## DAC Resources Investment

Dolphyn.DAC_investmentMethod
DAC_investment(EP::Model, inputs::Dict, setup::Dict)

Sets up constraints common to all DAC resources.

This function defines the expressions and constraints keeping track of total available DAC CO2 capture capacity $y_{d}^{\textrm{C,DAC}}$ as well as constraints on capacity.

The expression defined in this file named after vCapacity\textunderscore{DAC}\textunderscore{per}\textunderscore{type} covers all variables $y_{d}^{\textrm{C,DAC}}$.

The total capacity of each DAC resource is defined as the sum of newly invested capacity based on the assumption there are no existing DAC resources.

Cost expressions

This module additionally defines contributions to the objective function from investment costs of DAC (fixed O\&M plus investment costs) from all generation resources $d \in \mathcal{D}$:

$$$\begin{equation*} \textrm{C}^{\textrm{C,DAC,c}} = \sum_{d \in \mathcal{D}} \sum_{z \in \mathcal{Z}} y_{d, z}^{\textrm{C,DAC}}\times \textrm{c}_{d}^{\textrm{DAC,INV}} + \sum_{d \in \mathcal{D}} \sum_{z \in \mathcal{Z}} y_{g, z}^{\textrm{C,DAC,total}} \times \textrm{c}_{d}^{\textrm{DAC,FOM}} \end{equation*}$$$

Constraints on DAC capacity

For resources where upper bound $\overline{y_{d}^{\textrm{C,DAC}}}$ and lower bound $\underline{y_{d}^{\textrm{C,DAC}}}$ of capacity is defined, then we impose constraints on minimum and maximum capture capacity.

$$$\begin{equation*} \underline{y_{d}^{\textrm{C,DAC}}} \leq y_{d}^{\textrm{C,DAC}} \leq \overline{y_{d}^{\textrm{C,DAC}}} \quad \forall d \in \mathcal{D} \end{equation*}$$$

## DAC Variable Cost

Dolphyn.DAC_var_costMethod
DAC_var_cost(EP::Model, inputs::Dict, setup::Dict)

Sets up variables common to all direct air capture (DAC) resources.

This module defines the DAC decision variable $x_{d,z,t}^{\textrm{C,DAC}} \forall k \in \mathcal{K}, z \in \mathcal{Z}, t \in \mathcal{T}$, representing CO2 injected into the grid by DAC resource $d$ in zone $z$ at time period $t$.

The variable defined in this file named after vDAC\textunderscore{CO2}\textunderscore{Captured} covers all variables $x_{d,z,t}^{\textrm{C,DAC}}$.

Cost expressions

This module additionally defines contributions to the objective function from variable costs of generation (variable OM plus fuel cost) from all resources over all time periods.

$$$\begin{equation*} \textrm{C}^{\textrm{C,DAC,o}} = \sum_{d \in \mathcal{K}} \sum_{t \in \mathcal{T}} \omega_t \times \left(\textrm{c}_{d}^{\textrm{DAC,VOM}} + \textrm{c}_{d}^{\textrm{DAC,FUEL}}\right) \times x_{d,z,t}^{\textrm{C,DAC}} \end{equation*}$$$

## Emissions

Dolphyn.emissions_cscMethod
emissions_csc(EP::Model, inputs::Dict, setup::Dict)

This function creates expression to add the CO2 emissions for carbon supply chain in each zone, which is subsequently added to the total emissions.

These include emissions from fuel utilization in DAC minus CO2 captured by flue gas CCS and also pipeline losses.

In addition, there is a constraint that specify that amount of CO2 that undergoes compression in each zone has to be equal to the amount of CO2 captured by DAC

$$$\begin{equation*} x_{z,t}^{\textrm{C,DAC}} = x_{z,t}^{\textrm{C,COMP}} \quad \forall z \in \mathcal{Z}, t \in \mathcal{T} \end{equation*}$$$