Inverter Sizing¶

Power-electronic conversion is modelled explicitly for the two DC-coupled assets — renewable generation and battery storage — so that converter capacity is sized and costed alongside the energy assets rather than folded into them. The two follow different but consistent philosophies.

Renewable inverters (deterministic)¶

Each renewable technology is sized on the DC side (installed panel/turbine capacity), and its inverter/converter AC capacity is derived deterministically from a fixed DC/AC ratio:

\[ P^{\text{inv,ac}}_{j} = \frac{C^{\text{dc}}_{j}}{\text{dc\_ac\_ratio}_{j}} \]

The ratio (renewables.yaml → technical.dc_ac_ratio, default 1.0) encodes the design choice of deliberately oversizing the array relative to the inverter. The derived AC capacity carries its own investment cost (inverter_specific_investment_cost_per_kw_ac), lifetime (inverter_lifetime_years), and fixed O&M (inverter_fixed_om_share_per_year), and a conversion efficiency (inverter_efficiency) is applied to renewable output. Because the AC capacity is a fixed function of the DC sizing decision, no extra optimisation variable is introduced — the inverter is a deterministic sidecar to the renewable sizing.

Battery inverter (explicit, component-based)¶

The battery converter is treated as a first-class sizing decision, on the same component-based footing as the other assets:

\[ P^{\text{inv}} = u^{\text{inv}}\; P^{\text{inv,nom}} \]

where \(u^{\text{inv}}\) is the number of battery-inverter units and \(P^{\text{inv,nom}}\) is the nominal power per unit (battery.yaml → technical.inverter_nominal_power_kw). Discrete unit sizing therefore applies naturally to the battery inverter as an integer unit count. The installed inverter power bounds the battery charge and discharge power in every period (see Battery storage), and may optionally be coupled to the installed energy through a maximum charge/discharge C-rate:

\[ P^{\text{ch}}_{t} \le P^{\text{inv}}, \qquad P^{\text{dis}}_{t} \le P^{\text{inv}}, \qquad P^{\text{inv}} \le c^{\text{rate}}\, C^{\text{bat}} \]

The battery inverter has its own CAPEX (inverter_specific_investment_cost_per_kw), lifetime (inverter_lifetime_years), and fixed O&M, all amortised on the calendar convention like the other assets (it is not subject to the battery's cycle-fade replacement).

Across the planning modes¶

Both formulations size the inverters with the same logic. In the typical-year model the inverter powers are single design variables; in the multi-year model they are resolved per investment step — renewable inverter/converter capacity per renewable technology and explicit battery-inverter sizing by step — and the inverter costs enter the discounted objective and the structured exports on the same cohort/step basis as the energy assets.