Cost Accounting¶

MicroGridsPy follows a bottom-up cost-accounting approach: every cost component is explicitly parameterized and mapped to decision variables. The same conceptual structure is used in both planning modes, but the temporal treatment of costs differs between the typical-year and multi-year formulations.

Total system cost is decomposed into four categories:

Annualized investment costs,
Fixed operation and maintenance costs,
Variable operational costs and revenues,
Externalities and penalty terms.

Investment-related costs depend on capacity-sizing decisions and are therefore scenario-independent. Most operational costs, revenues, and reliability penalties depend on scenario-specific dispatch variables. The two modes differ mainly in how time is represented:

In the typical-year formulation, all costs are interpreted as (steady-state) annual equivalents.
In the multi-year formulation, costs are tracked explicitly by year and discounted to present value. If capacity expansion is enabled, investments are introduced at discrete steps and tracked as capacity cohorts, with annualized costs active from the commissioning year to the end of the horizon.

Investment cost¶

Installed capacity of technology \(j\) is unit-based:

\[ C_j = N_j \cdot P_j \]

where \(N_j\) is the number of installed units and \(P_j\) the nominal capacity per unit. The annualized investment cost is

\[ \text{Annuity}_j = C_j \cdot \text{CAPEX}^{\text{eff}}_j \cdot \text{CRF}_j \]

where \(\text{CAPEX}^{\text{eff}}_j = (1-g_j)\,\text{CAPEX}_j\) accounts for investment grants \(g_j\), and \(\text{CRF}_j\) is the capital recovery factor computed from \(\text{WACC}_j\) and the lifetime \(LT_j\).

Fixed operation and maintenance cost¶

Fixed O&M costs are capacity-dependent, hence scenario-independent. For technology \(j\):

\[ \text{FixedO}\&\text{M}_j = C_j \cdot \text{CAPEX}_j \cdot f^{\text{FOM}}_j \]

where \(f^{\text{FOM}}_j\) is the fixed-O&M fraction. In the typical-year formulation, total annual fixed O&M is computed once from installed capacities and added outside the scenario expectation:

\[ \text{FixedO}\&\text{M} = \sum_j \text{FixedO}\&\text{M}_j \]

In the multi-year formulation, it is computed per active cohort and included in yearly system costs:

\[ \text{FOM}_y = \sum_{j,k} \alpha_{j,k,y}\cdot \text{FOM}_{j,k} \]

where \(\alpha_{j,k,y}\) is the cohort activation mask.

Operational costs and revenues¶

Operational costs depend on dispatch variables at hourly resolution. For each scenario \(\omega\):

Fuel costs

\[ \text{FuelCost}_{\omega} = \sum_{t,g} f_{t,\omega,g}\cdot c^{\text{fuel}}_g \]

Grid interaction (net cost)

\[ \text{GridNetCost}_{\omega} = \sum_t \left( e^{\text{imp}}_{t,\omega}\,c^{\text{imp}}_{t,\omega} - e^{\text{exp}}_{t,\omega}\,c^{\text{exp}}_{t,\omega} \right) \]

Renewable production subsidies

\[ \text{Subsidy}_{\omega} = \sum_{t,r} p^{\text{ren}}_{t,\omega,r}\cdot s_r \]

Lost-load penalties

\[ \text{LLCost}_{\omega} = \sum_t \ell_{t,\omega}\cdot c^{\text{LL}} \]

The expected annual operational cost is the probability-weighted sum across scenarios. Grid costs and revenues are computed on the raw interchange variables at the point of common coupling — see Grid Cost and Emissions.

Externalities¶

Externalities include direct operational emissions, optional grid-related (scope-2) emissions, and embodied emissions. In the typical-year formulation, embodied emissions are annualized consistently with the steady-state interpretation:

\[ \text{Externalities}_{\omega} = c^{\text{CO}_2} \left( \sum_{t,g} f_{t,\omega,g}\,\epsilon^{\text{fuel}}_g + \sum_j \frac{C_j\,\epsilon^{\text{emb}}_j}{LT_j} + \sum_t e^{\text{imp}}_{t,\omega}\,\epsilon^{\text{grid}}_t \right) \]

where the three terms are direct fuel emissions, annualized embodied emissions, and grid-related indirect emissions. In the multi-year formulation, embodied emissions are tracked explicitly by year and cohort rather than annualized:

\[ \text{Externalities}_{y,\omega} = c^{\text{CO}_2} \left( \sum_{t,g} f_{t,y,\omega,g}\,\epsilon^{\text{fuel}}_g + \sum_{j,k} \beta_{j,k,y}\,\epsilon^{\text{emb}}_j + \sum_t e^{\text{imp}}_{t,y,\omega}\,\epsilon^{\text{grid}}_t \right) \]

where \(\beta_{j,k,y}\) activates embodied emissions at commissioning. Direct fuel-emission costs and optional grid-emission costs are evaluated within each modelled year and scenario, then discounted together with the other annual system costs.

Same economics, different time representation

Both modes rely on the same bottom-up cost structure. In the typical-year formulation costs are annualized into horizon-independent equivalents; in the multi-year formulation they are resolved year by year and discounted to present value. The typical-year model is the steady-state limit of the multi-year one.