Combustion system having a fuel cell to produce blue hydrogen

A method of operating a combustion system, the combustion system having a fuel cell with an anode side, a cathode side, and an electrolyte, the method comprising:

• supplying fuel to the anode side of the fuel cell with an anode inlet line;
• supplying oxidants to the cathode side of the fuel cell with a cathode inlet line;
• producing, with the fuel cell, anode output products containing a first portion of hydrogen;
• providing the anode output products from the anode side to a separation system, the separation system comprising a water gas shift reactor;
• producing a second portion of hydrogen with from the anode output products with the water gas shift reactor;
• removing, with the separation system, water and carbon dioxide from the anode output products;
• and
• providing the hydrogen to a combustion section of a gas turbine engine.