World Energy Projection System (WEPS): 

Electricity Model

Independent Statistics & Analysis

www.eia.gov

U.S. Department of Energy

Washington, DC 20585

Last Updated 2020
U.S. Energy Information Administration | World Energy Projection System: Electricity Model i

This report was prepared by the U.S. Energy Information Administration (EIA), the statistical and 

analytical agency within the U.S. Department of Energy. By law, EIA’s data, analyses, and forecasts are 

independent of approval by any other officer or employee of the United States Government. The views 

in this report therefore should not be construed as representing those of the U.S. Department of Energy 

or other federal agencies.
U.S. Energy Information Administration | World Energy Projection System: Electricity Model 1

Table of Contents

1. Introduction .............................................................................................................................................. 2

2. Objective Function .................................................................................................................................... 2

3. Key Constraints ......................................................................................................................................... 3

3.1 Summary of Key Constraints.............................................................................................................. 3

3.2 Discussion of Key Constraints............................................................................................................ 3

3.3 Optional Constraints.......................................................................................................................... 4

3.4 Renewables Penetration Limits......................................................................................................... 4

4. Interaction with Other WEPS Models....................................................................................................... 5

5. Energy System Structure........................................................................................................................... 6

6. Shadow Prices and Cost-of-Service Regimes............................................................................................ 7

7. Model Data Sources.................................................................................................................................. 8

7.1 Existing generation stock................................................................................................................... 8

7.2 Operating and maintenance costs..................................................................................................... 8

7.3 Wind and solar potential ................................................................................................................... 8

7.4 Hydro potential and generation profile............................................................................................. 9

7.5 Inter-regional transmission capacity ............................................................................................... 10

7.6 Historical generation and consumption .......................................................................................... 10

Table of Figures

Figure 1. Energy system structure and WEPS linkages for each model region ............................................ 7
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1. Introduction

The International Electricity Market Model (IEMM) projects the following key quantities:

• Electricity generating capacity, including additions and retirements

• Electricity generation

• Electricity added and removed from storage 

• Electricity sold and purchased

• Electricity delivered to consumers

• Fuel consumed in electricity generation

• Carbon dioxide emissions

• Electricity prices

The model projects these quantities for each of the WEPS regions by year and time-slice. A time-slice is 

a time period, specified by EIA analysts, as a period of the day during a particular month or season (e.g., 

January from 7:00 p.m. to 9:00 p.m.). In some cases, some of the quantities listed above are also broken 

out by other characteristics such as the type of technology used to generate the electricity. 

The model projects these quantities by minimizing an objective function subject to several constraints. 

The objective function represents the total cost to electricity suppliers of meeting all of the electricity 

demands, by year and time-slice, as projected by the WEPS demand models. Examples of constraints 

include limits on fuel-specific electricity generating equipment, policy constraints (e.g., renewable 

portfolio standards), and emissions caps. The IEMM uses linear programming to perform the 

constrained optimization.

2. Objective Function

To minimize the total system cost of meeting electricity demands projected by WEPS demand models, 

the IEMM breaks the cost into several components:

• Capital costs for investment in new electricity generating capacity–these costs are annualized 

over the generating unit’s economic life, at either the system discount rate or a technologyspecific discount rate estimated by EIA analysts,

• Fixed and variable annual Operation and Maintenance (O&M) costs of electricity generating 

equipment,

• Costs for fuel consumed, including purchases at regional fuel prices and any delivery costs

identified by EIA analysts

• Projected taxes and subsidies minus the salvage value of generators with remaining economic 

life

In some cases, the IEMM includes additional costs in the analysis. Other possible costs include:

• Decommissioning costs (e.g., capital expenditures and/or annual operation and maintenance 

costs) for equipment that incurs costs for dismantling at the end of its useful life,

• Damage costs from pollutant emissions (e.g., from acid rain or health impacts), and

• Welfare loss/gain resulting from changes in quantity of electricity demanded.
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The additional costs are included when we configure the IEMM to allow the quantity of electricity 

demanded in each region to be affected by price changes rather than fixed at the value received from 

the main WEPS system. In this case, the minimization of system costs, including welfare gains/losses, is 

equivalent to maximizing total consumer plus producer surplus.1

3. Key Constraints

3.1 Summary of Key Constraints

The cost minimization is subject to constraints that impose physical, operational, and policy restrictions 

on the electricity supply costs. These constraints account for:

• Retrofits and retirements of electricity generating equipment, based on equipment age

• Fuel-specific equipment efficiencies and fuel shares for fuel-flexible generating units

• Equipment availability

• Reserve capacity requirements, which require suppliers to maintain sufficient generating

capacity to exceed peak demand by a specified amount

• Commodity balance and demand satisfaction

• Projected policy constraints, including renewable portfolio requirements, emissions limits, and 

minimum and maximum addition and operation of generating units by type

3.2 Discussion of Key Constraints

This section provides more information on the first five constraints listed above.

• Equipment retrofits and retirements. When computing the available capacity for a certain time 

period, the model accounts for the capacity resulting from all investments up to that period. 

Some of these capacity investments may have been made before the initial period but the 

equipment is still in operating condition and other capacity investments may have been 

projected at or after the initial period, up to and including the period in question. Investments in 

a particular technology increase its projected installed capacity for the duration of the technical 

life of the technology. When the technology is retired, the projected capacity for this technology 

decreases.

• Equipment efficiencies and fuel shares. These constraints specify that the amount of electricity 

produced (output) is in fixed proportion to the sum of the fuels used in electricity generation 

(inputs). For example, we may have a fuel-flexible power plant that can burn different 

combinations of fuels, but the total amount of electricity generated must be proportional to the 

sum of the quantities of fuel used. 

• Use of available capacity. For each time period, the model may project the use of some or all of 

the installed electricity generating capacity, according to the technology-specific availability 

factor, which defines a maximum capacity usage. 

• Reserve capacity requirements. This constraint requires that the total capacity of all processes 

producing electricity in each year, region, and time-slice must exceed the average demand in the 

time-slice where peak demand occurs (e.g., a daytime hour in summer), by a certain percentage.

 1 See Loulou, R., Remne, U., Kanudia, A., Lehtila, A., Goldstein, G., 2005. Documentation for the TIMES Model Part I, Energy 

Technology Systems Analysis Programme, https://www.iea-etsap.org/docs/Documentation_for_the_TIMES_Model-Part-I_July2016.pdf, Section 3.2.3.2, for an explanation of the equivalence.
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• Commodity balance and demand satisfaction. In each year and time-slice, the production of 

electricity within each region, plus any imports from other regions, must balance the amount of 

electricity consumed in the region and exported to other regions.

3.3 Optional Constraints

In addition to the core constraints discussed above, EIA analysts may add bounds to model variables. 

This section describes the major additional bounds and constraints that we added to IEMM. 

A bound is an upper, lower, or fixed limit on a single model variable. For example, bounds can be 

imposed on:

• Capacity, investment, generation, fuel consumption, or emissions from any technology (e.g., to 

project the effects of operational or policy limits on technology investment and behavior in 

each region)

• Total production, consumption, or net level of any commodity (e.g., to set emissions caps)

EIA analysts may include constraints specifying more complex relationships between variables. Common 

applications of such constraints include:

• Imposing bounds on selected technologies/commodities for a group of regions (e.g., a common 

emission cap on a group of regions that are allowed to trade)

• Imposing renewable portfolio, clean energy standards, carbon emissions intensity, and other 

policies based on relationships between fractions of generation by different plant types or 

between emissions and generation 

• Creating banking schemes for cap and trade programs

• Imposing build-rate penalties (e.g., any capacity created beyond x GW per year will cost an 

additional $y / GW)

Constraints that relate variables across periods or time-slices can be used to

• Impose a limit on the rate of growth (or decay) in capacity/activity of a new technology type 

from one period to the next

• Limit the ramping rate—the percentage increase or decrease in the utilization level of a thermal 

power plant from one time-slice to the next

3.4 Renewables Penetration Limits

IEMM uses the bound and constraint facilities to construct two sets of limitations to the penetration of 

variable renewable (VRE) generation. The need for these limits arises because VRE has inherently 

granular temporal and spatial dependencies. No matter how detailed the time and space resolution of a 

global model such as IEMM, it will always be insufficient to capture these dependencies fully. 

Specifically, we wish to address two challenges:

• Limiting the use of country-level wind and solar penetration in large, possibly multi-country 

regions

• Limiting the ability of variable resources to meet average loads in model time-slices
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IEMM contains country-level wind and solar potentials, but it projects demand at a regional level. In 

multi-country regions, as well as in large countries, resources may not be located near loads and 

transmission capacity may not exist from resources to load. We do not want the model to satisfy an 

unrealistic portion of regional load with renewables that may be located in a small, and potentially 

distant, portion of the region. 

To provide a generic structure to control the penetration of these technologies, IEMM allows each 

country to produce a maximum level of generation from wind-plus-solar before it has to incur a grid 

extension cost. To allow generation beyond that limit, we provided three levels of grid extension

investment—notionally representing short distance, medium distance, and long distance transmission—

each with assumed bounds and investment costs. 

The bounds for the initial maximum generation and the three levels of grid extension are initially driven 

by projected country-level electricity demand, which is based on a logistic curve fitted to minimize the 

sum of squared errors of per capita consumption from historical values and population projections. EIA 

analysts may add similar constraints to prevent the IEMM from projecting over utilization of 

hydroelectric resources in countries with large hydroelectric potential that don’t have the corresponding 

electricity transmission investment. 

IEMM time-slices are designed to capture two important types of temporal variation in load and 

generation: season and time-of-day. They do not capture day-to-day variation within seasons; rather, 

they average over such variation. When penetrations of VRE sources become large relative to total load, 

such averaging may run the risk of implicitly assuming free storage between days, or even hours, within 

the same time-slice. 

To avoid such an outcome, EIA implemented constraints that limit the maximum projected share of total 

electricity production in each region and time-slice from VRE sources. Output from storage technologies 

is included in the denominator of the constraint, resulting in a requirement for storage investment and 

operation when VRE penetrations become very high. The maximum VRE share is currently set at 65%. 

4. Interaction with Other WEPS Models

The IEMM receives regional annual sectoral electricity demands and power sector fuel prices from other 

WEPS models. IEMM also receives nuclear capacity and generation projections from the WEPS nuclear 

model. For each of the four WEPS end-use sectors (residential, commercial, industrial, and 

transportation), the IEMM provides to other WEPS models the projections for

• Regional electricity capacity and generation by fuel and technology

• Power sector fuel consumption

• Wholesale and retail prices. 

IEMM provides an economic projection of global electricity generating capacity and dispatch. IEMM 

tracks existing equipment by region and age (or vintage), along with analyst-specified planned capacity 

builds, and evaluates options to build new capacity and retire existing capacity. At the same time, it 

optimizes the dispatch, subject to technology- and region-specific dispatch limitations and policy 
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requirements. It also tracks existing inter-regional transmission capacity and can project new 

transmission capacity. The IEMM projects electricity demand by end-use sector and time-slice using 

sector-specific data provided by other WEPS models. The model uses a linear programming approach to 

find the lowest cost capacity-plus-dispatch solution. 

5. Energy System Structure

The IEMM energy system structure within each WEPS region is depicted in Figure 1, along with the 

information flows between IEMM and other WEPS models. 

Stepped fuel supply curves: IEMM receives regional delivered power sector fuel prices for coal, natural 

gas, and oil products from the WEPS supply models. It also retains a delivered quantity from a previous 

run of the WEPS system. IEMM constructs a stepped supply curve, shaped by analyst-provided

elasticities, around these initial points. These supply curves allow some supply-price adjustment to help 

speed convergence of the WEPS system. IEMM also receives projected fuel-based emissions factors 

from the WEPS emissions model.

Renewable potential and cost: The IEMM knowledgebase contains detailed country-level potentials for 

onshore and offshore wind, photovoltaic, and hydroelectric capacity. Wind potentials are segmented by 

resource class, distance from transmission, and, for offshore wind, depth. Each country-level segment 

has its own cost, resulting in a detailed global wind supply curve. PV potential is similarly segmented by 

resource class within each country. Hydroelectric capacity is specified by a three-step cost supply curve. 

EIA developed hourly wind and solar generation profiles for each country using geospatial solar and 

win7d speed data. The hourly data are aggregated into model time-slices. Country-level availability 

factors constrain hydroelectricity production at the annual and seasonal levels, based on historical 

seasonal generation, where available, or seasonal precipitation data. Moderate (20%) additional 

seasonal flexibility is provided to represent the capacity for reservoirs to allow seasonal shifting of 

production.
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Coal, natural gas, and oil 

supply curves built around 

WEPS prices and 

quantities

Wind, solar, and hydro 

potential and time profile 

by class and country.

New fossil units, available 

with regional costs and 

efficiencies

Existing units, aggregated 

per user specification into 

model regions and plant 

types, tracked by vintage

New wind and solar units, 

with country-specific costs 

and characteristics

Annual sectoral electricity 

load, shaped into model 

time slices and combined 

into total load curve

Nuclear capacity and 

generation projections

New hydro units, with 

country-specific costs and 

annual and seasonal 

availabilities

Resource supplies

Power plants

Demands

WEPS nuclear module

fuels

WEPS fuel 

modules

electricity

transmission exchange 

with other model 

regions

storage moves 

electricity between 

model time slices

Sectoral retail prices, capacity, generation, 

and fuel consumption, and emissions by 

type to other WEPS modules 

WEPS 

end-use 

modules

Figure 1. Energy system structure and WEPS linkages for each model region

6. Shadow Prices and Cost-of-Service Regimes

IEMM sends capacity, generation, and fuel consumption projections to the main WEPS system for each 

region and technology type. In addition to these outputs, IEMM produces 

• Marginal prices (shadow prices) of generation by region and time-slice

• Average cost of electricity generation by region

• The shadow price on meeting reserve capacity requirements by region

The WEPS system uses these inputs to produce electricity generation prices under cost-of-service and 

competitive pricing regulatory regimes. 

Under cost-of-service regimes, the generation price is calculated as the average cost of generation, 

which is simply the sum of all system costs (including capital, operating, fuel, and policy compliance 

costs) divided by total generation. Under competitive pricing regimes, the retail price is the sum of an 

energy component based on the marginal price of generation and a capacity component based on the 

shadow price on the reserve requirement constraint. EIA analysts specify the ratio of cost-of-service and 

competitive pricing, along with end-use sector markups representing transmission and distribution 

adders, taxes, and subsidies. 
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7. Model Data Sources

7.1 Existing generation stock

The Platts UDI World Electric Power Plants Database (WEPP) is used for existing and under-construction 

capacity by country and state. Planned builds may be adjusted by EIA analysts to reflect the most recent 

information on national plans.

7.2 Operating and maintenance costs

Country-level O&M costs are based on the 2010 and 2015 IEA Generation Cost studies

(https://www.oecd-nea.org/ndd/pubs/2015/7057-proj-costs-electricity-2015.pdf) which provide 

national O&M cost estimates for new units. Because of incomplete coverage, EIA divided countries into 

five reporting peer groups, and we used data from the Bureau of Labor Statistics on international wage 

differentials to establish which countries were most closely aligned in labor costs. On this basis, we 

assigned non-reporting countries to a peer group paired with countries that did report. Calculations 

based on the two capacity factor scenarios IEA reported were used to distinguish fixed and variable 

O&M. We used data from EIA’s recently commissioned Sargent & Lundy study on operating costs of U.S. 

generation to develop ratios for large versus small units. This ratio was applied to the base costs for all 

countries.

7.3 Wind and solar potential

Wind resource data by country come from a resource assessment performed at the National Renewable 

Energy Laboratory (NREL), based on the National Center for Atmospheric Research's (NCAR) Climate 

Four Dimensional Data Assimilation (CFDDA) mesoscale climate database. Resources are defined by 

country and resource quality. We further differentiated onshore supply curves by distance to nearest 

large load or power plant and offshore supply curves by distance to shore and water depth. Resources 

are calculated from hourly wind velocity vectors at a 40 kilometer (km) grid at 90 meter hub heights. 

Output is derated for outages and wake losses to obtain the net capacity factor. Protected, urban, and 

high-elevation areas are fully excluded, and certain land cover types are fractionally excluded. Areas

within 5 nautical miles of or farther than 100 nautical miles from shore are excluded. Protected marine 

areas are also excluded. Marine areas are assigned to countries based on exclusive economic zones; 

unassigned or disputed areas are excluded.

The estimated solar potential is obtained from NREL and represents an annual average of the daily total 

solar resource averaged over surface cells of 10 km resolution at the country level. The data are based 

on the State University of New York, Albany satellite radiation model, which uses several factors to 

calculate the hourly total insolation (sun and sky) falling on a horizontal surface output over a 12-year 

period (1998–2009):

• Hourly radiance images from geostationary weather satellites

• Daily snow cover data

• Monthly averages of atmospheric water vapor, trace gases, and the amount of aerosols in the 

atmosphere
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The values returned are the kilowatthours per square meter per day (kWh/m2/day) available to fixed, 

flat plate systems titled toward the equator at an angle equal to the latitude. The total solar resources 

within each country are then organized by class, starting at 3 kWh/m2

/day or less and increasing in 0.5 

kWh/m2

/day increments, with the highest solar class being 6 kWh/m2/day or more. Each solar class in 

each country is then converted into total potential solar energy available per year as a function of land 

area per solar class, conversion efficiency (10%), and number of days per year (365).

7.4 Hydro potential and generation profile

Hydropower potential and installed cost are based on an article published in Gernaat et al. (2017)2 that 

only evaluated data for river power plants (or conventional hydropower). Currently, countries with 

specific cost and potential include 

• Angola

• Argentina

• Australia

• Bolivia

• Brazil

• Cameroon

• Canada

• Central African Republic

• Chile

• China

• Colombia

• Congo (Brazzaville)

• Democratic Republic of Congo

• Egypt

• Ethiopia

• France

• Gabon

• India

• Indonesia

• Italy

• Japan

• Madagascar

• Malaysia

• Mexico

• Mozambique

• Myanmar

• Nepal

• New Zealand

• Pakistan

• Papua New Guinea

• Peru

 2 Gernaat, D. E. H. J., Bogaart, P. W., Van Vuuren, D. P., Biemans, H., and Niessink, R. “High-resolution assessment of global 

technical and economic hydropower potential,” Nature Energy, Vol 2 (October 2017), p. 821-828.
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• Russia

• Sudan

• Tanzania

• Turkey

• Uganda

• United States

• Venezuela

• Vietnam

• Zambia

Countries with no specific installed cost information use regional costs, which are based on data from 

the International Renewable Energy Agency (IRENA, Renewable Power Generation Costs in 2017) and 

Oak Ridge National Laboratory (ORNL).

The annual availability factor for hydropower generation for each country is an average capacity factor, 

calculated from historical (2000 to 2015) capacity and generation data from EIA International Energy 

Statistics. Monthly capacity factor is based on historical hydropower generation for 

• OECD countries

• Argentina

• Brazil

• China

• Colombia

• India

• Russia

• Vietnam

For other countries with no historical hydro generation, monthly capacity factor is based loosely on 

monthly share of precipitation. 

7.5 Inter-regional transmission capacity

Inter-country transmission capacity data is derived from ENTSO-E data 

(https://www.entsoe.eu/data/data-portal/exchange/Pages/default.aspx) for European countries. For 

other major electricity trading countries, historical trades are derived from the UN Comtrade database 

(https://comtrade.un.org/data/) and converted into an implied capacity.

7.6 Historical generation and consumption

We used the International Energy Agency’s historical data on generation and fuel consumption by 

country, fuel, and major unit type and electricity consumption by sector for 

• Calibration

• Derivation of sector load shapes

• Projecting country-level load to set renewable bounds