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The inscrutable baseline and the problem of attribution 难以捉摸的基线和归因问题
IF 3.2 4区 工程技术 Q3 ENERGY & FUELS Pub Date : 2024-03-20 DOI: 10.1007/s12053-024-10207-y
Stephen P. Waite

This paper examines the problem of attribution in the evaluation of energy efficiency program impact. The methodological problem concerns the observability of consumer behavior under the baseline condition of no program intervention. The statistical solution to the problem, which entails randomized exposure of targeted individuals to program influence, is not a viable alternative in most applications. Randomized opt-in and randomized encouragement designs do not conform to this requirement because all targeted individuals are encouraged to participate in the program, resulting in negative exposure bias. Quasi-experimental methods which utilize non-targeted individuals or targeted nonparticipants as baseline surrogates are further subject to selection bias of unknown magnitude and direction. Valid attribution in the general case of unrestricted eligibility depends on prior knowledge of the determinants of measure adoption and program participation. In default of such knowledge, evaluators must rely upon structural assumptions that have no foundation in empirical science. On the other hand, established measurement and verification methods which exploit scientific knowledge of the determinants of end-use energy consumption should be utilized to obtain unbiased estimates of individual measure and gross program energy savings.

本文探讨了能效项目影响评估中的归因问题。方法论问题涉及在无项目干预的基线条件下消费者行为的可观察性。该问题的统计解决方案需要将目标个体随机暴露于项目影响之下,但这在大多数应用中并不可行。随机选择加入和随机鼓励设计不符合这一要求,因为所有目标个体都被鼓励参与计划,从而导致负面暴露偏差。利用非目标个人或目标非参与者作为基线替代物的准实验方法会进一步受到选择偏差的影响,其程度和方向未知。在无限制资格的一般情况下,有效的归因取决于事先对采用措施和参与计划的决定因素的了解。如果不具备这些知识,评估人员就必须依赖于在实证科学中毫无根据的结构性假设。另一方面,应利用成熟的测量和验证方法,利用对终端能源消耗决定因素的科学知识,对单个措施和项目总节能效果进行无偏见的评估。
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引用次数: 0
The potential of decentral heat pumps as flexibility option for decarbonised energy systems 分散式热泵作为脱碳能源系统灵活性选择的潜力
IF 3.2 4区 工程技术 Q3 ENERGY & FUELS Pub Date : 2024-03-20 DOI: 10.1007/s12053-024-10206-z
Franziska Schöniger, Philipp Mascherbauer, Gustav Resch, Lukas Kranzl, Reinhard Haas

Decarbonising the energy system requires high shares of variable renewable generation and sector coupling like power to heat. In addition to heat supply, heat pumps can be used in future energy systems to provide flexibility to the electricity system by using the thermal storage potential of the building stock and buffer tanks to shift electricity demand to hours of high renewable electricity production. Bridging the gap between two methodological approaches, we coupled a detailed building technology operation model and the open-source energy system model Balmorel to evaluate the flexibility potential that decentral heat pumps can provide to the electricity system. Austria in the year 2030 serves as an example of a 100% renewable-based electricity system (at an annual national balance). Results show that system benefits from heat pump flexibility are relatively limited in extent and concentrated on short-term flexibility. Flexible heat pumps reduce system cost, CO2 emissions, and photovoltaics and wind curtailment in all scenarios. The amount of electricity shifted in the assessed standard flexibility scenario is 194 GWhel and accounts for about 20% of the available flexible heat pump electricity demand. A comparison of different modelling approaches and a deterministic sensitivity analysis of key input parameters complement the modelling. The most important input parameters impacting heat pump flexibility are the flexible capacity (determined by installed capacity and share of control), shifting time limitations, and cost assumptions for the flexibility provided. Heat pump flexibility contributes more to increasing low residual loads (up to 22% in the assessed scenarios) than decreasing residual load peaks. Wind power integration benefits more from heat pump flexibility than photovoltaics because of the temporal correlation between heat demand and wind generation.

能源系统的去碳化需要高比例的可变可再生能源发电和部门耦合,如电力与热力的耦合。除供热外,热泵还可用于未来的能源系统,通过利用建筑存量和缓冲罐的蓄热潜力,将电力需求转移到可再生能源发电量高的时段,从而为电力系统提供灵活性。为了缩小两种方法之间的差距,我们将详细的建筑技术运行模型与开源能源系统模型 Balmorel 结合起来,以评估分散式热泵为电力系统提供灵活性的潜力。以奥地利 2030 年的电力系统为例,该电力系统 100% 采用可再生能源(年度全国平衡)。结果表明,热泵灵活性带来的系统效益相对有限,且集中在短期灵活性上。在所有方案中,灵活的热泵都能降低系统成本、二氧化碳排放量以及光伏和风能削减量。在评估的标准灵活性方案中,转移的电量为 194 GWhel,约占可用灵活性热泵电力需求的 20%。不同建模方法的比较和关键输入参数的确定性敏感性分析对建模起到了补充作用。影响热泵灵活性的最重要输入参数是灵活性容量(由装机容量和控制份额决定)、转移时间限制以及所提供灵活性的成本假设。热泵灵活性对增加低剩余负荷(在评估方案中高达 22%)的贡献大于减少剩余负荷峰值的贡献。由于热需求与风力发电之间的时间相关性,风力发电整合比光伏发电更能从热泵灵活性中获益。
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引用次数: 0
Determination of household electricity expenditures using quantile regression with Kennedy approach 利用肯尼迪方法的量子回归确定家庭电费支出
IF 3.2 4区 工程技术 Q3 ENERGY & FUELS Pub Date : 2024-03-19 DOI: 10.1007/s12053-024-10204-1
Kübranur Çebi Karaaslan, Esma Kesriklioğlu, Erkan Oktay

The electrical energy expenditure of households in Turkey has been increasing over the years, and households account for one-fifth of the overall electrical energy consumption. For this reason, it is of vital importance to determine the factors that affect household electricity expenditure, reveal consumption patterns for different consumer groups, and propose suggestions for the efficient use of electrical energy. In the present study, determinants of household electricity expenditure were analyzed with the quantile regression approach using the Household Budget Survey published by the Turkish Statistical Institute. In conclusion, it was determined that demographic, economic, and residential factors had significant effects on the electricity expenditures of households. The present study will serve as a guide for policymakers and decision-makers in developing strategies and conducting studies toward reducing the electricity expenditures of households, which is an important factor for energy usage.

多年来,土耳其家庭的电能支出一直在增加,家庭占总电能消耗的五分之一。因此,确定影响家庭电能支出的因素、揭示不同消费群体的消费模式以及提出有效利用电能的建议至关重要。在本研究中,利用土耳其统计研究所发布的家庭预算调查,采用量子回归法对家庭电费支出的决定因素进行了分析。最后确定,人口、经济和居住因素对家庭电费支出有显著影响。本研究将为政策制定者和决策者制定战略和开展研究提供指导,以减少作为能源使用重要因素的家庭电费支出。
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引用次数: 0
Drivers of clean fuel adoption and consumption intensity at the household level in Pakistan 巴基斯坦家庭采用清洁燃料和消费强度的驱动因素
IF 3.2 4区 工程技术 Q3 ENERGY & FUELS Pub Date : 2024-03-15 DOI: 10.1007/s12053-024-10208-x
Ashar Awan, Dil Bahadur Rahut, Maqsood Sadiq, Daniel Balsalobre Lorente

The use of solid fuel (dirty fuel) that includes firewood, coal, charcoal, crop residue, kerosene, and dung cake is hazardous to human health and the environment. Therefore, it is crucial to understand the factors influencing the household-level transition to clean fuel. Against this backdrop, the present study analyzes the clean fuel choice and consumption intensity using the latest HIES 2018–2019 data. Findings revealed that 76 and 14% of households in Pakistan use dirty cooking fuel in rural and urban areas, respectively. In addition, choices of fuel for cooking, heating, and lighting fuel vary across provinces. Probit and Tobit model shows that income, wealth, urban location, small family size, and fewer women and children influence households’ transition towards clean fuel. The study underscores the importance of tailored policies, including tariff structures, pricing mechanisms, and financial incentives, to accelerate the adoption of energy-efficient and clean technologies. These recommendations aim to drive sustainable energy access, economic growth, and environmental sustainability in Pakistan.

使用木柴、煤炭、木炭、农作物秸秆、煤油和粪饼等固体燃料(脏燃料)对人类健康和环境有害。因此,了解影响家庭向清洁燃料过渡的因素至关重要。在此背景下,本研究利用最新的 2018-2019 年家庭收入和支出调查数据分析了清洁燃料的选择和消费强度。研究结果显示,巴基斯坦农村和城市地区分别有 76% 和 14% 的家庭使用不洁烹饪燃料。此外,各省对烹饪、取暖和照明燃料的选择也不尽相同。Probit 和 Tobit 模型显示,收入、财富、城市位置、小家庭规模以及妇女和儿童较少等因素影响着家庭向清洁燃料的过渡。这项研究强调了量身定制的政策(包括关税结构、定价机制和财政激励措施)对于加快采用节能和清洁技术的重要性。这些建议旨在推动巴基斯坦的可持续能源获取、经济增长和环境可持续性。
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引用次数: 0
Air emission and health impacts of a US industrial energy efficiency program 美国工业能效计划对空气排放和健康的影响
IF 3.2 4区 工程技术 Q3 ENERGY & FUELS Pub Date : 2024-03-13 DOI: 10.1007/s12053-024-10210-3
Elaheh Safaei Kouchaksaraei, Kerry Elizabeth Kelly

Energy efficiency opportunities in the industrial sector can reduce air emissions and benefit human health. One national-level energy efficiency program, the Department of Energy (DOE)-funded Industrial Assessment Center (IAC), provides US manufacturing facilities with cost-effective energy efficiency recommendations. However, the effect of the IAC on air quality and human health has not been explored. While several studies have evaluated the health impacts of air emissions reduction associated with energy efficiency, most of them did not consider regional differences in electricity grid profiles. These differences can change both emissions and health outcomes. This study focuses on air quality and health impacts of electricity and natural gas-related recommendations from the IAC program in 2022. It estimates 248 GWh of electricity, and 1.1E6 MMBtu of natural gas savings will result from the recommendations. Using the Environmental Protection Agency (EPA)’s Avoided Emissions and GeneRation Tool (AVERT) to estimate regional electricity emissions, published natural gas emission rates, and EPA’s co-benefit risk assessment (COBRA) tool, the total annual health outcomes associated with these savings range from 4.85 to 16.9 million USD (2023). This range includes different NOx emission rates and high and low COBRA estimates. Additionally, we introduce an energy savings health estimator (ESHE) tool that calculates air emissions and associated health outcomes of energy savings measures. We also apply it to the 2022 IAC recommendations and compare the health outcomes to those calculated using AVERT and COBRA separately. This tool can quickly estimate the health impacts of various energy efficiency projects or programs.

摘要 工业领域的节能机会可以减少空气排放,有益于人类健康。能源部(DOE)资助的工业评估中心(IAC)是一项国家级能效计划,它为美国的制造设施提供具有成本效益的能效建议。然而,IAC 对空气质量和人类健康的影响尚未得到探讨。虽然有几项研究评估了与能源效率相关的空气减排对健康的影响,但其中大多数都没有考虑电网分布的地区差异。这些差异会改变排放和健康结果。本研究重点关注 2022 年 IAC 计划中与电力和天然气相关的建议对空气质量和健康的影响。据估计,这些建议将节省 248 千兆瓦时的电力和 1.1E6 百万英热单位的天然气。利用环境保护局 (EPA) 的避免排放和基因重组工具 (AVERT) 估算区域电力排放量、已公布的天然气排放率以及 EPA 的共同效益风险评估 (COBRA) 工具,与这些节约相关的年度健康成果总额介于 485 万美元至 1690 万美元之间(2023 年)。这一范围包括不同的氮氧化物排放率以及高和低 COBRA 估计值。此外,我们还引入了节能健康估算工具(ESHE),用于计算空气排放和节能措施的相关健康结果。我们还将其应用于 2022 年 IAC 建议,并将健康结果与分别使用 AVERT 和 COBRA 计算得出的结果进行比较。该工具可快速估算各种能效项目或计划对健康的影响。
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引用次数: 0
A numerical investigation of the influence of ozone on combustion to improve the performance of spark ignition engines 臭氧对燃烧影响的数值研究,以提高火花点火发动机的性能
IF 3.2 4区 工程技术 Q3 ENERGY & FUELS Pub Date : 2024-03-13 DOI: 10.1007/s12053-024-10209-w
Marco D’Amato, Antonio Cantiani, Angelo Basso, Vinicio Magi, Annarita Viggiano

The aim of this work is to exploit the influence of using ozonized air to achieve stable and efficient combustion of lean mixtures in a gasoline-fuelled Spark-Ignition (SI) engine. The influence of ozone on the combustion of near-stoichiometric mixtures, which are typical of SI engines, has also been assessed. A Computational Fluid Dynamics (CFD) model has been employed to simulate compression, combustion, and expansion of a spark ignition, axisymmetric engine fuelled with iso-octane/air/ozone mixtures. The aim is to assess how ozone improves the engine performance under different engine speeds, ignition timings and equivalence ratios. The model has been validated against experimental data available in the literature. Parametric analyses have been carried out by considering three values of engine speeds (800, 1000 and 1200 rpm), three different ozone concentrations at Intake Valve Closure (IVC) (0, 100 and 200 ppm) and two equivalence ratios (0.9 and 0.7). The results show that ozone enables reactions in the Low Temperature Combustion (LTC) regime, modifies the mixture chemical composition and the auto-ignition tendency. Specifically, for all the cases under examination, the addition of ozone to the air/fuel mixture reduces the combustion duration, leading to an increase in terms of work output and a reduction of the specific fuel consumption. Moreover, the advantage of using ozone is greater for lean mixtures than for near-stoichiometric mixtures. Finally, for the near-stoichiometric cases, when the residence time of the mixture is high enough, auto-ignition occurs in the end gases.

这项工作的目的是利用臭氧空气的影响,在以汽油为燃料的火花点火(SI)发动机中实现贫油混合物的稳定高效燃烧。此外,还评估了臭氧对接近公称混合气(SI 发动机的典型特征)燃烧的影响。采用计算流体动力学(CFD)模型模拟了以异辛烷/空气/臭氧混合物为燃料的轴对称火花点火发动机的压缩、燃烧和膨胀过程。目的是评估在不同的发动机转速、点火时间和当量比条件下,臭氧如何改善发动机的性能。该模型已根据文献中的实验数据进行了验证。通过考虑三种发动机转速值(800、1000 和 1200 rpm)、进气阀关闭时的三种不同臭氧浓度(0、100 和 200 ppm)以及两种当量比(0.9 和 0.7),进行了参数分析。结果表明,臭氧可以促进低温燃烧(LTC)机制中的反应,改变混合物的化学成分和自燃趋势。具体来说,在研究的所有情况下,向空气/燃料混合物中添加臭氧都会缩短燃烧时间,从而增加功输出并降低特定燃料消耗。此外,在贫油混合物中使用臭氧的优势要大于在接近公称混合气中使用臭氧的优势。最后,在接近化学计量的情况下,当混合气的停留时间足够长时,尾气中会出现自燃现象。
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引用次数: 0
Subjective indicators of fuel poverty in Zarqa Governorate, Jordan 约旦扎尔卡省燃料贫困的主观指标
IF 3.2 4区 工程技术 Q3 ENERGY & FUELS Pub Date : 2024-03-08 DOI: 10.1007/s12053-024-10197-x
Mohammad M. Jaber, Tekla Szép

Fuel poverty is a pressing global issue for households, particularly low-income ones. This study employs a subjective approach to examine fuel poverty in Jordan. Analyzing data from a survey of 490 participants in Zarqa Governorate, it evaluates the main determinants of subjective fuel poverty. The survey was conducted over 1 month, from March 10 to April 10, 2022. Findings reveal that the sample households experience challenges related to fuel poverty. The modeling of subjective indicators indicates an association between income level and the probability of being in arrears with utility bills. Moreover, the results highlight issues such as an inability to maintain adequate summer and winter temperatures and the presence of leaks, damp, and rot. In light of these findings, policy interventions should focus on enhancing energy efficiency and supporting vulnerable low-income households, particularly those in rural areas.

摘要 燃料贫困是全球家庭,尤其是低收入家庭面临的一个紧迫问题。本研究采用主观方法研究约旦的燃料贫困问题。研究分析了来自扎尔卡省 490 名参与者的调查数据,评估了主观燃料贫困的主要决定因素。调查时间为 2022 年 3 月 10 日至 4 月 10 日,历时一个月。调查结果显示,样本家庭经历了与燃料贫困相关的挑战。主观指标建模表明,收入水平与拖欠水电费的概率之间存在关联。此外,研究结果还凸显了一些问题,如无法保持足够的夏季和冬季温度,以及存在漏水、潮湿和腐烂等问题。鉴于这些研究结果,政策干预措施应侧重于提高能源效率和支持弱势低收入家庭,特别是农村地区的弱势低收入家庭。
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引用次数: 0
Understanding transaction costs of energy efficiency renovations in the Swedish residential sector 了解瑞典住宅领域节能改造的交易成本
IF 3.2 4区 工程技术 Q3 ENERGY & FUELS Pub Date : 2024-03-05 DOI: 10.1007/s12053-024-10198-w
Robert Lundmark

The residential sector has a large potential to reduce its energy use. Improving the energy performance of buildings is one way to realise this potential. For single-family buildings, improving the energy efficiency by energy renovations can produce a net financial gain. However, there are unaccounted barriers that act as impediments for house-owners to undertake energy efficiency measures. This study postulates that transaction costs are such a barrier. Transaction costs are defined as the cost of making an economic exchange on a market in addition to the market price. The purpose is to empirically estimate the magnitude of the transactions costs and its determinants for energy efficiency measures in the residential sector. Specifically, the transaction costs for heat insulation and energy-saving windows in Swedish single-family buildings are assessed. The analysis is based on a unique dataset, constructed from a web-based survey. The results indicate that transaction costs for energy efficiency measures are considerable. The average transaction cost to make additional heat insulation is SEK 18,046 (EUR 1,510) and SEK 21,106 (EUR 1,766) to install energy-saving windows. The determinants of the transaction costs are cognitive limitations, social connectedness, asset specificity and previous experiences. Therefore, to reduce the transaction costs, the complexity of energy efficiency measures must be addressed, potential opportunistic behaviour must be reduced, and financial options expanded.

住宅部门在减少能源消耗方面潜力巨大。提高建筑能效是实现这一潜力的途径之一。对于单户建筑而言,通过能源改造提高能源效率可以产生净经济收益。然而,有一些无法估量的障碍阻碍了房屋所有者采取节能措施。本研究假设交易成本就是这样一种障碍。交易成本是指在市场上进行经济交换时除市场价格以外的成本。本研究的目的是根据经验估算住宅领域节能措施的交易成本及其决定因素。具体来说,对瑞典单户建筑隔热和节能窗的交易成本进行了评估。该分析基于一个基于网络调查的独特数据集。结果表明,节能措施的交易成本相当高。额外隔热的平均交易成本为 18,046 瑞典克朗(1,510 欧元),安装节能窗的平均交易成本为 21,106 瑞典克朗(1,766 欧元)。交易成本的决定因素包括认知限制、社会联系、资产特殊性和以往经验。因此,要降低交易成本,必须解决能效措施的复杂性问题,减少潜在的机会主义行为,并扩大金融选项。
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引用次数: 0
Forecasting long-term energy demand and reductions in GHG emissions 预测长期能源需求和减少温室气体排放
IF 3.2 4区 工程技术 Q3 ENERGY & FUELS Pub Date : 2024-03-05 DOI: 10.1007/s12053-024-10203-2
Parvin Golfam, Parisa-Sadat Ashofteh, Hugo A. Loáiciga

This work projects the long-term energy demand and assesses the effects of using renewable-energy technologies on greenhouse gas (GHG) emissions in the Marun Basin, Iran. Energy projections are made with the Low Emissions Analysis Platform (LEAP) model. Demographic and macro-economic data, per capita energy use in the urban and agricultural sectors in the Marun Basin, were gathered and input to the LEAP model to simulate the energy system in the period 2016–2040. This work’s results show that under the Business As Usual (BAU) scenario the electricity demand trend in the domestic sector would increase from 1783 MWh in 2016 to 2341 MWh by 2040. The fossil fuels consumed by the urban sector would increase from 738 million barrel of oil equivalents (BOE) in 2016 to 968 million BOE in 2040. The CO2 emissions under the BAU scenario would increase from 27.33 million tons in 2016 to 35.87 million tons in 2040. A scenario was created to provide electricity service by means of residential solar panels (RSPs) to rural areas currently not connected to the national power grid. The LEAP model’s results show CO2 emissions would be reduced by 17%, and 20% of the domestic diesel use would be replaced by electricity generated with solar panels.

摘要 本研究预测了伊朗马伦盆地的长期能源需求,并评估了使用可再生能源技术对温室气体(GHG)排放的影响。能源预测采用低排放分析平台(LEAP)模型。我们收集了马伦盆地的人口和宏观经济数据、城市和农业部门的人均能源使用量,并将其输入 LEAP 模型,以模拟 2016-2040 年期间的能源系统。这项工作的结果表明,在 "一切照旧"(BAU)情景下,国内部门的电力需求趋势将从 2016 年的 1783 兆瓦时增至 2040 年的 2341 兆瓦时。城市部门消耗的化石燃料将从 2016 年的 7.38 亿桶石油当量增加到 2040 年的 9.68 亿桶石油当量。在 BAU 情景下,二氧化碳排放量将从 2016 年的 2733 万吨增加到 2040 年的 3587 万吨。通过住宅太阳能电池板(RSPs)为目前尚未与国家电网连接的农村地区提供电力服务的情景被创建出来。LEAP 模型的结果显示,二氧化碳排放量将减少 17%,20% 的家用柴油将被太阳能电池板产生的电力取代。
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引用次数: 0
Dynamical assessment of multi-dimensional energy poverty at the national and sub-national levels in Pakistan 巴基斯坦国家和国家以下各级多维能源贫困的动态评估
IF 3.2 4区 工程技术 Q3 ENERGY & FUELS Pub Date : 2024-03-02 DOI: 10.1007/s12053-024-10190-4
Zilong Wang, Asad Amin, Abbas Ali Chandio, Aadil Hameed Shah, Muhammad Imdad Ullah

The primary objective of the current study is to examine the social issue of energy poverty from a multi-dimensional perspective in Pakistan’s national, sub-national, and urban-rural regions. The universally attributed Alkire and Foster indexing approach and globally organized PSLM (Pakistan Social and Living Standard Measurement) data from 2010–2011 to 2019–2020 were used to calculate numerical results. The study’s empirical findings emphasize that multiple-attribute energy poverty is primarily a rural phenomenon in Pakistan and its provinces. Furthermore, the time-variant situation reveals that with a shorter (longer) period, energy poverty exhibits a hybrid (declining) trend for Pakistan as a whole, its four provinces, and its regions. Finally, decomposability analyses of population subgroups and key dimensions show that households in two provinces (Sindh and KPK) and three attributes (cooking, home appliances, and entertainment) are the primary contributors to multi-dimensional energy poverty. Hence, to achieve the UN’s Millennium Development Goals, i.e., SDG7, by 2030, several measures must be implemented rapidly, particularly in rural areas and the provinces, especially Sindh and KPK, such as providing easy access to modern energy services, reducing load shedding and energy shortfalls through advanced technology adoption, and improving households’ living standards by reducing financial poverty. All of these solutions will assist in rapidly reducing energy poverty at all levels, paving the way for achieving the zero energy poverty goal (SDG7) by 2030.

本研究的主要目的是从多维角度研究巴基斯坦国家、次国家和城乡地区的能源贫困社会问题。研究采用了普遍认可的阿尔基勒和福斯特指数化方法以及全球组织的 2010--2011 年至 2019-2020 年巴基斯坦社会和生活水平测量(PSLM)数据来计算数值结果。研究的实证结果强调,多属性能源贫困主要是巴基斯坦及其各省的农村现象。此外,随时间变化的情况表明,随着时间的缩短(延长),整个巴基斯坦、其四个省份和地区的能源贫困呈现混合(下降)趋势。最后,对人口分组和关键维度的可分解性分析表明,两个省份(信德省和肯塔基米尔省)的家庭和三个属性(烹饪、家用电器和娱乐)是造成多维度能源贫困的主要因素。因此,为了在 2030 年前实现联合国千年发展目标,即可持续发展目标 7,必须迅速实施多项措施,特别是在农村地区和各省,尤其是信德省和开伯尔-开伯尔邦,例如提供便捷的现代能源服务,通过采用先进技术减少负荷中断和能源短缺,以及通过减少金融贫困提高家庭生活水平。所有这些解决方案都将有助于在各个层面迅速减少能源贫困,为到 2030 年实现零能源贫困目标(可持续发展目标 7)铺平道路。
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引用次数: 0
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