A method of controlling the effective impedance of a low-impedance high-temperature superconducting cable (“HTS cable”). Passive or active control circuitry is used to create a current in the shielding conductor of the HTS cable which opposes the current in the primary conductor. In the case of a three-phase conductor, magnetic cross-coupling between the phases is exploited. The magnitude of the magnetic field is used to alter the HTS cable's effective impedance. The result is the creation of a controlled and substantially-higher effective impedance for the HTS cable. The creation of the higher impedance allows the HTS cable to be connected in parallel with conventional lines while regulating the amount of current flowing through the HTS cable.