Abstract: A method of operating a multi-phase arc furnace by controlling the required values in the secondary circuits comprising the measurement and computation of such values from selected primary and/or secondary circuit measurements excluding secondary phase voltages measured with respect to the furnace bath, computing the desired values for effecting control of the furnace on the basis of an assumption that the behavior of the inductances of the secondary circuits is predictable during other variations in the particular furnace, and, applying such computed values to the furnace control optionally subject to any desired limits imposed on the variables of the furnace.