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Mathematical Modeling and Optimization of Energy Systems
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Mathematical Modeling and Optimization of Energy Systems

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E2: Control Theory and Mechanics".

Deadline for manuscript submissions: closed (15 September 2024) | Viewed by 22113

Special Issue Editor

Dr. Kotb Basem Tawfiq

E-Mail Website
Guest Editor
Department of Electromechanical, Systems, and Metal Engineering, Ghent University, 9000 Ghent, Belgium
Interests: matrix converter; inverter; space vector modulation; symmetrical sequence algorithm; wind energy conversion system; synchronous reluctance machine; multiphase machine; vector control; winding function; harmonic analysis; star-pentagon and optimization techniques
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Rapid global economic growth has resulted in continually rising energy consumption. Since the industrial revolution, conventional petroleum derivatives, such as coal, oil, and flammable gas, have been the primary energy sources. As a result, significant efforts are being made to generate energy from renewable sources, such as wind, solar, and so on. The main advantage of adopting renewable energy is that these methods generate no hazardous emissions. Wind energy has been used for energy generation for over 3000 years. Furthermore, it has been used by individuals for over 120 years. Wind turbines are commonly used in autonomous systems. Electricity harvested from wind energy conversion systems (WECS) and PV covers a significant proportion of the electrical power needs. The recent focus of research has been targeted toward the reliable and improved performance of renewable energy systems, with a focus on all components of the systems, including the power converter and its controlling techniques.

We invite the submission of original research or review papers to this Special Issue of Mathematics, entitled “Mathematical Modeling and Optimization of Energy Systems”. The main objective of this Special Issue is to promote new advancements, developments, and applications of control, modeling and optimization in the field of energy systems. Additionally, we aim to highlight the possibilities of the careful integration of the energy system within the electric grid. Moreover, it is important to consider this impact, especially under fault conditions.

Dr. Kotb Basem Tawfiq
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.

Keywords

  • mathematical modeling
  • control methods
  • optimization algorithms
  • fault diagnosis
  • differential equations
  • stochastical methods
  • numerical analysis
  • operations research
  • energy systems
  • renewable resources
  • PV systems
  • wind energy systems
  • power converters
  • switching losses
  • maximum power point tracking techniques
  • modulation techniques

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Published Papers (11 papers)

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Editorial

Jump to: Research

3 pages, 142 KiB  
Editorial
Preface to the Special Issue “Mathematical Modeling and Optimization of Energy Systems”
by Kotb B. Tawfiq
Mathematics 2025, 13(5), 860; https://doi.org/10.3390/math13050860 - 5 Mar 2025
Viewed by 438
Abstract
The rapid growth of the global economy has led to a continuous increase in energy consumption [...] Full article
(This article belongs to the Special Issue Mathematical Modeling and Optimization of Energy Systems)

Research

Jump to: Editorial

26 pages, 6712 KiB  
Article
Enhanced Virtual Synchronous Generator with Angular Frequency Deviation Feedforward and Energy Recovery Control for Energy Storage System
by Alisher Askarov, Vladimir Rudnik, Nikolay Ruban, Pavel Radko, Pavel Ilyushin and Aleksey Suvorov
Mathematics 2024, 12(17), 2691; https://doi.org/10.3390/math12172691 - 29 Aug 2024
Cited by 6 | Viewed by 956
Abstract
Frequency control is one of the most important tasks in electric power systems. At the same time, in modern power systems with inertia-free converter-interfaced generation, this task has become more complex. Such an issue is especially relevant for microgrids, which are characterized by [...] Read more.
Frequency control is one of the most important tasks in electric power systems. At the same time, in modern power systems with inertia-free converter-interfaced generation, this task has become more complex. Such an issue is especially relevant for microgrids, which are characterized by a significant increase in the rate of change of frequency and its nadir or zenith. An effective way is through the use of energy storage systems (ESSs) with a grid-forming control in microgrids. For this purpose, this paper proposes a novel structure of the control algorithm based on a current-control virtual synchronous generator (CC-VSG), in which the damping is performed using a feedforward controller. In addition, a simple proportional–integral controller is added to the CC-VSG structure to control the state of charge of the ESS. The performed frequency analysis proves the independence of the different control loop operations within the developed CC-VSG. At the same time, a methodology based on the bandwidth separation of different control loops is proposed for the CC-VSG tuning, which allows for the achievement of the desired quality of frequency regulation in the microgrid, taking into account both the energy recovery and the permissible frequency variation. Finally, the time-domain simulation using PSCAD/EMTDC is performed to confirm the obtained results. Full article
(This article belongs to the Special Issue Mathematical Modeling and Optimization of Energy Systems)
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15 pages, 7261 KiB  
Article
Transformerless Partial Power AC-Link Step-Down Converter
by Rodrigo A. Bugueño, Hugues Renaudineau, Ana M. Llor and Christian A. Rojas
Mathematics 2024, 12(13), 1939; https://doi.org/10.3390/math12131939 - 22 Jun 2024
Cited by 1 | Viewed by 1559
Abstract
DC–DC power converters are essential for various applications, including photovoltaic systems, green hydrogen production, battery charging, and DC microgrids. Partial Power Converters (PPC) are notable for their efficiency, processing only a fraction of total power and reducing conversion losses, but this performance is [...] Read more.
DC–DC power converters are essential for various applications, including photovoltaic systems, green hydrogen production, battery charging, and DC microgrids. Partial Power Converters (PPC) are notable for their efficiency, processing only a fraction of total power and reducing conversion losses, but this performance is overshadowed by the high cost of its construction, associated with high-frequency transformers (HFT). This paper introduces a transformerless partial power AC-link step-down converter, eliminating the need for an HFT and reducing costs while improving power density. An experimental validation using a reduced-scale prototype demonstrates the converter’s operation with a peak efficiency of 93.2% and overall efficiency above 92%, demonstrating the experimental viability of the converter. The proposed AC-link seen as a two-port network is shown to be very attractive for DC–DC step-down operations, and as a possible replacement of traditional PPC. Full article
(This article belongs to the Special Issue Mathematical Modeling and Optimization of Energy Systems)
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26 pages, 2269 KiB  
Article
Design of a Novel Chaotic Horse Herd Optimizer and Application to MPPT for Optimal Performance of Stand-Alone Solar PV Water Pumping Systems
by Rabeh Abbassi and Salem Saidi
Mathematics 2024, 12(4), 594; https://doi.org/10.3390/math12040594 - 17 Feb 2024
Cited by 9 | Viewed by 1951
Abstract
A significant part of agricultural farms in the Kingdom of Saudi Arabia (KSA) are in off-grid sites where there is a lack of sufficient water supply despite its availability from groundwater resources in several regions of the country. Since abundant agricultural production is [...] Read more.
A significant part of agricultural farms in the Kingdom of Saudi Arabia (KSA) are in off-grid sites where there is a lack of sufficient water supply despite its availability from groundwater resources in several regions of the country. Since abundant agricultural production is mainly dependent on water, farmers are forced to pump water using diesel generators. This investigation deals with the increase in the effectiveness of a solar photovoltaic water pumping system (SPVWPS). It investigated, from a distinct perspective, the nonlinear behavior of photovoltaic modules that affects the induction motor-pump because of the repeated transitions between the current and the voltage. A new chaotic Horse Herd Optimization (CHHO)-based Maximum Power Point Tracking technique (MPPT) is proposed. This algorithm integrates the capabilities of chaotic search methods to solve the model with a boost converter to maximize power harvest while managing the nonlinear and unpredictable dynamical loads. The analytical modeling for the proposed SPVWPS components and the implemented control strategies of the optimal duty cycle of the DC–DC chopper duty cycle and the Direct Torque Control (DTC) of the Induction Motor (IM) has been conducted. Otherwise, the discussions and evaluations of the proposed model performance in guaranteeing the maximum water flow rate and the operation at MPP of the SPVWPS under partial shading conditions (PSC) and changing weather conditions have been carried out. A comparative study with competitive algorithms was conducted, and the proposed control system’s accuracy and its significant appropriateness to improve the tracking ability for SPVWPS application have been proven in steady and dynamic operating climates and PSC conditions. Full article
(This article belongs to the Special Issue Mathematical Modeling and Optimization of Energy Systems)
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21 pages, 3356 KiB  
Article
A Stackelberg Game-Based Model of Distribution Network-Distributed Energy Storage Systems Considering Demand Response
by Zezhong Li, Xiangang Peng, Yilin Xu, Fucheng Zhong, Sheng Ouyang and Kaiguo Xuan
Mathematics 2024, 12(1), 34; https://doi.org/10.3390/math12010034 - 22 Dec 2023
Cited by 4 | Viewed by 1444
Abstract
In the context of national efforts to promote country-wide distributed photovoltaics (DPVs), the installation of distributed energy storage systems (DESSs) can solve the current problems of DPV consumption, peak shaving, and valley filling, as well as operation optimization faced by medium-voltage distribution networks [...] Read more.
In the context of national efforts to promote country-wide distributed photovoltaics (DPVs), the installation of distributed energy storage systems (DESSs) can solve the current problems of DPV consumption, peak shaving, and valley filling, as well as operation optimization faced by medium-voltage distribution networks (DN). In this paper, firstly, a price elasticity matrix based on the peak and valley tariff mechanism is introduced to establish a master–slave game framework for DN-DESSs under the DPV multi-point access environment. Secondly, the main model optimizes the pricing strategy of peak and valley tariffs with the objective of the lowest annual operating cost of the DN, and the slave model establishes a two-layer optimization model of DESSs with the objective of the maximum investment return of the DESSs and the lowest daily operating costs and call the CPLEX solver and particle swarm optimization algorithm for solving. Finally, the IEEE33 node system is used as a prototype for simulation verification. The results show that the proposed model can not only effectively reduce the operating cost of the distribution network but also play a role in improving the energy storage revenue and DPV consumption capacity, which has a certain degree of rationality and practicality. Full article
(This article belongs to the Special Issue Mathematical Modeling and Optimization of Energy Systems)
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28 pages, 5295 KiB  
Article
A Novel Balanced Arithmetic Optimization Algorithm-Optimized Controller for Enhanced Voltage Regulation
by Serdar Ekinci, Haluk Çetin, Davut Izci and Ercan Köse
Mathematics 2023, 11(23), 4810; https://doi.org/10.3390/math11234810 - 28 Nov 2023
Cited by 11 | Viewed by 1507
Abstract
This work introduces an innovative approach that unites a PIDND2N2 controller and the balanced arithmetic optimization algorithm (b-AOA) to enhance the stability of an automatic voltage regulator (AVR) system. The PIDND2N2 controller, tailored for precision, stability, and [...] Read more.
This work introduces an innovative approach that unites a PIDND2N2 controller and the balanced arithmetic optimization algorithm (b-AOA) to enhance the stability of an automatic voltage regulator (AVR) system. The PIDND2N2 controller, tailored for precision, stability, and responsiveness, mitigates the limitations of conventional methods. The b-AOA optimizer is obtained through the integration of pattern search and elite opposition-based learning strategies into the arithmetic optimization algorithm. This integration optimizes the controller parameters and the AVR system’s response, harmonizing exploration and exploitation. Extensive assessments, including evaluations on 23 classical benchmark functions, demonstrate the efficacy of the b-AOA. It consistently achieves accurate solutions, exhibits robustness in addressing a wide range of optimization problems, and stands out as a promising choice for various applications. In terms of the AVR system, comparative analyses highlight the superiority of the proposed approach in transient response characteristics, with the shortest rise and settling times and zero overshoot. Additionally, the b-AOA approach excels in frequency response, ensuring robust stability and a broader bandwidth. Furthermore, the proposed approach is compared with various state-of-the-art control methods for the AVR system, showcasing an impressive performance. These results underscore the significance of this work, setting a new benchmark for AVR control by advancing stability, responsiveness, and reliability in power systems. Full article
(This article belongs to the Special Issue Mathematical Modeling and Optimization of Energy Systems)
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17 pages, 3490 KiB  
Article
Six-Segment Strategy for Prosumers’ Financial Benefit Maximization in Local Peer-to-Peer Energy Trading
by Pratik Mochi, Kartik Pandya, Ricardo Faia and Joao Soares
Mathematics 2023, 11(18), 3933; https://doi.org/10.3390/math11183933 - 15 Sep 2023
Cited by 3 | Viewed by 1482
Abstract
The notion of prosumers, people who create and consume energy, has emerged in the energy sector as a result of the fast integration of renewable energy sources and advances in digital technology. Platforms for peer-to-peer (P2P) energy trading have come to light as [...] Read more.
The notion of prosumers, people who create and consume energy, has emerged in the energy sector as a result of the fast integration of renewable energy sources and advances in digital technology. Platforms for peer-to-peer (P2P) energy trading have come to light as viable ways to allow prosumers to conduct direct energy transactions within small groups. Existing P2P trading models, however, frequently lack an optimized approach to maximize the advantages for prosumers. In this article, we provide a novel six-segment strategy (SSS) that is intended to increase prosumers′ ability to maximize their benefits in P2P energy trading systems. Additionally, the SSS promotes prosumers′ active market engagement by supporting community-driven energy exchanges. Through extensive mathematical modeling, simulations, and case studies, we demonstrate the effectiveness of the six-segment strategy in enhancing the economic benefits of prosumers participating in P2P energy trading. The proposed optimization strategy holds the potential to revolutionize the energy landscape by promoting more sustainable and consumer-centric energy trading. The cost savings of 12.9% are distributed among prosumers by the SSS, which is an improvement compared with previously proposed strategies. Full article
(This article belongs to the Special Issue Mathematical Modeling and Optimization of Energy Systems)
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23 pages, 10634 KiB  
Article
Robust Control for Torque Minimization in Wind Hybrid Generators: An H∞ Approach
by Amina Mseddi, Omar Naifar, Mohamed Rhaima, Lassaad Mchiri and Abdellatif Ben Makhlouf
Mathematics 2023, 11(16), 3557; https://doi.org/10.3390/math11163557 - 17 Aug 2023
Cited by 3 | Viewed by 1577
Abstract
This study focuses on implementing a wind turbine emulator based on a permanent magnet synchronous machine with excitation auxiliary windings and thoroughly investigates the space harmonics created by this innovative topology in MATLAB/Simulink. A Hybrid Generator (HG) is a robust generator that does [...] Read more.
This study focuses on implementing a wind turbine emulator based on a permanent magnet synchronous machine with excitation auxiliary windings and thoroughly investigates the space harmonics created by this innovative topology in MATLAB/Simulink. A Hybrid Generator (HG) is a robust generator that does not have slip rings or brushes in its structure. Furthermore, the flux of the hybrid generator HG may be easily adjusted as it is created by direct current excitation coils and permanent magnets. Unfortunately, the space harmonic rate in the HG is relatively high. In other words, the mechanical vibrations caused by the electromagnetic torque ripple threaten the drive train’s behaviour and, ultimately, the wind turbine’s lifespan. This study describes two methods for decreasing the ripple in electromagnetic torque. Both circuit architecture and robust H∞ control techniques are considered. After simulating the two approaches, a list of requirements is provided for the maximum allowable amplitude of the inductance and the flux harmonics. Full article
(This article belongs to the Special Issue Mathematical Modeling and Optimization of Energy Systems)
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10 pages, 347 KiB  
Article
SOS Approach for Practical Stabilization of Tempered Fractional-Order Power System
by Hamdi Gassara, Dhouha Kharrat, Abdellatif Ben Makhlouf, Lassaad Mchiri and Mohamed Rhaima
Mathematics 2023, 11(13), 3024; https://doi.org/10.3390/math11133024 - 7 Jul 2023
Cited by 5 | Viewed by 1154
Abstract
Fractional systems have been widely utilized in various fields, such as mathematics, physics and finance, providing a versatile framework for precise measurements and calculations involving partial quantities. This paper aims to develop a novel polynomial controller for a power system (PS) with fractional-order [...] Read more.
Fractional systems have been widely utilized in various fields, such as mathematics, physics and finance, providing a versatile framework for precise measurements and calculations involving partial quantities. This paper aims to develop a novel polynomial controller for a power system (PS) with fractional-order (FO) dynamics. It begins by studying the practical stability of a general class of tempered fractional-order (TFO) nonlinear systems, with broad applicability and potential for expanding its applications. Afterward, a polynomial controller is designed to guarantee the practical stability of the PS, encompassing the standard constant controller as a specific instance. The design conditions for this controller are resolved using the sum of squares (SOS) approach, a powerful technique for guaranteeing stability and control design. To showcase the practical value of the analytical findings, simulations of the PS are conducted utilizing SOSTOOLS. Full article
(This article belongs to the Special Issue Mathematical Modeling and Optimization of Energy Systems)
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20 pages, 1194 KiB  
Article
Rolling Horizon Robust Real-Time Economic Dispatch with Multi-Stage Dynamic Modeling
by Luyu Wang, Houbo Xiong, Yunhui Shi and Chuangxin Guo
Mathematics 2023, 11(11), 2557; https://doi.org/10.3390/math11112557 - 2 Jun 2023
Viewed by 1806
Abstract
A multi-stage robust real-time economic dispatch model (MRRTD) for power systems is proposed in this paper. The MRRTD takes the dynamic form of multi-stage robust optimization as the framework to naturally simulate the operation of equipment that is temporally coupled, e.g., utility-level energy [...] Read more.
A multi-stage robust real-time economic dispatch model (MRRTD) for power systems is proposed in this paper. The MRRTD takes the dynamic form of multi-stage robust optimization as the framework to naturally simulate the operation of equipment that is temporally coupled, e.g., utility-level energy storage systems. For normal systems, the MRRTD can work directly in short time slots with a rolling horizon. For large-scale systems, the MRRTD expands the time-slot scale and generates optimal dispatch policies. With this guidance, the real-time dispatch decision can be swiftly made thereafter. In addition, a dynamic uncertainty set based on deep learning is proposed, which can dynamically refine the covering ability for probable occurred wind power scenarios. To efficiently solve the MRRTD, a novel fast robust dual dynamic programming method is employed. The effectiveness of the proposed model and solution algorithm, especially the improved scalability compared to several other dynamic economic dispatch methods, are demonstrated by simulation results from six benchmark test cases ranging from a modified IEEE 6-bus system to a 6495-bus system. Full article
(This article belongs to the Special Issue Mathematical Modeling and Optimization of Energy Systems)
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18 pages, 6813 KiB  
Article
Mathematical Design and Analysis of Three-Phase Inverters: Different Wide Bandgap Semiconductor Technologies and DC-Link Capacitor Selection
by Kotb B. Tawfiq, Arafa S. Mansour and Peter Sergeant
Mathematics 2023, 11(9), 2137; https://doi.org/10.3390/math11092137 - 2 May 2023
Cited by 4 | Viewed by 6591
Abstract
This paper introduces a mathematical design and analysis of three-phase inverters used in electric drive applications such as aerospace, electric vehicles, and pumping applications. Different wide bandgap (WBG) semiconductor technologies are considered in this analysis. Using SiC MOSFETs and Si IGBTs, two drive [...] Read more.
This paper introduces a mathematical design and analysis of three-phase inverters used in electric drive applications such as aerospace, electric vehicles, and pumping applications. Different wide bandgap (WBG) semiconductor technologies are considered in this analysis. Using SiC MOSFETs and Si IGBTs, two drive systems are developed in order to show the improvement in the efficiency of the inverter. The efficiency, total losses of the drive systems and the power losses of two inverters are computed and compared for both drive systems at the same operating condition. The drive system with SiC MOSFET shows much better performance compared to the drive system with Si IGBT. The SiC MOSFET system provides a 59.39%, 86.13%, and 29.76% lower conduction losses, switching losses and drive’s total losses, respectively, compared to the Si IGBT system. The efficiency of the SiC MOSFET system is 2.46%pu higher than the efficiency of the Si IGBT drive system. Moreover, this paper introduces a detailed analysis for the dc-link voltage and current ripples in three-phase inverters. Furthermore, the minimal dc-link capacitor needed to deal with the ripple current and voltage is investigated. Finally, the performance of the drive with Si IGBT is experimentally tested under different operating speeds and loads. Full article
(This article belongs to the Special Issue Mathematical Modeling and Optimization of Energy Systems)
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