  The hydrogen production curve of the electrolyzer describes the non-linear
and non-convex relationship between its power consumption and hydrogen
production. An accurate representation of this curve is essential for the
optimal scheduling of the electrolyzer. The current state-of-the-art approach
is based on piece-wise linear approximation, which requires binary variables
and does not scale well for large-scale problems. To overcome this barrier, we
propose two models, both built upon convex relaxations of the hydrogen
production curve. The first one is a linear relaxation of the piece-wise linear
approximation, while the second one is a conic relaxation of a quadratic
approximation. Both relaxations are exact under prevalent operating conditions.
We prove this mathematically for the conic relaxation. Using a realistic case
study, we show that the conic model, in comparison to the other models,
provides a satisfactory trade-off between computational complexity and solution
accuracy for large-scale problems.
