Renewable Technologies¶

Renewable technologies are modelled with a generic, technology-agnostic formulation based on installed capacity, resource availability, and conversion efficiency. This common structure — driven by time-series inputs and a small set of techno-economic parameters — represents photovoltaics, wind turbines, hydropower, or any renewable source describable through a production profile.

Renewable production is always treated as an upper-bounded quantity: curtailment is implicitly allowed whenever available renewable energy exceeds demand or network capability. The mathematical structure differs slightly between the typical-year and multi-year formulations because the latter treats capacity evolution explicitly.

Renewable production constraint¶

Typical-year formulation¶

For each time period \(t\), scenario \(\omega\), and renewable technology \(r\), production is bounded by installed capacity and resource availability:

\[ E_{t,\omega,r} \;\le\; A_{t,\omega,r}\cdot \eta_r\cdot P_r\cdot N_r \]

where \(E_{t,\omega,r}\) is renewable production, \(A_{t,\omega,r}\) is the normalized resource- availability profile (e.g. capacity factor), \(\eta_r\) is the inverter/conversion efficiency, and \(P_r\cdot N_r\) is the installed nominal capacity.

Multi-year formulation¶

Renewable capacity is built incrementally through investment cohorts and evolves over time due to aging and replacement. Let \(k\) denote the investment step (cohort) and \(y\) the year. The available capacity in year \(y\) is

\[ C^{\text{avail}}_{y,r} = \sum_k N_{k,r}\cdot P_r\cdot \alpha_{k,y}\cdot \delta_{k,y,r} \]

where \(N_{k,r}\) is the number of units installed at step \(k\), \(\alpha_{k,y}\) is the cohort activation mask (accounting for lifetime and replacement), and \(\delta_{k,y,r}\) is the degradation factor applied to capacity. Renewable production is then bounded by the available capacity:

\[ E_{t,y,\omega,r} \;\le\; A_{t,y,\omega,r}\cdot \eta_r\cdot C^{\text{avail}}_{y,r} \]

Maximum installable capacity (optional)¶

Physical, spatial, or regulatory limits can bound the installed capacity of each renewable technology.

Typical-year — applies to the total installed capacity:

\[ N_r\cdot P_r \;\le\; \overline{C}_r \]

Multi-year — applies to the cumulative capacity across all cohorts:

\[ \sum_k N_{k,r}\cdot P_r \;\le\; \overline{C}_r \]

where \(\overline{C}_r\) is the maximum allowable installed capacity.

Land availability constraint (optional)¶

When spatial limitations are relevant, MicroGridsPy can bound the total land area used by renewables. Let \(a_r\) be the specific land requirement of technology \(r\) (\(\text{m}^2/\text{kW}\)) and \(A^{\max}\) the total available area.

Typical-year — with \(C_r = N_r P_r\):

\[ \sum_{r} C_r\, a_r \;\le\; A^{\max} \]

Multi-year — land use is computed on the cumulative renewable design across all steps:

\[ \sum_k \sum_r N_{k,r}\, P_r\, a_r \;\le\; A^{\max} \]

so renewable land occupation is a cumulative design-side constraint over all installed cohorts.