Methods and apparatus for differential current measurement in a three-phase power system

A method for measuring the differential current between a first terminal of a device in a three-phase power system and a, second terminal of the device, wherein the device introduces a phase shift between said first and second terminals on each phase of the power system, the method comprising:

• obtaining, for each phase, a measure of the current (I1) through the first terminal of the device;
• obtaining, for each phase, a measure of the current (I2) through the second terminal of the device;
• normalizing the measured currents of each phase of the first and second terminals in accordance with the following transformations:
• {overscore (I)}1G(0) I1=cos(0)U I1+sin(0)J I1, and
• {overscore (I)}2=G(P) I2=cos(P)U I2+sin(P)J I2
• where G( ) is a generalized normalization transform comprising a quadrature combination of U and J, P represents the phase angle by which the phase of I1 lags the phase of I2, U represents a unit zero degree phase shift with zero sequence components removed, J represents a unit ninety degree phase shift with zero sequence components removed, and {overscore (I1)} and {overscore (I2)} represent the normalized measured currents of I1 and I2 respectively;
• and
• calculating from the normalized measured currents a differential current for each phase.

Apparatus for measuring the differential current between a first terminal of a device in a three-phase power system and a second terminal of the device, wherein the device introduces a phase shift between said first and second terminals on each phase of the power system, the apparatus comprising:

• a first sensor coupled to the first terminal and obtaining, for each phase, a measure of the current through the first terminal;
• a second sensor coupled to the second terminal and obtaining, for each phase, a measure of the current through the second terminal;
• and
• a processor connected to receive the measures of current obtained by the first and second sensors and to normalize the measured currents in order to compensate for changes in at least one of phase and magnitude introduced by the device, said processor performing such normalization in accordance with the following transformation:
• G(θ)=cos(θ)U+sin(θ)J
• where G( ) is a generalized normalization transform comprising a quadrature combination of U and J, U represents a unit zero degree phase shift with zero sequence components removed, and J represents a unit ninety degree phase shift with zero sequence components removed, said processor further calculating from the normalized measured currents a differential current for each phase.

A transformer protection unit for detecting faults in a power transformer of a three-phase power system, the transformer having a plurality of primary windings and a plurality of secondary windings, one of each for each of the different phases of the power system, the transformer protection unit comprising:

• a first plurality of current sensors, each coupled to a respective one of the primary windings of the transformer for obtaining a measure of the current through that winding;
• a second plurality of current sensors, each coupled to a respective one of the secondary windings of the transformer for obtaining a measure of the current through that winding;
• and
• a processor connected to receive the measures of current obtained by the first and second pluralities of current sensors and to normalize the measured currents in order to compensate for changes in at least one of phase and magnitude introduced by the transformer, said processor performing such normalization in accordance with the following transformation:
• G(θ)=cos(θ)U+sin(θ)J
• where G( ) is a generalized normalization transform comprising a quadrature combination of U and J, U represents a unit zero degree phase shift with zero sequence components removed, and J represents a unit ninety degree phase shift with zero sequence components removed, said processor further calculating from the normalized measured currents a differential current for each phase.

A computer-readable medium having program code stored thereon for use in measuring the differential current between a first terminal of a device in a three-phase power system and a second terminal of the device, wherein the device introduces a phase shift between said first and second terminals on each phase of the power system, the program code, when executed by a processor, causing the processor to:

• receive, for each phase, a measure of the current through the first terminal of the device and a measure of the current through the second terminal of the device;
• normalize the measured currents of each phase of the first and second terminals in order to compensate for changes in at least one of phase and magnitude introduced by the device, said normalization being performed in accordance with the following transformation:
• G(θ)=cos(θ)U+sin(θ)J
• where G( ) is a generalized normalization transform comprising a quadrature combination of U and J, U represents a unit zero degree phase shift with zero sequence components removed, and J represents a unit ninety degree phase shift with zero sequence components removed;
• and
• calculate from the normalized measured currents a differential current for each phase.