## 2 Model Development
### Supply-Side Model  
This study uses the Model of Energy Supply Systems and Their Common Environmental Impacts (MESSAGE) developed by the International Institute for Applied Systems Analysis (IIASA) as an energy supply model based on dynamic linear mathematical programming to find a plausible combination of power supply technologies to meet the projected power demand calculated above. The optimal solution is based on the least costs, the availability of technologies, as well as constraints and bounds set on technologies over the horizon. The model also finds an optimal timing for adding new energy supply technologies based on future needs [22]. The models' objective function denotes the discounted cost of the energy system through the model horizon. Discounting ensures that the costs incurred at different points in the time slice are comparable in the optimization [23]. The supply model is then used to minimize the objective function subject to the technical, environmental, and economic constraints, as follows:  
\[\text{Min C}=\sum_{x}\text{df}_{x}\cdot\text{c}_{x} \tag{2}\]  
Subject to:  
**Economic constraint:**  
\[\text{c}_{x}=\sum_{s,h}\text{Ia}_{v,h}\cdot\text{F}\text{x}_{v,h}+\sum_{\text{tec }}\text{Hd}_{\text{tec}}\cdot\text{AddCap}_{\text{tec}}+\sum_{\text{tec}} \text{Md}_{\text{tec}}\cdot\text{Cap}_{\text{tec}}+\sum_{\text{tec}}\text{Td} _{\text{tec}}\cdot\text{D}_{\text{tec}}+\sum_{\text{tec, e}}\text{F}_{\text{tec,e}}\cdot\text{F}_{\text{tec,e}} \tag{3}\]  
\[\text{df}_{x}=\frac{1}{\left(1+\text{DR}\right)^{x}} \tag{4}\]  
**Demand constraint:**  
\[\sum_{x}\sum_{t}\sum_{\text{tec}}\text{D}_{\text{tec, y},t}\geq\sum_{x}\sum_{t}\text{E}_{y,t}^{0} \tag{5}\]  
**Capacity constraint:**  
\[\sum_{m}\text{D}_{\text{tec,m,x}t}\leq\text{DUR}_{t}\cdot\text{kf}_{\text{tec,x,m,t}}\cdot\text{K}_{\text{tec,x,m,t}} \tag{6}\]  
**Resource constraint:**  
\[\text{F}\text{Y}_{t,x}\leq\text{R}_{u,h,x^{\prime}}\cdot(\text{ST}_{u,h}\ -\sum_{x^{\prime}<y}\text{DUR}_{x^{\prime}}\cdot\text{F}_{\text{d,h,x^{\prime}}} \tag{7}\]  
**Emission constraint:**  
\[\sum_{\text{tec}}\text{FS}_{\text{tec,e},x}=\text{FN}\_\text{bound}_{\text{ e},x} \tag{8}\]  
where in the above equations, C is the total cost; df is the capital recovery factor computed based on the discount rate over the model horizon; DR is the discount rate; x is the year; and t is the load region (i.e., different months of the year); for the year x, c\({}_{x}\) is the total cost. \(\text{Ia}_{v,h}\) and \(\text{F}\text{x}_{v,h}\) denote the cost and extracted resources of each type v and grade h. For each technology tec, \(\text{Hd}_{\text{tec}}\), \(\text{Md}_{\text{tec}}\), and \(\text{Td}_{\text{tec}}\) represent the investment, fixed, and variable costs. \(\text{Addcap}_{\text{tec}}\), \(\text{K}_{\text{tec}}\), \(\text{kf}_{\text{tec}}\) and \(\text{D}_{\text{tec}}\) each denote the added, maintained capacities, capacity  
Figure 4: General process for forecasting using an ARIMA model (adapted from [21]). factor, and generation (energy outflow) of each conversion technology. The emission tax and emission amount for each technology \(\mathrm{t}\)c and emission category \(\mathrm{e}\) are \(\mathrm{F}_{\mathrm{t}\mathrm{c},\mathrm{e}}\) and \(\mathrm{F}_{\mathrm{t}\mathrm{c},\mathrm{e}}\), and \(\mathrm{E}_{y,\mathrm{t}}^{0}\) is the electricity demand predicted by the SARIMA model; \(\mathrm{D}\mathrm{U}\mathrm{R}_{\mathrm{t}}\) is its \(\mathrm{e}\) duration of the load region \(\mathrm{t}\). \(\mathrm{F}\mathrm{Y}_{\mathrm{t}\mathrm{x}}\) is the extracted resource \(\mathrm{r}\) in a specified year \(\mathrm{x}\), when the value is lower than the resource volume \(\mathrm{ST}_{\mathrm{u},\mathrm{h}}\), while also considering the amount extracted in the previous year \(\mathrm{x}^{\prime}\) utilizing the \(\mathrm{R}_{\mathrm{u},\mathrm{h},\mathrm{z}}\), the rate at which the remaining resource is extracted.