4.1. Mathematical Formulation
The core of the model is a linear optimization problem minimizing total annual cost $C_{total}$:
$\min C_{total} = \sum_{t,i} (C_{cap,i} \cdot G_{i} + C_{op,i} \cdot g_{i,t}) + \sum_{l} C_{trans,l} \cdot T_l + \sum_s C_{store,s} \cdot S_s$
Subject to:
1. Energy Balance (hourly): $\sum_i g_{i,t} + \sum_s (p_{s,t}^{dis} - p_{s,t}^{ch}) + \sum_l I_{l,t} = D_{t}^{elec} + D_{t}^{PtG} + D_{t}^{Desal}$
2. Capacity Constraints: $0 \le g_{i,t} \le CF_{i,t} \cdot G_i$
3. Storage Dynamics: $E_{s,t+1} = E_{s,t} + \eta_s^{ch} \cdot p_{s,t}^{ch} - p_{s,t}^{dis} / \eta_s^{dis}$
Where $G_i$ is capacity of technology $i$, $g_{i,t}$ is its generation at time $t$, $T_l$ is transmission capacity, $S_s$ is storage capacity, and $D_t$ represents various demands.
4.2. Input Data & Assumptions
Key assumptions include 2005-2009 meteorological data for VRE, technology cost projections for 2030 from literature, an 8% weighted average cost of capital (WACC), and estimated demands for electricity (1813 TWh), water, and gas.