Total Final Energy Use Research Articles

Representative typology of buildings: case study of hellenic non residential buildings

ABSTRACT Buildings have a significant energy and environmental footprint. In Greece, there are about 4.1 million buildings, a quarter of which are exclusive-use nonresidential buildings. The aim of this work is to define the average construction and technical characteristics of the existing Hellenic nonresidential buildings, and to assess their energy performance, responding to the need for more information and insight on this sector. The work exploits data from about 2400 building energy audits that include general information as well as specific characteristics on the envelope construction and the electromechanical installations. The information were first screened by a data quality control and were then organized into 239 classes that correspond to the Hellenic nonresidential building typology, defined in terms of building use, vintage, and location. The analysis revealed that there is a great potential for upgrading the existing building stock, since only 4% of the audited buildings meet the current minimum thermal envelope code requirements and 15% are in compliance with code recommendations for the technical installations. Overall, only 1% of the buildings have fully compliant envelope and technical installations. The calculated total final energy use averages 217.5kWh/m2 for the entire NR sector, ranging between 89.0kWh/m2 and 530.0kWh/m2 among the different building uses.

Decarbonization of industry: Guidelines towards a harmonized energy efficiency policy program impact evaluation methodology

The decarbonization of EU energy system is under way, but manufacturing industry is still using approximately 25% of the EU total final energy use. To maintain long-term competitiveness while contributing to the EU goal of carbon neutrality by 2050, manufacturing industry needs to improve energy efficiency in a cost-effective way. One important way to achieve this is through energy audits. The Energy Efficiency Directive promotes member states’ development of energy efficiency programs to encourage industry to undergo energy audits. Previous studies have reviewed industrial energy efficiency policy program evaluations and argued that there is no harmonized way to conduct them. This leads to difficulties in: i) comparing energy efficiency and cost saving potentials throughout different programs, and ii) providing necessary information that supports the improvement of the policy program. Therefore, we argue that a harmonized methodology for industrial energy efficiency policy program evaluation is of great importance, and, we have developed a set of five-steps guidelines that lay the foundation for an ex-ante energy efficiency policy program evaluation methodology. The guidelines are to be be conducted during the lifetime of the program, in five steps, as follows: (s1) define key issues, (s2) set the objectives for each key issue, (s3) identify the options for each key issue, (s4) analyze options from an energy and environmental perspective, and (s5) compare options and select the recommended one. Our proposed methodology will support policymakers and evaluators answer questions such as: i) how can the objectives of the policy program be achieved? ii) is there any need to change the policy program? Furthermore, a comparison in terms of relevance, efficiency, effectiveness, and sustainability of all major policy options developed, including the status quo option is proposed in the methodology. This paper can be seen an important step towards the goal of creating a harmonized policy evaluation methodology.

Decarbonisation Pathways of Industry in TIMES Model

Abstract The industry sector in many countries has a significant role in reaching national long-term emission reductions, energy efficiency and renewable energy targets. New technologies, wide implementation of energy efficiency measures and smart energy management are needed for the industry to ensure local and global competitiveness and reduce emissions. Since the industrial sector is often comprised of sub-sectors that are unique and with local specifics, this paper focuses on three of them, taking Latvia as the case. The sectors are: manufacture of wood and wood products, non-metallic mineral products, as well as food products and tobacco. These sub-sectors together consume around 80 % of the total final energy use in the country’s industrial sector. Comprehensive analysis and decomposition of the sub-sectors was made to identify future development pathways. TIMES model was used to elaborate a process-oriented modelling approach to analyze the impact of measures defined in the National Energy and Climate Plan until 2030 as well to gauge the impact of additional measures. Results show that these measures promote the use of renewable energy and improve energy efficiency, however it is necessary to set new measures and activities for the period beyond to reach climate neutrality by 2050.

A cross-sectoral integrated assessment of alternatives for climate mitigation in Madagascar

ABSTRACT Using the integrated assessment model TIAM-ECN, we analyze how Madagascar's nationally determined contribution (NDC) to the Paris Agreement can be implemented in both the energy and non-energy sectors. We explore how the country's national climate goal for 2030 can be reached under two different cost levels for climate change mitigation through land-use change. We find that land use is the main sector in which large greenhouse gas (GHG) emission reductions must be achieved, but there are opportunities to also exploit the country's abundant domestic low-carbon energy resources. We explore the options for such a transformation of Madagascar's energy system, which today largely relies on the use of biomass. If GHG emissions reduction in land use is hard or too costly to implement, e.g. as a result of land property rights or forest logging practices, total final energy use needs to be almost entirely renewable by 2050. The power sector needs to rely on 100% renewables already by 2030. In our scenario runs, biomass, hydropower, solar and wind energy account for the vast majority of electricity generation in Madagascar from 2030 onwards. Electrification is introduced in the residential sector – notably for cooking. Cumulative additional undiscounted investment requirements may be as high as US$ 8 billion up to 2050. Key policy insights Madagascar could reach its 14% GHG emission reduction target relative to 2030 business-as-usual levels through the land use sector only. However, given the potential higher mitigation costs in land use and its links with the energy system, overlooking mitigation options in the energy sector could be a missed opportunity to exploit abundant domestic low-carbon energy resources. Biomass may well remain the most important energy resource in Madagascar until 2050, mainly driven by residential cooking demand. Solid biomass stoves with efficient combustion should be promoted hand-in-hand with alternative fuels, e.g. electricity and bioethanol. Promoting GHG mitigation in both AFOLU and energy sectors maximizes co-benefits, which enables achieving a higher number of sustainable development goals (SDGs). Providing electricity for household services is an important part of climate change mitigation. Investments in power distribution infrastructure and decentralized electricity generation are needed to achieve electrification of rural households.

Experimental investigation of a wind to thermal energy hydraulic system

Abstract In EU households, heating and hot water alone account for 79% of total final energy use (192.5 Mtoe) [ 1 ]. The development of smart technologies to cover the heating requirements of the building sector constitutes a major challenge of the EU scientific community. Wind to thermal energy technologies, although they have been investigated thoroughly since the 50’s, did not gain much interest in the recent years. This study aims to analyse a novel wind to thermal energy conversion system, which could potentially be used in the EU building sector, in regions with high wind potential and increased requirements for space heating. The rationale of the proposed solution is based on a hydraulic system and the heat produced mainly due to friction losses of this system. The main idea behind the system is that the energy required to drive the hydraulic pump will be directly provided by a wind turbine. For the investigation of the proposed system, a scale-down test facility, which simulates the performance of the proposed system, was developed and operated at the Kaunas University of Technology. The wind turbine was simulated with the use of an electric motor with variable rotational frequency. Flow control valves were used both as the main energy converter of mechanical energy of the hydraulic fluid to heat as well as to regulate the load of the hydraulic pump. The optimal working conditions of the experimental set-up were defined in terms of the maximum thermal power delivered. The results of the research were summarized by empirical equations, which can be used for further development of the proposed hydraulic system. The study concluded that under optimal conditions, the system may reach an overall efficiency of 58.8%, which is comparable to efficiencies delivered by solar thermal systems for space heating in regions with increased solar potential (EU Mediterranean countries).

Energy savings and overheating risk of deep energy renovation of a multi-storey residential building in a cold climate under climate change

Here, we analyse final and primary energy savings and overheating risk of deep energy renovation of a Swedish multi-storey residential building of the 1970s under climate change and consider overheating control measures to reduce cooling demand and risk of overheating. The energy-efficiency measures include additional insulation to basement walls, exterior walls, and attic floor as well as improved energy-efficient windows and doors, balanced ventilation with heat recovery (VHR), lighting, household appliances as well as water taps and shower heads. The future climates are based on the representative concentration pathways scenarios. We find that implementing improved energy-efficient windows and doors, VHR and additional insulation to external walls give significant final and primary energy savings for space heating. The total operation final and primary energy use decrease averagely by 58% and 54%, respectively when all the measures are cumulatively applied under both current and future climate scenarios. Efficient household appliances and lighting as well as appropriate overheating control measures significantly reduce cooling demand and risk of overheating. The indoor air temperature and overheating risk as well as the final energy savings are influenced by the considered climate scenarios.

DOES INTELLECTUAL PROPERTY RIGHTS PROTECTION CONSTITUTE A BARRIER TO RENEWABLE ENERGY? AN ECONOMETRIC ANALYSIS

This study uses an econometric approach to investigate the role of IPR protection on renewable energy adoption using panel data of 102 countries at five-year intervals over the period 1990–2005. The Ginarte-Park index is used as a measure of the strength of intellectual property protection while the adoption of renewable energy is measured by the share of renewable energy in total final energy use. The results reveal that the level of intellectual property rights protection and reform of the intellectual property rights regime do not have significant impact on renewable energy adoption, suggesting that IPR protection is not a cause for concern in the global quest for clean energy transition. On the contrary, we find that trade openness has a stronger influence in the transition to clean energy. Based on the findings of the study, we conclude that IPR protection does not influence renewable energy adoption except in high R&D countries; rather policy makers should concentrate efforts on economic factors, such as trade openness, that drive the adoption of renewable energy technologies.

Impact of space layout on energy performance of office buildings coupling daylight with thermal simulation

Space layout design is one of the most important phases in architectural design, and current studies have shown that it can affect building energy performance. However, its influence has not been quantified. This paper aims at investigating the impact of space layouts on building energy performance. We use the floor plan of an office building in the Netherlands as reference, and propose eleven space layouts based on the reference. Calculations are performed with the tools Honeybee and Ladybug in Grasshopper, which are developed based on Daysim and EnergyPlus, to simulate lighting, cooling and heating demand of these layouts. In addition, we couple daylight with thermal simulation, by importing the artificial lighting schedule calculated in Daysim to EnergyPlus. The result shows that the heating demand of the worst layout is 12% higher than the best layout, the cooling demand of the worst layout is 10% higher than the best layout, and the lighting demand of the worst layout is 65% higher than the best layout. The total final energy use of the worst layout is 19% higher than the best layout.

Modelling development and analysis on the Balanced Energy Networks (BEN) in London

In the UK up to 40% of total final energy use is accounted for by the heating and hot water systems, which makes up 20% of greenhouse gas emissions. One path to low carbon heating is to electrify heat, and then meet the electricity demand via a smarter grid. This article presents a novel approach to electrifying heat based on a balanced energy network (BEN) system located at the London South Bank University (LSBU) campus. The BEN system includes borehole thermal storage, an ambient temperature heat network (heat transmission and distribution), water source heat pumps, smart hot water storage, and demand side response (DSR) service. Its thermal and electrical energy performances were mainly investigated. A novel energy performance index (TSE: total system efficiency) was also proposed and applied in assessing the performances. Several key findings were achieved as follows: (1) The TSE varied from 1.4 to 2.2 in one of the coldest months of the year, indicating a great improvement on energy efficiency. (2) The ICAX high-temperature heat pumps in BEN operate with a higher COP fluctuating between 3.1 and 3.2 with a Carnot efficiency of 0.5. (3) With an acceptable level of thermal comfort, the BEN system can reduce CO2 emissions up to 3.62 t for two weeks. (4) Corresponding with the initial design setting, 70 °C has been proved as the optimal operating output temperature of heat pump.

The Societal Costs of Deep Decarbonization in China

The deeply decarbonized energy economy would be achieved by the efficient power generation and low-carbon end-use equipment and infrastructure, which relies on the fixed cost investments in these items. In this study, we calculated the societal costs by the incremental energy system costs, which are defined the cost of producing, distributing, and consuming energy in a decarbonized energy system. We assess the transformation of the energy system including the major changes in energy supply and end use technology and infrastructure and its related energy costs. The investments in the highly efficient end use of energy, decarbonization of electricity and other fuels including biomass, petroleum, coal, natural gas and switching of end uses to electricity and other low-carbon supplies are calculated. The primary results show that the reference case shows a modest 15% increase in total final energy use, a 9% increase in CO2 emissions relative to 2014 levels, while the deep decarbonization case shows a 20% decrease in total final energy use and an 65% reduction in total emissions. The total societal costs, calculated by summing these three categories costs can be used for assessing the expected cost to achieve the target of greenhouse gas emissions reduction, which can provide theory for implications of low-carbon technology and infrastructure changes for the energy economy and policy.

A state of art review on methodologies for control strategies in low energy buildings in the period from 2006 to 2016

Building sector accounts for significant portion of total final energy use in most countries. One way to reduce significantly building energy consumption is to adopt energy efficiency technologies and strategies. Due to environmental concerns and high cost of energy in current years there has been a renewed interest in building energy efficiency. Advanced control strategies provide a more efficient way of minimizing energy demand of buildings and maintaining indoor environmental quality in accordance with global principle of sustainability, which has also proven reliable for diverse applications such as Heating, Ventilation and Air Conditioning (HVAC) control and thermal comfort control etc. The objective of this paper is to review the control strategies in buildings, particularly focusing on low energy buildings (LEB), in recent 10 years. Present work consists of why to use control strategies in buildings, categories of control strategies, research literature for building performance affected by diverse control strategies from the perspective of theoretical modelling, physical experimental study and numerical simulation investigation. Following that, more than 20 parameters affecting control performance have been analyzed and evaluated. The literature has illustrated that the best overall performance of control strategy is proportional integral derivative control-model predictive control (PID-MPC); the effects of those parameters on control performance are completely different, depending on which exact initial conditions and the interaction between different factors.

Development of a Concept for Energy Optimization of Existing Greek Hotel Buildings

Hotel buildings are unique compared to other public, commercial buildings due to their varying size as well as their facilities and operating schedules. Recent studies indicate that hotels are the second highest energy consuming category after hospitals. Even though they represent only 0.82% of the building stock, they reflect 28% of the total final energy use in the tertiary building sector of Greece. The reported average energy consumption for Greek hotels is 273kWh/m2 annually. Purpose of this Master Thesis was to evaluate different energy optimization scenarios for an existing hotel building as a case study and calculate the potential energy savings using the Greek software TEE-KENAK. Three main subjects were investigated: the building envelope, the electromechanical systems and the application of renewable energy technologies. Based on the results from several simulations, it is concluded that it is possible to reach an average reduction of 60% in the annual primary energy consumption.

A cross-country comparison of the building energy consumptions and their trends

Although it is often stated that the energy consumption in buildings accounts for more than 30% of total global final energy use, only a few studies analyze updated data about the current building energy consumptions or focus on comparing different countries. Similarly, models that predict future trends in building energy demand often use contrasting algorithms which result in diverse forecasts. Scope of this paper is to present and discuss data taken from several studies about the building energy consumptions in US, EU, and BRIC (Brazil, Russia, India, and China) countries and to provide an updated inventory of useful figures. Comparisons among countries are used to show historical, actual, and future energy consumption trends. Data presented by the World Bank, the United Nations Environment Program, the Intergovernmental Panel on Climate Change, and the International Energy Agency are compared with national reports as well as with research studies. The variety of the approaches used in each of the previous sources was considered fundamental to allow a complete review. The paper shows that the total building energy consumptions in BRIC countries have already overcome those in developed countries, and the continuous increase in the building stock of the BRIC countries creates an urgency for promoting building energy efficiency policies in these countries. At the same time, the policies actually adopted in developed countries are insufficient to guarantee a significant reduction in their building energy consumption in the years to come. In the current scenario, at least a doubling of the global energy demand in buildings compared to today’s levels will occur by 2050. To avoid this forecast, cost-effective best practices and technologies as well as behavioral and lifestyle changes need to be diffused and accepted globally.

People and energy use in the indoor and built environment

The increasing potential for dramatic climatic changes, the need to protect the future of our energy supply and rising fuel prices, mean that there is an urgent need to reduce energy consumption. This Special Issue of Indoor and Built Environment on ‘People and energy use in the indoor and built environment’ recognises that while buildings account for 32% of total global final energy use, the role of people in buildings’ energy use is often overlooked, despite the fact that ‘buildings don’t use energy: people do.’ The papers in this Special Issue demonstrate a broadening of the social science contribution to understanding energy use in the indoor and built environment. As well as focusing on ‘routine actions’ (or behaviours) using technologies and buildings, many papers presented here focus on ‘one-off actions’ to change technologies or buildings. Several papers go beyond a focus on individual building occupants, to include chains of actors or intermediaries (e.g. landlords) that influence the choice and/or use of technologies or buildings. These papers often also address the processes or chains of actions entailed in introducing new technology or buildings – such as service design or the communication process. Many papers explore the social, economic or technical context for actors and their actions. Most papers explore motivations for actions. Indeed, for many authors in this Special Issue, context is motivation and, combined with existing technologies and buildings, it creates the conditions that virtually require the routine actions that are observed. A few papers report on experiments with relatively ‘deep’ interdisciplinarity; approaches that might help the social and technical sciences learn from each other and so improve our understanding of people and energy use in the indoor and built environment. Three papers focus on the use of technology. Moore et al. note that the installation of heat pumps into homes has traditionally been seen as a purely technical matter, but if heat pumps are not used effectively, they won’t save energy. Examining the installation of domestic heat pumps in UK social housing, they focus on the design of the service to support the user experience of this new technology. Landlords and installers thought heat pumps were too complicated for users and more complicated than necessary. Tenants felt they were given insufficient information on how to use their heat pump, and many lacked confidence using heat pump controls, resulting in feelings of frustration and dependence. However, the authors’ prototype leaflet on using the heat pump controls was not favourably evaluated by users and tenants wanted a personal follow-up visit from the landlord or installer to answer any questions. Belatedly trying to explain how to use a too-complicated technology seems a less-promising approach than developing a technology and its control interface to suit its users. Dimitrokali et al. also examine the use of technology – smart home heating controls. Participants were customers of a UK utility company who volunteered to take part; nearly all were men who felt they had a good understanding of the purpose of smart home heating controls. Participants felt the trial positively changed their heating behaviour but wanted better capacity to control schedules when away from home and personalised tips on how to control their heating. The use of technology is also explored by Watson, focusing on a recently built UK ‘passive design’ office development, featuring a range of natural ventilation technologies and newly inhabited by a tenant organisation. The building was using significantly more energy than predicted, even after a post-occupancy evaluation helped fine-tune the technologies. The author uses social practice theory to understand this ‘performance gap’. Although the material element (technologies) of social practice theory was eventually functioning correctly, this was not the case for the three other elements of the practices framework: embodied habits, engagement (developing shared meaning) and institutionalised knowledge. The habits of building users were deeply

Energy Performance Database of Building Heritage in the Region of Umbria, Central Italy

Household energy consumption has been increasing in the last decades; the residential sector is responsible for about 40% of the total final energy use in Europe. Energy efficiency measures can both reduce energy needs of buildings and energy-related CO2 emissions. For this reason, in recent years, the European Union has been making efforts to enhance energy saving in buildings by introducing various policies and strategies; in this context, a common methodology was developed to assess and to certify energy performance of buildings. The positive effects obtained by energy efficiency measures need to be verified, but measuring and monitoring building energy performance is time consuming and financially demanding. Alternatively, energy efficiency can also be evaluated by specific indicators based on energy consumption. In this work, a methodology to investigate the level of energy efficiency reached in the Umbria Region (Central Italy) is described, based on data collected by energy certificates. In fact, energy certificates, which are the outcomes of simulation models, represent a useful and available tool to collect data related to the energy use of dwellings. A database of building energy performance was developed, in which about 6500 energy certificates of residential buildings supplied by Umbria region were inserted. On the basis of this data collection, average energy and CO2 indicators related to the building heritage in Umbria were estimated and compared to national and international indicators derived from official sources. Results showed that the adopted methodology in this work can be an alternative method for the evaluation of energy indicators; in fact, the ones calculated considering simulation data were similar to the ones reported in national and international sources. This allowed to validate the adopted methodology and the efficiency of European policies.

Energy efficiency improvements utilising mass flow control and a ring topology in a district heating network

Heating and cooling have a major role in the energy sector, covering 46% of total final energy use worldwide. District heating (DH) is a significant technology for improving the energy efficiency of heating systems in communities, because it enables waste heat sources to be utilised economically and therefore significantly reduces the environmental impacts of power generation. As a result of new and more stringent construction regulations for buildings, the heat demands of individual buildings are decreasing and more energy-efficient heating systems have to be developed. In this study, the energy efficiency of a new DH system which includes both a new control system called mass flow control and a new network design called a ring network is examined. A topology in the Helsinki region is studied by using a commercial DH network modelling tool, Grades Heating. The district heating network is attached to a wood-burning heat station which has a heat recovery system in use. Examination is performed by means of both technical and economic analysis. The new non-linear temperature programme that is required is adopted for supply and return temperatures, which allows greater temperature cooling and smaller flow rates. Lower district heating water temperatures are essential when reducing the heat losses in the network and heat production. Mass flow control allows smaller pressure drops in the network and thus reduces the pumping power. The aim of this study was to determine the most energy-efficient DH water supply temperatures in the case network. If the ring network design is utilised, the district heating system is easier to control. As a result the total heat consumption within the heating season is reduced compared to traditional DH systems. On the basis of the results, the new DH system is significantly more energy-efficient in the case network that was examined than the traditional design. For example, average energy losses within the constraints (which consist of heat losses, pumping energy, and surplus energy from the heat recovery system) are reduced from 4.4% to 3.1%.

Technological Alternatives or Use of Wood Fuel in Combined Heat and Power Production

Abstract Latvia aims for 40% share of renewable energy in the total final energy use. Latvia has large resources of biomass and developed district heating systems. Therefore, use of biomass for heat and power production is an economically attractive path for increase of the share of renewable energy. The optimum technological solution for use of biomass and required fuel resources have to be identified for energy planning and policy purposes. The aim of this study was to compare several wood fuel based energy conversion technologies from the technical and economical point of view. Three biomass conversion technologies for combined heat and electricity production (CHP) were analyzed: • CHP with steam turbine technology; • gasification CHP using gas engine; • bio-methane combined cycle CHP. Electricity prices for each alternative are presented. The results show the level of support needed for the analyzed renewable energy technologies and time period needed to reach price parity with the natural gas - fired combined cycle gas turbine (CCGT) CHPss. The results also show that bio-methane technology is most competitive when compared with CCGT among the considered technologies regarding fuel consumption and electricity production, but it is necessary to reduce investment costs to reach the electricity price parity with the natural gas CCGT.

Long-term energy efficiency analysis requires solid energy statistics: The case of the German basic chemical industry

Analyzing the chemical industry’s energy use is challenging because of the sector’s complexity and the prevailing uncertainty in energy use and production data. We develop an advanced bottom-up model (PIE-Plus) which encompasses the energy use of the 139 most important chemical processes. We apply this model in a case study to analyze the German basic chemical industry’s energy use and energy efficiency improvements in the period between 1995 and 2008. We compare our results with data from the German Energy Balances and with data published by the International Energy Agency (IEA). We find that our model covers 88% of the basic chemical industry’s total final energy use (including non-energy use) as reported in the German Energy Balances. The observed energy efficiency improvements range between 2.2 and 3.5% per year, i.e., they are on the higher side of the values typically reported in literature. Our results point to uncertainties in the basic chemical industry’s final energy use as reported in the energy statistics and the specific energy consumption values. More efforts are required to improve the quality of the national and international energy statistics to make them useable for reliable monitoring of energy efficiency improvements of the chemical industry.

Potential of best practice technology to improve energy efficiency in the global chemical and petrochemical sector

The chemical and petrochemical sector is by far the largest industrial energy user, accounting for 30% of the industry’s total final energy use. However, due to its complexity its energy efficiency potential is not well understood. This article analyses the energy efficiency potential on a country level if Best Practice Technologies (BPT) were implemented in chemical processes. Two approaches are applied and an improved dataset referring to Europe has been developed for BPT energy use. This methodology has been applied to 66 products in fifteen countries that represent 70% of chemical and petrochemical sector’s energy use worldwide. The results suggest a global energy efficiency potential of 16% for this sector, excluding savings in electricity use and by higher levels of process integration, combined heat and power (CHP) and post-consumer plastic waste treatment. The results are more accurate than previous estimates. The results suggest significant differences between countries, but a cross-check based on two different methods shows that important methodological and data issues remain to be resolved. Further refinement is needed for target setting, monitoring and informing energy and climate negotiation processes. For the short and medium term, a combination of benchmarking and country level analysis is recommended.

Indicators for industrial energy efficiency in India

Abstract India accounts for 4.5% of industrial energy use worldwide. This share is projected to increase as the economy expands rapidly. The level of industrial energy efficiency in India varies widely. Certain sectors, such as cement, are relatively efficient, while others, such as pulp and paper, are relatively inefficient. Future energy efficiency efforts should focus on direct reduced iron, pulp and paper and small-scale cement kilns because the potentials for improvement are important in both percentage and absolute terms. Under business as usual, industrial energy use is projected to rise faster than total final energy use. A strong focus on energy efficiency can reduce this growth, but CO2 emissions will still rise substantially. If more substantial CO2 emissions reductions are to be achieved then energy efficiency will need to be combined with measures that reduce the carbon intensity of the industrial fuel mix.