Environmental issues and concerns about depletion of fossil fuels have driven rapid growth in the generation of renewable energy (RE) and its use in electricity grids. Similarly, the need for an alternative to hydrocarbon fuels means that the number of fuel cell vehicles is also expected to increase. The ability of electricity networks to balance supply and demand is greatly affected by the variable, intermittent output of RE generators; however, this could be relieved using energy storage and demand-side response (DSR) techniques. One option would be production of hydrogen by electrolysis powered from wind and solar sources. The use of tariff structures would provide an incentive to operate electrolysers as dispatchable loads. The aim of this paper is to compare the cost of hydrogen production by electrolysis at garage forecourts in Libya, for both dispatchable and continuous operation, without interruption of fuel supply to vehicles. The coastal city of Derna was chosen as a case study, with the renewable energy being produced via a wind turbine farm. Wind speed was analysed in order to determine a suitable turbine, then the capacity was calculated to estimate how many turbines would be needed to meet demand. Finally, the excess power was calculated, based on the discrepancy between supply and demand. The study looked at a hydrogen refueling station in both dispatchable and continuous operation, using an optimisation algorithm. The following three scenarios were considered to determine whether the cost of electrolytic hydrogen could be reduced by a lower off-peak electricity price. These scenarios are: Standard Continuous, in which the electrolyser operates continuously on a standard tariff of 12 p/kWh; Off-peak Only, in which the electrolyser operates only during off-peak periods at the lower price of 5 p/kWh; and 2-Tier Continuous, in which the electrolyser operates continuously on a low tariff at off-peak times and a high tariff at other times. The results indicate that Scenario 2 produced the cheapest electricity at £2.90 per kg of hydrogen, followed by Scenario 3 at £3.80 per kg, and the most expensive was Scenario 1 at £6.90 per kg.