Digital current differential system

A method of detecting faults on a power transmission line system including a plurality of transmission terminals, the method including:

• simultaneously measuring phase current samples at each phase of each transmission terminal;
• calculating real and imaginary phaselets comprising partial sums of the phase current samples;
• for each phaselet, calculating a respective partial sum of squares of each phase current sample;
• calculating the sums of the real and imaginary phaselets over a variable size sliding sample window;
• calculating real and imaginary phasor components from the phaselets over the sample window;
• calculating a sum of the partial sums of the squares over the sample window;
• using the sums of the real and imaginary phaselets, the real and imaginary phasor components, and the sum of the partial sums of the squares to calculate, for each phase, a sum of squares of errors between the phase current samples and a fitted sine wave representative of the real and imaginary phasor components;
• for each terminal,
• calculating sequence current phasors from the phase current samples;
• calculating a sequence sums of squares of the errors from the sums of squares of errors;
• using the sequence sums of squares of errors to calculate a sequence variance matrix defining an elliptical uncertainty region;
• transmitting the sequence current phasors and the sequence variance matrix to a remote location;
• and
• at the remote location,
• determining whether a disturbance has occurred, and, if so, re-initializing the sample window;
• and
• determining whether any of the sequence current phasors falls outside the elliptical uncertainty region.

A method of detecting faults on a transformer, the method comprising:

• measuring phase current samples at each of a plurality of transformer windings;
• calculating real and imaginary phaselets comprising partial sums of the phase current samples;
• for each phaselet, calculating a respective partial sum of the squares of each phase current sample of the each phaselet;
• calculating the sums of the real and imaginary phaselets over a variable size sliding sample window;
• calculating real and imaginary phasor components from the phaselets over the sample window;
• calculating a sum of the partial sums of the squares over the sample window;
• using the sums of the real and imaginary phaselets, the real and imaginary phasor components, and the sum of the partial sums of the squares to calculate a sum of squares of errors between the phase current samples and a fitted sine wave representative of the real and imaginary phasor components;
• using the sum of squares of errors to calculate a variance matrix defining an elliptical uncertainty region;
• applying a symmetrical component transform to the real and imaginary phasor components to obtain symmetrical component current phasors including a negative sequence current phasor for each of the transformer windings;
• determining a baseline residual current phasor;
• adding the negative sequence current phasors of the transformer windings in the direction of a coupling region to obtain a calculated residual current phasor;
• subtracting the baseline residual current phasor from the calculated residual current phasor to obtain a resulting phasor;
• and
• determining whether the resulting phasor falls outside of the elliptical uncertainty region.

A system for detecting faults on a power transmission line system including a plurality of transmission terminals, the system including:

• current sensors for simultaneously measuring phase current samples at each phase of each transmission terminal;
• and
• a computer for
• calculating real and imaginary phaselets comprising partial sums of the phase current samples;
• for each phaselet, calculating a respective partial sum of squares of each phase current sample;
• calculating the sums of the real and imaginary phaselets over a variable size sliding sample window;
• calculating real and imaginary phasor components from the phaselets over the sample window;
• calculating a sum of the partial sums of the squares over the sample window;
• using the sums of the real and imaginary phaselets, the real and imaginary phasor components, and the sum of the partial sums of the squares to calculate a sum of squares of errors between the phase current samples and a fitted sine wave representative of the real and imaginary phasor components;
• using the sum of squares of errors to calculate a variance matrix defining an elliptical uncertainty region;
• determining whether a disturbance has occurred, and, if so, re-initializing the sample window;
• and
• determining whether a sum of current phasors from each terminal for a respective phase falls outside of the elliptical uncertainty region for the respective phase.

A system for detecting faults on a power transmission line system including a plurality of transmission terminals, the system including:

• current sensors for simultaneously measuring phase current samples at each phase of each transmission terminal;
• and
• a computer for
• calculating real and imaginary phaselets comprising partial sums of the phase current samples;
• for each phaselet, calculating a respective partial sum of squares of each phase current sample;
• calculating the sums of the real and imaginary phaselets over a variable size sliding sample window;
• calculating real and imaginary phasor components from the phaselets over the sample window;
• calculating a sum of the partial sums of the squares over the sample window;
• using the sums of the real and imaginary phaselets, the real and imaginary phasor components, and the sum of the partial sums of the squares to calculate, for each phase, a sum of squares of errors between the phase current samples and a fitted sine wave representative of the real and imaginary phasor components;
• for each terminal,
• calculating sequence current phasors from the phase current samples;
• calculating a sequence sums of squares of the errors from the sums of squares of errors;
• using the sequence sums of squares of errors to calculate a sequence variance matrix defining an elliptical uncertainty region;
• transmitting the sequence current phasors and the sequence variance matrix to a remote location;
• and
• at the remote location,
• determining whether a disturbance has occurred, and, if so, re-initializing the sample window;
• and
• determining whether any of the sequence current phasors falls outside the elliptical uncertainty region.

A system for detecting faults on a transformer, the system comprising:

• current sensors for measuring phase current samples at each of a plurality of transformer windings;
• and
• a computer for
• calculating real and imaginary phaselets comprising partial sums of the phase current samples;
• for each phaselet, calculating a respective partial sum of the squares of each phase current sample of the each phaselet;
• calculating the sums of the real and imaginary phaselets over a variable size sliding sample window;
• calculating real and imaginary phasor components from the phaselets over the sample window;
• calculating a sum of the partial sums of the squares over the sample window;
• using the sums of the real and imaginary phaselets, the real and imaginary phasor components, and the sum of the partial sums of the squares to calculate a sum of squares of errors between the phase current samples and a fitted sine wave representative of the real and imaginary phasor components;
• using the sum of squares of errors to calculate a variance matrix defining an elliptical uncertainty region;
• applying a symmetrical component transform to the real and imaginary phasor components to obtain symmetrical component current phasors including a negative sequence current phasor for each of the transformer windings;
• determining a baseline residual current phasor;
• adding the negative sequence current phasors of the transformer windings in the direction of a coupling region to obtain a calculated residual current phasor;
• subtracting the baseline residual current phasor from the calculated residual current phasor to obtain a resulting phasor;
• and
• determining whether the resulting phasor falls outside of the elliptical uncertainty region.