Providing a frequency of an electrical quantity in an electrical power system
A method for providing a frequency of an electrical quantity in an electrical power system comprises obtaining, with respect to a first time, a first discrete Fourier transform (DFT) phasor of an electrical quantity in the electrical power system, estimating a second DFT phasor at a time interval before the first time, where the time interval depends on an approximated frequency, and determining the frequency at the first time based on the first and the second DFT phasor.
1. A method for providing a frequency of an electrical quantity in an electrical power system, the method comprising:
obtaining, with respect to a first time at which the electrical quantity is sampled, a first discrete Fourier transform (DFT) phasor of the electrical quantity in the electrical power system,
estimating a second DFT phasor at a first time interval before the first time, said first time interval depending on an approximated frequency, wherein the second DFT phasor is estimated by interpolation using DFT phasors obtained at sampling times around the time at which the second DFT phasor is to be estimated,
determining the frequency (fnew) at the first time based on the first and the second DFT phasor, and
control the electrical power system based on the determined frequency, wherein the control comprises one or more of controlling a circuit breaker, disconnecting a load, or restoring a frequency of the electrical power system.
2. The method according to claim 1 , wherein the second DFT phasor is estimated by linear interpolation using a DFT phasor obtained at a sampling time directly preceding the time at which the second DFT phasor is to be estimated and another DFT phasor obtained at a sampling time directly following the time at which the second DFT phasor is to be estimated.
3. The method according to claim 1 , wherein the second DFT phasor is estimated by higher order interpolation using at least three DFT phasors obtained at sampling times around the time at which the second DFT phasor is to be estimated.
4. The method according to claim 1 , wherein the approximated frequency is a frequency at a second time preceding the first time, in particular the frequency at the second time is determined based on a previous DFT phasor at the second time and a previous estimated DFT phasor at a second time interval before the second time.
5. The method according to claim 1 , wherein the first time interval is given by one divided by a product, where the product is two times the approximated frequency.
6. The method according to claim 1 , wherein determining the frequency at the first time based on the first and the second DFT phasor comprises determining a difference in phase angle between the first and the second DFT phasor.
7. The method according to claim 1 , further comprising applying the determined frequency at the first time in a fault handling measure in the electrical power system.
8. The method according to claim 1 , further comprising:
applying the determined frequency to a correction function, which correction function is based on an analytical expression for the phasor; and
adjusting the phasor with a correction factor obtained from the correction function.
9. The method according to claim 8 , wherein the analytical expression is based on a sinusoidal function.
10. The method according to claim 8 , wherein the correction function comprises a phase of the phasor as a parameter and the method further comprises estimating the phase for the correction function based on the phasor.
11. The method according to claim 10 , further comprising estimating an initial phase to be used in the correction function based on the analytical expression and a zero phase angle.
12. The method according to claim 8 , further comprising applying the adjusted phasor in a fault handling measure in the electrical power system.
13. The method according to claim 12 , wherein the fault handling measure is a Rate of Change of Frequency (ROCOF) protection measure.
14. The method according to claim 12 , wherein the fault comprises short circuit faults and/or the protection is the protection of a generator.
15. A phasor processing device for use in an electrical power system, the phasor processing device comprising a processor configured to:
obtain, with respect to a first time at which an electrical quantity is sampled, a first discrete Fourier transform (DFT) phasor of the electrical quantity in the electrical power system,
estimate a second DFT phasor at a first time interval before the first time, said first time interval depending on an approximated frequency, wherein the second DFT phasor is estimated by interpolation using DFT phasors obtained at sampling times around the time at which the second DFT phasor is to be estimated, and
determine the frequency (fnew) at the first time based on the first and the second DFT phasor, and
control the electrical power system based on the determined frequency, wherein the control comprises one or more of controlling a circuit breaker, disconnecting a load, or restoring a frequency of the electrical power system.
16. The phasor processing device according to claim 15 , wherein the second DFT phasor is estimated by linear interpolation using a DFT phasor obtained at a sampling time directly preceding the time at which the second DFT phasor is to be estimated and another DFT phasor obtained at a sampling time directly following the time at which the second DFT phasor is to be estimated.
17. The phasor processing device according to claim 15 , wherein the second DFT phasor is estimated by higher order interpolation using at least three DFT phasors obtained at sampling times around the time at which the second DFT phasor is to be estimated.
18. The phasor processing device according to claim 15 , wherein the device is selected from the group of: an intelligent electronic device, a protection relay, a phasor measurement unit, a grid controller, and a merging unit.
19. A non-transitory computer-readable medium storing computer program code for providing a frequency of an electrical quantity in an electrical power system, said computer program code configured to cause a processor to, when said computer program code is being operated upon by the processor:
obtain, with respect to a first time at which the electrical quantity is sampled, a first discrete Fourier transform (DFT) phasor of the electrical quantity in the electrical power system,
estimate a second DFT phasor at a first time interval before the first time, said first time interval depending on an approximated frequency, wherein the second DFT phasor is estimated by interpolation using DFT phasors obtained at sampling times around the time at which the second DFT phasor is to be estimated, and
determine the frequency (fnew) at the first time based on the first and the second DFT phasor, and
control the electrical power system based on the determined frequency, wherein the control comprises one or more of controlling a circuit breaker, disconnecting a load, or restoring a frequency of the electrical power system.
20. The non-transitory computer-readable medium according to claim 19 ,
wherein the second DFT phasor is estimated by linear interpolation using a DFT phasor obtained at a sampling time directly preceding the time at which the second DFT phasor is to be estimated and another DFT phasor obtained at a sampling time directly following the time at which the second DFT phasor is to be estimated, or
wherein the second DFT phasor is estimated by higher order interpolation using at least three DFT phasors obtained at sampling times around the time at which the second DFT phasor is to be estimated.