Generation Expansion Planning

GEP · IRP · MIP

Multi-decade · Capacity Investment · Technology Mix

Which new generators should a utility, system operator, or sovereign build over the next ten, twenty, or forty years? How much of each technology — coal, gas, wind, solar, nuclear, hydrogen, storage? Where, exactly, and in which year? Generation Expansion Planning (GEP) answers these questions as a mixed-integer program that couples multi-billion-dollar investment decisions with an operational dispatch subproblem. Decisions made today lock in capital stock that lasts 30–60 years; getting GEP wrong is one of the most expensive mistakes a utility can make.

The problem

Capital stock decisions that last decades

A 600-MW combined-cycle gas plant costs roughly $500–$800 million and lasts 30 to 40 years. A gigawatt of onshore wind or utility-scale solar costs $1–$1.5 billion and lasts 25 years. A nuclear reactor runs north of $10 billion and operates for 60–80 years. GEP decides how many of each to build, where, and when, to meet demand that itself grows and evolves over the planning horizon. Unlike day-ahead unit commitment, the wrong answer cannot be corrected tomorrow — it is locked in by concrete and steel for a generation.

The mathematical structure is a two-level decision problem. The upper level chooses investment binaries $x_{g,y} \in \{0, 1\}$ (build generator $g$ in year $y$?) and continuous capacity variables $K_{g,y} \ge 0$ (how many MW?). The lower level, for each year and for representative operating periods (clusters of typical hours), dispatches the installed capacity to meet demand at minimum operational cost. Investment decisions constrain operations; operations inform the value of investment through dual variables. The resulting problem is a large-scale MIP with investment binaries, capacity variables, operational dispatch variables, and coupling constraints between them.

Historical note

Early GEP used screening curves — an analytical technique due to Masters (1957) and Turvey (1963) that plotted fixed cost vs annual utilization for each technology and picked intersections. Anderson (1972) formalized the first linear-programming GEP formulation at the World Bank. The modern multi-period MIP with representative hours was canonicalized in the MARKAL/TIMES family of models (IEA-ETSAP, 1976 onwards), the MESSAGE model at IIASA, and OSeMOSYS (open-source, 2011). Conejo, Baringo, Kazempour & Siddiqui (2016) is the contemporary textbook reference; Koltsaklis & Dagoumas (2018) is the authoritative review.

Modern GEP under deep uncertainty is a stochastic or robust MIP. Uncertain fuel prices, demand growth, technology learning rates, and policy paths motivate scenario-based two-stage formulations (investment first-stage, operations second-stage) or adaptive robust formulations (investment now, redispatch against worst-case realizations). The choice shapes both computational difficulty and the risk-preference of the recommended investment plan.

Mathematical formulation

Two-level investment-operations MIP

Notation

Sets, parameters, decision variables
Symbol	Meaning	Units
$\mathcal{Y}$	Planning years $\{1, \dots, Y\}$	—
$\mathcal{T}$	Representative operating periods per year	—
$\mathcal{G}$	Candidate generation technologies	—
$I_g$	Overnight capital cost of tech $g$	$/MW
$FOM_g$	Fixed O&M cost	$/MW-yr
$VOM_g$	Variable O&M (fuel + non-fuel)	$/MWh
$CF_g$	Capacity factor or availability	pu
$D_{y,t}$	Load in year $y$, period $t$	MW
$\tau_t$	Duration of representative period $t$	h
$r$	Discount rate	pu
$x_{g,y}$	Build decision (binary)	{0,1}
$K_{g,y}$	New capacity of tech $g$ in year $y$	MW
$K_{g,y}^{\mathrm{tot}}$	Cumulative installed capacity	MW
$p_{g,y,t}$	Dispatch output	MW

Objective · discounted total cost

Minimize net-present value of investment, fixed O&M, and variable operations:

\min \; \sum_{y \in \mathcal{Y}} \frac{1}{(1+r)^{y-1}} \left[ \sum_{g} I_g K_{g,y} + \sum_{g} FOM_g \, K_{g,y}^{\mathrm{tot}} + \sum_{g,t} \tau_t \cdot VOM_g \, p_{g,y,t} \right] \qquad \text{(1)}

The three terms are the upfront capital investment, annual fixed O&M proportional to installed capacity, and per-MWh variable costs over the operational dispatch. All discounted back to year one by $(1+r)^{y-1}$. Salvage-value terms are sometimes added at the horizon end.

Constraints

Capacity accumulation: new builds add to cumulative installed:

K_{g,y}^{\mathrm{tot}} \;=\; K_{g,y-1}^{\mathrm{tot}} + K_{g,y} - R_{g,y} \qquad \forall g, y \qquad \text{(2)}

where $R_{g,y}$ is retirement (end-of-life) capacity. Build logic: capacity only added if binary is on:

K_{g,y} \;\le\; K_g^{\max} \cdot x_{g,y} \qquad \forall g, y \qquad \text{(3)}

Demand balance in every year and representative period:

\sum_{g \in \mathcal{G}} p_{g,y,t} \;=\; D_{y,t} \qquad \forall y, t \qquad \text{(4)}

Operational capacity limit: dispatch bounded by available capacity times availability:

p_{g,y,t} \;\le\; CF_g \cdot K_{g,y}^{\mathrm{tot}} \qquad \forall g, y, t \qquad \text{(5)}

Reserve / reliability: total firm capacity must exceed peak load + margin:

\sum_{g} \phi_g \, K_{g,y}^{\mathrm{tot}} \;\ge\; (1 + m) \, D_y^{\mathrm{peak}} \qquad \forall y \qquad \text{(6)}

where $\phi_g$ is the firm-capacity contribution (ELCC) of tech $g$ and $m$ is the planning reserve margin. Optional emissions cap:

\sum_{g, t} \tau_t \cdot \epsilon_g \, p_{g,y,t} \;\le\; E_y^{\max} \qquad \forall y \qquad \text{(7)}

Complexity & solution methods

GEP is NP-hard (inherits from integer investment binaries). Real instances have 10–30 year horizons, 50–200 representative periods per year, and 20–100 candidate technologies, producing MIPs with 10$^4$ to 10$^5$ binaries and 10$^6$ continuous variables.

Industrial solution methods include:

Direct MIP: Gurobi / CPLEX branch-and-cut on the full problem. Feasible up to a few thousand binaries.
Benders decomposition: Master problem (investment binaries) with a subproblem per year/scenario (operational LP). Cuts propagate dual information from operations back to investment.
Nested Benders / SDDP: For multi-stage stochastic variants with interstage dependent uncertainty.
Progressive hedging: For scenario-based stochastic GEP with non-anticipativity constraints.

Industry-standard GEP solvers include PLEXOS, Aurora, PROMOD, and open-source GenX, Switch, PyPSA, TIMES, OSeMOSYS.

Real-world data

Cost curves · learning rates · planning benchmarks

NREL Annual Technology Baseline (ATB)

The NREL Annual Technology Baseline publishes current-year and projected overnight capital cost, fixed O&M, variable O&M, and capacity-factor trajectories for every major electric-power technology through 2050. The most-cited open source of GEP cost inputs in US research.

IEA World Energy Outlook scenarios

IEA WEO 2023 and similar publications provide demand growth, fuel price, and technology learning rate scenarios under alternative climate-policy pathways (Stated Policies, Announced Pledges, Net Zero). These are the standard boundary conditions for global GEP exercises.

Open-source GEP models

GenX (MIT), Switch (Infrastructure Policy Institute), PyPSA (TU Berlin), TIMES (IEA-ETSAP), OSeMOSYS (KTH) are open GEP / energy-systems frameworks. Most accept NREL ATB / IEA inputs directly and run the full GEP MIP.

Illustrative 5-technology case (this page)

The interactive solver below covers five technologies (coal, gas-CC, wind, solar, battery) over a 10-year horizon in 2-year steps. Capital costs, fixed O&M, variable O&M, and capacity factors are illustrative of 2024 US wholesale markets; replace with NREL ATB numbers for real analysis.

Interactive solver

10-year GEP with capacity-mix evolution

Scenario parameters

Year-1 peak demand (MW)

1500

Annual demand growth (%)

Gas fuel price ($/MMBtu)

Carbon price ($/tCO2)

Renewable standard (% min)

20%

Discount rate (%)

Adjust parameters and press Plan.

Capacity mix evolution

Installed capacity by technology (MW) over 10-year horizon · white line = peak demand + reserve margin

New investment by year (MW added, stacked by technology)

Solution interpretation

What the capacity-mix chart tells you

The capacity-mix evolution chart is the iconic GEP deliverable. The x-axis is time, the y-axis is installed MW, and each color band is one technology. Reading it top-to-bottom at any year gives the full fleet composition; reading left-to-right along any band shows that technology's trajectory. A good plan fills the chart below the demand+reserve line without gross over-build; a bad one either leaves the line exposed (insufficient capacity) or stacks redundant build (wasted capital).

The chart reveals the economics behind the decisions: cheap, dispatchable baseload (coal, gas combined-cycle) fills the base when fuel prices are low; as gas or carbon prices rise, the mix tilts toward renewables and storage; when a renewable-portfolio standard is binding, wind and solar are forced in regardless of their unsubsidized economics. Retirement of end-of-life thermal units shows as a shrinking band mid-horizon, typically backfilled by the cheapest replacement the solver can find given the constraints.

The duals of the demand-balance and reserve-margin constraints give time-varying shadow prices on energy and capacity. These are direct analogs of LMPs (from OPF) extended to a planning horizon — and they tell capacity-market designers what the equilibrium capacity price should be.

The investment-schedule canvas shows which years see the biggest new builds. Concentrated investment in one year is usually a signal of a discrete step-change in demand, retirement, or policy; smooth investment is the sign of well-calibrated growth parameters. Real planners study both: the mix chart for the portfolio view, the investment schedule for cash-flow planning.

Extensions & variants

From deterministic GEP to stochastic, bilevel, integrated

Stochastic GEP (scenario-based)

Uncertain fuel prices, demand growth, technology costs, and policy expand into a scenario tree. First-stage (today's) investments are scenario-independent; future investments adapt. Solved via extensive-form LP, Benders, or progressive hedging.

Refs: Wang & Liu (2011); Park & Baldick (2015); Conejo et al. (2016), ch. 5.

Adaptive Robust GEP

Investments optimize against the worst-case realization inside an uncertainty set; operations adapt after uncertainty resolves. Less sensitive to scenario-distribution assumptions than stochastic GEP.

Refs: Dehghan et al. (2014); Baringo & Conejo (2013).

Integrated GEP + TEP

Joint optimization of generation and transmission investments. Generation and transmission are substitutes: a new line may replace the need for a local generator, or vice versa. Couples GEP constraints (1)–(6) with TEP's line-building binaries.

Refs: Hemmati, Saboori & Dehghanian (2013); Aghaei et al. (2014).

Bi-level GEP (producer equilibrium)

When one firm plans investment anticipating market-clearing prices, the problem is a Mathematical Program with Equilibrium Constraints (MPEC). The firm's investment is upper-level; market clearing is lower-level. Used to study strategic investment, market power, and capacity auctions.

Refs: Wogrin, Centeno & Barquín (2011); Kazempour & Conejo (2012).

Low-carbon / Net-zero GEP

Increasingly the dominant variant: GEP with hard emissions constraints or net-zero trajectories. Requires modeling hydrogen production, long-duration storage, carbon capture, nuclear, and policy constraints like the US Inflation Reduction Act.

Refs: Sepulveda et al. (2018); Jenkins, Luke & Thernstrom (2018); Jenkins et al. Net-Zero America (2021).

Integrated Resource Planning (IRP)

The regulatory-practice form of GEP: a utility's multi-year plan filed with a state public utility commission showing how it will meet demand at least cost subject to reliability and environmental standards. Uses the same underlying MIP plus public-interest criteria.

Refs: Wilson & Biewald (2013); US-specific PUC filings.

Key references

Cited above · DOIs and permanent URLs

[1]

Conejo, A. J., Baringo, L., Kazempour, S. J., & Siddiqui, A. S. (2016).

Investment in Electricity Generation and Transmission: Decision Making under Uncertainty.

Springer. doi:10.1007/978-3-319-29501-5

[2]

Koltsaklis, N. E., & Dagoumas, A. S. (2018).

“State-of-the-art generation expansion planning: A review.”

Applied Energy, 230, 563–589. doi:10.1016/j.apenergy.2018.08.087

[3]

Anderson, D. (1972).

“Models for determining least-cost investments in electricity supply.”

The Bell Journal of Economics and Management Science, 3(1), 267–299. doi:10.2307/3003078

[4]

Pfenninger, S., Hawkes, A., & Keirstead, J. (2014).

“Energy systems modeling for twenty-first century energy challenges.”

Renewable and Sustainable Energy Reviews, 33, 74–86. doi:10.1016/j.rser.2014.02.003

[5]

Kazempour, S. J., & Conejo, A. J. (2012).

“Strategic generation investment under uncertainty via Benders decomposition.”

IEEE Transactions on Power Systems, 27(1), 424–432. doi:10.1109/TPWRS.2011.2159251

[6]

Park, H., & Baldick, R. (2015).

“Stochastic generation capacity expansion planning reducing greenhouse gas emissions.”

IEEE Transactions on Power Systems, 30(2), 1026–1034. doi:10.1109/TPWRS.2014.2331279

[7]

Sepulveda, N. A., Jenkins, J. D., De Sisternes, F. J., & Lester, R. K. (2018).

“The role of firm low-carbon electricity resources in deep decarbonization of power generation.”

Joule, 2(11), 2403–2420. doi:10.1016/j.joule.2018.08.006

[8]

Howells, M., Rogner, H., Strachan, N., et al. (2011).

“OSeMOSYS: The Open Source Energy Modeling System.”

Energy Policy, 39(10), 5850–5870. doi:10.1016/j.enpol.2011.06.033

[9]

DeCarolis, J., Daly, H., Dodds, P., et al. (2017).

“Formalizing best practice for energy system optimization modelling.”

Applied Energy, 194, 184–198. doi:10.1016/j.apenergy.2017.03.001

[10]

NREL. (2024).

“Annual Technology Baseline (ATB).”

National Renewable Energy Laboratory. atb.nrel.gov

The in-browser solver uses a simplified 5-technology 10-year model with linear capacity variables (LP relaxation of the GEP MIP). Production GEP tools (GenX, Switch, PyPSA, TIMES, OSeMOSYS, PLEXOS) handle full binary decisions, hundreds of technologies, and decades-long horizons.