the real loads of the consumers integrated into the smart metering system (SMS), and the typical load profiles for the consumers non-integrated in the SMS. The algorithm was tested in a real network, having a hybrid structure of the consumption points, on a by 24-h interval. The obtained results were analyzed and compared with other algorithms from the heuristic (minimum count of loads adjustment algorithm) and the metaheuristic (particle swarm optimization and genetic algorithms) categories. The best performances were provided by the proposed algorithm, such that the unbalance coefficient had the smallest value (1.0017). The phase load balancing led to the following technical effects: decrease of the average current in the neutral conductor and the energy losses with 94%, respectively 61.75%, and increase of the minimum value of the phase voltage at the farthest pillar with 7.14%, compared to the unbalanced case. Full article
(This article belongs to the Special Issue Mathematical Methods applied in Power Systems)
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27 pages, 5564 KiB  
Article
A New Vision on the Prosumers Energy Surplus Trading Considering Smart Peer-to-Peer Contracts
by Bogdan-Constantin Neagu, Ovidiu Ivanov, Gheorghe Grigoras and Mihai Gavrilas
Mathematics 2020, 8(2), 235; https://doi.org/10.3390/math8020235 - 12 Feb 2020
Cited by 26 | Viewed by 3085
Abstract
A growing number of households benefit from government subsidies to install renewable generation facilities such as PV panels, used to gain independence from the grid and provide cheap energy. In the Romanian electricity market, these prosumers can sell their generation surplus only at [...] Read more.
A growing number of households benefit from government subsidies to install renewable generation facilities such as PV panels, used to gain independence from the grid and provide cheap energy. In the Romanian electricity market, these prosumers can sell their generation surplus only at regulated prices, back to the grid. A way to increase the number of prosumers is to allow them to make higher profit by selling this surplus back into the local network. This would also be an advantage for the consumers, who could pay less for electricity exempt from network tariffs and benefit from lower prices resulting from the competition between prosumers. One way of enabling this type of trade is to use peer-to-peer contracts traded in local markets, run at microgrid (μG) level. This paper presents a new trading platform based on smart peer-to-peer (P2P) contracts for prosumers energy surplus trading in a real local microgrid. Several trading scenarios are proposed, which give the possibility to perform trading based on participants’ locations, instantaneous active power demand, maximum daily energy demand, and the principle of first come first served implemented in an anonymous blockchain trading ledger. The developed scheme is tested on a low-voltage (LV) microgrid model to check its feasibility of deployment in a real network. A comparative analysis between the proposed scenarios, regarding traded quatities and financial benefits is performed. Full article
(This article belongs to the Special Issue Mathematical Methods applied in Power Systems)
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22 pages, 2995 KiB  
Article
Energy Efficiency and Fuel Economy of a Fuel Cell/Renewable Energy Sources Hybrid Power System with the Load-Following Control of the Fueling Regulators
by Nicu Bizon and Phatiphat Thounthong
Mathematics 2020, 8(2), 151; https://doi.org/10.3390/math8020151 - 21 Jan 2020
Cited by 24 | Viewed by 3359
Abstract
Two Hybrid Power System (HPS) topologies are proposed in this paper based on the Renewable Energy Sources (RESs) and a Fuel Cell (FC) system-based backup energy source. Photovoltaic arrays and wind turbines are modeled as RESs power flow. Hydrogen and air needed for [...] Read more.
Two Hybrid Power System (HPS) topologies are proposed in this paper based on the Renewable Energy Sources (RESs) and a Fuel Cell (FC) system-based backup energy source. Photovoltaic arrays and wind turbines are modeled as RESs power flow. Hydrogen and air needed for FC stack to generate the power requested by the load are achieved through the Load-Following control loop. This control loop will regulate the fueling flow rate to load level. A real-time optimization strategy for RES/FC HPS based on Extremum Seeking Control will find the Maximum Efficiency Point or best fuel economy point by control of the boost converter. Therefore, two HPS configurations and associated strategies based on Load-Following and optimization loops of the fueling regulators were studied here and compared using the following performance indicators: the FC net power generated on the DC bus, the FC energy efficiency, the fuel consumption efficiency, and the total fuel consumption. An increase in the FC system’s electrical efficiency and fuel economy of up to 2% and 12% respectively has been obtained using the proposed optimization strategies compared with a baseline strategy. Full article
(This article belongs to the Special Issue Mathematical Methods applied in Power Systems)
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