Weld circuit inductance tracking

An apparatus for welding or cutting comprising:

• a power supply to supply an output voltage to, and deliver a current associated with the output voltage through, a weld circuit to a welding torch to produce an arc;
• and
• a controller coupled to the power supply and configured to perform:
• receiving a measured current from a current sense point of the power supply or the weld circuit and that is representative of the current;
• receiving, from a voltage sense point of the power supply or the weld circuit that is spaced-apart from the welding torch, a measured voltage that differs from an arc voltage at the arc by a voltage drop resulting from the current and an inductance of the weld circuit;
• compensating the measured voltage for the voltage drop using the measured current and an inductance value that is an estimate of the inductance, to produce a compensated voltage;
• computing a derivative of the compensated voltage;
• computing a second derivative of the measured current;
• and
• upon determining that the inductance value and the inductance differ based on the derivative and the second derivative, adjusting the inductance value toward the inductance and repeating compensating with the inductance value as adjusted.