There are major discussions worldwide on how the production of clean fuels, such as hydrogen, could facilitate the whole-energy system decarbonization. From a power system perspective, green hydrogen production results in massive grid integration of electrolyzers, that needs to be considered in power system analysis. This tutorial presents the modelling foundations of utility-scale hydrogen electrolyzers with alkaline and proton exchange membrane (PEM) technology, including electrolysis stack models, power electronics interface (PEI) and control, thermodynamics, hydrogen production formulations, and operational constraints in downstream hydrogen process/buffer, required for system-level steady-state and dynamic studies in both transmission and distribution grids. Possible PEIs for grid integration of electrolyzers will be discussed, along with the associated control schemes in particular grid-forming load control. It will be discussed how and to what extent electrolysis plants could impact system stability and operation, from both steady-state and dynamic perspectives