Water electrolysis and cryogenic liquefaction system

A method for electrolyzing water and cryogenically forming liquid oxygen therefrom, comprising:

• directing a water stream to at least one of an anode side chamber or a cathode side chamber of an electrolyzer;
• the electrolyzer comprising the anode side chamber, the cathode side chamber, and an electrolyzer membrane and electrode assembly located between the anode side chamber and the cathode side chamber;
• directing a separated oxygen stream from the anode side chamber of the electrolyzer to a deep space oxygen radiator;
• directing a cooled oxygen stream from the deep space oxygen radiator to an oxygen storage tank of a cryogenic heat exchanger;
• directing a separated hydrogen stream from the cathode side chamber to an electrochemical hydrogen compressor;
• directing a cooled hydrogen stream from the electrochemical hydrogen compressor to a hydrogen storage tank and cooling the cooled hydrogen stream in at least one recuperative heat exchanger and at least one deep space hydrogen radiator upstream of the hydrogen storage tank;
• expanding at least a portion of the cooled hydrogen stream in an expansion valve to form a refrigerant hydrogen stream and directing the refrigerant hydrogen stream to the cryogenic heat exchanger;
• directing a warmed hydrogen stream from the hydrogen storage tank to the electrochemical hydrogen compressor and warming the warmed hydrogen stream via the at least one recuperative heat exchanger;
• and
• directing a heat-exchanged hydrogen stream from the cryogenic heat exchanger to the warmed hydrogen stream upstream of the electrochemical hydrogen compressor.