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Energies, Volume 11, Issue 7 (July 2018)

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Open AccessArticle Thermo–Economical Evaluation of Producing Liquefied Natural Gas and Natural Gas Liquids from Flare Gases
Energies 2018, 11(7), 1868; https://doi.org/10.3390/en11071868 (registering DOI)
Received: 18 June 2018 / Revised: 28 June 2018 / Accepted: 12 July 2018 / Published: 18 July 2018
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Abstract
In many industrial plants including petrochemicals and refineries, raw hydrocarbons (mostly flammable gas) are released during unplanned operations. These flammable gases (usually called flare gases) are sent to a combustor and the process is called flaring. Flaring wastes energy and produces environmental pollution.
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In many industrial plants including petrochemicals and refineries, raw hydrocarbons (mostly flammable gas) are released during unplanned operations. These flammable gases (usually called flare gases) are sent to a combustor and the process is called flaring. Flaring wastes energy and produces environmental pollution. Consequently, recovering the flare gases is an important subject in these industries. In this work, an economical and technical analysis is presented for the production of valuable products, namely, liquefied natural gas and natural gas liquids from flare gas. The flare gas of Fajr Jam refinery, a refinery located in the south part of Iran, is selected as a case study. One of the issues in recovering flare gases is the nonconstant flow rate of these gases. For this reason, an auxiliary natural gas flow rate is employed to have a constant feed for the flare recovery process. The Poly Refrigerant Integrated Cycle Operations (PRICO) refrigeration cycle is employed for producing liquefied natural gas and natural gas liquids. In the PRICO cycle, the mixed refrigerant is used as the working fluid. The other issue is the existence of H2S in the flare gases. The main idea is that the flare gas components, including H2S, have different boiling points and it is possible to separate them. Consequently, flare gases are separated into several parts during a number of successive cooling and heating stages and passing through phase separators. It is shown that the proposed flare gas recovery process prevents burning of 12 million cubic meters of the gases with valuable hydrocarbons, which is almost 70% of the current flare gases. Furthermore, about 11,000 tons of liquefied natural gas and 1230 tons of natural gas liquids are produced in a year. Finally, the economic evaluation shows a payback period of about 1.6 years. Full article
(This article belongs to the Section Sustainable Energy)
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Open AccessArticle Gas Content Evaluation of Coalbed Methane Reservoir in the Fukang Area of Southern Junggar Basin, Northwest China by Multiple Geophysical Logging Methods
Energies 2018, 11(7), 1867; https://doi.org/10.3390/en11071867 (registering DOI)
Received: 11 June 2018 / Revised: 5 July 2018 / Accepted: 11 July 2018 / Published: 17 July 2018
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Abstract
To study the gas potential of coalbed methane (CBM) in the Fukang area, southern Junggar Basin (SJB) of North China, different methods including multiple geophysical logging, the Kim method with proximate analysis data, and Langmuir adsorption were used to evaluate the gas content.
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To study the gas potential of coalbed methane (CBM) in the Fukang area, southern Junggar Basin (SJB) of North China, different methods including multiple geophysical logging, the Kim method with proximate analysis data, and Langmuir adsorption were used to evaluate the gas content. Furthermore, the geological controls on gas content were evaluated. One hundred sixteen CBM wells with geophysical logging and 20 with field-measured gas content were adopted to assess the gas content in the Fukang area of SJB, NW China. The results show that the two geophysical logging variables (DEN and CNL) were favorable for evaluating the gas content due to the perfect correlation with the measured gas content. The gas content varies from 4.22 m3/t to 16.26 m3/t, and generally increases with increasing burial depth. The gas content in coal seams along the synclinal axis is significantly higher than that along the synclinal wing in the west zone. In the east zone, the gas content of the westward is higher than that of the eastward because of the fault coating effect by reverse fault. Generally, the gas content of the SJB is in the order of syncline > surrounding reverse fault > slope of syncline > slope of anticline > central of reverse fault, if only geological structure features are considered. The favorable areas for CBM concentration appear to be a composite gas controlling result of multiple geological factors. Two typical geological scenarios with low gas content and high gas content were revealed. In the Fukang area of SJB, the low gas content is mainly due to the normal fault and roof lithology of sandstone. The most favorable area of high gas content for CBM exploration and development is in the northeast, where reversed fault, synclinal axis, mudstone roof lithology, and burial depth coincide with high gas content. Full article
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Open AccessArticle Design and Experimental Implementation of a Hysteresis Algorithm to Optimize the Maximum Power Point Extracted from a Photovoltaic System
Energies 2018, 11(7), 1866; https://doi.org/10.3390/en11071866 (registering DOI)
Received: 12 June 2018 / Revised: 2 July 2018 / Accepted: 13 July 2018 / Published: 17 July 2018
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Abstract
In the several last years, numerous Maximum Power Point Tracking (MPPT) methods for photovoltaic (PV) systems have been proposed. An MPPT strategy is necessary to ensure the maximum power efficiency provided to the load from a PV module that is subject to external
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In the several last years, numerous Maximum Power Point Tracking (MPPT) methods for photovoltaic (PV) systems have been proposed. An MPPT strategy is necessary to ensure the maximum power efficiency provided to the load from a PV module that is subject to external environmental perturbations such as radiance, temperature and partial shading. In this paper, a new MPPT technique is presented. Our approach has the novelty that it is a MPPT algorithm with a dynamic hysteresis model incorporated. One of the most cited Maximum Power Point Tracking methods is the Perturb and Observer algorithm since it is easily implemented. A comparison between the approach presented in this paper and the known Perturb and Observer method is evaluated. Moreover, a new PV-system platform was properly designed by employing low cost electronics, which may serve as an academical platform for further research and developments. This platform is used to show that the proposed algorithm is more efficient than the standard Perturb and Observer method. Full article
(This article belongs to the Special Issue Energy Systems Engineering)
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Open AccessFeature PaperArticle A Novel Two-Stage Photovoltaic Grid-Connected Inverter Voltage-Type Control Method with Failure Zone Characteristics
Energies 2018, 11(7), 1865; https://doi.org/10.3390/en11071865 (registering DOI)
Received: 16 May 2018 / Revised: 22 June 2018 / Accepted: 13 July 2018 / Published: 17 July 2018
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Abstract
This paper investigates how to develop a two-stage voltage-type grid-connected control method for renewable energy inverters that can make them simulate the characteristics of a synchronous generator governor. Firstly, the causes and necessities of the failure zone are analyzed, and thus the traditional
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This paper investigates how to develop a two-stage voltage-type grid-connected control method for renewable energy inverters that can make them simulate the characteristics of a synchronous generator governor. Firstly, the causes and necessities of the failure zone are analyzed, and thus the traditional static frequency characteristics are corrected. Then, a novel inverter control scheme with the governor’s failure zone characteristics is proposed. An enabling link and a power loop are designed for the inverter to compensate fluctuations and regulate frequency automatically. Outside the failure zone, the inverter participates in the primary frequency regulation by disabling the power loop. In the failure zone, the droop curve is dynamically moved to track the corrected static frequency characteristic by enabling the power loop, resisting the fluctuation of grid frequency. The direct current (DC) bus voltage loop is introduced into the droop control to stabilize the DC bus voltage. Moreover, the designed dispatch instruction interface ensures the schedulability of the renewable energy inverter. Finally, the feasibility and effectiveness of the proposed control method are verified by simulation results from MATLAB (R2016a). Full article
(This article belongs to the Special Issue Power Electronics in Renewable Energy Systems)
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Open AccessArticle Bubble Size and Bubble Concentration of a Microbubble Pump with Respect to Operating Conditions
Energies 2018, 11(7), 1864; https://doi.org/10.3390/en11071864 (registering DOI)
Received: 8 June 2018 / Revised: 11 July 2018 / Accepted: 12 July 2018 / Published: 17 July 2018
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Abstract
The present paper describes some aspects of the bubble size and concentration of a microbubble pump with respect to flow and pressure conditions. The microbubble pump used in the present study has an open channel impeller of a regenerative pump, which generates micro-sized
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The present paper describes some aspects of the bubble size and concentration of a microbubble pump with respect to flow and pressure conditions. The microbubble pump used in the present study has an open channel impeller of a regenerative pump, which generates micro-sized bubbles with the rotation of the impeller. The bubble characteristics are analyzed by measuring the bubble size and concentration using the experimental apparatus consisting of open-loop facilities; a regenerative pump, a particle counter, electronic flow meters, pressure sensors, flow control valves, a torque meter, and reservoir tanks. To control the intake, and the air flowrate upstream of the pump, a high precision flow control valve is introduced. The bubble characteristics have been analyzed by controlling the intake air flowrate and the pressure difference of the pump while the rotational frequency of the pump impeller was kept constant. All measurement data was stored on the computer through the NI (National Instrument) interface system. The bubble size and concentration are mainly affected by three operating parameters: the intake air flowrate, the pressure difference, and the water flowrate supplied to the pump. It is noted that the operating conditions that can most effectively generate microbubbles in the range of 20 to 30 micrometers are at the pressure of 5 bar and at the air flowrate ratio of 4.0 percent for the present pump. Throughout the experimental measurements, it was found that the pump efficiency changed by less than 1.2 percent, depending on the intake air supply. The performance characteristics of microbubble generation obtained by experimental measurements are analyzed and discussed in detail. Full article
(This article belongs to the Special Issue Fluid Flow and Heat Transfer)
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Open AccessArticle Multi-Objective Optimisation of the Energy Performance of Lightweight Constructions Combining Evolutionary Algorithms and Life Cycle Cost
Energies 2018, 11(7), 1863; https://doi.org/10.3390/en11071863 (registering DOI)
Received: 19 June 2018 / Revised: 11 July 2018 / Accepted: 16 July 2018 / Published: 17 July 2018
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Abstract
This paper discusses the thermal and energy performance of a detached lightweight building. The building was monitored with hygrothermal sensors to collect data for building energy model calibration. The calibration was performed using a dynamic simulation through EnergyPlus® (EP) (Version 8.5, United
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This paper discusses the thermal and energy performance of a detached lightweight building. The building was monitored with hygrothermal sensors to collect data for building energy model calibration. The calibration was performed using a dynamic simulation through EnergyPlus® (EP) (Version 8.5, United States Department of Energy (DOE), Washington, DC, USA) with a hybrid evolutionary algorithm to minimise the root mean square error of the differences between the predicted and real recorded data. The results attained reveal a good agreement between predicted and real data with a goodness of fit below the limits imposed by the guidelines. Then, the evolutionary algorithm was used to meet the compliance criteria defined by the Passive House standard for different regions in Portugal’s mainland using different approaches in the overheating evaluation. The multi-objective optimisation was developed to study the interaction between annual heating demand and overheating rate objectives to assess their trade-offs, tracing the Pareto front solution for different climate regions throughout the whole of Portugal. However, the overheating issue is present, and numerous best solutions from multi-objective optimisation were determined, hindering the selection of a single best option. Hence, the life cycle cost of the Pareto solutions was determined, using the life cycle cost as the final criterion to single out the optimal solution or a combination of parameters. Full article
(This article belongs to the Special Issue Building Energy Use: Modeling and Analysis)
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Open AccessArticle An Improved Centralized Control Structure for Compensation of Voltage Distortions in Inverter-Based Microgrids
Energies 2018, 11(7), 1862; https://doi.org/10.3390/en11071862 (registering DOI)
Received: 13 June 2018 / Revised: 10 July 2018 / Accepted: 12 July 2018 / Published: 17 July 2018
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Abstract
Recently, increased use of non-linear loads has intensified the harmonic distortion and voltage unbalance in distribution systems. Inverter Based Distributed Generators (IBDGs) can be employed as distributed compensators to improve the power quality, as well as to supply distribution systems. In this paper,
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Recently, increased use of non-linear loads has intensified the harmonic distortion and voltage unbalance in distribution systems. Inverter Based Distributed Generators (IBDGs) can be employed as distributed compensators to improve the power quality, as well as to supply distribution systems. In this paper, an enhanced hierarchical control scheme for the compensation of voltage disturbance in an AC Micro Grid (MG) that includes of two control levels is proposed. The secondary control level is performed by a centralized controller. Data of voltage harmonics and voltage unbalance at the MG Sensitive Load Bus (SLB) is sent to the centralized controller by a measurement unit. A general case with a combined voltage harmonic and unbalance distortion is considered. The compensation coefficients for IBDG units are computed by the centralized controller, and reference commands are sent to the local controllers of the IBDG units that act as a primary level of control. In the secondary control level, harmonic analysis is performed for the MG in order to provide a guide for properly assigning the harmonics and unbalance compensation priorities to IBDGs at different locations in the distribution system. Some buses have more participation in exciting the MG resonance modes; therefore, larger harmonic compensation factors are considered for the IBDGs that are near to these buses. For other IBDGs, the voltage unbalance compensation factor is selected bigger. The control system of the IBDGs mainly includes a current controller, a virtual damping resistor loop, and a load compensation block. Effectiveness of the proposed control scheme is demonstrated through simulation studies. Full article
(This article belongs to the Section Electrical Power and Energy System)
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Open AccessArticle Hybrid Modulated Model Predictive Control in a Modular Multilevel Converter for Multi-Terminal Direct Current Systems
Energies 2018, 11(7), 1861; https://doi.org/10.3390/en11071861 (registering DOI)
Received: 17 May 2018 / Revised: 10 July 2018 / Accepted: 11 July 2018 / Published: 17 July 2018
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Abstract
In this paper a hybrid modulated model predictive control (HM2PC) strategy for modular-multilevel-converter (MMC) multi-terminal direct current (MTDC) systems is proposed for supplying power to passive networks or weak AC systems, with the control objectives of maintaining the DC voltage, voltage
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In this paper a hybrid modulated model predictive control (HM2PC) strategy for modular-multilevel-converter (MMC) multi-terminal direct current (MTDC) systems is proposed for supplying power to passive networks or weak AC systems, with the control objectives of maintaining the DC voltage, voltage stability and power balance of the proposed system. The proposed strategy preserves the desired characteristics of conventional model predictive control method based on finite control set (FCS-MPC) methods, but deals with high switching frequency, circulating current and steady-state error in a superior way by introducing the calculation of the optimal output voltage level in each bridge arm and the specific duty cycle in each Sub-Module (SM), both of which are well-suited for the control of the MMC system. In addition, an improved multi-point DC voltage control strategy based on active power balanced control is proposed for an MMC-MTDC system supplying power to passive networks or weak AC systems, with the control objective of coordinating the power balance between different stations. An MMC-HVDC simulation model including four stations has been established on MATLAB/Simulink (r2014b MathWorks, Natick, MA, USA). Simulations were performed to validate the feasibility of the proposed control strategy under both steady and transient states. The simulation results prove that the strategy can suppress oscillations in the MMC-MTDC system caused by AC side faults, and that the system can continue functioning if any one of the converters are tripped from the MMC-MTDC network. Full article
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Open AccessArticle Impact of Partial Shading on the P-V Characteristics and the Maximum Power of a Photovoltaic String
Energies 2018, 11(7), 1860; https://doi.org/10.3390/en11071860 (registering DOI)
Received: 1 June 2018 / Revised: 21 June 2018 / Accepted: 26 June 2018 / Published: 17 July 2018
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Abstract
A photovoltaic system is highly susceptible to partial shading. Based on the functionality of a photovoltaic system that relies on solar irradiance to generate electrical power, it is tacitly assumed that the maximum power of a partially shaded photovoltaic system always decreases as
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A photovoltaic system is highly susceptible to partial shading. Based on the functionality of a photovoltaic system that relies on solar irradiance to generate electrical power, it is tacitly assumed that the maximum power of a partially shaded photovoltaic system always decreases as the shading heaviness increases. However, the literature has reported that this might not be the case. The maximum power of a partially shaded photovoltaic system under a fixed configuration and partial shading pattern can be highly insusceptible to shading heaviness when a certain critical point is met. This paper presents an investigation of the impact of partial shading and the critical point that reduce the susceptibility of shading heaviness. Photovoltaic string formed by series-connected photovoltaic modules is used in this research. The investigation of the P-V characteristic curve under different numbers of shaded modules and shading heaviness suggests that the photovoltaic string becomes insusceptible to shading heaviness when the shaded modules irradiance reaches a certain critical point. The critical point can vary based on the number of the shaded modules. The formulated equation in this research contributes to determining the critical point for different photovoltaic string sizes and numbers of shaded modules in the photovoltaic string. Full article
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Open AccessArticle Design, Analysis and Model Predictive Control of an Axial Field Switched-Flux Permanent Magnet Machine for Electric Vehicle/Hybrid Electric Vehicle Applications
Energies 2018, 11(7), 1859; https://doi.org/10.3390/en11071859
Received: 8 June 2018 / Revised: 13 July 2018 / Accepted: 15 July 2018 / Published: 16 July 2018
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Abstract
In this paper, an axial field switched-flux permanent magnet (AFSFPM) machine with stator-PM, which has a high power/torque density and efficiency feature as well as shorter axial length, is designed, analyzed and controlled. The topology, operating principle and design procedure of the AFSFPM
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In this paper, an axial field switched-flux permanent magnet (AFSFPM) machine with stator-PM, which has a high power/torque density and efficiency feature as well as shorter axial length, is designed, analyzed and controlled. The topology, operating principle and design procedure of the AFSFPM machine are labored and discussed. The electromagnetic performance, including the flux linkage, back-EMF, cogging torque, winding inductance and field-control capability, are studied based on 3-D finite-element analysis (FEA). In order to investigate the operating performance of the machine in the whole speed range, a continuous-control-set model predictive control (MPC) method for the AFSFPM machine is proposed. Based on the stage control targets, the maximum torque per ampere (MTPA) and maximum output power flux-weakening strategies are presented in constant torque and constant power regions, respectively. Finally, a prototype of AFSFPM machine has been manufactured and experimentally evaluated and the results show that the MTPA strategy increases the load capability and the flux-weakening strategy broadens the constant power operation range. Moreover, the anti-load-disturbance capacity and dynamic response performance are improved under the MPC method. As a result, the proposed AFSFPM machine drive system is excellent alternative for electrical vehicles (EVs) or hybrid EVs (HEVs). Full article
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Open AccessArticle A Green Quality Management Decision Model with Carbon Tax and Capacity Expansion under Activity-Based Costing (ABC)—A Case Study in the Tire Manufacturing Industry
Energies 2018, 11(7), 1858; https://doi.org/10.3390/en11071858
Received: 22 May 2018 / Revised: 26 June 2018 / Accepted: 12 July 2018 / Published: 16 July 2018
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Abstract
Issues related to global environmental protection are highly important. Under the global trend of energy saving and carbon reduction, in order to lower the carbon emissions of products or services offered by enterprises, the Taiwanese government aims to control carbon emissions by constructing
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Issues related to global environmental protection are highly important. Under the global trend of energy saving and carbon reduction, in order to lower the carbon emissions of products or services offered by enterprises, the Taiwanese government aims to control carbon emissions by constructing a carbon tax system and mandating enterprises to pay a carbon tax. The collection of a carbon tax can minimize the total social environmental cost and increase the efficiency of carbon reduction; the need to control the green quality cost can serve as a criterion of green management decision-making. This study aimed to reorganize carbon emissions in different stages of production in order to lower the total carbon emissions of products. Activity-based costing (ABC) was adopted to assess green quality management and production cost. The optimal green quality production portfolio was selected via a mathematical programming model to focus on the expansion of productivity and outsourcing strategy in order to effectively lessen the harmful effects on the environment and maximize profits. Besides academic contributions, the findings of this study could serve as a reference to enterprises on assessing the effects of carbon emissions, carbon taxes, and environmental management on production decision-making. Full article
(This article belongs to the Special Issue Modeling and Simulation of Carbon Emission Related Issues)
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Open AccessArticle E-City Web Platform: A Tool for Energy Efficiency at Urban Level
Energies 2018, 11(7), 1857; https://doi.org/10.3390/en11071857
Received: 20 June 2018 / Revised: 11 July 2018 / Accepted: 13 July 2018 / Published: 16 July 2018
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Abstract
Cities, as main energy consumers, play a crucial role in achieving a more sustainable energy future. This means that there is an urgent need to transform the way of planning urban areas, focusing on more efficient and self-reliant energy production and consumption modes
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Cities, as main energy consumers, play a crucial role in achieving a more sustainable energy future. This means that there is an urgent need to transform the way of planning urban areas, focusing on more efficient and self-reliant energy production and consumption modes overall. In this framework, the aim of this study is to explore the Net-Zero energy balance between two spatial scales: the whole city with its diversified energy consumption patterns, and those urban blocks, neighborhoods, or industrial areas that can produce energy and supply it to other areas. This approach leads to the development of an energy zoning for the city, based on the geographical urban delimitation of solar energy exporters cells and the energy consuming ones. On the production side, cells are delimited according to their solar energy production potential. On the demand side, cells are delimited according to four specific criteria: construction timeline, population density, urban morphologies, and land-use patterns that permit the definition of a classification of urban areas, based on the different energy consumption levels. In this paper, the web platform “E-City”, a tool for planning energy balance at urban level is presented, by describing its practical application in the city of Oeiras, Portugal. The platform integrates itself with the existing municipal Geographic Information System, exploring both spatial and statistical dimensions associated with zoning and the overall energy network system. Results from the use of this tool are relevant for urban planning practices, formulation of policies, and management of public investment that can be guided to more energy efficient solutions and supporting the transition towards nearly zero-energy cities. Full article
(This article belongs to the Section Sustainable Energy)
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Open AccessErratum Erratum: Rogada, J.R.; et al. Comparative Modeling of a Parabolic Trough Collectors Solar Power Plant with MARS Models. Energies 2018, 11, 37
Energies 2018, 11(7), 1856; https://doi.org/10.3390/en11071856
Received: 2 July 2018 / Accepted: 3 July 2018 / Published: 16 July 2018
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Abstract
Due to the difference in date between the sending and the publication of the article [...] Full article
(This article belongs to the Special Issue Solar and Wind Energy Forecasting)
Open AccessArticle A Framework for the Selection of Optimum Offshore Wind Farm Locations for Deployment
Energies 2018, 11(7), 1855; https://doi.org/10.3390/en11071855
Received: 23 April 2018 / Revised: 25 June 2018 / Accepted: 9 July 2018 / Published: 16 July 2018
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Abstract
This research develops a framework to assist wind energy developers to select the optimum deployment site of a wind farm by considering the Round 3 available zones in the UK. The framework includes optimization techniques, decision-making methods and experts’ input in order to
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This research develops a framework to assist wind energy developers to select the optimum deployment site of a wind farm by considering the Round 3 available zones in the UK. The framework includes optimization techniques, decision-making methods and experts’ input in order to support investment decisions. Further, techno-economic evaluation, life cycle costing (LCC) and physical aspects for each location are considered along with experts’ opinions to provide deeper insight into the decision-making process. A process on the criteria selection is also presented and seven conflicting criteria are being considered for implementation in the technique for the order of preference by similarity to the ideal solution (TOPSIS) method in order to suggest the optimum location that was produced by the nondominated sorting genetic algorithm (NSGAII). For the given inputs, Seagreen Alpha, near the Isle of May, was found to be the most probable solution, followed by Moray Firth Eastern Development Area 1, near Wick, which demonstrates by example the effectiveness of the newly introduced framework that is also transferable and generic. The outcomes are expected to help stakeholders and decision makers to make better informed and cost-effective decisions under uncertainty when investing in offshore wind energy in the UK. Full article
(This article belongs to the Special Issue Optimisation Models and Methods in Energy Systems)
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Open AccessArticle Effects of Asymmetric Gas Distribution on the Instability of a Plane Power-Law Liquid Jet
Energies 2018, 11(7), 1854; https://doi.org/10.3390/en11071854
Received: 17 May 2018 / Revised: 22 June 2018 / Accepted: 27 June 2018 / Published: 16 July 2018
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Abstract
As a kind of non-Newtonian fluid with special rheological features, the study of the breakup of power-law liquid jets has drawn more interest due to its extensive engineering applications. This paper investigated the effect of gas media confinement and asymmetry on the instability
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As a kind of non-Newtonian fluid with special rheological features, the study of the breakup of power-law liquid jets has drawn more interest due to its extensive engineering applications. This paper investigated the effect of gas media confinement and asymmetry on the instability of power-law plane jets by linear instability analysis. The gas asymmetric conditions mainly result from unequal gas media thickness and aerodynamic forces on both sides of a liquid jet. The results show a limited gas space will strengthen the interaction between gas and liquid and destabilize the power-law liquid jet. Power-law fluid is easier to disintegrate into droplets in asymmetric gas medium than that in the symmetric case. The aerodynamic asymmetry destabilizes para-sinuous mode, whereas stabilizes para-varicose mode. For a large Weber number, the aerodynamic asymmetry plays a more significant role on jet instability compared with boundary asymmetry. The para-sinuous mode is always responsible for the jet breakup in the asymmetric gas media. With a larger gas density or higher liquid velocity, the aerodynamic asymmetry could dramatically promote liquid disintegration. Finally, the influence of two asymmetry distributions on the unstable range was analyzed and the critical curves were obtained to distinguish unstable regimes and stable regimes. Full article
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