Fuel cell system and method of estimating content of metal ions

A fuel cell system comprising:

• a fuel cell that includes a membrane-electrode assembly, the membrane-electrode assembly including an electrolyte membrane, and an anode catalyst layer and a cathode catalyst layer sandwiching the electrolyte membrane;
• an impedance measuring device that measures alternating-current impedance of the fuel cell when an alternating-current voltage is applied to the fuel cell;
• an impedance acquisition unit configured to obtain a first imaginary part value of the alternating-current impedance of the fuel cell measured by the impedance measuring device when an alternating-current voltage with a fixed frequency satisfying
• Fixed frequency [Hz]×(Thickness of the electrolyte membrane [μm])2≤500 [Hz×μm2]
• is applied to the fuel cell in a state where a relative humidity of the membrane-electrode assembly is 20% or greater, and a fuel gas is present and an oxidant gas is absent in the anode catalyst layer and the cathode catalyst layer;
• and
• a metal ion estimation unit configured to estimate a content of metal ions in the electrolyte membrane on a basis of the first imaginary part value of the alternating-current impedance obtained by the impedance acquisition unit.