This work aims at developing an approach for modelling and optimizing the operation of a reference alkaline electrolysis unit operating in transient state using orthogonal collocation on finite elements (OCFE). The main goal is to define the set of operating conditions that minimize the processing cost (associated to electricity cost) given a hydrogen yield. Three components of the electrolyzer are considered: the stack of electrolytic cells and two separators that single out the hydrogen and oxygen gas streams. The dynamic behavior is considered for the mass holdup in the separators as well as the energy accumulation for these three components. The associated mathematical model is derived in the paper. Its solving allows characterizing the influence of the transient operating parameters of the system on its working and associated final hydrogen production. Mathematical optimization aims at defining the ideal operating load in order to minimize costs associated to fluctuating price of electricity consumed by the stack given a defined hydrogen yield. The model has been validated according to experimental test runs and operating conditions have been optimized under a proof of concept scenario saving 17% of electricity costs if compared to constant plant capacity.