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Artykuły w czasopismach na temat "Power resources Australia Mathematical models"

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Austin, Oshin Ola. "Advanced Control And Development of Hydro and Diesel Generator Hybrid Power System Models for Renewable Energy Microgrids." Journal La Multiapp 2, no. 3 (August 11, 2021): 16–32. http://dx.doi.org/10.37899/journallamultiapp.v2i3.383.

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The Nigerian power problem resulted to incessant and erratic supply of electricity and this has destroyed many industrial processes in the country. It has reduced productivity and has increased unemployment rate in the country to over 50million (this figure is over 70% of Nigerian youths). This has led many of the youths in the country to crime. It has led to the deaths of many innocent people in the country. As of 2016, the electricity energy consumption in the world from the world fact book revealed that the average power per capita (watts per person) in the United States is 1,377 Watts. In
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Barragán-Escandón, Antonio, Jonathan Miguel Olmedo Ruiz, Jonnathan David Curillo Tigre, and Esteban F. Zalamea-León. "Assessment of Power Generation Using Biogas from Landfills in an Equatorial Tropical Context." Sustainability 12, no. 7 (March 28, 2020): 2669. http://dx.doi.org/10.3390/su12072669.

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This work evaluates the biogas production potential of the Ceibales landfill for feeding a power plant in the southern region of Ecuador. Biogas production is estimated through mathematical models that consider energy generation and technologies available to supply electricity plants. Characteristic landfill data are accounted for to analyze and develop these mathematical models. Once the generation capability of each source is identified, a decision can be made on the most suitable electricity generation technology. A local model (Ecuadorian model) is applied to calculate the potential of bio
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Iakubovskii, Dmitrii, and Dmitry Krupenev. "Analysis power shortage minimization methods in the modern processing software for adequacy assessment of electric power systems." E3S Web of Conferences 209 (2020): 06008. http://dx.doi.org/10.1051/e3sconf/202020906008.

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Analysis of domestic and foreign software systems for assessing the resource adequacy showed a variety of models and methods used in them. Many software systems use both linear and nonlinear models, these models are optimized according to various criteria to simulate the operation of the system. As tools for solving, software usually use commercial high-level modelling systems for mathematical optimization. However, in addition to the existing ready-made commercial solutions, the authors consider the effectiveness of optimization methods, as well as their parallelized versions, which can be in
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Clarke, David C., and Philip F. Skiba. "Rationale and resources for teaching the mathematical modeling of athletic training and performance." Advances in Physiology Education 37, no. 2 (June 2013): 134–52. http://dx.doi.org/10.1152/advan.00078.2011.

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A number of professions rely on exercise prescription to improve health or athletic performance, including coaching, fitness/personal training, rehabilitation, and exercise physiology. It is therefore advisable that the professionals involved learn the various tools available for designing effective training programs. Mathematical modeling of athletic training and performance, which we henceforth call “performance modeling,” is one such tool. Two models, the critical power (CP) model and the Banister impulse-response (IR) model, offer complementary information. The CP model describes the relat
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Rayaral, Naveen, and Prashanth Revankar. "MODELING OF RENEWABLE ENERGY SYSTEMS FOR POWER GENERATION." International Journal of Engineering Applied Sciences and Technology 6, no. 7 (November 1, 2021): 151–58. http://dx.doi.org/10.33564/ijeast.2021.v06i07.025.

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Sustainable energy systems are termed as the systems which deliver energy and power, utilizing the Renewable and natural resources, which is cost effective and has an environmental concern. The Modeling of the systems and its components is itself a complex procedure. The basic Modeling through Physical law applied to each component of the system, its subsystem and the result of the overall system is more time consuming and requires thorough understanding of physical concept and the results obtained are more accurate. Alternatively, the Mathematical Modeling techniques or the procedures are sim
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Saravanan, G., and I. Gnanambal. "Mathematical Model and Control Design of Micro Turbine Generation System." Journal of Computational and Theoretical Nanoscience 13, no. 10 (October 1, 2016): 7610–16. http://dx.doi.org/10.1166/jctn.2016.5760.

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In this modern era power generation seems to be a very demanding factor. New models and methods have been proposed to derive from various natural and man made resources. In such instances this paper gives a detailed report on the power generation from micro turbines. To enlist the microturbines as a prime source of energy utility restructuring, technology evolution, public environmental policy and expanding power demand are some of the most notable factors. Gas turbines plays a very important role in electric power generation. Especially they are used in the Combined cycle process power Plants
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Komyakov, A. A. "Нормирование и прогнозирование расхода топливно- энергетических ресурсов в производственных процессах на железнодорожном транспорте с использованием информационных технологий". Herald of the Ural State University of Railway Transport, № 2 (2020): 35–43. http://dx.doi.org/10.20291/2079-0392-2020-2-35-43.

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The article reflects issues of improvement of norm setting and forecasting of power resources consumption through improvement of scientific and methodological principles of efficiency enhancement of railway resource-saving operating systems, they including transition from operational methods of fuel and power resources consumption, from the achieved level of power consumption to the methods which imply elaboration and application of mathematical models of power resources and development of organizational structure of control over railway fuel and power resources with reference to delegation of
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Issa, H. I., H. J. Mohammed, L. M. Abdali, A. G. Al Bairmani, and M. Ghachim. "Mathematical Modeling and Controller for PV System by Using MPPT Algorithm." Bulletin of Kalashnikov ISTU 24, no. 1 (April 6, 2021): 96. http://dx.doi.org/10.22213/2413-1172-2021-1-96-101.

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In this research, the study theory of system includes the use of an important source of renewable energy sources (solar source) and linking this system with an electrical load. The world is witnessing a significant rise in fossil fuel prices since the ending of the 20th century and now, this rise in price increases with the decrease in inventory day after day. Therefore, it turned that the field of attention to researchers of power generation to expand in non-conventional energy sources (new and renewable energy sources).New and renewable energy is inexhaustible in use because they rely on ren
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Park, Heejung. "Generation Capacity Expansion Planning Considering Hourly Dynamics of Renewable Resources." Energies 13, no. 21 (October 27, 2020): 5626. http://dx.doi.org/10.3390/en13215626.

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As more generation capacity using renewable sources is accommodated in the power system, methods to represent the uncertainty of renewable sources become more important, and stochastic models with different methods for uncertainty representation are introduced. This paper investigates the impacts of hourly variability representation of random variables on a stochastic generation capacity expansion planning model. In order to represent the hourly variability as well as uncertainty of the random parameters such as wind power availability, solar irradiance, and load, AutoRegressive-To-Anything (A
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Perkins, Greg. "Mathematical modelling of in situ combustion and gasification." Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy 232, no. 1 (August 2, 2017): 56–73. http://dx.doi.org/10.1177/0957650917721595.

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The total worldwide resources of oil sands, heavy oil, oil shale and coal far exceed those of conventional light oil. In situ combustion and gasification are techniques that can potentially recover the energy from these unconventional hydrocarbon resources. In situ combustion can be used to produce oil, especially viscous and immobile crudes, by heating the oil and reducing the viscosity of the hydrocarbon liquids allowing them to flow to production wells. In situ gasification can be used to convert deep carbonaceous materials into synthesis gas which can be used at surface for power generatio
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Rozprawy doktorskie na temat "Power resources Australia Mathematical models"

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Jaforullah, Mohammad. "Energy modelling in a general equilibrium framework with alternative production specifications." Title page, contents and astract only, 1988. http://web4.library.adelaide.edu.au/theses/09PH/09phj23.pdf.

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Vichare, Nitin Shrikrishna. "Robust Mahalanobis distance in power systems state estimation." Diss., Virginia Tech, 1993. http://hdl.handle.net/10919/40024.

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Anasis, John George. "A Combined Energy and Geoengineering Optimization Model (CEAGOM) for Climate Policy Analysis." PDXScholar, 2015. https://pdxscholar.library.pdx.edu/open_access_etds/2620.

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One of the greatest challenges that will face humanity in the 21st century is the issue of climate change brought about by emissions of greenhouse gases. Energy use is one of the primary sources of greenhouse gas emissions. However, it is also one of the most important contributors to improved human welfare over the past two centuries and will continue to be so for years to come. This quandary has led a number of researchers to suggest that geoengineering may be required in order to allow for continued use of fossil fuels while at the same time mitigating the effects of the associated greenhou
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Roufberg, Lewis Marlin. "DC analysis of quasi-resonant buck and forward converters including effects of parasitic elements." Thesis, Virginia Tech, 1987. http://hdl.handle.net/10919/45924.

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<p>The need for smaller and more efficient power supplies steadily grows. Many power supplies incorporate high-frequency dc-to-dc switching converters to meet these demands. Recently, a new class of switching converters has been introduced which can operate at very high frequencies to further reduce size and increase efficiency. They are called quasi-resonant converters. Previously, the dc characteristics of many of these converters had been determined, assuming ideal components and circuit operating conditions. However, as the frequency of operation increases, the circuit behavior becom
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Yee, Victoria E. "Predicting the renewable energy portfolio for the southern half of the United States through 2050 by matching energy sources to regional needs." Scholarly Commons, 2012. https://scholarlycommons.pacific.edu/uop_etds/808.

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Worldwide energy consumption is estimated to double between 2008 and 2035. Over-dependence on energy imports from a few, often politically unstable countries, and unpredictable oil and gas prices, pushes energy to a critical agenda. While there is an agreement that we need to change the production and consumption of energy, there is still disagreement about the specific changes that are needed and how they can be achieved. The conventional energy plans relying primarily on fossil fuels and nuclear technologies, which are in need of transformation due to limited resources and carbon dioxide emi
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Jaforullah, Mohammad. "Energy modelling in a general equilibrium framework with alternative production specifications / Mohammad Jaforullah." Thesis, 1988. http://hdl.handle.net/2440/18835.

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Bowden, G. J. (Gavin James). "Forecasting water resources variables using artificial neural networks." 2003. http://web4.library.adelaide.edu.au/theses/09PH/09phb7844.pdf.

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"February 2003." Corrigenda for, inserted at back Includes bibliographical references (leaves 475-524 ) A methodology is formulated for the successful design and implementation of artificial neural networks (ANN) models for water resources applications. Attention is paid to each of the steps that should be followed in order to develop an optimal ANN model; including when ANNs should be used in preference to more conventional statistical models; dividing the available data into subsets for modelling purposes; deciding on a suitable data transformation; determination of significant model inputs;
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Gilmour, Juliet Karla. "An integrated modelling approach for assessing land use change and water allocation policy options." Phd thesis, 2003. http://hdl.handle.net/1885/148557.

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Paracha, Zahir Javed. "Design and development of intelligent computational techniques for power quality data monitoring and management." Thesis, 2011. https://vuir.vu.edu.au/19381/.

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The most important requirement of power system operations is sustained availability and quality supply of electric power. In Electrical Power Distribution System (EPDS), non-linear loads are the main cause of power quality (PQ) degradation. The PQ problems generated by these non-linear loads are complex and diversified in nature. The power system which is not capable to handle non-linear loads faces the problem of voltage unbalance, sag, swell, momentary or temporary interruption and ultimately complete outage of EPDS. The PQ problems have motivated power system engineers to design and develop
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Książki na temat "Power resources Australia Mathematical models"

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G, Saneev B., Gamm Aleksandr Zelʹmanovich, and Makarov Alekseĭ Aleksandrovich, eds. Approksimat͡s︡ii͡a︡ modeleĭ ėnergeticheskikh sistem: Planirovanie i analiz regressionnykh ėksperimentov. Novosibirsk: Izd-vo "Nauka," Sibirskoe otd-nie, 1985.

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Liang, Qiyuan. Taiwan neng yuan jing ji mo xing zhi yan jiu. Zhonghua min guo Taibei Shi Nan'gang: Zhong yang yan jiu yuan jing ji yan jiu suo, 1987.

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Cichy, Marian. Modelowanie systemów energetycznych. Gdańsk: Wydawn. Politechniki Gdańskiej, 2001.

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Qiyuan, Liang. Taiwan neng yuan jing ji mo xing zhi yan jiu. Zhonghua min guo Taibei Shi Nan'gang: Zhong yang yan jiu yuan jing ji yan jiu suo, 1987.

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C, Greengard, and Ruszczyński Andrzej P, eds. Decision making under uncertainty: Energy and power. New York: Springer, 2002.

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Kim, Dae-Wook. Biases in static oligopoly models?: Evidence from the California electricity market. Cambridge, MA: National Bureau of Economic Research, 2004.

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Conference:, Applied Optimization Techniques in Energy Problems (1984 Linz Austria). Proceedings of the Conference, Applied Optimization Techniques in Energy Problems: June 25-29, 1984, Linz, Austria. Stuttgart: B.G. Teubner, 1985.

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Optimizing reservoir resources: Including a new model for reservoir reliability. New York: Wiley, 1999.

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Johnsen, Tor Arnt. Ressursbruk og produksjon i kraftsektoren. Oslo: Statistisk sentralbyrå, 1992.

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Arzamast͡sev, D. A. Modeli optimizat͡sii razvitii͡a ėnergosistem. Moskva: "Vysshai͡a shkola", 1987.

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Części książek na temat "Power resources Australia Mathematical models"

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Tasneem, Rayeesa, and M. A. Jabbar. "An Insight into Load Balancing in Cloud Computing." In Proceeding of 2021 International Conference on Wireless Communications, Networking and Applications, 1125–40. Singapore: Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-2456-9_113.

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AbstractCloud Computing has emerged as a High-performance computing model providing on-demand computing resources as services via the Internet. Services include applications, storage, processing power, allocation of resources and many more. It is a pay-per-use model. Despite of providing various services, it is also experiencing numerous challenges like data security, optimized resource utilization, performance management, cost management, Cloud migration and many more. Among all, Load Balancing is another key challenge faced by Cloud. Effective load balancing mechanism will optimize the utilization of resources and improve the cloud performance. Load balancing is a mechanism to identify the overloaded and under loaded nodes and then balance the load by uniformly distributing the workload among the nodes. Various load balancing mechanisms are proposed by various researchers by taking different performance metrics. However existing load balancing algorithms are suffering from various drawbacks. This paper emphasizes the comparative review of various algorithms on Load Balancing along with their advantages, shortcomings and mathematical models.
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Stennikov, Valery A., and Ivan V. Postnikov. "Problems of Modeling and Optimization of Heat Supply Systems." In Sustaining Power Resources through Energy Optimization and Engineering, 102–26. IGI Global, 2016. http://dx.doi.org/10.4018/978-1-4666-9755-3.ch005.

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This chapter deals with the problem of comprehensive analysis of heat supply reliability for consumers. It implies a quantitative assessment of the impact of all stages of heat energy production and distribution on heat supply reliability for each consumer of the heat supply system. A short review of existing methods for the analysis of fuel and heat supply reliability is presented that substantiates the key approaches to solving the problem of comprehensive analysis of heat supply reliability. A methodological approach is suggested, in which mathematical models and methods for nodal evaluation of heat supply reliability for consumers are developed and the studies on the impact of different elements of fuel and heat supply systems on its level are described. Mathematical modeling is based on the Markov random processes, models of flow distribution in a heat network, deterministic dependences of thermal processes of heat energy consumption and some other models.
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Arbaiy, Nureize, Junzo Watada, and Pei-Chun Lin. "Fuzzy Random Regression-Based Modeling in Uncertain Environment." In Sustaining Power Resources through Energy Optimization and Engineering, 127–46. IGI Global, 2016. http://dx.doi.org/10.4018/978-1-4666-9755-3.ch006.

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The parameter value determination is important to avoid the developed mathematical model is troublesome and may yield inappropriate results. However, estimating the weights of the parameter or objective functions in the mathematical model is sometimes not easy in real situations, especially when the values are unavailable or difficult to decide. Additionally, various uncertainties include in the statistical data makes common mathematical analysis is not competent to deal with. Hence, this paper presents the Fuzzy Random Regression approach to determine the coefficient whereby statistical data used contain uncertainties namely, fuzziness and randomness. The proposed methods are able to provide coefficient information in the model setting and consideration of uncertainties in the evaluation process. The assessment of coefficient value is given by Weight Absolute Percentage Error of Fuzzy Decision. It clarifies the results between fuzzy decision and non-fuzzy decision that shows the distance of different between both approaches. Finally, a real-life application of production planning models is provided to illustrate the applicability of the proposed algorithms to a practical case study.
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Stennikov, Valery, Andrey Penkovskii, and Oleg Khamisov. "Problems of Modeling and Optimization of Heat Supply Systems." In Sustaining Power Resources through Energy Optimization and Engineering, 54–75. IGI Global, 2016. http://dx.doi.org/10.4018/978-1-4666-9755-3.ch003.

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In the chapter, one of widespread models of the organization of heat supply of consumers presented in the “Single buyer” format is considered. The scientific and methodical base for its description and research offers to accept the fundamental principles of the theory of hydraulic circuits, bi-level programming, principles of economics in the energy sector. Distinctive feature of the developed mathematical model is that it, along with traditionally solved tasks within the bilateral relations heat sources – consumers of heat, considers a network component with physics and technology properties of a heat network inherent in it, and also the economic factors connected with costs of production and transport of heat energy. This approach gives the chance to define the optimum levels of load of heat sources, providing the set demand for heat energy from consumers taking into account receiving with heat sources of the greatest possible profit and performance thus of conditions of formation of the minimum costs in heat networks during the considered time period. Practical realization of the developed mathematical model is considered by the example of the heat supply system with two heat sources, working for single heat networks. With the help of the developed model are carried plotting optimal load heat sources during the year, as well as a nomogram for determining the average tariffs for heat energy heat sources.
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Ranganathan, Prakash, and Kendall Nygard. "Design Models for Resource Allocation in Cyber-Physical Energy Systems." In Sustainable ICTs and Management Systems for Green Computing, 111–30. IGI Global, 2012. http://dx.doi.org/10.4018/978-1-4666-1839-8.ch005.

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Today’s and tomorrow’s smart grid systems are made more efficient, cleaner, and reliable by “smart” control mechanisms and decision models that deliver information to consumers so they can better manage energy resources. The rapidly changing needs and opportunities of today’s electric grid market require unprecedented levels of interoperability to integrate diverse information systems to share knowledge and collaborate among sub-devices or sub-systems in the grid. This book chapter focuses on optimal mathematical models for resource allocation. A series of mathematical models is presented in this book chapter for solving large-scale energy allocation problems with partially observable states, utility functions, and constrained action is introduced. The authors’ techniques use a Linear Programming (LP) approach to determine resource allocations among a set of fuzzy rules that allocates Distributed Energy Resources (DER’s) or power sources/sinks and uses to determine improving resource management.
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Brahimi, Tayeb, and Ion Paraschivoiu. "Aerodynamic Analysis and Performance Prediction of VAWT and HAWT Using CARDAAV and Qblade Computer Codes." In Entropy and Exergy in Renewable Energy [Working Title]. IntechOpen, 2021. http://dx.doi.org/10.5772/intechopen.96343.

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Wind energy researchers have recently invited the scientific community to tackle three significant wind energy challenges to transform wind power into one of the more substantial, low-cost energy sources. The first challenge is to understand the physics behind wind energy resources better. The second challenge is to study and investigate the aerodynamics, structural, and dynamics of large-scale wind turbine machines. The third challenge is to enhance grid integration, network stability, and optimization. This chapter book attempts to tackle the second challenge by detailing the physics and mathematical modeling of wind turbine aerodynamic loads and the performance of horizontal and vertical axis wind turbines (HAWT &amp; VAWT). This work underlines success in the development of the aerodynamic codes CARDAAV and Qbalde, with a focus on Blade Element Method (BEM) for studying the aerodynamic of wind turbines rotor blades, calculating the induced velocity fields, the aerodynamic normal and tangential forces, and the generated power as a function of a tip speed ration including dynamic stall and atmospheric turbulence. The codes have been successfully applied in HAWT and VAWT machines, and results show good agreement compared to experimental data. The strength of the BEM modeling lies in its simplicity and ability to include secondary effects and dynamic stall phenomena and require less computer time than vortex or CFD models. More work is now needed for the simulation of wind farms, the influence of the wake, the atmospheric wind flow, the structure and dynamics of large-scale machines, and the enhancement of energy capture, control, stability, optimization, and reliability.
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Streszczenia konferencji na temat "Power resources Australia Mathematical models"

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Gu¨len, S. Can. "A Simple Parametric Model for the Analysis of Cooled Gas Turbines." In ASME Turbo Expo 2010: Power for Land, Sea, and Air. ASMEDC, 2010. http://dx.doi.org/10.1115/gt2010-22160.

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A natural gas fired gas turbine combined cycle power plant is the most efficient option for fossil fuel based electric power generation that is commercially available. Trade publications report that currently available technology is rated near 60% thermal efficiency. Research and development efforts are in place targeting even higher efficiencies in the next two decades. In the face of diminishing natural resources and increasing carbon dioxide emissions, leading to greenhouse gas effect and global warming, these efforts are even more critical today than in the last century. The main performan
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Meckesheimer, Martin, Russell R. Barton, Timothy W. Simpson, and Andrew J. Booker. "Computationally Inexpensive Metamodel Assessment Strategies." In ASME 2001 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/detc2001/dac-21028.

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Abstract In many scientific and engineering domains, it is common to analyze and simulate complex physical systems using mathematical models. Although computing resources continue to increase in power and speed, discipline-specific computer simulation modules continue to grow in complexity and remain computationally expensive, limiting their use in design optimization. The use of different approximation strategies as inexpensive metamodels of the discipline-specific simulation models has led to the development of various metamodel-based integration frameworks and associated research topics. In
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Bischi, Aldo, Stefano Campanari, Alberto Castiglioni, Giampaolo Manzolini, Emanuele Martelli, Paolo Silva, and Ennio Macchi. "Tri-Generation Systems Optimization: Comparison of Heuristic and Mixed Integer Linear Programming Approaches." In ASME Turbo Expo 2014: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/gt2014-27028.

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This work compares two optimization approaches for combined cooling, heating and power (CCHP or Tri-generation) energy systems scheduling. Both approaches are developed through dedicated software codes and are based on simulation models capable of evaluating of the best operating strategy (both economically and energy-wise) to run a given trigeneration plant while dealing with time-variable loads and tariffs. The simultaneous use of different prime movers operating in parallel is taken into consideration as well as their part load performance, the influence of ambient temperature and the usage
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Suk, Hailie, Abhishek Yadav, and John Hall. "Scalability Considerations in the Design of Microgrids to Support Socioeconomic Development in Rural Communities." In ASME 2018 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/imece2018-88441.

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The interaction between technology and people is characterized by sociotechnical models. In the context of design, these types of systems are analyzed to increase productivity. The level of productivity is expected to increase as the technology evolves. Still, a lack of focus on adaptive design hinders the success of sociotechnical systems. The problem is evident in the relationship between microgrid technology and the residents of developing communities. An analysis of this type of sociotechnical system is analyzed in this paper. Rural villages in the developing world often lack access to the
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Ancona, M. A., M. Bianchi, L. Branchini, A. De Pascale, F. Ferrari, F. Melino, and A. Peretto. "Optimal Design of Renewable Hydrogen Production for Gas Turbine Test Facilities." In ASME Turbo Expo 2021: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/gt2021-59218.

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Abstract The growing attention to environmental issues has led to an increase in renewable source exploitation. These resources, in addition to their characteristic of zero emissions, can be employed where there is no connection to the electricity grid or to produce synthetic fuels (e.g. hydrogen or synthetic natural gas) via power-to-gas technologies. In the context of the ERA-Net Project ZEHTC (Zero Emission Hydrogen Turbine Center), the aim of this paper is the development of a design calculation model for the ZEHTC pilot plant, consisting in the first gas turbine test facility making use o
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Cremanns, Kevin, Dirk Roos, Andreas Penkner, Simon Hecker, and Christian Musch. "Steam Turbine Exhaust Optimization Based on Gaussian Covariance Networks Using Transient CFD Simulations." In ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/gt2018-75261.

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Renewable energies are increasingly contributing to the overall volume of the electricity grid and demand besides high efficiency, greater flexibility of the conventional fossil power plants. To optimize these objectives, extensive CFD calculations are required in most cases. For example, transient CFD calculations are only rarely combined with an optimizer because of their high demand on computational resources and time. Surrogate models, which are mathematical methods to learn and approximate the relationship between input and output parameters, are a common way to solve these problems. Once
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