Network Expansion Planning

The decision being supported

Where and when to build lines, transformers, interconnectors, and storage; whether a project’s benefits exceed its cost; and what generation mix and network are jointly consistent with a decarbonisation target. Time horizons run 10–40 years, and the assets are lumpy, irreversible, and slow — a European transmission line takes roughly a decade from concept to energisation, which is longer than the useful life of most of the assumptions used to justify it.

That last observation should govern the modelling: the objective is not to identify the optimal network but to find investments that are robust across the futures you cannot distinguish between.

Formulation

The canonical transmission expansion planning (TEP) problem is a two-stage optimisation: invest, then operate.

min   Σ_l  I_l · x_l                                  (annualised investment)
    + Σ_s w_s Σ_t Σ_g c_g · P_{g,s,t}                 (expected operating cost)

s.t.  DC power flow in every scenario s and snapshot t
      |P_{l,s,t}| ≤ x_l · P_l^max                     (capacity only if built)
      generation limits, ramping, storage dynamics
      x_l ∈ {0,1}   or   x_l ≥ 0 continuous

Three structural choices dominate the result.

Binary or continuous investment. Binary variables represent real, lumpy projects and give a mixed-integer problem whose difficulty grows quickly. Continuous capacities (“transmission volume in MW·km”) keep the problem linear and are appropriate for strategic studies where the output is a corridor, not a project. Note that the disjunctive constraint linking a candidate line’s flow to its build decision (the “big-M” formulation) is where MILP formulations of TEP get numerically fragile — the bound must be tight or the relaxation is useless.¹

Generation co-optimisation. Network and generation investment are substitutes: a transmission line can replace local peaking capacity, and vice versa. Optimising the network against a fixed generation fleet overstates the value of the network in some places and understates it in others. Modern European studies co-optimise, which is what makes them large.²

Anticipation of operation. Whether the operational layer is a copper plate, DC-OPF, or a security-constrained problem changes the answer materially — a network built against an N-0 operational model is systematically under-built.

Managing the size

An honest formulation is computationally intractable: decades × 8760 hours × thousands of nodes × scenarios × integer investment. Every practical model reduces it, and the reductions are where the credibility is won or lost.

Temporal aggregation. Representative periods (typically 5–20 clustered days or weeks) with weights. This is safe for thermal-dominated systems and dangerous for storage- and renewables-dominated ones, where inter-period linkage matters — a seasonal store cannot be represented by disconnected representative days. Techniques for preserving inter-period state exist and should be used when long-duration storage is in scope.³

Spatial aggregation. Cluster nodes into regions, preserving the aggregate transfer capability between them. Fine for continental studies, fatal for questions about a specific substation. PyPSA-Eur implements this explicitly and lets you sweep the number of clusters, which is a good way to demonstrate that your conclusion is not an artefact of the resolution.⁴

Candidate pre-screening. Restrict candidate lines to a plausible set derived from congestion patterns in an unconstrained run, rather than allowing every node pair.

Decomposition. Benders decomposition separates the investment master problem from operational subproblems, which parallelise. This is the standard route to large instances.⁵

Uncertainty

Scenario uncertainty here is not noise around a forecast; it is structural. Demand electrification pace, hydrogen’s role, nuclear policy, weather years, and fuel prices are not independently distributed quantities with known moments.

Three treatments, in ascending order of what they demand and deliver:

• Deterministic per scenario, compared afterwards. Run each scenario independently, then look at which investments appear in all of them. Simple; the intersection is a genuinely useful robustness signal. This is essentially what TYNDP does.
• Stochastic programming. One optimisation over probability-weighted scenarios, giving a single hedged investment plan. Requires probabilities you do not have, and the answer is sensitive to them.
• Robust or adaptive optimisation. Optimise worst-case or regret over an uncertainty set, with recourse. Conservative but honest when probabilities are genuinely unknown.⁶

Reporting regret — how much worse a plan performs in a scenario other than the one it was designed for — is more decision-useful than reporting an expected cost, because the decision maker’s actual concern is asymmetric.

Cost-benefit analysis

European projects are assessed with ENTSO-E’s CBA methodology, which is worth understanding even if you never run it, because it defines what “benefit” means in this domain.⁷ The benefit categories:

• Socio-economic welfare — the reduction in total system generation cost, computed as the difference between market simulations with and without the project.
• RES integration — avoided curtailment.
• CO₂ variation — emissions change from the altered dispatch.
• Losses variation — grid losses, which can go either way.
• Adequacy / security of supply — change in expected energy not served.
• Flexibility and stability — largely qualitative.

Against these sit CAPEX, OPEX, and environmental and social impacts. The methodology’s key structural feature is the “take-out-one-at-a-time” (TOOT) approach: assess each project by removing it from a fully built reference network, which values a project against a world where the others exist. The alternative (“put-in-one-at-a-time”) gives systematically different numbers, and projects that are complements can look poor under one and good under the other. Any CBA result should be read with the counterfactual named.

Failure modes

Optimising a network for a single weather year. Renewable-driven congestion patterns vary substantially between years. Use several, and report the spread.

Ignoring AC feasibility. A DC-optimal expansion can be reactive-power-infeasible. Verify the final plan with AC power flow at stress points, even though the optimisation was linear.

Treating the objective’s optimum as meaningful to the last euro. The cost surface near the optimum is typically flat: many quite different networks are within 1–2% of each other. Explore that near-optimal space explicitly — “modelling to generate alternatives” — and present the family, not the point.⁸

Omitting the deliverability of the plan. Permitting, supply chains, and public acceptance are the binding constraints on European transmission, not optimisation. A plan that assumes 12 GW of new corridors in eight years is arithmetic, not a plan.

Tooling

PyPSA / PyPSA-Eur and PyPSA-Eur-Sec for open European studies with expansion built in; Calliope and OSeMOSYS for broader energy-system scope with a coarser network; GENeSYS-MOD, TIMES for policy-facing work; commercial tools (PLEXOS, Antares, PowerFactory for the AC verification step) where required. Solver choice matters at this scale — Gurobi or a well-tuned HiGHS with Benders decomposition.⁹

Summary

Expansion planning is investment optimisation wrapped around an operational model, made tractable by temporal, spatial, and candidate reduction, and made credible by explicit treatment of structural uncertainty. The deliverable that survives contact with reality is a robust set of investments plus a characterisation of near-optimal alternatives — not a single optimal network.

References