En-ROADS Technical Reference


Population, GDP, and Capital🔗

The demand sector defines the global energy demand for transport (transportation), residential and commercial, and industry end uses, all of which may be met by electric and non-electric carriers. The model determines the energy demand according to the stock of energy-consuming capital and its associated energy requirements.

Capital grows according to GDP as calculated by specified population scenarios and GDP per capita rates. GDP exogenously uses data reported by the World Development Indicators (2022) for each region. Projections assume GDP per capita growth rates converge from what they are in the period leading up to the last historical year and converge to 1.5% through 2100. Population uses the UN historical data through 2021, followed by their projections for different fertility scenarios. By default, En-ROADS assumes the medium fertility projections, but the model can vary continuously between the lower and upper 95% confidence intervals.

The capital-output ratio is assumed to be fixed such that capital and GDP rates are equivalent. Damage functions relating to GDP impacts from temperature change are described in detail in Damage to GDP. Energy requirements are embodied in the capital stock at the time of investment, which introduces a lag between the energy intensity of new capital and the average energy intensity of the capital stock.

The energy intensity of new capital is governed by a response to the total cost of ownership of each carrier for each end use and an exogenous user-specified technology trend. For each end use and carrier, two price effects, one based on energy costs and the other based on non-energy costs, also affect its energy intensity of new capital. Each price effect is formulated according to a distinct constant elasticity, such that as the cost relative to the reference increases, the energy intensity of that end use and carrier decreases. Likewise, as the cost relative to the reference decreases, the energy intensity of that end use and carrier increases.

The demand sector includes energy intensity of new and average energy consuming capital, which is disaggregated into three vintages, with energy requirements of each vintage, accounting for aging, early discarding and retiring, and retrofitting. Capital and energy requirements of that capital are disaggregated by end use (residential & commercial, industry, and transport), as well as by carrier (electricity and four fuels). The nonelectric carriers are coal, oil, gas, and biomass. The model carefully tracks final and primary energy demand, where the former is the energy consumed by the end use capital, and the latter is the energy needed to be generated to meet that demand accounting for thermal efficiency that is less than 100% and other losses.

Carrier Choice🔗

Energy is delivered to end use capital via five potential carriers; there are four nonelectric carriers and one electric carrier. Each of the nonelectric carriers matches 1:1 with each of the fuels, i.e., coal, oil, gas, and bio. The choice between each carrier is made in the carrier choice sector.

Shares of each carrier are allocated on the basis of the relative attractiveness of options according to a logit-type choice function, e.g.:

$$ Share[Carrier] = \frac{Attractiveness[Carrier]}{\sum Attractiveness[Carrier]} $$

Attractiveness is an exponential function of cost, complementary assets (for transport only), and other factors including phase-out policies, technical feasibility, and other effects. Cost attractiveness is determined according to the weighted average of attractiveness based on upfront capital costs and that based on the total cost of ownership (TCO), i.e., sticker price plus annual operation and maintenance costs plus energy costs. The weight reflects the value of how the buyers' attention is distributed between the sticker price and the TCO while making purchasing decisions and is specified for each end use.

Costs associated with the market price of energy are driven by the energy dynamics (e.g., extracted fuel commodity cycle, market clearing algorithms). Costs associated with the end use capital may be reduced by learning from end use experience, and for the electric carrier, adjusted with subsidies.

Complementary assets (CAs) reflect the availability of infrastructure to support the carrier; the effect applies only to transport end uses, reflecting fueling points/charging stations for vehicles. The installation of CAs is a function of the embodied carrier demand and, for the electric carrier, a policy to increase that. However, it is also constrained by a third order delay of the installation capacity. CAs have a normal lifetime but can also be retired early if the level exceeds the carrier demand. The level of CAs relative to that which is needed factors into the attractiveness of each carrier. Coal is assumed to have adequate availability for the relatively small amount of demand, notably for trains. The bio carrier uses the complementary assets of the oil carrier.

Fuel phase-out mandates also affect attractiveness, as described in Drivers of Cost of Supply.

The logit-determined shares are also subject to policies of phasing out fuel-powered capital, thereby electrifying new capital. These policies are phased in over time. For transport, the logit and fuel phase-outs only apply to the 85% of capital that is road and rail. To electrify the remaining 15% that is for shipping and aviation, another policy must be implemented.

Energy Intensity of New Capital🔗

In the demand sector energy requirements are embodied separately for each fuel and for electricity. Energy intensity of each new unit of capital drives the embodied long-term requirements. Technological improvements and price of energy affect the energy intensity of new capital. The technological effect defaults to the historically observed improvements, assuming those persist into the future. However, the user may change those rates of improvement. Price effects for each end use and carrier are determined according to the long-term demand elasticities to the price of energy and to the non-energy costs of capital. The indicated price effect for each, which is the product of the effect of energy costs and the effect of non-energy costs, is delayed over time. There is also a fraction of the residential and commercial sector that is by definition electric, e.g., lighting and electronics. The energy intensity of this share grows with the closure of the gap between the average GDP per capita of developing countries and the initial average of developed GDP per capita.

Long Term Energy Requirements🔗

The energy demanding capital that is installed is a function of the desired capital and that which is lost through discarding and retiring. The long term energy requirements are a function of the energy intensity of the capital that is installed and tracked through the capital lifetime through each vintage. Retrofitting for each end use also occurs, with the retrofits at the capital share and intensity of new energy.

Model Structure🔗

Figure 3.1 Elements of Carrier Attractiveness
Figure 3.2 Carrier Choice

Model Equations🔗

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