Harmonic component measuring method for power system

A harmonic component measuring method for a power system, for finding an impedance for a measurement harmonic or an equivalent circuit comprising the impedance and a current source in series, wherein an mth-degree harmonic of a frequency which is m times (m is an integer) a frequency fs of a fundamental wave in the power system is used as the measurement harmonic, said harmonic component measuring method comprising the steps of:

• synchronizing voltages of inter-harmonics with the measurement harmonic, wherein the voltages of inter-harmonics comprises voltages of frequencies fx which are non-integral multipies of the fundamental wave above and below the measurement harmonic;
• finding and determining the frequencies fx of the voltages of inter-harmonics between the mth-degree measurement harmonic and (m±1)th-degree harmonics from an expression of fx=(fs*m)±{(fs/n)*k)} where n is an integer of 1, 2, . . . , n responsive to measurement accuracy 1/n (0<1/n<1) and k is an integer of 1, 2, . . . , n for frequency setting;
• applying the voltages of inter-harmonics to a harmonic inject point in the power system in n cycles of the fundamental wave;
• measuring voltages at the harmonic inject point based on the applied voltages of inter-harmonics and measuring currents at least either upstream or downstream from the harmonic inject point in the power system;
• calculating impedances for the applied voltages of inter-harmonics on at least either an upstream or a downstream side from the harmonic inject point from the measurement results;
• and
• performing interpolation processing based on the calculation results to find the impedance for the measurement harmonic on at least either the upstream or the downstream side from the harmonic inject point.

A harmonic component measuring method for a power system, for finding an admittance for a measurement harmonic or an equivalent circuit comprising the admittance and a current source in parellel wherein an nth-degree harmonic of a frequency which is n times (n is an integer) a frequency fs of a fundamental wave in the power system is used as the measurement harmonic, said harmonic component measuring method comprising the steps of:

• performing a frequency analysis of system voltage data at a harmonic inject point in the power system and detecting (n±m)th-degree (0<m<1) intermediate-degree harmonic components in an order starting at the component closest to the measurement harmonic, wherein the (n±m) th-deqree intermediate-degree harmonic components are components of frequencies of non-integral multiples of the fundamental wave, synchronized therewith, above and below the measurement harmonic of the system voltage;
• determining inject frequencies above and below the measurement harmonic at a measurement time, wherein the inject frequencies above and below the measurement harmonic comprises first detected frequencies of the intermediate-degree harmonic components above and below the measurement harmonic at which the harmonic components are equal to or less than a setup value;
• injecting currents of the inject frequencies into the harmonic inject point at the measurement time;
• measuring voltages at the harmonic inject point based on the injected currents of the inject frequencies and measuring currents at least either upstream or downstream from the harmonic inject point in the power system;
• calculating admittances for the injected currents of the inject frequencies on at least either an upstream or a downstream side from the harmonic inject point from the measurement results;
• and
• performing interpolation processing based on the calculation results to find the admittance for the measurement harmonic on at least either the upstream or the downstream side from the harmonic inject point.

A harmonic component measuring method for a power system, for finding an impedance for a measurement harmonic or an equivalent circuit comprising the impedance and a current source in series, wherein an nth-degree harmonic of a frequency which is n times (n is an integer) a frequency fs of a fundamental wave in the power system is used as the measurement harmonic, said harmonic component measuring method comprising the steps of:

• perfoming a frequency analysis of system voltage data at a harmonic inject point in the power system and detecting (n±m)th-degree (0<m<1) intermediate-degree harmonic components in an order starting at the component closest to the measurement harmonic, wherein the (n±m) th-degree intermediate-degree harmonic components are components of frequencies of non-integral multiples of the fundamental wave, synchronized therewith, above and below the measurement harmonic of the system voltage;
• determining apply frequencies above and below the measurement harmonic at a measurement time, wherein the apply frequencies above and below the measurement harmonic comprises first detected frequencies of the intermediate-degree harmonic components above and below the measurement harmonic at which the harmonic components are equal to or less than a setup value;
• applying voltages of the apply frequencies to the harmonic inject point at the measurement time;
• measuring voltages at the harmonic inject point based on the applied voltages of the apply frequencies and measuring currents at least either upstream or downstream from the harmonic inject point in the power system;
• calculating impedances for the applied voltages of the apply frequencies on at least either an upstream or a downstream side from the harmonic inject point from the measurement results;
• and
• performing interpolation processing based on the calculation results to find the impedance for the measurement harmonic on at least either an upstream or the downstream side from the harmonic inject point.

A harmonic component measuring method for a power system comprising the steps of:

• injecting currents of frequencies of non-integral multiples of a fundamental wave above and below a measurement harmonic into a harmonic inject point in the power system while gradually increasing the currents until a distortion voltage measured at the harmonic inject point rises to almost a predetermined upper limit voltage, wherein the measurement harmonic is a harmonic of a frequency of an integral multiple of the fundamental wave;
• calculating admittances for the injected currents on at least either an upstream or a downstream side from the harmonic inject point in the power system from voltage measurement results at the harmonic inject point based on the injected currents and current measurement results on at least either the upstream or the downstream side from the harmonic inject point in the power system;
• and
• performing interpolation processing based on the calculation results to find an admittance for the measurement harmonic on at least either the upstream or the downstream side from the harmonic inject point.

A harmonic component measuring method for a power system comprising the steps of:

• injecting currents of frequencies of non-integral multiples of a fundamental wave above and below a measurement harmonic into a harmonic inject point in the power system while gradually increasing the currents until a distortion voltage measured at the harmonic inject point rises to almost a predetermined upper limit voltage, wherein the measurement harmonic is a harmonic of a frequency of an integral multiple of the fundamental wave;
• calculating admittances for the injected currents on at least either an upstream or a downstream side from the harmonic inject point in the power system from voltage measurement results at the harmonic inject point based on the injected currents and current measurement results on at least either the upstream or the downstream side from the harmonic inject point in the power system;
• performing interpolation processing based on the calculation results to find an admittance of an equivalent circuit for the measurement harmonic on at least either the upstream or the downstream side from the harmonic inject point;
• finding and determining a current source of the equivalent circuit for the measurement harmonic on at least either the upstream or the downstream side from the harmonic inject point from the admittance determined for the measurement harmonic and a measurement harmonic voltage and current measurement results in the power system at the harmonic inject point;
• and
• finding the equivalent circuit for the measurement harmonic on at least either the upstream or the downstream side from the harmonic inject point from a parallel circuit of the determined admittance and the determined current source.

A harmonic component measuring method for a power system, for finding an admittance for a measurement harmonic or an equivalent circuit comprising the admittance and a current source in parallel, wherein an nth-degree harmonic of a frequency which is n times (n is an integer) a frequency fs of a fundamental wave in a power system is used as the measurement harmonic, said harmonic component measuring method comprising the steps of:

• simultaneously injecting currents of frequencies of non-integral multiples of the fundamental wave above and below the measurement harmonic into a harmonic inject point in the power system;
• measuring voltages at the harmonic inject point based on the injected currents and measuring currents at least either upstream or downstream from the harmonic inject point in the power system;
• calculating admittances for the injected currents on at least either an upstream or a downstream side from the harmonic inject point in the power system from the measurement results;
• and
• performing interpolation processing based on the calculation results to find the admittance for the measurement harmonic on at least either the upstream or the downstream side from the harmonic inject point.

A harmonic component measuring method for a power system comprising the steps of:

• injecting currents of frequencies of non-integral multiples of a fundamental wave above and below a measurement harmonic into a harmonic inject point in the power system wherein the measurement harmonic is a harmonic of a frequency of an integral multiple of the fundamental wave;
• measuring voltages at the harmonic inject point based on the injected currents and currents at least either upstream or downstream from the harmonic inject point in the power system;
• determining equivalent circuits on an upstream and a downstream side from the harmonic inject point wherein each equivalent circuit comprises a parallel circuit of an admittance and a current source;
• calculating admittances for the injected currents on at least either the upstream or the downstream side from the harmonic inject point from the measurement results;
• and
• performing interpolation processing based on the calculation results to find an admittance for the measurement harmonic on at least either the upstream or the downstream side from the harmonic inject point.

A harmonic component measuring method for a power system comprising the steps of:

• injecting currents of frequencies of non-integral multiples of a fundamental wave above and below a measurement harmonic into a harmonic inject point in the power system wherein the measurement harmonic is a harmonic of a frequency of an integral multiple of the fundamental wave;
• measuring voltages at the harmonic inject point based on the injected currents and currents at least either upstream or downstream from the harmonic inject point in the power system;
• determining equivalent circuits on an upstream and a downstream side from the harmonic inject point wherein each equivalent circuit comprises a parallel circuit of an admittance and a current source;
• calculating admittances for the injected currents on at least either the upstream or the downstream side from the harmonic inject point from the measurement results;
• performing interpolation processing based on the calculation results to find an admittance for the measurement harmonic on at least either the upstream or the downstream side from the harmonic inject point;
• finding and determining a current source for the measurement harmonic on at least either the upstream or the downstream side from the harmonic inject point from the admittance determined for the measurement harmonic and a measurement harmonic voltage and current measurement results in the power system at the harmonic inject point;
• and
• finding the equivalent circuit for the measurement harmonic on at least either the upstream or the downstream side from the harmonic inject point.

A harmonic component measuring method for a power system comprising the steps of:

• applying voltages of frequencies of non-integral multiples of a fundamental wave above and below a measurement harmonic into a harmonic inject point in the power system wherein the measurement harmonic is a harmonic of a frequency of an integral multiple of the fundamental wave;
• measuring voltages at the harmonic inject point based on the applied voltages and currents at least either upstream or downstream from the harmonic inject point in the power system;
• determining equivalent circuits on an upstream and a downstream side from the harmonic inject point wherein each equivalent circuit comprises a series circuit of an impedance and a voltage source;
• calculating impedances for the applied voltages on at least either the upstream or the downstream side from the harmonic inject point from the measurement results;
• and
• performing interpolation processing based on the calculation results to find an impedance for the measurement harmonic on at least either the upstream or the downstream side from the harmonic inject point.

A harmonic component measuring method for a power system comprising the steps of:

• applying voltages of frequencies of non-integral multiples of the fundamental wave above and below a measurement harmonic into a harmonic inject point in the power system wherein the measurement harmonic is a harmonic of a frequency of an integral multiple of the fundamental wave;
• measuring voltages at the harmonic inject point based on applied voltages and currents at least either upstream or downstream from the harmonic inject point in the power system;
• determining equivalent circuits on an upstream and a downstream side from the harmonic inject point wherein each equivalent circuit comprises a series circuit of an impedance and a voltage source;
• calculating impedances for the applied voltages on at least either the upstream or the downstream side from the harmonic inject point from the measurement results;
• performing interpolation processing based on the calculation results to find an impedance for the measurement harmonic on at least either the upstream or downstream side from the harmonic inject point;
• finding and determining a voltage source for the measurement harmonic on at least either the upstream or the downstream side from the harmonic inject point from the impedance determined for the measurement harmonic and a measurement harmonic voltage and current measurement results in the power system at the harmonic inject point;
• and
• finding the equivalent circuit for the measurement harmonic on at least either the upstream or the downstream side from the harmonic inject point.