PEM electrolyzers convert water and power into hydrogen and oxygen. In this article, we will focus on the principles behind an electrolyzer. Everything below refers primarily to PEM electrolyzers, but much of it can be applied to other types of electrolyzers as well. The spreadsheet linked at the bottom of this article will help you determine the cell voltage, efficiency, and output rate of hydrogen and oxygen of your electrolyzer.
Current
The amount of hydrogen or oxygen the electrolyzer generates is determined solely by the current.
This makes sense when you look at the physics of the electrolysis cell. Since current is defined as the flow of electrons (or protons) and a hydrogen molecule is only 2 protons and 2 electrons, it follows that when you put a certain number of electrons across the membrane (current), it will generate an equivalent number of Hydrogen molecules.
The exact amount is 0.007 Liters/minute @ STP (aka standard Liters per min, or SLPM) of hydrogen for every Amp that is put through each cell (0.007 SLPM/A/cell)
In practice, this gives you two variables: Current and Number of Cells. For example. If you wanted 7 SLPM of H2 you could design a single cell electrolyzer and pump 1000 A through it (0.007SLPM/A/cell * 1000A * 1 cell) or you could design one with 10 cells and only have to put 100 A through it (0.007 * 100A * 10 cells).
This allows you to get a rough estimate of how many cells you might need based on the current available.
Since hydrogen and oxygen production is completely dictated by current, this can sometimes be a convenient way to control production rates without actually having to measure the gas production or rely on other parameters that may change with time.
Voltage
The voltage that it takes to provide this current determines the overall efficiency, and thus the amount of power (P=V*I) required to generate your Hydrogen and Oxygen.
The voltage each cell will operate at is an experimentally determined value that can vary depending on the properties of the Membrane Electrode Assembly (MEA), temperature, current density, mechanical design, etc. At any given set of conditions, an MEA will have a Voltage vs Current parameter (usually called an IV curve).
These curves will have lower voltages at lower current densities. This means less power per unit of gas generated. Since there is less current you must have larger active areas and/or more cells to generate the same total amount of gas.
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