Energy end-use - IMACLIM
| Corresponding documentation | |
|---|---|
| Previous versions | |
| Model information | |
| Model link | |
| Institution | Centre international de recherche sur l'environnement et le développement (CIRED), France, http://www.centre-cired.fr., Societe de Mathematiques Appliquees et de Sciences Humaines (SMASH), France, http://www.smash.fr. |
| Solution concept | General equilibrium (closed economy) |
| Solution method | SimulationImaclim-R is implemented in Scilab, and uses the fonction fsolve from a shared C++ library to solve the static equilibrium system of non-linear equations. |
| Anticipation | Recursive dynamics: each year the equilibrium is solved (system of non-linear equations), in between two years parameters to the equilibrium evolve according to specified functions. |
Transport
Modeling the dynamics of the transportation sector
In static equilibrium, the transport of passengers and merchandise are characterized by the following parameters:
- The number and charachteristics of households personal vehicles,
- The efficiency of the fleet of personal vehicles,
- The physical capacities of the different modes of transport,
- The coefficients of intermediary energy use in the transport sectors,
- The coefficients of intermediary consumption of transport in all sectors.
In the recursive dynamic structure of Imaclim-R the "transport" dynamic module represents the evolutions of these parameters.
Waisman et al. (2013) give a detailed description of the representation of the transportation sector in Imaclim-R, and analyze the sector's role in the development of low-carbon pathways. The section below gives a description of the representation of the dynamics of the sector in Imaclim-R.
Personal vehicles: stock and energy intensity
The evolution in the rate of motorization in each region has been found to be strongly linked to the evolution of average income per inhabitant and to the distribution of income in the population. It is however only slightly sensitive to variations in fuel prices (Storchmann, 2005). The representation of these links in IMACLIM-R are based upon the SMP model, a sectorial model of energy use in the transport sector developed in a collaboration between the International Energy Agency and the World Energy Council (Fulton and Eads, 2004). The key feature of the SMP model is that it uses an income elasticity that varies depending on the rate of motorization. In practice this means an elasticity that varies with income. Regional variation resulting from historical and geographical factors, mean that the correlation between an absolute level of wealth and the possession of a vehicle is not transposable from one region to another. The saturation effect on the possession of personal vehicles thus appears at a level of average income that depends on the region.
The income elasticity, ?k, is linked to the rate of motorization according to a formula adapted from the SMP model and schematized in Figure 1. In the regions where the annual average income (measured in purchasing power parity) does not exceed $5000 per capita, this elasticity is maintained equal to 0.3 regardless of the rate of motorization, in order to represent the threshold effects linked to accessing auto-mobility in today?s least developed economies. By multiplying Cars_pc by the total population one obtains the total size of the car fleet, denoted CARS. The size of the personal vehicle fleet, CARS, then determines the capacity of transport associated with the automobile mode, a parameter which is taken into account in the budget-time constraint of households in static equilibrium.
Figure 1 Evolution of the ?k elasticity income according to the rate of motorization.
The efficiency of the automobile fleet depends both upon technical progress and upon technological choices households make upon acquisition of their vehicles. In the model the automobile fleet is charachterised by differentgenerations of vehicles categorised according to the year in which they were put into service and further grouped into four types of vehicles: conventional or hybrid with, in both cases, standard or improved technology. This schematic representation, includes contrasting characteristics for the four types of vehicles : purchase price, energy efficiency and fixed and variable maintenance costs. All costs are calibrated with data from the International Energy Agency (IEA, 2006) and evolve over time in resopnce to technical progress. Hybrid vehicle technology is assumed to improve so as to make possible consumption levels in the order of 1.5 litres per 100 kilometres. This figure can also be understood as being an average of electrical vehicles and rechargeable hybrid vehicles.
At every time step, the technological composition of the new generation of vehicles results from the households? choosing from among the four specific technologies. This choice is carried out by comparing, for each of the four available vehicle technologies, the levelised average cost associated with the production of a vehicle-kilometre. This average cost is calculated using technological characteristics of the different types of vehicles in a manner similar to that used in calculating the complete cost of the technologies used to produce electricity. In doing so it is assumed that households formulate a myopic view of the trajectory of future energy prices, that is to say, they consider that future prices will be equal to those of the preceding static equilibrium. In the case where an explicit carbon policy in introduced, it is assumed that households anticipate perfectly future values of the tax and add it to their myopic scenario of energy prices. The levelized average production cost of a vehicle-kilometer for a specific technology, denoted TECH in the following, is obtained using Equation 1 by summing up the fixed and variable costs linked to the possession and usage of the vehicle respectively. The fixed costs are made up of the levelized purchase cost (denoted CINV_carsk,TECH) and the annual fixed running costs associated with the possession of a vehicle (e.g. insurance).Both fixed and running costs are normalised to a kilometre covered on the basis of a hypothesis on the annual average distance covered by vehicles (denoted average_km_per_yeark) applied to each region on. Variable costs group the fuel costs which depend both on the anticipated final price scenarios (denoted _p_fuel_anticip_taxed_cars_) and the fuel consumption of the vehicle type per vehicle.kilometre (denoted sym). In all of these calculations, the discount rate adopted by the households, denoted disck,CAR, is fixed as a scenario hypothesis between 0.12 and 0.18, according to the region.
(1)
with:
(2)
The market shares of each new vehicle technology is obtained by a logit function which makes it possible to take into account heterogeneities in household choices and the coexistence on the market of several different vehicle types (Clarke and Edmonds, 1993):
(3)
These shares are then allocated to the new generation of vehicles, denoted CAR_new, obtained by the difference between the new total size of the CARS fleet and the old depreciated fleet.
Finally, the new average energy intensity of automobile transport (expressed in Mtoe per passenger.kilometre) is obtained by taking into account the composition of the fleet and the levels of use of the different generations and types of vehicles:
(4)
This equation includes two behavioural parameters drawn from the SMP model which are necessary togo from the theoretical energy use levels for the four types of vehicles to the average energy intensity of the whole fleet per passenger.kilometer: (1) the average occupation rate of the vehicles, denoted occupancy'k, and (2) the relationship between the theoretical energy use level of the vehicles and actual observed energy use level, denoted on_road_gap_factor'k.
Other means of transport: capacities and energy use
The evolution of passenger transport capacity is directly linked to the evolution in transport infrastructures that follows from public and private sector decisions. By default, these public and private sector decisions finance capacity evolution in responce to demand increases either explicitly through state spending on road infrastructures or via the investment decisions of the respective transport sectors. The evolution in the levels of capacity then modifys the ?time-efficiency? of the different transport modes used in the calculation of the time-budget constraint in the households? utility maximization program in the static equilibrium (Figure 2).
Figure 2 The effect of the extension of capacities on the marginal efficiency of transport time.
The non-automobile transport intermediary energy use respond to reduced, simple forms of efficiency improvement:
- In the air sector, fuel use declines by 0.7% per year due to autonomus technical progress that includes both advances in airplane design and the improved use of flight and destination organizational measures aimed at filling plane seats.
- In the maritime sector, intermediary energy use per unit of transport remains unchanged.
- In the which includes sector of freight and passenger transport by land, the average use of liquid fuels evolves in response to a price elasticity of fuels, denoted elast_Et_OT'k, which is fixed at -0.3 but does not go below an asymptote fixed at 25% of its initial level (See Equation 5). This aggregated representation is a preliminary step towards a more detailed representation of this sector divided into sub-sectors. In fact, in the present version of the model, the sector ?public land transport? groups road and rail freight and road (bus) and rail passenger transport. This level of aggregation follows directly from the GTAP data format upon which the model is calibrated. This format does not distuinguish different sub-sectors of transport. The dynamic evolution of the energy use of this sector is thus a function of vehicle technological progress, modal shifts (particularly shifts in freight between road and rail) and modifications in the structural composition of the sector arising from changes in the relative weights of the comprising sub-sectors.
(5)
Evolution in the transport demand of other sectors
Production technologies used in each sector are described using Leontief functions. The functions have fixed levels of labor, energy and other intermediary inputs. This means that at a given point in time, that the transport demand of production sectors in each of the three freight transportation modes (air, water and land ) is measured by input-output coefficients, FjIC, which describe a linear dependence in a given mode of freight transport, j, to production volumes.
The input-output coefficients, FjIC, capture implicitly (a) the spatial organization of the production processes in terms of specialization/concentration of production units and (b) the constraints imposed on distribution in terms of distance to markets and just-in-time processes, and these two factors drive the modal breakdown and the intensity of demand for freight mobility. The input-output coefficients can evolve exogenously over time to capture assumptions on changes in the energy efficiency of freight vehicles, in the logistic organization of the production/distribution process and in the modal breakdown.
For enterprises making organizational and production decisions an uncertainty exists regarding their reaction to variations in the price of transport however small. Therefore it has been decided to fix the evolution of these parameters exogenously. In the default model setting, these coefficients of intermediate consumption of transport by sectors are maintained constant. This is in line with observed historical tendencies.
Residential and commercial sectors
Residential sector
In the structure of the IMACLIM-R model, the use of energy in the residential sector is determined in each static equilibrium via the ?m2 parameters. The parameters acts as a physical constraint on household budgets because they are directly linked to the physical stock of buildings available during the current period, and to the coefficients of unit consumption of energy (kWh/m2) rather than to the maximization of utility. Determining residential sector energy use in the static equilibrium thus means assuming that its energy demand for various end-uses is inelastic to price and income variations over the short term. Hence, households' energy demand depends mainly on the equipment choices they have made over the preceeding years.
In the dynamic modules, the amount of living space per capita changes according to the income per capita which isdetermined endogenously in the preceding static equilibrium. It is assumed that there is an asymptote of floor area per capita specific to each region, and that the asymptote incorporates spatial constraints, choices in the styles of building development and density and cultural habits. In the construction of scenarios, the assumptions made about these asymptotes are kept consistent with those concerning the development of transport infrastructure, bearing in mind that all such dynamics are linked to territorial and urban zoning policies.
The equation below relates the evolution of floor area per capita for the residential sectorto the evolution ofincome per capita, Income_pck, over the two preceding static equilibrium periods and an elasticity, ?k(m2_pc(t)), which decreases as floor area per capita increases:
The total residential floor area, Sk;housing, is the product of this surface per capita and of the total population. The newly constructed residential surface is equal to the difference between this total surface and the old residential surface depreciated by the surfaces at end of life (lifetime, Life_timek;housing): 
Energy use per m2 depends on the average composition of equipment installed in the housing stock, and of the thermal charachteristics of building construction. Their evolution depends on the choices agents' technological make in responce to different economic signals and the available technologies.
In the reference scenario, energy use per m2, ?m2k;ener (t + 1), evolves according to an exogenous trajectory calibrated to outputs from the POLES energy model, that have themselves been calculated to be coherent with macroeconomic trajectories from IMACLIM-R during coupling exercises between the two models. This trajectory encompasses the evolution dynamics of household equipment, the conversion efficiency betweenbetween final energy and energy services and the buildings physical characteristics (insulation, use of renewable energies).
In the emission reduction scenarios the carbon price signal induces efficiency gains in building phyisical charachteristics and equipment. These technological options are represented with a unique type of alternative housing called a Very Low Energy building (VLE) whoose annual energy consumption is 50kWh/m2 (80% electricity and 20% gas). Technologies which can bring about this level of unit energy consumption are already commercialised e.g. on-site energy production of energy and efficient insulation of buildings, and are represented in the model in an aggregated manner. To increse the deployment of VLE?s we assume the introduction of what we call technological rupture policies, expected to launch large scale thermal renovation plans and the tightening of building regulations in the developing countries. Following this scheme, two types of housing can coexist in the same stock: (i) standard homes (BAU) which have the same energy characteristics as those of the reference scenario and incorporate progressive gains in energy efficiency and (ii) newly built Very Low Energy (VLE) homes. The penetration speed of VLE?s into the building stock is determined by two reduced functional forms that link the level of a carbon tax to (i) the percentage of new built dwellings that are VLE?s (written share__{}VLE{}_{}new_) and (ii), the annual rate of renovation in the existing building stock (written share__{}renov{}_{}VLE_) that converts a BAU into a VLE (with a maximum annual rate fixed at 2,5%). This maximum level is reached at a carbon price of $100 per ton of CO2 while VLE buildings begin to penetrate the market from $10 per ton of CO2.
Unit consumption of the existing dwelling stock is then obtained by averaging the energy characteristics of the BAU and VLE housing stocks, weighted by their shares in the total dwelling stock.
Commercial sector
The evolution of this composite sectors (aggregating light industries and services) intermediate consumption of energy follows the same structure of representation as that of the industrial sector (see following section).
Industrial sector
Energy use by productive sectors
Induced technical change in productive sectors of the economy is modelled in Imaclim-R according to two assumptions. First, energy efficiency improvements are induced by devolopments in energy prices. Second, energy substitution occurs driven by learning-by-doing processes. At the aggregate level, energy efficiency improvements and energy substitution may result from structural changes in economic activity.
Energy efficiency improvements in productive sectors
For each productive sector (industry, construction, services, agriculture), the region with the lowest final energy use per unit of production at base year is identified as the most energy efficient region, thus dividing the world into one leader region and eleven followers for each sector. The energy efficiency of the leader evolves as a function of an energy price index, and an exogenous trend in energy efficiency improvements at constant energy prices. The energy price index is determined endogenously, and the energy efficiency growth rate of the leader will increase (resp. decrease) in response to increases (resp. decreases) in energy prices. For each sector, the energy intensity of the followers is assumed to converge towards the performance of the leader. The speed of convergence also depends on the level of energy prices. Some emerging economies appear to be more energy efficient in some sectors at the year of calibration [1]. In these regions, the energy intensity of the relevant sectors is allowed to start with lower levels of energy intensity then the leader, before converging towards the leader. Energy efficiency improvements are assumed to be in part free, and in part linked to higher cost of capital. Energy efficiency improvements in productive sectors are not biased towards low carbon energy sources meaning that the use of fossil and non-fossil energy decreases uniformly. A shift from carbon intensive to low carbon energy use in these sectors may be induced by an increase in fossil fuel energy prices brought about by the introduction of a carbon price. In general, substitutions between energy carriers (coal, oil, gas, electricity, refined fuel) and transportation modes (road, rail, air, water) are driven by relative prices given explicit constraints on energy production and end-use equipment.
Energy efficiency improvements induce lower energy consumption per unit of output (ICu'ener) in each productive sector. This may result in higher or lower aggregated energy consumption (IC'ener), depending on the relative effects of lower unit consumption and higher sectoral production (Q) induced by lower prices. Lower overall energy consumption affects energy prices in two ways: a decrease in wholesale energy prices because of lower energy use (IC'ener) and lower emissions lead to a relaxation of the carbon tax required to reach a set climate objective. Overall, lower energy consumption thus results in lower tax-inclusive energy prices. As energy efficiency improvements are driven by the energy price index, lower energy prices may in turn counterbalance energy efficiency improvements. On the production side, lower unitary energy requirements (ICu'ener) decrease production costs and prices (p), driving up demand and production (Q).
Substitution and structural change
Substitution between energy carriers (i.e. coal, oil, natural gas, electricity, refined liquid fuels) and substitution between transportation modes (i.e. by road, rail, air or water) are driven by relative prices, given explicit constraints on energy production and end-use infrastructure e.g. energy production and conversion capacities and available end-use equipment. These substitutions occur at the end-use sector level.
At the micro level, learning-by-doing may induce substitution between technologies, which may in turn induce energy carrier substitution e.g. from coal to gas for electricity production. Technology substitution is also explicitly modelled at the end-use level for transport, e.g. between conventional and electric cars. Energy efficiency improvements are not biased towards low or high carbon energy carriers, as the consumption of all types of energy decreases uniformly. However, for the sectors using fossil fuels, carbon pricing will increase the energy price index. The substitution between energy carriers however depends on relative prices and relies on a logit decision function for new vintages of productive capacities and equipment (the sectoral energy mix being the sum of energy demands of all vintages). Technical change may occur at the level of specific technologies through learning-by-doing processes. The cost of technologies is assumed to decrease with cumulative investment and production through learning-by-doing, using learning curves for all explicit technologies. The pace of cost reductions down the learning curve depends on the initial installed capacity, the learning rate and the cost floor. This approach has been used to characterise energy technologies, see for instance (McDonald and Schrattenholzer, 2001; Neij, 2008). It is used in Imaclim-R to model electricity and oil production technologies, or for demand technologies (such as cars). In energy production sectors, learning-by-doing for low-carbon electricity production technologies (triggered by carbon prices) may improve the carbon efficiency of energy transformation through the substitution from fossil energy towards low carbon-alternatives. At the macro level, carbon pricing policies may induce a change in the structure of demand both at the household and firm levels by altering energy prices. This may in turn change the nature of the goods produced, and hence the structure of each sector and in the relative weight of each sector in total economic output.
[1] From combining IEA energy matrices and GTAP input-output tables, agriculture in Africa appears to be 12% more efficient than the leader (Japan). This can be due to missing data, or difference in the structures of the sectors, and thus suggests precaution with the use of the data. Conforti and Giampietro (1997) also reports that some African countries display a very high energy output to input ratio (Uganda is 380 times more ?efficient? than Japan).
Other
Agriculture, industry, construction and services
By default, supply-side energy consumption in these four sectors changes according to global energy efficiency improvements and shifts in the energy carrier mix for new vintages of capital. Both are driven by the relative prices of energy. On the demand side, income elasticities of consumption of industrial and agricultural goods are assumed to decline to represent saturation, when per-capita income increases. This leads to an endogenous dematerialisation.