Supply Chain-Constrained Generation Expansion Planning

• The paper integrates upstream supply-chain feasibility—including material availability, component production, and lead times—into generation expansion planning to assess cost and reliability risks.
• It employs a multi-stage MILP with intertemporal linking constraints, demonstrating that ignoring upstream limitations understates investment costs and reliability challenges.
• Scenario analyses reveal that constrained supply chains favor fast-deployment technologies (SPV/BSS) and that tighter material sourcing leads to persistent reserve margin shortfalls and load shedding risks.

Supply Chain-Constrained Generation Expansion Planning (SC-GEP) is a generation expansion framework that integrates upstream supply-chain feasibility into long-term capacity expansion decisions. In the formulation introduced in “Integrating Upstream Supply Chains into Generation Expansion Planning,” the planning problem endogenizes critical materials, component production, product assembly, deployment lead times, field availability, and material reuse from retired assets alongside the usual downstream generation and reliability constraints. The resulting model is a multi-stage MILP in which upstream limits can delay the availability of planned resources, shift technology choice toward shorter lead-time and lower-material-intensity options, increase investment cost, and create reserve margin or load-shedding outcomes that do not appear in traditional unconstrained GEP formulations (Yao et al., 5 Aug 2025).

1. Scope and conceptual basis

SC-GEP links upstream supply-chain stages—material availability $u_{my}$, component production $v_{cy}$, product assembly $w_{py}$, deployment lead times $T^{\mathrm{LEAD}}_{g}$, and field availability $f^k_{iy}$—to downstream expansion and operations. Material limits include primary supply $\overline{M}_{my}$, stock $s_{my}$, and recovery from retirements $R^{\mathrm{RM}}_{mg}$. Material-to-component mappings use $D^{\mathrm{CO}}_{mc}$ in tonnes per unit component, while component-to-product mappings use $D^{\mathrm{PR}}_{cp}$ in units per MW of product. Spatial deployment feasibility is represented through capacity density $v_{cy}$0 and area $v_{cy}$1, with available field evolving as assets retire (Yao et al., 5 Aug 2025).

Within this structure, material and production limits cap annual product output, and product output bounds the capacity that can be built. Lead times couple “plan now” to “operate later,” so a time-consistent build schedule must be initiated early enough to satisfy reserve margin and RPS requirements. Field availability constrains siting across regions and is replenished only when assets retire. Retirements also return recoverable material at rate $v_{cy}$2 per MW, so reuse enters the intertemporal material stock dynamics.

The contrast with traditional GEP is explicit. Traditional GEP models typically assume unconstrained supply: they choose capacity additions and assume instant availability with unlimited upstream materials and manufacturing. SC-GEP shows that such assumptions understate both cost and reliability risk. In Maryland, ignoring upstream supply constraints enabled reactive, just-in-time builds with no reliability issues, whereas adding those constraints raised total investment costs in the low-demand scenario from $v_{cy}$323.7 billion and created reserve margin shortfalls in years when retirements coincided with material bottlenecks. Under high demand, ignoring upstream limits masked persistent load shedding from 2037 onward and reserve margin violations driven by silicon, nickel, and cobalt bottlenecks together with binding lead times (Yao et al., 5 Aug 2025).

2. Mathematical structure of the SC-GEP model

The formulation is posed over zones $v_{cy}$4, transmission corridors $v_{cy}$5, technologies $v_{cy}$6, generator types $v_{cy}$7, units $v_{cy}$8, materials $v_{cy}$9, components $w_{py}$0, products $w_{py}$1, years $w_{py}$2, representative days $w_{py}$3, and hours $w_{py}$4. Parameters cover demand $w_{py}$5 and peak load $w_{py}$6, generator and line ratings, renewable availability $w_{py}$7, storage limits and efficiencies, ELCC factors, reserve margin and RPS targets, penalty coefficients, supply-chain intensities, material limits, lead times, lifetimes, fixed retirement years, field areas, capacity densities, and discounted investment and operating costs (Yao et al., 5 Aug 2025).

The model minimizes discounted total system cost:

$w_{py}$8

Here $w_{py}$9 denotes investment cost, $T^{\mathrm{LEAD}}_{g}$0 fixed and variable operating cost, and $T^{\mathrm{LEAD}}_{g}$1 penalty cost associated with load shedding, reserve margin slack, and RPS slack. The operational variables include dispatch $T^{\mathrm{LEAD}}_{g}$2, transmission flows $T^{\mathrm{LEAD}}_{g}$3, load shedding $T^{\mathrm{LEAD}}_{g}$4, storage charging $T^{\mathrm{LEAD}}_{g}$5, discharging $T^{\mathrm{LEAD}}_{g}$6, and state of charge $T^{\mathrm{LEAD}}_{g}$7. Reliability and policy slack are represented by $T^{\mathrm{LEAD}}_{g}$8 and $T^{\mathrm{LEAD}}_{g}$9. Status variables include planned $f^k_{iy}$0, built $f^k_{iy}$1, retired $f^k_{iy}$2, and operational $f^k_{iy}$3, with thermal-unit statuses binary and renewable/storage statuses continuous on $f^k_{iy}$4.

The supply-chain module imposes material-to-component and component-to-product feasibility:

$f^k_{iy}$5

Material balance combines primary supply, recovery from retirements, and stock:

$f^k_{iy}$6

with intertemporal stock dynamics in $f^k_{iy}$7. Product availability then limits build decisions:

$f^k_{iy}$8

Field use and dynamics make siting cumulative and intertemporal. The deployed capacity of technology $f^k_{iy}$9 in zone $\overline{M}_{my}$0 uses field according to:

$\overline{M}_{my}$1

and available field evolves with retirements and prior builds. Lead times and lifetimes connect planning, construction, operation, and retirement:

$\overline{M}_{my}$2

$\overline{M}_{my}$3

Existing units have fixed retirement year $\overline{M}_{my}$4.

The downstream GEP module includes nodal energy balance, output limits for thermal and renewable generators, transmission limits, storage constraints, reserve margin, and RPS compliance. The reserve margin condition is:

$\overline{M}_{my}$5

The RPS condition is technology-specific and uses annual energy generation plus slack $\overline{M}_{my}$6.

The physical meaning of these constraints is central. Material balance and stock dynamics ensure physical feasibility of manufacturing; when $\overline{M}_{my}$7 exceeds $\overline{M}_{my}$8 plus recovery and stock, planned products $\overline{M}_{my}$9 must be reduced, cutting builds $s_{my}$0. Product-capacity linking ties the physical availability of assembled MW-equivalents to the build decision. Field use and status track area depletion and return, making siting a cumulative resource. Lead time and lifetime equations couple plan-build-operate-retire arcs, while reserve margin and RPS constraints translate upstream-constrained capacity and generation into reliability and policy outcomes (Yao et al., 5 Aug 2025).

3. Intertemporal coupling and decomposition

SC-GEP is a multi-stage MILP with cross-year linking constraints and year-local operational constraints. The cross-year links arise from lead times, lifetimes, material stocks, field availability, and build/retire status; the operational layer contains hourly dispatch together with reserve margin and RPS conditions. This induces a block-angular structure that is amenable to nested Benders decomposition (Yao et al., 5 Aug 2025).

In the compact form, the problem is written as

$s_{my}$1

subject to stage-local constraints

$s_{my}$2

and cross-stage constraints

$s_{my}$3

The state variables $s_{my}$4 collect cross-stage quantities such as $s_{my}$5, $s_{my}$6, $s_{my}$7, $s_{my}$8, and $s_{my}$9, while $R^{\mathrm{RM}}_{mg}$0 contains other stage variables, including operations, storage, and logistics.

Year-wise isolation is obtained through duplicated states $R^{\mathrm{RM}}_{mg}$1 and linking constraints of the form

$R^{\mathrm{RM}}_{mg}$2

Subproblems are then solved year by year with a cost-to-go approximation $R^{\mathrm{RM}}_{mg}$3, and the backward pass generates optimality cuts:

$R^{\mathrm{RM}}_{mg}$4

Convergence criteria are standard, namely $R^{\mathrm{RM}}_{mg}$5 or an iteration cap.

The computational emphasis is structural rather than benchmark-oriented. The model description highlights that upstream constraints are inter-year linkages whereas operations are year-local, producing separable subproblems coordinated by a compact set of cross-year cuts. The paper emphasizes the structural benefits and algorithmic fit rather than reporting specific runtimes or iteration counts (Yao et al., 5 Aug 2025).

4. Data requirements and calibration

The SC-GEP implementation requires calibration of material intensities $R^{\mathrm{RM}}_{mg}$6 and $R^{\mathrm{RM}}_{mg}$7, critical material lists, technology-specific lead times, recovery rates, field availability, capacity densities, and system-planning inputs. Material intensities and critical material lists are calibrated from USGS and DOE sources. Lead times use technology-specific values: BSS 1 year, SPV 2 years, LBW 3 years, and OSW 4 years. Reuse yields $R^{\mathrm{RM}}_{mg}$8 reflect conservative recovery of 10% for wind, solar, and storage. Manufacturing and product capacity are implicit in $R^{\mathrm{RM}}_{mg}$9 and are bounded by material and component flows; in the Maryland implementation, manufacturing is aggregated to a single supply node and multi-node logistics flows are not modeled (Yao et al., 5 Aug 2025).

The Maryland case study uses four utility zones—BGE, APS, DPL, and PEPCO—as nodes, with four representative days, one per season, each containing 24 hours. Transmission is modeled as a transportation network, and PJM Window 3 upgrades are assumed online. The planning horizon is 2024–2053. The reserve margin is 15% with ELCC, and RPS penalties are enacted. The penalty parameters are VOLL $D^{\mathrm{CO}}_{mc}$0, RPS penalty $D^{\mathrm{CO}}_{mc}$1, and reserve margin penalty $D^{\mathrm{CO}}_{mc}$2.

The technologies considered for new builds are LBW, OSW, SPV, and BSS, while thermal builds are restricted consistent with Maryland policy. Lifetimes are SPV/LBW/OSW 30 years, BSS 15 years, NUC 60 years, and NGCC approximately 30 years, with existing thermal retirements fixed per data. The supply-chain representation includes 14 critical materials: aluminum, cobalt, dysprosium, gallium, graphite, lithium, manganese, neodymium, nickel, praseodymium, silicon, terbium, tin, and titanium. Maryland’s share of national supply is scaled to approximately 1.6% by GDP and electricity consumption. Field availability is calibrated from land and offshore studies, and capacity densities include SPV 36 MW/km$D^{\mathrm{CO}}_{mc}$3, LBW approximately 3.09 MW/km$D^{\mathrm{CO}}_{mc}$4, OSW approximately 5.2 MW/km$D^{\mathrm{CO}}_{mc}$5, and BSS approximately 900 MW/km$D^{\mathrm{CO}}_{mc}$6 under an equivalent land assumption.

These calibration choices are not merely data inputs; they determine how and when upstream constraints bind. The details imply that SC-GEP is highly sensitive to the joint specification of materials, lead times, siting density, and retirement timing, because each of these parameters governs a different intertemporal bottleneck.

5. Scenario structure and Maryland results

Three scenario families are evaluated. The baseline SC-GEP case imposes realistic constraints on materials, lead times, and field availability under both Low and High demand. The “w/o SC” case relaxes material constraints, removes lead times, and expands land and offshore area. The “lim. SC” case imposes more restrictive material sourcing, domestic/allied only, tightening rare earths and nickel (Yao et al., 5 Aug 2025).

Scenario	Constraint structure	Reported outcome
Baseline (SC-GEP)	Realistic constraints on materials, lead times, and field	Earlier SPV/BSS deployment; reliability stress under retirements
w/o SC	No material constraints, no lead times, expanded land/offshore area	Reactive, just-in-time builds; no reliability issues
lim. SC	Domestic/allied-only sourcing; tighter rare earths and nickel	Wind curtailed after 2045; persistent reserve margin shortfalls

By 2053, the Low baseline reaches 4.1 GW BSS, 1.5 GW LBW, 1.4 GW OSW, and 8.5 GW SPV. The High baseline reaches 7.3 GW BSS, 0.5 GW LBW, 0.4 GW OSW, and 19.5 GW SPV. These trajectories reflect systematic technology substitution under upstream pressure. Early years favor short-lead, low-material-intensity technologies, especially SPV and BSS. Before 2031, silicon and nickel bottlenecks limit battery growth, and SPV mixes c-Si and CdTe to diversify away from silicon saturation. In the Low baseline, as loads ease after 2031, accumulated material stocks allow more LBW and OSW after 2044. In the High baseline, sustained load growth prolongs the priority on fast builds, with SPV dominating and LBW/OSW entering later, after approximately 2047, when SPV alone cannot satisfy adequacy (Yao et al., 5 Aug 2025).

Lead times amplify retirement shocks. Forced retirements in 2025 cannot be replaced instantly, so reserve margin shortfalls arise despite planned builds. Additional retirement waves include Essential Power Rock Springs in 2033, Calvert Cliffs units in 2035 and 2037, and an NGCC cluster in 2047–2048. These events require early planning and sufficient material availability to avoid reliability penalties. This timing effect is central: in the unconstrained case, builds can be timed exactly to retirements, but once upstream supply and delivery are modeled explicitly, the same retirement profile creates temporary or persistent adequacy failures.

Reliability outcomes differ sharply by scenario. In the Low baseline SC-GEP case, load shedding is avoided, but reserve margin shortfalls appear mainly in 2025–2041 because of lead-time and material limits. In the High baseline SC-GEP case, load shedding begins in 2037 and persists, while reserve margin violations recur; around 2048–2049 there is an unresolved 1.8 GW gap caused by approximately 2 GW of NGCC retirements coinciding with binding upstream constraints. In the limited-supply scenario, tighter rare earth and nickel limits halt wind additions after 2045, reserve margin violations persist across the horizon, and batteries shift from nickel-intensive NMC 811 to lower-nickel NMC 111 to conserve scarce nickel (Yao et al., 5 Aug 2025).

Cost effects are also explicit. In the low-demand case, total investment cost rises from $D^{\mathrm{CO}}_{mc}$723.7 billion in SC-GEP, a $1.2 billion increase attributable to lead-time-driven reserve margin penalties and constrained material and product availability that force earlier or alternative investments. The reported interpretation is that integrating upstream constraints materially changes GEP outcomes because it reveals the need to start investments earlier, forces substitutions such as SPV/BSS for LBW/OSW, turns siting into a cumulative constraint with delayed replenishment, and can induce reserve margin violations and load shedding even when nominal capacity additions appear sufficient.

6. Planning implications, limitations, and related research directions

The planning insights reported for SC-GEP concern the conditions under which upstream constraints bind and the levers available to relax them. Binding clusters occur when retirements coincide with tight materials—silicon, nickel, cobalt, and rare earths for wind—and finite lead times. Technologies with long lead times, such as OSW, or with rare-earth intensity, such as LBW and direct-drive OSW, are most affected, while SPV and BSS are preferred under time pressure. The reported policy and regulatory levers include strategic stockpiles and recycling incentives for nickel, silicon, cobalt, and neodymium; streamlined permitting and workforce expansion for field availability; domestic manufacturing incentives that raise effective $D^{\mathrm{CO}}_{mc}$8 limits and cut lead times $D^{\mathrm{CO}}_{mc}$9; reliability oversight requiring SC-aware adequacy checks; and trade or ally-sourcing policies that reduce the severity of the limited-supply case (Yao et al., 5 Aug 2025).

The framework also has stated limitations. SC-GEP is deterministic; robust or stochastic variants could capture demand and supply uncertainty, trade and geopolitical risk, and lead-time variability. Suggested extensions include multi-objective formulations with emissions caps, local siting constraints, and equity criteria; endogenous expansion of upstream facilities; endogenous cost declines and supply-chain learning effects; and dynamic allocation among sectors for critical materials. These are presented as extensions rather than features of the published formulation.

A related line of work broadens the supply-chain lens from generation technologies to grid-supporting equipment. “Grid-Supporting Equipment Supply Chains Constrain the Feasible Pace of Power System Expansion” develops a framework integrating dynamic stock-flow modeling, bill-of-materials accounting, multi-regional supply-use analysis, and expansion optimization to quantify GSE deployment requirements and upstream material dependence. In a U.S. case study, GSE shortages reach 269.6–274.1 GVA, or 28.5%–28.6%, by 2030 under high-growth conditions; copper becomes fully binding, with steel and nickel forming additional constraints; trade disruption intensifies shortages; and grid-enhancing technologies provide limited relief (Yao et al., 20 Apr 2026). This related literature suggests that SC-GEP can be interpreted not only as a generation-capacity planning framework, but also as part of a broader class of deliverability-aware expansion models in which upstream manufacturability, replacement cycles, material dependence, and logistics jointly determine whether nominal expansion plans are physically feasible.

Within that broader context, SC-GEP’s distinctive contribution is the direct integration of upstream constraints into endogenous generation expansion decisions. Its central result is not simply that supply chains matter, but that the timing, composition, and reliability consequences of expansion planning change once materials, production, lead times, and field availability are modeled as binding intertemporal constraints rather than as exogenous background conditions (Yao et al., 5 Aug 2025).