Impedance measurement using line-to-line current injection

A method for measuring impedance in a multi-phase alternating current (ac) circuit, the multi-phases ac circuit having a source portion and a load portion that are integrally connected at each phase of the multi-phase ac circuit, the method comprising:

• injecting a first unbalanced line-to-line shunt current at an injected current frequency in the multi-phase ac circuit;
• obtaining a first set of line voltages and a first set of phase currents of the multi-phase ac circuit;
• determining a first fundamental electrical frequency for the first set of line voltages and the first set of phase currents;
• determining a first set of transformed voltages and a first set of transformed currents by
• applying a fast Fourier transform to the first set of line voltages and the first set of phase currents at a frequency of interest and
• transforming the first set of line voltages and the first set of phase currents to a q-d synchronous reference frame using the first fundamental electrical frequency;
• injecting at least a second unbalanced line-to-line shunt current at a frequency linearly independent of the injected current frequency in the multi-phase ac circuit;
• obtaining at least a second set of line voltages and at least a second set of phase currents of the multi-phase ac circuit;
• determining at least a second fundamental electrical frequency for the at least a second set of line voltages and the at least a second set of phase currents;
• determining at least a second set of transformed voltages and at least a second set of transformed currents by
• applying a fast Fourier transform to the at least a second set of line voltages and the at least a second set of phase currents at a frequency of interest and
• transforming the at least a second set of line voltages and the at least a second set of phase currents to a q-d synchronous reference frame using the at least a second fundamental electrical frequency;
• and
• calculating an impedance for one of the set consisting of the source portion of the multi-phase ac circuit and the load portion of the multi-phase ac circuit using the first set of transformed voltages, the first set of transformed currents, the at least a second set of transformed voltages, and the at least a second set of transformed currents.

A system for measuring impedance of a multi-phase ac circuit, the multi-phases ac circuit having a source portion and a load portion that are integrally connected at each phase of the multi-phase ac circuit, the system comprising:

• a current injection device configured for injecting in the multi-phase ac circuit a first unbalanced line-to-line shunt current at an injected current frequency and for injecting in the multi-phase ac circuit at least a second unbalanced line-to-line shunt current at a frequency linearly independent of the injected current frequency;
• and
• an interface device configured for determining an impedance of a portion of the multi-phase ac circuit, the interface device including
• a circuit interface adapted for measuring a first set of line voltages and a first set of phase currents of the multi-phase ac circuit when the first unbalanced line-to-line shunt current is injected and for measuring at least a second set of line voltages and at least a second set of phase currents of the multi-phase ac circuit when the at least a second unbalanced line-to-line shunt current is injected,
• an extraction module adapted for determining a first fundamental electrical frequency for the first set of line voltages and the first set of phase currents, and determining at least a second fundamental electrical frequency for the at least a second set of line voltages and the at least a second set of phase currents,
• a transform module adapted for applying a fast Fourier transform to the first set of line voltages and the first set of phase currents at a frequency of interest and transforming the first set of line voltages and the first set of phase currents to a q-d synchronous reference frame using the first fundamental electrical frequency to produce the first set of transformed voltages and the first set of transformed currents, and applying a fast Fourier transform to the at least a second set of line voltages and the at least a second set of phase currents at a frequency of interest and transforming the at least a second set of line voltages and the at least a second set of phase currents to a q-d synchronous reference frame using the at least a second fundamental electrical frequency to produce the at least a second set of transformed voltages and the at least a second set of transformed currents;
• and
• an impedance calculation module adapted for calculating an impedance for at least one of the set consisting of the source portion of the multi-phase ac circuit and the load portion of the multi-phase ac circuit using the first set of transformed voltages, the first set of transformed currents, the at least a second set of transformed voltages, and the at least a second set of transformed currents.