The Generation Expansion Problem asks how an electricity system should evolve over time. Its purpose is not merely to operate an existing fleet efficiently, but to determine what new generating assets should be added so that future electricity demand can be met at minimum total cost.

A good way to contrast it with Economic Dispatch is this:

So the problem combines two levels of decision-making:

1. Investment decisions — which technologies to build and when,
2. Operational decisions — how those technologies are used after they are installed.

That is why Generation Expansion is one of the central models in long-term power-system planning, energy policy analysis, and adequacy studies. It links engineering constraints, technology costs, reliability requirements, and public policy in a single optimization framework.

In Economic Dispatch, installed capacity is taken as fixed. The system operator only decides generation levels.

In Generation Expansion, installed capacity itself becomes a decision variable. The planner is not only deciding how many megawatts to generate, but also how many megawatts of each technology should be built and carried forward into future years.

This changes the structure of the problem in three deep ways.

That is why the Generation Expansion Problem is often described as a multi-period investment-and-operation optimization model.

Imagine a system planner looking 15 years ahead.

Demand is expected to grow. Some old plants may retire. Fuel prices may change. Emissions policy may tighten. Wind and solar may become cheaper. Storage may become more valuable.

The planner must decide whether to rely more on:

• firm thermal plants,
• variable renewables,
• storage,
• low-carbon firm technologies,
• or some mix of all of them.

We begin by defining the sets used in the model.

Let \( g \in G \) denote a generation technology or candidate plant type.

Typical examples of \(g\) are: nuclear, combined-cycle gas turbine (CCGT), open-cycle gas turbine (OCGT), solar PV, wind, hydro, battery storage, coal.

Let \( t \in T \) denote the planning periods, usually years.

For example, \(t = 1,2,\dots,T\), or calendar years such as 2027, 2028, …, 2040.

Let \( h \in H \) denote representative operational periods inside each year.

These might be: representative hours, load blocks, seasons, day/night segments, peak and off-peak periods.

This extra index matters because installed capacity is only useful if it can produce at the moments when the system needs it.

Parameters are known inputs. The model does not choose them.

The model chooses the following variables.

A standard least-cost Generation Expansion model minimizes the present value of total system cost:

where \(\text{VOLL}\) is the value of lost load.

Interpretation of each term:

This objective function formalizes the basic planning trade-off: pay now in capital cost, or pay later in operating cost or unreliability.

8.1 Capacity accumulation

A common lifetime-based formulation is:

This means that installed capacity in year \(t\) consists of:

• the remaining existing fleet,
• plus still-active past investments.

This is one of the defining equations of expansion planning, because it connects current investment decisions with future system capability.

8.2 Demand balance

This ensures that demand is met in every time slice, either through generation or, if allowed, through penalized unserved energy.

8.3 Generation limited by available capacity

This says that generation cannot exceed available installed capacity. This is the key bridge between the investment layer and the operating layer.

8.4 Adequacy or reserve requirement

This ensures enough firm capacity is available to satisfy peak load plus reserve.

8.5 Non-negativity

The model compares two types of technologies.

This is the structural logic behind why power systems contain different types of resources.

For technologies used many hours per year, low variable cost matters a lot. For technologies used only rarely, low capital cost matters more.

That basic idea is what later appears graphically in screening curves.

A technology is valuable not only because it exists, but because of how it can be used.

• A gas peaker may produce little annual energy yet have high adequacy value.
• Solar may produce a lot of annual energy but little during evening peaks.
• Wind may lower fuel consumption but not fully replace firm capacity.
• Storage may not generate net energy at all, yet still be valuable because it shifts energy across time.

So the planner cannot choose the best investment mix without also representing operation.

That is why \(P_{g,t,h}\) is essential.

For intuition, consider a simplified one-year version of the model. Associate \(\lambda_h\) with the demand balance constraint, and \(\mu_{g,h}\) with the generation-capacity constraint.

Then the Lagrangian is:

The multiplier \(\lambda_h\) measures the marginal system value of serving one more unit of demand in time slice \(h\). The multipliers \(\mu_{g,h}\) measure the marginal value of relaxing the capacity limit of technology \(g\) in that slice.

Economically, this means that capacity becomes valuable precisely when it helps the system avoid expensive operation or scarcity. That is the reason building an extra MW can be worthwhile.

Suppose a planner is studying a 5-year horizon with annual peak demand growth. The candidate technologies are: utility-scale solar PV, land-based wind, CCGT, OCGT peaker, 4-hour battery storage, advanced nuclear.

Let the system begin with: existing CCGT: 2,000 MW, existing OCGT: 500 MW, existing hydro: 800 MW.

These values deliberately preserve the classic structural differences. The cost and performance logic is informed by current NREL Annual Technology Baseline data and EIA data.

Suppose each year is represented by four slices:

Nuclear: \(a \approx 0.9\). Hydro: limited annual energy and partial peak contribution. Battery: available subject to state-of-charge and charging limits.

Even before solving the model, the structure suggests several things.

If one MW runs for \(H\) hours per year, the simplified annual cost of technology \(g\) is:

Suppose stylized annualized fixed costs are: Solar PV: \(A_{\text{PV}} = 75{,}000\) €/MW-year, Wind: \(A_{\text{W}} = 130{,}000\), CCGT: \(A_{\text{CCGT}} = 110{,}000\), OCGT: \(A_{\text{OCGT}} = 45{,}000\), Nuclear: \(A_{\text{NUC}} = 500{,}000\).

CCGT vs OCGT crossover:

So if a capacity block is expected to be used more than about 1,182 hours per year, CCGT becomes cheaper than OCGT despite higher fixed cost.

Nuclear vs CCGT crossover:

This means nuclear only becomes economically attractive in this stylized setup if it is heavily utilized or if additional policy or adequacy value is recognized.

Suppose peak demand is rising, evening peaks are increasingly important, and gas remains allowed but costly in energy terms.

A plausible optimal result from this stylized setup might be:

• Add solar because it provides low-cost daytime energy,
• Add some batteries because they raise the effective value of solar and help with evening peak,
• Retain or expand some CCGT because firm mid-merit capacity is still needed,
• Add little OCGT except for residual rare adequacy need,
• Add nuclear only if the horizon is long enough, the discount rate is low, or carbon policy strongly rewards firm low-emission capacity.

A Generation Expansion solution is always conditional on assumptions.

If demand, costs, policy, or financing assumptions change, the optimal build mix may change substantially. That is why students should not think of the model as producing "the answer," but rather as producing the least-cost answer under a specific set of assumptions.

The best way to teach this is to vary one parameter at a time and see how the solution shifts.

Suppose base-case peak demand in year 5 is 5,100 MW, but the forecast is revised upward to 5,600 MW.

The adequacy constraint changes from:

If \(\rho_5 = 0.15\), required firm capacity rises from \(1.15 \times 5{,}100 = 5{,}865\) MW to \(1.15 \times 5{,}600 = 6{,}440\) MW. So the system suddenly needs 575 MW more firm capacity.

Covering an additional 575 MW of firm requirement could be done approximately by:

• ~605 MW of new CCGT (\(\phi=0.95\)), or
• ~605 MW of OCGT (\(\phi=0.95\)), or
• ~676 MW of battery (\(\phi=0.85\)), or
• ~3,833 MW of solar alone (\(\phi=0.15\)).

This immediately shows why adequacy problems cannot usually be solved with energy-only thinking.

Suppose solar capex falls from \(I_{\text{PV}} = 700{,}000\) €/MW to \(I_{\text{PV}} = 500{,}000\) €/MW.

The investment term in the objective changes from \(700{,}000 \, x_{\text{PV},t}\) to \(500{,}000 \, x_{\text{PV},t}\). So every MW of solar becomes 200,000 € cheaper to install.

If the model was considering 1,200 MW of solar in year 3, the investment bill falls by:

The model will tend to build more solar, but the increase is usually not unlimited. Why not? Because solar still has:

• zero output at night,
• limited contribution to evening peak,
• possible curtailment if too much is built,
• lower marginal value when penetration rises.

Suppose CCGT variable cost rises from 75 €/MWh to 100 €/MWh, and OCGT rises from 130 €/MWh to 160 €/MWh. This could represent a higher gas price or a higher carbon price.

If annual CCGT generation is 8 TWh, then a cost increase of 25 €/MWh raises total annual operating cost by:

That is often enough to change expansion decisions materially.

The system may respond by:

• adding more wind and solar,
• adding more storage,
• considering nuclear earlier,
• reducing reliance on gas for energy,
• but still retaining some gas for adequacy.

Suppose the model includes:

and the cap is tightened by 30%. Assume in the original solution annual emissions are 6 million tCO₂, but the new cap is 4.2 million.

If CCGT emits approximately 0.35 tCO₂/MWh, then reducing emissions by 1.8 million tCO₂ requires roughly:

of gas generation to be displaced. That is over 5 TWh.

This may require: a few GW of renewables, plus some storage, or some combination of renewables and nuclear, or demand-side flexibility.

Suppose the discount rate rises from 5% to 10%.

The discount factor changes from \(\delta_t = \frac{1}{(1.05)^{t-1}}\) to \(\delta_t = \frac{1}{(1.10)^{t-1}}\). This makes future operating savings less valuable in present-value terms.

Suppose a technology costs 400 million € more upfront but saves 35 million €/year for 20 years. At 5%, that stream is worth much more than at 10%.

So high-discount-rate planning tends to penalize technologies that are: expensive upfront, economical only through long-run savings.

A higher discount rate generally favors:

• OCGT over CCGT at the margin,
• gas over nuclear,
• delayed investment,
• smaller early buildouts of capital-intensive clean technologies.

Suppose solar penetration rises strongly. Then the system has abundant midday energy and scarcer evening energy.

In that case, battery storage may become more valuable even if its standalone economics initially looked weak.

Now suppose excess midday solar would otherwise be curtailed by 1.5 TWh/year. A 500 MW / 2,000 MWh battery fleet may be able to shift part of that energy into evening peak hours, displacing OCGT generation at 130 €/MWh.

If batteries shift 0.6 TWh/year and avoid 130 €/MWh peaker output, the gross avoided variable cost is roughly:

Suppose solar capacity credit falls from 0.25 to 0.10 because system peak moves later into the evening.

Previously, 1,000 MW of solar counted as \(0.25 \times 1{,}000 = 250\) MW of firm contribution. Now it counts as only \(0.10 \times 1{,}000 = 100\) MW.

So the same solar fleet contributes 150 MW less toward adequacy.

The model may still build solar for energy, but it will need more complementary firm or flexible resources, such as: batteries, CCGT, OCGT, hydro, demand response, firm low-carbon capacity.

Suppose utility-scale solar is very cheap, but the planner adds a practical build cap:

Even if the model would like to build 2,000 MW immediately, supply-chain, siting, or interconnection constraints prevent it.

The model may:

• invest earlier,
• rely temporarily on gas,
• build more storage or wind in the interim,
• or accept higher total cost.

If the model must decide not only capacity and generation, but also whether plants are on or off in each hour, introduce binary commitment variables: \(u_{g,t,h} \in \{0,1\}\), and start-up variables \(y_{g,t,h} \in \{0,1\}\) with:

Generation is then limited by commitment status:

and possibly by minimum stable output:

The objective gains startup cost: \(\sum_{t,h,g} SU_g \, y_{g,t,h}\)

This extension is useful when operational flexibility is crucial, but it makes the problem much harder because the model becomes mixed-integer.

If the system has multiple nodes \(n \in N\), then demand and generation must be represented by location. Let \(P_{g,n,t,h}\) be generation of technology \(g\) at node \(n\), and \(f_{\ell,t,h}\) be flow on line \(\ell\).

Nodal balance becomes:

Transmission limits are:

If transmission expansion is also allowed, define line investment variables \(z_{\ell,t} \ge 0\) and let transmission capacity evolve analogously to generation capacity.

This extension matters because a technology may be cheap in one zone but unusable if transmission is congested.

Instead of a hard cap, emissions can enter directly in the objective through a carbon price \(\pi_t^{CO_2}\):

This simply raises the effective variable cost of emitting technologies.

If CCGT emits 0.35 tCO₂/MWh and the carbon price is 80 €/tCO₂, then carbon adds:

to gas generation cost.

This is mathematically simpler than a hard emissions cap and very intuitive economically.

If a minimum renewable share is required:

where \(G^{REN}\) is the set of renewable technologies.

If a clean-energy standard is broader, use \(G^{CLEAN}\) instead, possibly including nuclear and storage-linked clean output.

This extension is useful for modeling policy mandates directly.

A more explicit battery model introduces: charging power \(C_{t,h}\), discharging power \(D_{t,h}^{\text{bat}}\), state of charge \(E_{t,h}\), power capacity \(K^{\text{pow}}_{\text{BAT},t}\), energy capacity \(K^{\text{ene}}_{\text{BAT},t}\).

The system balance becomes:

This makes the intertemporal operational value of storage explicit.

Suppose the planner may retire capacity early. Let \(R_{g,t} \ge 0\) be retired capacity in year \(t\). Then:

Retirement can be bounded by available capacity:

If retirement has a cost or salvage value, add it to the objective.

This extension is useful when old plants become uneconomic under carbon policy or declining utilization.

If uncertainty matters, define scenarios \(s \in S\) with probabilities \(p_s\).

Investment decisions may be here-and-now: \(x_{g,t}\), while dispatch decisions become scenario-dependent: \(P_{g,t,h,s}\).

Then the objective becomes expected discounted cost:

This allows the planner to hedge against uncertainty in demand, fuel prices, renewable availability, or policy.

Suppose some demand can be shifted or curtailed. Let \(DR_{t,h} \ge 0\) be flexible demand reduction.

Then balance becomes:

with bounds:

and possible annual energy-neutrality condition:

if shifting rather than permanent reduction is modeled.

This extension is important because flexible demand can substitute for peaking capacity.

A central teaching device for Generation Expansion is the screening curve.

For each technology, define annual cost for one MW as a function of annual usage hours \(H\):

where \(A_g\) is annualized fixed cost, and \(c_g\) is variable cost. This gives a straight line.

Technologies with:

• low \(A_g\) and high \(c_g\) are attractive for low utilization,
• high \(A_g\) and low \(c_g\) are attractive for high utilization.

That is why:

• OCGT tends to be a peaker,
• CCGT tends to be mid-merit,
• nuclear tends to be baseload,
• renewables complicate the picture because their usable energy depends on availability rather than dispatch freedom.

The screening-curve method is not a full expansion model, but it gives very strong intuition for why optimal portfolios contain multiple technologies.

The Generation Expansion Problem determines the least-cost evolution of the power system by deciding:

• what to build,
• when to build it,
• how to operate it,
• and how to satisfy reliability and policy constraints.

It is the long-run analogue of Economic Dispatch, but richer because it endogenizes the generation fleet itself.

If someone forgets many details but remembers the main logic, these are the key ideas.