A welding power supply, comprising: power conversion circuitry configured to convert supply power to welding current; a voltage sense circuit configured to measure an output voltage of the power conversion circuitry; and control circuitry, characterized in that the control circuitry is configured to: when the output voltage is between a first upper voltage limit and a lower voltage limit, control the power conversion circuitry to output the welding current to substantially match an amperage parameter; when the output voltage is above the first upper voltage limit and below a second upper voltage limit, control the power conversion circuitry to output the welding current based on a first voltage-amperage relationship; and in response to detecting that the output voltage has decreased below the lower voltage limit: control an increasing ramp rate of the welding current output by the power conversion circuitry; and in response to detecting that the output voltage has increased above the lower voltage limit, control a decreasing ramp rate of the welding current output by the power conversion circuitry. power conversion circuitry configured to convert supply power to welding current; a voltage sense circuit configured to measure an output voltage of the power conversion circuitry; and control circuitry, characterized in that the control circuitry is configured to: when the output voltage is between a first upper voltage limit and a lower voltage limit, control the power conversion circuitry to output the welding current to substantially match an amperage parameter; when the output voltage is above the first upper voltage limit and below a second upper voltage limit, control the power conversion circuitry to output the welding current based on a first voltage-amperage relationship; and in response to detecting that the output voltage has decreased below the lower voltage limit: control an increasing ramp rate of the welding current output by the power conversion circuitry; and in response to detecting that the output voltage has increased above the lower voltage limit, control a decreasing ramp rate of the welding current output by the power conversion circuitry. when the output voltage is between a first upper voltage limit and a lower voltage limit, control the power conversion circuitry to output the welding current to substantially match an amperage parameter; when the output voltage is above the first upper voltage limit and below a second upper voltage limit, control the power conversion circuitry to output the welding current based on a first voltage-amperage relationship; and in response to detecting that the output voltage has decreased below the lower voltage limit: control an increasing ramp rate of the welding current output by the power conversion circuitry; and in response to detecting that the output voltage has increased above the lower voltage limit, control a decreasing ramp rate of the welding current output by the power conversion circuitry. control an increasing ramp rate of the welding current output by the power conversion circuitry; and in response to detecting that the output voltage has increased above the lower voltage limit, control a decreasing ramp rate of the welding current output by the power conversion circuitry.