AI for AI: Optimizing Additional Infrastructure Build-out to Power Artificial Intelligence Data Centers

Alexander Crosier; Kyle Onghai; Ronnie Sircar

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AI for AI: Optimizing Additional Infrastructure Build-out to Power Artificial Intelligence Data Centers

Alexander Crosier, Kyle Onghai, Ronnie Sircar

arXiv:2609.08166v1Sep 8, 2026q-fin.GNcs.AIecon.GN

TL;DR

Rapid data-center load growth is putting pressure on an electricity grid whose supply response is slow, uncertain, and potentially weakened by investment-induced revenue cannibalization. The paper combines deterministic, stochastic, and stochastic-control models to study prices, capacity, and technology investment. It finds that prices can rise substantially despite optimal investment as capacity accumulates and reduces incentives for further entry.

Problem
Rapidly growing data-center electricity demand may outpace generation and grid expansion, creating higher and uncertain market-clearing prices.
Method
The paper models deterministic growth, stochastic arrivals of data-center load and generation capacity, and dynamic technology investment by a revenue-maximizing capacity developer.
Results
Prices rise from $30/MWh to roughly $46–49/MWh over six years despite optimal investment, while investment intensity falls as accumulated capacity lowers portfolio revenues.
Takeaways & Limitations
Uncertain demand, delayed build-outs, and value cannibalization can weaken supply investment incentives even when rapid data-center growth increases the need for generation.
Takeaways & Limitations
The framework would be extended by modeling endogenous data-center connection choices, project initiation and cancellation risk, uncertain time-to-build, and retail-rate effects.

Abstract

from arXiv · show

The twenty-first century's transformative technology, artificial intelligence, is increasingly constrained by the twentieth century's transformative technology, the electricity grid. Rapid growth in electricity demand from data centers is leading to higher electricity prices, without a compensating supply-side response. We develop a framework linking data-center load growth, available generation capacity, and market-clearing prices to understand this phenomenon. We first analyze a deterministic model to show how differing estimates of demand and supply growth rates affect prices. We then model the expansion of new data centers and their associated electricity demand, together with build-outs of new electricity supply, as stochastic processes,resulting in probabilistic distributions of supply, demand, and prices rather than a single forecast. Finally, we formulate generation expansion as a stochastic control problem in which a revenue-maximizing investor dynamically chooses the intensity of supply-side investments. The analysis highlights a central challenge of the data-center build-out: even when rapid demand growth increases the need for new generation, the uncertainties related to load forecasts, development execution risks, and value cannibalization from overbuilding capacity may weaken incentives to invest at the pace required to keep electricity prices stable.

1 Introduction

Rapid data-center growth is increasing electricity demand faster than grid infrastructure can expand, creating uncertainty about future prices and supply adequacy. The paper develops deterministic, stochastic, and investment models to connect load growth, generation capacity, and market-clearing prices.

Data-center electricity demand rose from 76 TWh in 2018 to more than 200 TWh in 2025, increasing its share of U.S. demand from 1.9% to 4.8%.
Forecasts vary widely, while grid operators and utilities expect data centers to increase peak demand by 20% to 40% or more over the next decade.ERCOT forecast 33 GW of new data-center and cryptocurrency-mining demand by 2031, equal to a 36% increase over its 91 GW system peak.
Data-center expansion is straining a grid whose infrastructure develops more slowly, with interconnection, transmission, supply-chain, permitting, and community constraints limiting new generation.New gas turbines may require five to seven years, while renewable projects can face multiyear delays.
Higher wholesale energy and capacity prices can raise costs for households and businesses that are not directly responsible for new data-center load.Capacity costs are only one component of retail bills, alongside energy, transmission, and distribution costs.
High prices may not induce timely or sufficient entry because generation projects are costly, slow, uncertain, and irreversible, while new capacity lowers revenues across the investor’s existing portfolio.This value cannibalization can cause optimal investment to stop even as aggregate electricity demand continues to grow.
The paper links load growth, available supply, and market-clearing prices through deterministic and stochastic models, then endogenizes investment intensity and technology choice under uncertainty.The investment framework considers natural gas, solar, wind, and nuclear technologies whose attractiveness depends on capital costs and expected build-out time.

2 Electricity Demand, Supply, and Price Formation

The paper models electricity demand, generation supply, and market-clearing prices, distinguishing traditional consumers from hyperscalers and examining deterministic and stochastic capacity growth. It shows that data-center growth raises prices under fixed or slow-growing supply, while rapid supply expansion can instead depress prices through revenue cannibalization.

2 Electricity Demand, Supply, and Price Formation: The model distinguishes traditional demand from faster-growing, less predictable hyperscaler demand and represents both through reference demand and price-response functions.Traditional and data-center demand are tracked separately, with price-responsive demand determined by elasticity functions.
2 Electricity Demand, Supply, and Price Formation: The ERCOT simulation uses P0 = $30/MWh, I0 = 55 GW, and X0 = 8 GW as initial reference price and demands.The parameters are chosen to approximate ERCOT’s average wholesale price and Texas demand conditions.
2.1 Market Clearing: Market-clearing price decreases with supply and increases with both traditional and data-center demand, with uniqueness established under decreasing demand-response functions.The implicit-function results give ∂sp∗ < 0, ∂xp∗ > 0, and ∂ip∗ > 0.
2.3.1 No New Build-out: With no supply growth, linear data-center demand growth raises prices substantially and crowds out traditional demand, but traditional demand does not reach zero for over 22 years.Under the stated simulation, prices would double from $30/MWh to $60/MWh over 10 years without additional infrastructure.
2.3.2 Linear Supply Growth: When supply grows linearly, slow additions allow demand growth to raise prices, whereas sufficiently rapid additions reduce prices through cannibalization.The comparison considers supply growth rates represented by cS in GW/year.
2.4.1 Poisson and Compound Poisson Processes: The stochastic model replaces smooth capacity and load growth with uncertain jump arrivals while preserving their underlying average growth rates.Generation technologies are represented through arrival intensities and capacity increments, with λjδj giving expected annual capacity contribution.
2.4.4 Simulations: The stochastic simulations produce a mean terminal price of $33.43/MWh with a standard deviation of $5.87/MWh.The simulations emphasize that prices may fall below the baseline P0 as well as rise above it.
2.4.4 Simulations: Data centers account for a mean 27.6% of price-responsive demand at the terminal date across the full Monte Carlo sample.This share remains significant after accounting for electricity-price responses.

3 Optimal Supply-Side Investment

The paper models generation expansion as a controlled-intensity investment problem under uncertain data-center demand and stochastic project completion. Results show that scarcity can attract investment, but additional capacity can depress prices and weaken incentives to build, with technology choices shaped by project size, costs, and timing.

Investment framework: The framework lets a revenue-maximizing owner choose supply-addition intensity while data-center load growth and project completion remain uncertain.Capacity expansion is endogenous, and completion delays can reflect supply-chain or permitting risks.
Investment framework: Investment intensity is increasing and convexly costly, so greater development effort raises costs at an increasing marginal rate.The cost function is increasing, convex, and satisfies C(0) = 0.
Single-technology results: Investment concentrates in states with low available supply and sufficiently high reference data-center demand, where scarcity preserves the value of additional capacity.The value function rises with demand but eventually falls as available supply increases.
Single-technology results: Demand arrivals raise market-clearing prices, while completed capacity lowers scarcity and prices, leaving terminal prices dispersed because both timings remain stochastic.The Monte Carlo results show that optimal investment does not eliminate price uncertainty.
Single-technology results: Revenue cannibalization can reduce investment intensity despite growing demand because new capacity lowers prices earned on the owner’s existing portfolio.In sufficiently well-supplied states, the incremental value of further capacity can become nonpositive.
Multiple-technology results: Across technologies, low-supply states prioritize large-capacity projects, while later investment reflects technology-specific project sizes, costs, and the remaining time horizon.A higher completion intensity does not necessarily imply a higher capacity-addition rate because completed projects differ in size.

4 Conclusion

The framework links data-center load growth, generation capacity, and market-clearing prices, showing that uncertain demand and capacity arrivals create broad outcomes. Endogenous investment can weaken as capacity accumulates because completed projects reduce portfolio-wide prices.

Absent a supply response, ERCOT-paced data-center demand roughly doubles average wholesale prices within a decade.
Discrete, uncertain arrivals of load and capacity turn point forecasts into wide distributions of supply, demand, and prices.
Each completed project lowers the price earned on the investor’s entire portfolio, causing optimal investment intensity to fall toward zero as capacity accumulates.
Historical evidence of load growth lowering residential prices may not generalize because it reflects modest growth and underused capacity rather than tight wholesale markets.
The paper identifies endogenous investment incentives as an additional reason supply response may lag even when physical constraints do not bind.
Future extensions include endogenous data-center connection choices, construction-pipeline and cancellation risks, and a retail-rate layer.

A Formulas & Figures for Section 2.3.1

The appendix derives how market-clearing prices and demand evolve when data-center demand and supply change over time. With fixed supply, traditional demand exits in finite time, while expanding supply can prevent that outcome.

When reference data-center demand grows with fixed supply, traditional demand reaches its effective choke price A1 in finite time.After that point, market clearing is determined entirely by price-responsive data-center demand.
The price approaches the hyperscaler choke price A2 only asymptotically, remaining below A2 at every finite time.
Figure 9 illustrates price growth under fixed supply as reference data-center demand increases.
Figure 10 contrasts rising reference demand with price-responsive demand, which declines for traditional consumers but increases for data centers until absorbing fixed supply.
With supply growth, the threshold is cX/k ≈ 2.67 GW/year when cX = 6 GW/year; all positive rates considered prevent traditional demand from reaching zero.

B Technical Foundations for the Controlled-intensity Model

The technical foundation specifies the state variables used by the controlled-intensity model: available supply, data-center demand, and deterministic traditional demand.

The dynamic-programming formulation uses available supply S, reference data-center demand X, and deterministic traditional demand It = I0e^γt as its state variables.
The appendix develops the controlled-intensity model using a point-process control framework specialized to these paper-specific states.
The model’s time horizon and state structure support dynamic optimization of generation investment under uncertainty.

B.1 Controlled-intensity Setup

The controlled-intensity setup represents supply additions as a stochastic process whose arrival intensity is chosen by the investor. It defines admissible controls, state dynamics, revenue net of investment cost, and the value function for dynamic programming.

An independent Poisson process with intensity μ models exogenous data-center arrivals, while the investor controls supply arrivals through a nonnegative predictable intensity λt.
The state vector Yt = (St, Xt) tracks available supply and data-center demand, with traditional demand represented by the deterministic path It = I0e^γt.
The market-clearing price is written as P(t, y), with deterministic traditional demand absorbed into the explicit time argument.
Admissible controls are predictable, nonnegative, stable under concatenation at stopping times, and may be represented as Markov feedback controls.
The running payoff is producer revenue sP(t, y) minus investment cost C(λ), and it may be negative when costs exceed contemporaneous revenue.
The dynamic-programming principle follows by decomposing payoff at a stopping time and concatenating an admissible control with an ε-optimal continuation.

B.3 Martingale Principle

The Bellman process is a supermartingale for every admissible control and becomes a martingale under an optimal control.

For any admissible control λ, the Bellman process M λ is a supermartingale.
Under an optimal control, the dynamic programming inequality is attained as equality, making M λ a martingale.The proof applies the DPP at a stopping time and incorporates accumulated and discounted continuation payoffs.

B.4 HJB equation

The HJB equation is derived from the dynamic programming principle by applying a short-interval argument to the controlled state generator, with a zero terminal condition.

The derivation assumes sufficient smoothness of the value function and continuity of the payoff rate in the state variables.
Forward differences describe changes in the test function from supply and demand state jumps.
The controlled generator acts only on state variables, so the time derivative is excluded from Aλ.
Applying the DPP over [t, t + h] yields the single-technology HJB, combining investment, state-transition, payoff, discount, and continuation terms.
The HJB has terminal condition v(T, s, x) = 0.

B.5 Verification Theorem

The verification result shows that a suitable HJB supersolution bounds the value function, and equals it when a measurable maximizing feedback control is admissible and attains the required equality.

The verification argument requires polynomial growth and sufficient integrability to justify Dynkin’s formula and passage to the terminal time.
If w(t, y) ≥ v(t, y), then w provides an upper bound on the value function.
A measurable selector ˆλ attaining the supremum, together with an admissible feedback control, is sufficient for verification when the stated equality condition holds.
Dynkin’s formula applied to the discounted state process establishes w(t, y) ≥ J(t, y; λ) for every admissible control.
Under the maximizing selector, the inequalities become equalities, proving w = v and establishing optimality of ˆλ.

B.6 Multi-technology Extension

The multi-technology extension uses independent controlled point processes for each supply technology and preserves the value-function, DPP, and martingale framework in higher dimensions.

Independent Poisson random measures and thinning construct controlled-intensity processes for each of d supply technologies.
Aggregate supply is formed by superposition, while aggregate supply and reference demand remain the state variables.
The expected remaining payoff, value function, DPP, and martingale principle extend to the higher-dimensional setting.
For λ = (λ1, . . . , λd), technology-specific supply jumps define the multivariate state generator and lead to the multi-technology HJB.
The verification theorem is stated to be a natural multivariate extension of the single-technology result.

C Numerical Implementation Details

The numerical implementation discretizes the supply-demand state space and solves the resulting first-order system backward in time using a semi-implicit Euler scheme. Sparse matrix structure, boundary handling, and precomputed jump matrices make the computation efficient and numerically stable.

State-space discretization: The solver operates on a tensor-product discrete state space combining supply and demand grid points.The grids use either δ_i or ηi for supply increments and κ_j for demand increments, depending on the solver formulation.
Time integration: A semi-implicit Euler method discretizes the first-order ODE system and updates the value function at each iteration.At iteration n, the control λ∗,(n) is computed with the value fixed before solving for the next value vector.
Time integration: The solver works backward in time because the terminal condition is V(T, ·) = 0.The updated V (n+1) approximates the value at the earlier time τn −∆t.
Linear-system solution: Vectorizing the discretized equations yields the linear system (I −∆tM λ∗,(n))V (n+1) = V (n) + ∆t [SP(t, S, X) −C(λ∗,(n))].The vectors are formed by stacking the state-space entries, with S and X filled along columns and rows respectively.
Linear-system solution: Boundary conditions use zero forward differences without wrap-around, while the resulting sparse matrix enables efficient solution of each update.Off-diagonal transitions and matching diagonal rates are omitted at the upper demand and supply boundaries.
Multi-technology extension: The multi-technology implementation uses a coarseness parameter η, technology-specific jump sizes wℓ = δℓ/η, and precomputed sparse jump matrices.Interpolation on the supply grid is used computationally to avoid floating-point arithmetic errors when computing wℓ.