6. Investment and sizing

el1xr_opt can size candidate assets alongside operation: a unit whose data carries a positive FixedInvestmentCost becomes an investment candidate, and the model decides its build fraction on the same discounted footing as the operating costs. The layer is built by oM_Investment.create_investment and is a no-op for cases with no candidates.

6.1. Candidates and the build decision

A candidate electricity or hydrogen unit \(\genindex\) gets a build-fraction variable

\[\vgeninvest_{\genindex} \in [\underline{x}_{\genindex}, \overline{x}_{\genindex}] \subseteq [0, 1]\]

(vEleGenInvest / vHydGenInvest, bounded by InvestmentLo / InvestmentUp). With BinaryInvestment set, the variable is binary – build all or nothing; left blank, the build is continuous, which keeps the problem an LP.

6.2. Capacity coupling

The build fraction scales every nameplate rating of the candidate, so an unbuilt candidate can do nothing and a half-built one has half of every capability («eEleInvestMaxOutput» / «eHydInvestMaxOutput», «eEleInvestMaxCharge» / «eHydInvestMaxCharge», «eEleInvestMaxInventory» / «eHydInvestMaxInventory»):

\[\veletotaloutput_{\periodindex,\scenarioindex,\timeindex,\genindex} \leq \overline{P}_{\periodindex,\scenarioindex,\timeindex,\genindex} \, \vgeninvest_{\genindex}\]

\[\veletotalcharge_{\periodindex,\scenarioindex,\timeindex,\genindex} \leq \overline{C}_{\periodindex,\scenarioindex,\timeindex,\genindex} \, \vgeninvest_{\genindex}\]

\[\veleinventory_{\periodindex,\scenarioindex,\timeindex,\storageindex} \leq \overline{S}_{\periodindex,\scenarioindex,\timeindex,\storageindex} \, \vgeninvest_{\storageindex}\]

where \(\overline{P}\), \(\overline{C}\) and \(\overline{S}\) are the MaximumPower, MaximumCharge and MaximumStorage ratings. The charge cap applies both to storage charging and to an electrolyser’s electricity input – for an electrolyser the input is the real design variable, since its hydrogen output is the input divided by the production function.

Note

The minimum-storage floor (MinimumStorage) and the initial inventory (InitialStorage) do not scale with the build fraction. A candidate store should therefore start empty with no inventory floor, otherwise satisfying its own floor forces it to be built (this is how the hydrogen sizing cases are set up; see data/sizing/README.md).

6.3. Investment cost

Each candidate pays its annualised investment cost \(\pinvestmentcost_{\genindex}\) (FixedInvestmentCost x FixedChargeRate) weighted by its build fraction. The total («eTotalICost») enters the objective next to the operating terms; see the Objective Function page, Eq. 4.2.

The sizing validation cases (HomeBatt, HoodBatt, H2Tank, Electrolyser and variants, generated by data/sizing/make_sizing_cases.py) each make exactly one asset a candidate and are regression-tested on both their cost and their build decision.