# Hydrogen Storage Investment

Dolphyn.h2_storage_investmentMethod
h2_storage_investment(EP::Model, inputs::Dict, setup::Dict)

This module defines the decision variable representing charging and energy components of hydrogen storage technologies

The total capacity of each resource is defined as the sum of the existing capacity plus the newly invested capacity minus any retired capacity.

$$$\begin{equation*} \Delta^{total,energy}_{y,z} =(\overline{\Delta^{energy}_{y,z}}+\Omega^{energy}_{y,z}-\Delta^{energy}_{y,z}) \quad \forall y \in \mathcal{O}, z \in \mathcal{Z} \end{equation*}$$$

One cannot retire more capacity than existing capacity.

$$$\begin{equation*} \Delta^{energy}_{y,z} \leq \overline{\Delta^{energy}_{y,z}} \quad \forall y \in \mathcal{O}, z \in \mathcal{Z} \end{equation*}$$$

For resources where $\overline{\Omega_{y,z}^{energy}}$ and $\underline{\Omega_{y,z}^{energy}}$ is defined, then we impose constraints on minimum and maximum power capacity.

\begin{aligned} & \Delta^{total,energy}_{y,z} \leq \overline{\Omega}^{energy}_{y,z} \hspace{4 cm} \forall y \in \mathcal{O}, z \in \mathcal{Z} \\ & \Delta^{total,energy}_{y,z} \geq \underline{\Omega}^{energy}_{y,z} \hspace{4 cm} \forall y \in \mathcal{O}, z \in \mathcal{Z} \end{aligned}

In addition, this function adds investment and fixed OM related costs related to charge capacity to the objective function:

\begin{aligned} & \sum_{y \in \mathcal{O} } \sum_{z \in \mathcal{Z}} \left( (\pi^{INVEST,energy}_{y,z} \times \Omega^{energy}_{y,z}) + (\pi^{FOM,energy}_{y,z} \times \Delta^{total,energy}_{y,z})\right) \end{aligned}