Method for diagnosing at least one fuel cell stack of a fuel cell device, computer-readable storage medium, and fuel cell diagnostic system

A method for diagnosing at least one fuel cell stack of a fuel cell device via a fuel cell diagnostic system, the method comprising:

• applying a sinusoidal first alternating current at a first frequency and applying at least one sinusoidal second alternating current at a second frequency different from the first frequency to the fuel cell stack;
• detecting a sinusoidal first voltage response of the fuel cell stack at the first frequency and detecting a sinusoidal second voltage response of the fuel cell stack at the second frequency;
• evaluating a first AC voltage as a function of the first voltage response and evaluating a second AC voltage as a function of the second voltage response via an analytical algorithm for a differential impedance analysis of the fuel cell stack by way of an electronic computing unit of the fuel cell diagnostic system, wherein the detected sinusoidal voltage response of the fuel cell stack at various excitation frequencies is used to determine a capacitance;
• determining a first resistance, a second resistance, and the capacitance of the fuel cell stack as a function of the evaluation by specifying an equivalent circuit diagram for the fuel cell stack, wherein the sinusoidal voltage response of the fuel cell stack at the various excitation frequencies is used to determine the second resistance;
• and
• diagnosing the fuel cell stack as a function of the determined first resistance, the determined second resistance, and the determined capacitance, wherein the diagnosis is carried out in real time, wherein the diagnosis is carried out during driving operation of a motor vehicle,
• wherein an undersupply of hydrogen in the fuel cell stack is diagnosed upon a determination of a drop of the capacitance and a uniform second resistance, or
• wherein an undersupply of oxygen in the fuel cell stack is diagnosed upon a determination of a constant capacitance and a rising second resistance.