Preface to the Special Issue “Mathematical Modeling and Optimization of Energy Systems”

1. Introduction

The rapid growth of the global economy has led to a continuous increase in energy consumption. Since the Industrial Revolution, conventional fossil fuels such as coal, oil, and natural gas have been the dominant energy sources [1,2]. However, the environmental impact and finite nature of these resources have driven significant efforts toward the adoption of renewable energy sources, including wind and solar power. A key advantage of renewable energy technologies is their ability to generate electricity with minimal harmful emissions, contributing to a more sustainable future [3,4].

Wind energy has been utilized for over 3000 years, with modern wind turbines playing a crucial role in autonomous energy systems [5]. Similarly, photovoltaic (PV) systems have become an essential component of the global energy landscape. Together, wind and solar energy contribute significantly to the world’s electricity supply [6]. Recent research has focused on enhancing the reliability and performance of renewable energy systems, addressing challenges in system components such as power converters and control strategies [7,8,9,10,11]. Mathematical modeling and optimization techniques have become indispensable tools in this pursuit, enabling researchers and engineers to improve efficiency, stability, and cost-effectiveness [12,13,14,15].

This Special Issue, “Mathematical Modeling and Optimization of Energy Systems”, showcases cutting-edge research on the modeling, control, and optimization of renewable energy systems. After a rigorous peer-review process, 10 high-quality papers were selected from 33 submissions. These studies present innovative approaches to improving the performance, integration, and management of energy systems, offering valuable insights for both researchers and practitioners in the field.

We extend our gratitude to all the authors who contributed their research, the reviewers for their constructive feedback, and the editorial team for their dedication in making this Special Issue possible. We hope that the findings presented in this collection will inspire further advancements in mathematical modeling and optimization techniques for energy systems.

2. Contributions

Contribution 1 presents a mathematical analysis and design of three-phase inverters for electric drive applications, comparing SiC MOSFET and Si IGBT technologies in terms of efficiency, power losses, and DC-link ripple characteristics, demonstrating the superior performance of SiC MOSFETs. Contribution 2 proposes a multi-stage robust real-time economic dispatch model that leverages deep learning-based uncertainty sets and a fast robust dual dynamic programming method to enhance scalability and efficiency in power system dispatch, validated through simulations on benchmark test cases. Contribution 3 develops a novel polynomial controller for power systems with fractional-order dynamics, ensuring practical stability using a sum of squares (SOS) approach and validated through simulations with SOSTOOLS. Contribution 4 investigates a wind turbine emulator based on a hybrid generator with excitation auxiliary windings, analyzing space harmonics in MATLAB/Simulink and proposing circuit architecture and robust H∞ control techniques to mitigate electromagnetic torque ripple. Contribution 5 introduces a novel six-segment strategy to optimize prosumer benefits in peer-to-peer energy trading, enhancing economic gains and community-driven energy exchanges, with simulations demonstrating a 12.9% cost saving over existing strategies. Contribution 6 presents a novel PIDND2N2 controller optimized using the balanced arithmetic optimization algorithm to enhance automatic voltage regulator system stability, demonstrating superior transient and frequency responses compared to existing control methods. Contribution 7 proposes a master–slave game framework to optimize distributed energy storage system operation in medium-voltage distribution networks with distributed photovoltaics (DPVs), demonstrating cost reduction and improved DPV consumption through simulation with the IEEE33 node system. Contribution 8 proposes a novel chaotic Horse Herd Optimization-based MPPT technique to enhance the performance of solar photovoltaic water pumping systems, demonstrating improved tracking accuracy and water flow efficiency under partial shading and dynamic weather conditions. Contribution 9 presents a novel transformerless partial power AC-link step-down converter, eliminating high-frequency transformers to reduce costs while enhancing power density. Experimental validation using a reduced-scale prototype demonstrates a peak efficiency of 93.2% and an overall efficiency above 92%, highlighting its viability as a cost-effective alternative to traditional partial power converters. Contribution 10 proposes a novel current control virtual synchronous generator (CC-VSG) structure for frequency regulation in microgrids, utilizing a feedforward controller for damping and a proportional–integral controller for the state-of-charge control of the energy storage system. The methodology based on bandwidth separation for tuning the CC-VSG ensures effective frequency regulation, balancing energy recovery and permissible frequency variation, with validation through time-domain simulations using PSCAD/EMTDC.