The penetration of intermittent renewable energies requires the development of energy storage technologies. High temperature electrolysis using solid oxide electrolyser cells (SOECs) as a potential energy storage technology, provides the prospect of a cost-effective and energy efficient route to clean hydrogen production. The development of optimal control strategies when SOEC systems are coupled with intermittent renewable energies is discussed. Hydrogen production is examined in relation to energy consumption. Control strategies considered include maximizing hydrogen production, minimizing SOEC energy consumption and minimizing compressor energy consumption. Optimal control trajectories of the operating variables over a given period of time show feasible control for the chosen situations. Temperature control of the SOEC stack is ensured via constraints on the overall temperature difference across the cell and the local temperature gradient within the SOEC stack, to link materials properties with system performance; these constraints are successfully managed. The relative merits of the optimal control strategies are analyzed.