Hydrogen Electrolyzers

electrolyzer!(EP::Model, inputs::Dict, setup::Dict)

This function defines the expressions and constraints for operation of hydrogen electrolyzers ($y \in \mathcal{EL} \subseteq \mathcal{G}$). This is a basic implementation of hydrogen electrolyzers that allows the specification of an hourly clean supply constraint. For a richer formulation, please see the DOLPHYN code at https://github.com/macroenergy/DOLPHYN.

Expressions

Consumption of electricity by electrolyzer $y$ in time $t$, denoted by $\Pi_{y,z}$, is subtracted from power balance expression ePowerBalance (as per other demands or battery charging) and added to Energy Share Requirement policy balance (if applicable), eESR.

Revenue from hydrogen production by each electrolyzer $y$, equal to $\omega_t \times \Pi_{y,t} / \eta^{electrolyzer}_y \times \$^{hydrogen}_y$, is subtracted from the objective function, where $\eta^{electrolyzer}_y$ is the efficiency of the electrolyzer $y$ in megawatt-hours (MWh) of electricity per metric tonne of hydrogen produced and $\$^{hydrogen}_y$ is the price of hydrogen per metric tonne for electrolyzer $y$.

Hourly consumption from electrolyzers $y$ in the zone, equal to:

\[\begin{aligned} \sum_{y \in {z \cap \mathcal{EL}}} \Pi_{y,t} \end{aligned}\]

is subtracted from the hourly matching policy balance eHM (if applicable).

Ramping limits

Electrolyzers adhere to the following ramping limits on hourly changes in power output:

\[\begin{aligned} \Pi_{y,t-1} - \Pi_{y,t} \leq \kappa_{y}^{down} \Delta^{\text{total}}_{y}, \hspace{1cm} \forall y \in \mathcal{EL}, \forall t \in \mathcal{T} \end{aligned}\]

\[\begin{aligned} \Pi_{y,t} - \Pi_{y,t-1} \leq \kappa_{y}^{up} \Delta^{\text{total}}_{y} \hspace{1cm} \forall y \in \mathcal{EL}, \forall t \in \mathcal{T} \end{aligned}\]

(See Constraints 1-2 in the code)

This set of time-coupling constraints wrap around to ensure the power output in the first time step of each year (or each representative period), $t \in \mathcal{T}^{start}$, is within the eligible ramp of the power output in the final time step of the year (or each representative period), $t+\tau^{period}-1$.

Minimum and maximum power output

Electrolyzers are bound by the following limits on maximum and minimum power output:

\[\begin{aligned} \Pi_{y,t} \geq \rho^{min}_{y} \times \Delta^{total}_{y} \hspace{1cm} \forall y \in \mathcal{EL}, \forall t \in \mathcal{T} \end{aligned}\]

\[\begin{aligned} \Theta_{y,t} \leq \rho^{max}_{y} \times \Pi^{total}_{y} \hspace{1cm} \forall y \in \mathcal{EL}, \forall t \in \mathcal{T} \end{aligned}\]

(See Constraints 3-4 in the code)