NOVELTY - Operating a fuel cell system (100) involves providing a fuel inlet stream (105) into a fuel cell stack (preferably solid oxide fuel cell (SOFC) stack) (101); operating the fuel cell stack to generate electricity and a hydrogen containing fuel exhaust stream (103); separating at least 95% of hydrogen contained in the fuel exhaust stream using a cascaded electrochemical hydrogen pump (1); and providing the hydrogen separated from the fuel exhaust stream into the fuel inlet stream. The hydrogen pump comprises a high temperature, low hydration ion exchange membrane cell stack.    USE - For operating a fuel cell system (claimed) useful for generating electrical energy.    ADVANTAGE - By recycling at least a portion of the hydrogen from the fuel exhaust (i.e., tail) gas stream into the fuel inlet stream, a high efficiency operation of the fuel cell system is obtained. The overall fuel utilization is increased. The system includes a cascaded electrochemical hydrogen pump unit, which recycles at least 95% of exhaust hydrogen, and therefore operates at a higher overall fuel efficiency (greater than 95%) and a higher AC electrical efficiency greater than 60%. Even higher efficiency may be obtained by increasing the per pass fuel utilization rate above 75%, such as 76-80%. At steady-state, there is no need for generating steam when steam methane reformation is used to create the feed gas to the fuel cell. The fuel exhaust stream contains enough water vapor to humidify the fuel inlet stream to the stack at steam to carbon ratios of 2-2.5. The increase in overall fuel utilization and the removal of heat requirement to generate steam increases the overall electrical efficiency.    DETAILED DESCRIPTION - Method of operating a fuel cell system (100) involves providing a fuel inlet stream (105) into a fuel cell stack (preferably solid oxide fuel cell (SOFC) stack) (101); operating the fuel cell stack to generate electricity and a hydrogen containing fuel exhaust stream (103); separating at least 95% of hydrogen contained in the fuel exhaust stream using a cascaded electrochemical hydrogen pump (1); and providing the hydrogen separated from the fuel exhaust stream into the fuel inlet stream. The cascaded electrochemical hydrogen pump comprises a high temperature, low hydration ion exchange membrane cell stack. The membrane cell stack comprises at least one membrane cell arranged in process fluid flow series with at least one other membrane cell. The high temperature, low hydration ion exchange membrane cell stack comprises a stack of acid doped non-fluorinated ion exchange ionomer membrane cells. Each membrane of the membrane cells comprises a polybenzimidazole (PBI) membrane doped with sulfuric and/or phosphoric acid. An INDEPENDENT CLAIM is included for fuel cell system comprising a fuel cell stack; a cascaded electrochemical hydrogen pump; a first conduit which operatively connects a fuel exhaust outlet of the fuel cell stack to a first inlet of the cascaded electrochemical hydrogen pump; and a second conduit which operatively connects a first outlet of the cascaded electrochemical hydrogen pump to a fuel inlet of the fuel cell stack.    DESCRIPTION OF DRAWING(S) - The figure shows a schematic view of fuel cell system.    Cascaded electrochemical hydrogen pump (100) Fuel cell system (1)    Fuel cell stack (101)    Fuel exhaust stream (103)    Fuel inlet stream. (105)