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Mathematical Methods in Renewable Energies
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Mathematical Methods in Renewable Energies

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

Deadline for manuscript submissions: closed (31 December 2021) | Viewed by 20681

Special Issue Editors

Dr. Pedro Beirão

E-Mail Website
Guest Editor
1. Polytechnic of Coimbra, Coimbra Institute of Engineering, Department of Mechanical Engineering, Rua Pedro Nunes—Quinta da Nora, 3030-199 Coimbra, Portugal
2. IDMEC—Mechanical Engineering Institute, Avenida Rovisco Pais, 1049-001 Lisbon, Portugal
Interests: wave energy; modeling; control; PLC programming; equipment development
Special Issues, Collections and Topics in MDPI journals
Dr. Duarte Valério

E-Mail Website
Guest Editor
Instituto de Engenharia Mecânica (IDMEC), Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal
Interests: fractional calculus; fractional control; wave energy conversion; data mining
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The importance of renewable energy is unquestionable, and several advantages arise from the use of renewable sources of energy. Immediately identified are environmental and economic benefits. Depending on the source, abundant availability and high power density may play important roles. However, technological aspects, such as resistance to harsh environments and conditions, power optimization, and energy harnessing and storing, involve great challenges.

The aim of this Special Issue is to publish original research articles covering the latest developments in mathematical methods applied to renewable energies, such as solar energy, wind energy, geothermal energy, tidal energy, wave energy, and biofuel.

Potential topics include but are not limited to modelling, control, resource prediction, optimization, grid connection, energy storage, management, price evolution, or any other aspect of renewable energy exploration.

Dr. Pedro Beirão
Prof. Dr. Duarte Valério
Guest Editors

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

  • Renewable energy
  • Mathematical models
  • Solar energy
  • Wind energy
  • Geothermal energy
  • Tidal energy
  • Wave energy

Published Papers (7 papers)

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Research

18 pages, 4512 KiB  
Article
AB-Net: A Novel Deep Learning Assisted Framework for Renewable Energy Generation Forecasting
by Noman Khan, Fath U Min Ullah, Ijaz Ul Haq, Samee Ullah Khan, Mi Young Lee and Sung Wook Baik
Mathematics 2021, 9(19), 2456; https://0-doi-org.brum.beds.ac.uk/10.3390/math9192456 - 02 Oct 2021
Cited by 35 | Viewed by 4106
Abstract
Renewable energy (RE) power plants are deployed globally because the renewable energy sources (RESs) are sustainable, clean, and environmentally friendly. However, the demand for power increases on a daily basis due to population growth, technology, marketing, and the number of installed industries. This [...] Read more.
Renewable energy (RE) power plants are deployed globally because the renewable energy sources (RESs) are sustainable, clean, and environmentally friendly. However, the demand for power increases on a daily basis due to population growth, technology, marketing, and the number of installed industries. This challenge has raised a critical issue of how to intelligently match the power generation with the consumption for efficient energy management. To handle this issue, we propose a novel architecture called ‘AB-Net’: a one-step forecast of RE generation for short-term horizons by incorporating an autoencoder (AE) with bidirectional long short-term memory (BiLSTM). Firstly, the data acquisition step is applied, where the data are acquired from various RESs such as wind and solar. The second step performs deep preprocessing of the acquired data via several de-noising and cleansing filters to clean the data and normalize them prior to actual processing. Thirdly, an AE is employed to extract the discriminative features from the cleaned data sequence through its encoder part. BiLSTM is used to learn these features to provide a final forecast of power generation. The proposed AB-Net was evaluated using two publicly available benchmark datasets where the proposed method obtains state-of-the-art results in terms of the error metrics. Full article
(This article belongs to the Special Issue Mathematical Methods in Renewable Energies)
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33 pages, 68585 KiB  
Article
A Comparative Analysis of Some Methods for Wind Turbine Maximum Power Point Tracking
by Constantin Voloşencu
Mathematics 2021, 9(19), 2399; https://0-doi-org.brum.beds.ac.uk/10.3390/math9192399 - 27 Sep 2021
Cited by 6 | Viewed by 1769
Abstract
The study in the paper is placed in the broad context of research for increasing the efficiency of capturing and converting wind energy. The purpose of the study is to analyze some mathematical methods for maximum power point tracking in wind turbines. The [...] Read more.
The study in the paper is placed in the broad context of research for increasing the efficiency of capturing and converting wind energy. The purpose of the study is to analyze some mathematical methods for maximum power point tracking in wind turbines. The mathematical methods studied are on–off control, fuzzy control, and neural predictive control. The rules developed for maximum power point tracking are presented. The related control structures and their design methods are presented. The behaviors of the control systems and their energy efficiency are analyzed. Maximum power point tracking ensures a significant increase in the energy generated compared to the unfavorable case of operation at a small and constant load torque. The differences in energy efficiency between the methods of maximum power point tracking studied are small. Full article
(This article belongs to the Special Issue Mathematical Methods in Renewable Energies)
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25 pages, 41042 KiB  
Article
A Fast Converging Hybrid MPPT Algorithm Based on ABC and P&O Techniques for a Partially Shaded PV System
by Carlos Restrepo, Nicolas Yanẽz-Monsalvez, Catalina González-Castaño, Samir Kouro and Jose Rodriguez
Mathematics 2021, 9(18), 2228; https://0-doi-org.brum.beds.ac.uk/10.3390/math9182228 - 10 Sep 2021
Cited by 12 | Viewed by 3071
Abstract
Among all the conventional maximum power point tracking (MPPT) techniques for a photovoltaic (PV) system that have been proposed, incremental conductance (INC) and perturb and observe (P&O) are the most popular because of their simplicity and ease of implementation. However, under partial shading [...] Read more.
Among all the conventional maximum power point tracking (MPPT) techniques for a photovoltaic (PV) system that have been proposed, incremental conductance (INC) and perturb and observe (P&O) are the most popular because of their simplicity and ease of implementation. However, under partial shading conditions (PSCs), these MPPT algorithms fail to track the global maximum power point (GMPP) and instead converge into local maximum power points (LMPPs), resulting in considerable PV power loss. This paper presents a new hybrid MPPT technique combining the artificial bee colony (ABC) and P&O algorithms named ABC-P&O. The P&O technique is used to track the MPP under uniform irradiance, and only during irradiance variations is the ABC algorithm employed. The effectiveness of the proposed hybrid algorithm at tracking the GMPP, under both uniform and nonuniform irradiance conditions, was assessed by hardware-in-the-loop (HIL) tests employed by a dc–dc boost converter. Then, the ABC-P&O strategy was applied to obtain the voltage reference for the outer PI control loop, which provided the current reference to the discrete-time sliding-mode current control. The ABC-P&O algorithm has a reasonable computational cost, allowing the use of a commercial, low-priced digital signal controller (DSC) with outer voltage and inner current control loops. Many challenging tests validated that the proposed ABC-P&O technique converges fast to the GMPP with high efficiency and superior performance under different PSCs. Full article
(This article belongs to the Special Issue Mathematical Methods in Renewable Energies)
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20 pages, 685 KiB  
Article
Sensitivity, Equilibria, and Lyapunov Stability Analysis in Droop’s Nonlinear Differential Equation System for Batch Operation Mode of Microalgae Culture Systems
by Abraham Guzmán-Palomino, Luciano Aguilera-Vázquez, Héctor Hernández-Escoto and Pedro Martin García-Vite
Mathematics 2021, 9(18), 2192; https://0-doi-org.brum.beds.ac.uk/10.3390/math9182192 - 08 Sep 2021
Cited by 6 | Viewed by 2406
Abstract
Microalgae-based biomass has been extensively studied because of its potential to produce several important biochemicals, such as lipids, proteins, carbohydrates, and pigments, for the manufacturing of value-added products, such as vitamins, bioactive compounds, and antioxidants, as well as for its applications in carbon [...] Read more.
Microalgae-based biomass has been extensively studied because of its potential to produce several important biochemicals, such as lipids, proteins, carbohydrates, and pigments, for the manufacturing of value-added products, such as vitamins, bioactive compounds, and antioxidants, as well as for its applications in carbon dioxide sequestration, amongst others. There is also increasing interest in microalgae as renewable feedstock for biofuel production, inspiring a new focus on future biorefineries. This paper is dedicated to an in-depth analysis of the equilibria, stability, and sensitivity of a microalgal growth model developed by Droop (1974) for nutrient-limited batch cultivation. Two equilibrium points were found: the long-term biomass production equilibrium was found to be stable, whereas the equilibrium in the absence of biomass was found to be unstable. Simulations of estimated parameters and initial conditions using literature data were performed to relate the found results to a physical context. In conclusion, an examination of the found equilibria showed that the system does not have isolated fixed points but rather has an infinite number of equilibria, depending on the values of the minimal cell quota and initial conditions of the state variables of the model. The numerical solutions of the sensitivity functions indicate that the model outputs were more sensitive, in particular, to variations in the parameters of the half saturation constant and minimal cell quota than to variations in the maximum inorganic nutrient absorption rate and maximum growth rate. Full article
(This article belongs to the Special Issue Mathematical Methods in Renewable Energies)
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26 pages, 4620 KiB  
Article
Simulation and Analysis of Renewable and Nonrenewable Capacity Scenarios under Hybrid Modeling: A Case Study
by José D. Morcillo, Fabiola Angulo and Carlos J. Franco
Mathematics 2021, 9(13), 1560; https://0-doi-org.brum.beds.ac.uk/10.3390/math9131560 - 02 Jul 2021
Cited by 4 | Viewed by 2003
Abstract
This work analyzes the response of the electricity market to varied renewable and nonrenewable installed capacity scenarios while taking into account the variability of renewables due to seasonality and El Niño-Southern Oscillation (ENSO) episodes. A hybrid system dynamics/dynamic systems (SD/DS) model was developed [...] Read more.
This work analyzes the response of the electricity market to varied renewable and nonrenewable installed capacity scenarios while taking into account the variability of renewables due to seasonality and El Niño-Southern Oscillation (ENSO) episodes. A hybrid system dynamics/dynamic systems (SD/DS) model was developed by first deriving an SD hypothesis and stock-flow structure from the Colombian electricity supply and demand dynamics. The model’s dynamic behavior was then transformed into a Simulink model and analyzed using the DS tools of bifurcation and control theory to provide deeper insights into the system, both from a Colombian perspective and from the perspective of other market scenarios. Applying the developed hybrid model to the Colombian electricity market provided a detailed description of its dynamics under a broad range of permanent (fossil fuel) and variable (renewable) installed capacity scenarios, including a number of counterintuitive insights. Greater shares of permanent capacity were found to guarantee the security of supply and system robustness in the short-term (2021–2029), whereas greater shares of variable capacity make the system more vulnerable to increased prices and blackouts, especially in the long-term (2040–2050). These critical situations can be avoided only if additional capacity from either conventional or non-conventional generation is quickly installed. Overall, the methodology proposed for building the hybrid SD/DS model was found to provide deeper insights and a broader spectrum of analysis than traditional SD model analysis, and thus can be exploited by policy makers to suggest improvements in their respective market structures. Full article
(This article belongs to the Special Issue Mathematical Methods in Renewable Energies)
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15 pages, 2364 KiB  
Article
Complementary Airflow Control of Oscillating Water Columns for Floating Offshore Wind Turbine Stabilization
by Fares M’zoughi, Payam Aboutalebi, Izaskun Garrido, Aitor J. Garrido and Manuel De La Sen
Mathematics 2021, 9(12), 1364; https://0-doi-org.brum.beds.ac.uk/10.3390/math9121364 - 12 Jun 2021
Cited by 10 | Viewed by 2754
Abstract
The implementation and integration of new methods and control techniques to floating offshore wind turbines (FOWTs) have the potential to significantly improve its structural response. This paper discusses the idea of integrating oscillating water columns (OWCs) into the barge platform of the FOWT [...] Read more.
The implementation and integration of new methods and control techniques to floating offshore wind turbines (FOWTs) have the potential to significantly improve its structural response. This paper discusses the idea of integrating oscillating water columns (OWCs) into the barge platform of the FOWT to transform it into a multi-purpose platform for harnessing both wind and wave energies. Moreover, the OWCs will be operated in order to help stabilize the FOWT platform by means of an airflow control strategy used to reduce the platform pitch and tower top fore-aft displacement. This objective is achieved by a proposed complementary airflow control strategy to control the valves within the OWCs. The comparative study between a standard FOWT and the proposed OWC-based FOWT shows an improvement in the platform’s stability. Full article
(This article belongs to the Special Issue Mathematical Methods in Renewable Energies)
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11 pages, 1618 KiB  
Article
Thermal Conductivity Estimation Based on Well Logging
by Jie Hu, Guangzheng Jiang, Yibo Wang and Shengbiao Hu
Mathematics 2021, 9(11), 1176; https://0-doi-org.brum.beds.ac.uk/10.3390/math9111176 - 23 May 2021
Cited by 4 | Viewed by 1863
Abstract
The thermal conductivity of a stratum is a key factor to study the deep temperature distribution and the thermal structure of the basin. A huge expense of core sampling from boreholes, especially in offshore areas, makes it expensive to directly test stratum samples. [...] Read more.
The thermal conductivity of a stratum is a key factor to study the deep temperature distribution and the thermal structure of the basin. A huge expense of core sampling from boreholes, especially in offshore areas, makes it expensive to directly test stratum samples. Therefore, the use of well logging (the gamma-ray, the neutron porosity, and the temperature) to estimate the thermal conductivity of the samples obtained from boreholes could be a good alternative. In this study, we measured the thermal conductivity of 72 samples obtained from an offshore area as references. When the stratum is considered to be a shale–sand–fluid model, the thermal conductivity can be calculated based on the mixing models (the geometric mean and the square root mean). The contents of the shale and the sand were derived from the natural gamma-ray logs, and the content of the fluid (porosity) was derived from the neutron porosity logs. The temperature corrections of the thermal conductivity were performed for the solid component and the fluid component separately. By comparing with the measured data, the thermal conductivity predicted based on the square root model showed good consistency. This technique is low-cost and has great potential to be used as an application method to obtain the thermal conductivity for geothermal research. Full article
(This article belongs to the Special Issue Mathematical Methods in Renewable Energies)
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