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Dos Santos Gonçalves PV, Campos LMS. A systemic review for measuring circular economy with multi-criteria methods. ENVIRONMENTAL SCIENCE AND POLLUTION RESEARCH INTERNATIONAL 2022; 29:31597-31611. [PMID: 35001284 DOI: 10.1007/s11356-022-18580-w] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/02/2021] [Accepted: 01/05/2022] [Indexed: 06/14/2023]
Abstract
Determining the circularity of a system through a criteria and indicators approach has been the focus of research in many branches of science. In this way, this work aims to review multiple criteria decision-making (MCDM) methods employed for measuring circular economy (CE) indicators and CE aspects at different levels (micro, meso, and macro). For this purpose, a systematic literature review (SLR) was conducted in ISI Web of Science and Scopus databases. Further, the results summarized 22 MCDM techniques, 27 CE aspects, and 36 CE indicators The SLR provides a concept map highlighting the relation of the level of circularity implementation (subdivided into micro-, meso-, and macro-levels) and MCDM techniques and demonstrates the interaction between CE aspects and indicators. The review provides an outline as to how MCDM techniques can solve problems related to CE aspects and marks the relevance in the use of CE indicators to support circularity aspects and to construct criteria in the methodologies applied.
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Affiliation(s)
- Paulo Vitor Dos Santos Gonçalves
- Graduate Program in Production Engineering (PPGEP), Universidade Federal de Santa Catarina (UFSC), Campus Universitario Trindade, Florianopolis, SC, 88062-451, Brazil
| | - Lucila M S Campos
- Graduate Program in Production Engineering (PPGEP), Universidade Federal de Santa Catarina (UFSC), Campus Universitario Trindade, Florianopolis, SC, 88062-451, Brazil.
- Department of Production Engineering (EPS), Universidade Federal de Santa Catarina (UFSC), Campus Universitario Trindade, Florianopolis, SC, 88062-451, Brazil.
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Unión-Sánchez JDD, Hermoso-Orzáez MJ, Hervás-Pulido MJ, Ogáyar-Fernández B. Impact of Thermal Dissipation on the Lighting Performance and Useful Life of LED Luminaires Applied to Urban Lighting: A Case Study. INTERNATIONAL JOURNAL OF ENVIRONMENTAL RESEARCH AND PUBLIC HEALTH 2022; 19:ijerph19020752. [PMID: 35055573 PMCID: PMC8776062 DOI: 10.3390/ijerph19020752] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/27/2021] [Revised: 01/05/2022] [Accepted: 01/07/2022] [Indexed: 12/22/2022]
Abstract
Currently, LED technology is an established form of lighting in our cities and homes. Its lighting performance, durability, energy efficiency and light, together with the economic savings that its use implies, are displacing other classic forms of lighting. However, some problems associated with the durability of the equipment related to the problems of thermal dissipation and high temperature have begun to be detected, which end up affecting their luminous intensity and the useful life. There are many studies that show a direct relationship between the low quality of LED lighting and the aging of the equipment or its overheating, observing the depreciation of the intensity of the light and the visual chromaticity performance that can affect the health of users by altering circadian rhythms. On the other hand, the shortened useful life of the luminaires due to thermal stress has a direct impact on the LCA (Life Cycle Analysis) and its environmental impact, which indirectly affects human health. The purpose of this article is to compare the results previously obtained, at different contour temperatures, by theoretical thermal simulation of the 3D model of LED street lighting luminaires through the ANSYS Fluent simulation software. Contrasting these results with the practical results obtained with a thermal imaging camera, the study shows how the phenomenon of thermal dissipation plays a fundamental role in the lighting performance of LED technology. The parameter studied in this work is junction temperature (Tj), and how it can be used to predict the luminous properties in the design phase of luminaires in order to increase their useful life.
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Affiliation(s)
- Juan de Dios Unión-Sánchez
- Centre for Advanced Studies in Energy and Environment, University of Jaén, 23071 Jaén, Spain; (J.d.D.U.-S.); (B.O.-F.)
| | - Manuel Jesús Hermoso-Orzáez
- Centre for Advanced Studies in Energy and Environment, University of Jaén, 23071 Jaén, Spain; (J.d.D.U.-S.); (B.O.-F.)
- Department of Graphic Engineering, Design and Projects, University of Jaén, 23071 Jaén, Spain;
- Correspondence: ; Tel.: +34-610-389-020
| | | | - Blas Ogáyar-Fernández
- Centre for Advanced Studies in Energy and Environment, University of Jaén, 23071 Jaén, Spain; (J.d.D.U.-S.); (B.O.-F.)
- Department of Electrical Engineering, University of Jaén, 23071 Jaén, Spain
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Abstract
The issue concerns the initial stage of work on a method for performing a rapid assessment of the energy efficiency and illuminance of a street lighting installation. The proposed method is based on simultaneous measurement of illuminance from three lux meters placed on the roof of the vehicle. The data are acquired in road traffic, while the vehicle is driving. The proposed solution will allow in the future to quickly and reproducibly obtain data about the lighting parameters of the studied road section. The illumination values are localised using Global Navigation Satellite System (GNSS). Based on the collected measurement data, with the use of terrain maps, geographic information system (GIS) data and installation design documentation, it will be possible to determine in detail the parameters of energy efficiency indicators for a selected section of the street for the entire street according to the EN13201-5 standard. Preliminary tests were conducted on a section of about one kilometer of street illuminated in class C3. Detailed measurements reveal high variation of obtained energy indicators DP and DE for each road section. The reason for this condition is the variation of power, installation geometry and the presence of obstacles to light.
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Development of an Indicator System for Local Governments to Plan and Evaluate Sustainable Outdoor Lighting. SUSTAINABILITY 2021. [DOI: 10.3390/su13031506] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/03/2023]
Abstract
Outdoor lighting offers many benefits to its users and is often considered a necessity for an active lifestyle when living in modern society. Sustainable outdoor lighting should fulfil the functional needs of the users, be cost- and energy-efficient, and result in minimal environmental impact. So far, a limited number of studies have been able to present clear strategies on how to plan and use outdoor lighting to ensure that it contributes towards sustainable development. Therefore, this study aimed to answer the following questions: (1) How many of the previously established sustainability indicators are already used by municipalities in their lighting planning? (2) Which types of indicators are not used by municipalities? Another aim of the study was to further develop the framework of sustainability indicators by adding new indicators that were identified from lighting plans of Swedish municipalities and the existing literature. In this study, lighting master plans from 16 randomly chosen Swedish municipalities with varying population sizes were analyzed. The results show that few sustainable indicators are used by the municipalities’ lighting plans, especially in the social dimension. The existing framework of sustainability indicators was developed by adding new indicators. Furthermore, 28 new indicators were identified, eight originated from new studies and the literature, and 20 originated from the municipalities’ lighting master plans. This study shows that there is a need for guidelines and recommendations for working with outdoor lighting from a sustainability perspective, especially in the social dimension of sustainability, where most of the new indicators were identified.
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The Contribution of Peripheral Large Scientific Infrastructures to Sustainable Development from a Global and Territorial Perspective: The Case of IFMIF-DONES. SUSTAINABILITY 2021. [DOI: 10.3390/su13020454] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Large scientific infrastructures are a major focus of progress. They have a big impact on the economic and social development of their surroundings. Departing from these well-known facts, it is not trivial to affirm whether the global contribution to Sustainable Development (SD) is higher when they are built in peripheral and not highly developed provinces instead of capitals and rich areas. Besides the economic impact on depressed areas, other SD-related parameters like the attachment of young and skilled people to their homeland, the avoidance of uncontrolled migrations from rural to dense urban zones, the growth of new focuses of knowledge independent from the lines of research established in the universities of the capitals, the indirect impact of auxiliary infrastructures and others must be analyzed. Concerning the next implementation of the “International Fusion Materials Irradiation Facility—Demo Oriented Neutron Source” (IFMIF-DONES) project in Granada (Spain), one depressed and tourism-dependent zone, an analysis and comparison with similar infrastructures were done and presented.
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Sustainability and Energy Efficiency: BIM 6D. Study of the BIM Methodology Applied to Hospital Buildings. Value of Interior Lighting and Daylight in Energy Simulation. SUSTAINABILITY 2020. [DOI: 10.3390/su12145731] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
One of the least used aspects of BIM (Building Information Modeling) is the ability to obtain the energy model of the building using the BIM methodology known as BIM 6D. This digital information model allows simulating the real energy behavior of the building and the improvement in the building’s lighting systems, both natural and artificial, in particular daylighting. In this way, the BIM 6D simulation allows us to make design and operation decisions for the building, not only for new buildings that must be, in accordance with current legislation, NZEB (Nearly Zero-Energy Building) but also for the rehabilitation of existing buildings. Particularly in buildings for sanitary use, BIM 6D allows an exhaustive analysis of the energy impact of said rehabilitation, guiding it towards an improvement in energy and light efficiency, which in turn provides greater quality and comfort in the use of the sustainable building. This subject of study is especially important in public buildings for hospital use. Buildings where energy efficiency and comfort, oriented towards optimal and efficient lighting, are two fundamental criteria highly appreciated by patients and citizens in general. Once the energy model of the building has been obtained, it is possible to study and identify possible alternatives to improve energy efficiency and improve lighting, as well as to analyze the possibilities of incorporating other more efficient forms of renewable energy, such as the use of daylight. In this work we can see how applying a set of simulated improvement actions in BIM 6D achieves an energy saving of 50% in general and up to 13% only by acting on lighting systems, allowing the decarbonization of buildings with high energy consumption, such as hospitals, and in turn, will lead to an improvement in the energy certification of these buildings; thus achieving a better and higher quality of habitability, using more efficient forms of lighting and transforming buildings into more sustainable spaces.
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Selection of the Best Method for Underpinning Foundations Using the PROMETHEE II Method. SUSTAINABILITY 2020. [DOI: 10.3390/su12135373] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
This article proposes applying the preference-ranking organization method for enrichment of evaluations (PROMETHEE) II in the selection of the optimal solution and ranking of selected methods for underpinning foundations. Analysis of the selected foundation-underpinning methods was based on a complex decision-making problem that included aspects of the three pillars of sustainable development, and it was extended to include technological and constructional criteria. The study used the following criteria for assessing proposed variants: price, bearing capacity, noise and vibrations, necessary equipment, necessary excavations under final structure, failure rates, and necessary foundation shoring. Analysis using the PROMETHEE II method allowed for identifying strengths and weaknesses of selected methods for underpinning foundations. The PROMETHEE II method enabled to create a ranking of foundation-underpinning methods. Jet-grouting and root-pile methods were the highest scorers in this ranking and those that fulfilled the identified criteria to the greatest extent. Moreover, analysis showed that the PROMETHEE II method was useful in solving problems of choice in the construction industry.
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Thermochemical and Economic Analysis for Energy Recovery by the Gasification of WEEE Plastic Waste from the Disassembly of Large-Scale Outdoor Obsolete Luminaires by LEDs in the Alto Alentejo Region (Portugal). APPLIED SCIENCES-BASEL 2020. [DOI: 10.3390/app10134601] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The recovery of urban waste is a social demand and a measure of the energy-environmental sustainability of cities and regions. In particular, waste of electrical origin, waste of electrical and electronic materials (WEEE) can be recovered with great success. The plastic fraction of these wastes allows their gasification mixed with biomass, and the results allow for producing syngas with a higher energy potential. This work allows for obtaining energy from the recovery of obsolete materials through thermochemical conversion processes of the plastic waste from the disassembly of the luminaires by mixing the said plastic waste in different proportions with the biomass of crop residues (olive). The gasification tests of these mixtures were carried out in a downstream fixed-bed drown daft reactor, at temperatures of approximately 800 °C. The results demonstrate the applied technical and economic feasibility of the technology by thermal gasification, for the production of LHV (Low Heating Value) syngas with highest power energy (more than 5 MJ/m3) produced in mixtures of up to 20% of plastic waste. This study was complemented with the economic-financial analysis. This research can be used as a case study for the energy recovery through gasification processes of plastic waste from luminaires (WEEE), mixed with agricultural biomass that is planned to be carried out on a large scale in the Alentejo (Portugal), as a solution applied in circular economy strategies.
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Circular Economy Practices and Strategies in Public Sector Organizations: An Integrative Review. SUSTAINABILITY 2020. [DOI: 10.3390/su12104181] [Citation(s) in RCA: 25] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Abstract
The concept of the Circular Economy (CE) is an increasingly attractive approach to tackling current sustainability challenges and facilitating a shift away from the linear “take-make-use-dispose” model of production and consumption. The public sector is a major contributor to the CE transition not only as a policy-maker but also as a significant purchaser, consumer, and user of goods and services. The circularization of the public sector itself, however, has received very little attention in CE research. In order to explore the current state of knowledge on the implementation of CE practices and strategies within Public Sector Organizations (PSOs), this research aims to develop an overview of the existing literature. The literature review was designed combining a systematic search with a complementary purposive sampling. Using organizational sustainability as a theoretical perspective, the main results showed a scattered landscape, indicating that the limited research on CE practices and strategies in PSOs has focused so far on the areas of public procurement, internal operations and processes, and public service delivery. As a result of this literature review, an organizational CE framework of a PSO is proposed providing a holistic view of a PSO as a system with organizational dimensions that are relevant for the examination and analysis of the integration process of CE practices and strategies. This innovative framework aims to help further CE research and practice to move beyond current sustainability efforts, highlighting that public procurement, strategy and management, internal processes and operations, assessment and communication, public service delivery, human resources dimensions, collaboration with other organizations, and various external contexts are important public sector areas where the implementation of CE has the potential to bring sustainability benefits.
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Revision of Threshold Luminance Levels in Tunnels Aiming to Minimize Energy Consumption at No Cost: Methodology and Case Studies. ENERGIES 2020. [DOI: 10.3390/en13071707] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
Because of the absence of lighting calculation tools at the initial stage of tunnel design, the lighting systems are usually over-dimensioned, leading to over illumination and increased energy consumption. For this reason, a fine-tuning method for switching lighting stages according to the traffic weighted L20 luminance is proposed at no additional cost. The method was applied in a real –case scenario, where L20 luminance of the access zone at eleven (11) existing tunnels was calculated. The traffic weighted method of CR14380 was used in order to calculate the actual luminance levels for the entrance zone. The new transition zone, which decreases luminance curves, was produced and compared with the existing ones. Thus, a new switching control was proposed and programed for the Supervisory Control and Data Acquisition (SCADA) system of the tunnel. The signals of the corresponding eleven L20 meters for a period of eight days were used and the corresponding annual energy consumptions were calculated using the proposed switching program for each tunnel. The results were compared with a number of scenarios in which the existing lighting system was retrofitted with Lighting Emitting Diodes (LED) luminaires. In these scenarios, the new luminaire arrangement was based not only on the existing luminance demand value for the threshold zone, but also on the newly proposed one with two different control techniques (continuous dimming and 10% step dimming). The fine-tuning method for switching resulted in energy savings between 11% and 54% depending on the tunnel when the scenario of the existing installation at no extra cost was used. Energy savings, when LED luminaires were installed, varied between 57% (for the scenario with existing luminance demand value for the threshold zone and 10% step dimming) and 85% (for the scenario with the new calculated luminance demand and continuous dimming).
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The Perspective of Total Lighting as a Key Factor to Increase the Sustainability of Strategic Activities. SUSTAINABILITY 2020. [DOI: 10.3390/su12072751] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
In the last decades, lighting has evolved from a branch of engineering ensuring safety and performance in indoor and outdoor installations, to a key discipline interacting with a wide spectrum of fields and having a deep impact on our daily lives. Although this evolution also applies to other areas of knowledge, the special features of lighting make its potential and also its limitations different. It is not the typical field where a well-established mathematical framework allows a departure from well-defined input and identifying clear effects and conclusions. The reason is that lighting is a field dealing with the interaction between a physical phenomenon and a physiological and psychological system, the human being. In addition to the complexity of its basis, the relationship between lighting and sustainability has become stronger in recent years. This relationship is bi-directional in some cases: on one hand, advanced societies require more and more complex lighting installations, which means high energy consumption, use of raw materials, financial costs, manufacturing and maintenance processes, waste and emissions to the atmosphere. On the other hand, good lighting has an impact on issues like productivity, well-being, happiness, disease avoidance, safety, and many other qualitative aspects whose direct or indirect impact on sustainability is remarkable. This work will analyze how lighting can give answers to questions related to sustainability, not only from the classic topics of energy consumption and waste management, but from a wider and global perspective. The results of these works are analyzed, and the basis of the new framework of total lighting, discussed.
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A Multi-Criteria Assessment Procedure for Outdoor Lighting at the Design Stage. SUSTAINABILITY 2020. [DOI: 10.3390/su12041330] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
This paper presents an attempt at a unified approach for the assessment of outdoor lighting solutions at the design stage. First of all, the lighting criteria for different types of outdoor lighting installations have been carefully described. Despite the differences in criteria, it is possible to find a common ground for the assessment of lighting solutions at the design stage. This is based on the need for the assessment of lighting solutions to be included in the requirements for the luminous environment, light pollution, and energy efficiency. The review and analysis of the standards and reports allows an experimental procedure to be created, the main aim of which is to find the best and most sustainable lighting solution for any outdoor situation. The procedure was tested by the example of an analysis of parking lot lighting solutions. In the case analyzed, 120 solutions were considered. It appeared that, in only 65 cases were the requirements referring to both lighting condition and light pollution met. Finally, based on the lighting energy efficiency assessment, ten solutions were selected as the most suitable. Furthermore, only one solution out of the ten was the most beneficial, taking into account the extra criterion of basic economic cost. The case study confirms that the assessment procedure allows the most beneficial solution to be selected, taking into account the luminous environment, as well as light pollution and energy efficiency criteria. The proposed multi-criteria assessment procedure may be used as a valuable tool by lighting designers to select the most beneficial solution in order to meet the needs of safety, visual efficiency, and comfort, as well as taking into account light pollution and energy efficiency restrictions.
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Co-Combustion of Waste Tires and Plastic-Rubber Wastes with Biomass Technical and Environmental Analysis. SUSTAINABILITY 2020. [DOI: 10.3390/su12031036] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The present work studies the possibility of energy recovery by thermal conversion of combustible residual materials, namely tires and rubber-plastic, plastic waste from outdoor luminaires. The waste has great potential for energy recovery (HHV: 38.6 MJ/kg for tires and 31.6 MJ/kg for plastic). Considering the thermal conversion difficulties of these residues, four co-combustion tests with mixtures of tires/plastics + pelletized Miscanthus, and an additional test with 100% Miscanthus were performed. The temperature was increased to the maximum allowed by the equipment, about 500 °C. The water temperature at the boiler outlet and the water flow were controlled (60 °C and 11 L/min). Different mixtures of residues (0–60% tires/plastics) were tested and compared in terms of power and gaseous emissions. Results indicate that energy production increased with the increase of tire residue in the mixture, reaching a maximum of 157 kW for 40% of miscanthus and 60% of tires. However, the automatic feeding difficulties of the boiler also increased, requiring constant operator intervention. As for plastic and rubber waste, fuel consumption generally decreased with increasing percentages of these materials in the blend, with temperatures ranging from 383 °C to 411 °C. Power also decreased by including such wastes (66–100 kW) due to feeding difficulties and cinder-fusing problems related to ash melting. From the study, it can be concluded that co-combustion is a suitable technology for the recovery of waste tires, but operational problems arise with high levels of residues in the mixture. Increasing pollutant emissions and the need for pre-treatments are other limiting factors. In this sense, the thermal gasification process was tested with the same residues and the same percentages of mixtures used in the co-combustion tests. The gasification tests were performed in a downdraft reactor at temperatures above 800 °C. Each test started with 100% acacia chip for reference (like the previous miscanthus), and then with mixtures of 0–60% of tires and blends of plastics and rubbers. Results obtained for the two residues demonstrated the viability of the technology, however, with mixtures higher than 40% it was very difficult to develop a process under stable conditions. The optimum condition for producing a synthesis gas with a substantial heating value occurred with mixtures of 20% of polymeric wastes, which resulted in gases with a calorific value of 3.64 MJ/Nm3 for tires and 3.09 MJ/Nm3 for plastics and rubbers.
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LCA Case Study to LED Outdoor Luminaries as a Circular Economy Solution to Local Scale. SUSTAINABILITY 2019. [DOI: 10.3390/su12010190] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The replacement of luminaires with discharge lamps with high luminous efficacy and long life-time LED based equipment is a reality worldwide promoted by policies that favor their gradual substitution. There is a great concern in this manufacturing industry to develop new luminaires with low environmental impact during the manufacturing and transportation processes and its end-of-life disposal (reducing greenhouse gas emissions, toxic or hazardous components, …). Life cycle assessment (LCA) is a very extended tool used to provide information on the quality and quantity of environmental impacts in the life cycle phases of any product, system, or service. This article includes all phases of the LCA analysis of a selected streetlight LED luminaire manufactured by a SME where a landfill deposit is the end-of-life scenario. In a second phase, alternatives are sought for the reuse of the most significant elements that improve its local economy. The results are classified and sorted according to the ISO 14040 standard.
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Closed Loop Control of a Series Class-E Voltage-Clamped Resonant Converter for LED Supply with Dimming Capability. ELECTRONICS 2019. [DOI: 10.3390/electronics8121380] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
In this work, a new closed-loop control system is applied to a class-E resonant DC–DC converter with voltage clamp used for light-emitting diode (LED) supply. The proposed power topology was first described by Ribas et al. in a recent work. In the present paper, the LED current is sensed and used to implement a feedback control loop instead of the simplified feedforward scheme used in this previous reference. To design the control, a novel, simplified small-signal model is presented. This model is used to analyze the converter behavior as a function of the output power. The proposed approximation is significantly simpler than the multifrequency averaging technique normally used to analyze resonant converters. The feedback control loop is designed to reduce the LED low frequency current ripple while providing dimming control. Both the model and the control are verified by simulation and laboratory experimentation and the results obtained are in good accordance with the expected values.
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