Frequency measuring and monitoring apparatus, methods and systems

• US 4,319,329 A
• Filed: 02/21/1980
• Issued: 03/09/1982
• Est. Priority Date: 02/21/1980
• Status: Expired due to Term

• Current Assignee: Iowa State University Research Foundation Incorporated (Iowa State University)
• Original Assignee: Iowa State University Research Foundation Incorporated (Iowa State University)
• Inventors: Ham, Fredric M., Girgis, Adly A.
• Primary Examiner(s): Wise, Edward J.
• Application Number:
  US06/123,213
• Time in Patent Office: 747 Days
• Field of Search: 364/493, 364/483, 364/484, 364/485, 364/900, 364/576, 361/80-84, 361/67, 361/68, 361/78, 324/77 B, 324/77 C, 324/77 CS, 324/78 D, 324/78 R, 324/78 Z
• US Class Current: 702/75
• CPC Class Codes: G01R 23/02 Arrangements for measuring frequency, e.g. pulse repetition rate; Arrangements for measuring period of current or voltage

Abstract

Waveform frequency measuring apparatus and methods utilizing zero-crossing triggered analog-to-digital conversion apparatus combined with Discrete Fourier Transform (DFT) digital computing apparatus accomplish measurement of waveform fundamental frequency using hitherto disadvantageous leakage of the Discrete Fourier Transform.

In an example, the frequency measuring apparatus and methods are used in an alternating current (AC) electrical power system for measuring and monitoring frequency deviation Δf from the nominal system frequency f and actuating protective relaying when the frequency deviation is excessive.

Claims

1. Apparatus for measurement, relative to a reference frequency f, of frequency deviation Δ

f of frequency of a substantially single-frequency sinusoidal waveform having electrical values including zero-crossings and being provided to said apparatus, said apparatus comprising;

means for generating triggering signals, each triggering signal being in response to a respective one of at least some of said zero-crossings of said waveform;

converting means being responsive to said waveform and to said each said triggering signal so that said converting means produces n digital representations, n being a whole number of at least 4, corresponding to n electrical values of said waveform occurring during a period 1/f of the reference frequency, one of said n digital representations corresponding to a time-wise first one of said n electrical values, said first one value being located fΔ

t reference cycles relative to the zero-crossing nearest said each said triggering signal, Δ

t being a time interval; and

stored program computing means for receiving said n digital representations and computing a leakage coefficient of the discrete Fourier transform of said n digital representations and then computing the measured frequency deviation Δ

f from at least the leakage coefficient so that the frequency deviation so computed is substantially accurate in view of the number n and the quantity fΔ

t.

2. Measurement apparatus as claimed in claim 1 wherein said converting means comprises

means for sampling said waveform at a rate equal to a multiple of said reference frequency f, said multiple being equal to said whole number n times f, said sampling means being responsive to said each said triggering signal so as to produce exactly n analog samples having said n electrical values and so that the timewise first one of said analog samples is always located the same said fΔ

t reference cycles relative to the zero-crossing nearest said each said triggering signal; and

means for producing said n digital representations from said n analog samples.

3. Measurement apparatus as claimed in claim 1 wherein said converting means comprises

means responsive to said waveform for producing a digital representation of any one of said electrical values of said waveform in response to a command pulse;

and

means responsive to said each said triggering signal for providing exactly n command pulses to said digital producing means such that said n command pulses recur at a rate equal to n times the reference frequency f and such that the timewise first one of said command pulses is always the same said fΔ

t reference cycles relative to the zero-crossing nearest said each said triggering signal,

whereby said digital producing means produces said n digital representations.

4. Measurement apparatus as claimed in claim 1 wherein

said triggering signal generating means, and said converting means cooperate so that said timewise first one of said n electrical values corresponding to a digital representation is always located less than the fraction 40/360 of one cycle of the reference frequency (fΔ

t<

40/360) relative to the zero-crossing nearest said each said triggering signal; and

said computing means computes the measured frequency deviation as proportional to the leakage coefficient and independent of the quantity fΔ

t.

5. Measurement apparatus as claimed in claim 4 wherein the reference frequency is 60 Hertz, the number n is 32, and the computing means computes the measured frequency deviation as equal to the leakage coefficient multiplied by a proportionality constant equal to the reciprocal of a number between 0.090 and 0.096.

6. Measurement apparatus as claimed in claim 1 wherein

said n digital representations correspond to the n electrical values being V(i), where i=0,1,2, . . . n-1, n being evenly divisible by two;

the leakage coefficient η

of the discrete Fourier transform computed by said computing means is substantially equal to ##EQU6## and the measured frequency deviation Δ

f computed by said computing means is substantially equal to the solution for Δ

f of the equation ##EQU7##

7. Electrical power relaying apparatus comprising

apparatus for measurement, relative to a reference frequency f, of frequency deviation Δ

f of frequency of a substantially single-frequency sinusoidal waveform having electrical values including zero-crossings and being provided to said measurement apparatus, said measurement apparatus comprising

means for generating triggering signals, each triggering signal being in response to a respective one of at least some of said zero-crossings of said waveform;

converting means being responsive to said waveform and to said each said triggering signal so that said converting means produces n digital representations, n being a whole number of at least 4, corresponding to n electrical values of said waveform occurring during a period 1/f of the reference frequency, one of said n digital representations corresponding to a timewise first one of said n electrical values, said first one value being located fΔ

t reference cycles relative to the zero-crossing nearest said each said triggering signal, Δ

t being a time interval; and

stored program computing means for receiving said n digital representations and computing a leakage coefficient of the discrete Fourier transform of said n digital representations and then computing the measured frequency deviation Δ

f from at least the leakage coefficient so that the frequency deviation so computed is substantially accurate in view of the number n and the quantity fΔ

t;

said electrical power relaying apparatus further comprising circuit breaking means capable of being actuated by an electrical breaker signal,

said computing means of said frequency deviation measurement apparatus further comparing said measured frequency deviation with at least one threshold frequency deviation quantity and producing said electrical breaker signal so as to actuate said circuit breaking means when said measured frequency deviation exceeds said threshold frequency deviation quantity in magnitude.

8. Protectable electrical power system apparatus comprising

a plurality of means for receiving electrical energy;

circuit breaker means connected to at least some of said plurality of energy-receiving means, each said circuit breaker means being able to disconnect one of said plurality of energy-receiving means when said each said circuit breaker means is fed a respective electrical breaker signal;

transmission line means connected to said circuit breaker means, said transmission line means being able to carry electrical energy having an alternating current frequency influenceable by the number of said plurality of energy-receiving means being permitted to receive said electrical energy by said circuit breaker means; and

frequency deviation measurement apparatus being apparatus for measurement, relative to a reference frequency f, of frequency deviation Δ

f of frequency of a substantially single-frequency sinusoidal waveform having electrical values including zero-crossings and being provided to said frequency deviation measurement apparatus, said frequency deviation measurement apparatus comprising

means for generating triggering signals, each triggering signal being in response to a respective one of at least some of said zero-crossings of said waveform;

converting means being responsive to said waveform and to said each said triggering signal so that said converting means produces n digital representations, n being a whole number of at least 4, corresponding to n electrical values of said waveform occurring during a period 1/f of the reference frequency, one of said n digital representations corresponding to a timewise first one of said n electrial values, said first one value being located fΔ

t reference cycles relative to the zero-crossing nearest said each said triggering signal, Δ

t being a time interval; and

stored program computing means for receiving said n digital representations and computing a leakage coefficient of the discrete Fourier transform of said n digital representations and then computing the measured frequency deviation Δ

f from at least the leakage coefficient so that the frequency deviation so computed is substantially accurate in view of the number n and the quantity fΔ

t;

said frequency deviation measurement apparatus being coupled to said transmission line means so that said alternating current frequency is provided to said frequency deviation measurement apparatus as said substantially single-frequency sinusoidal waveform having electrical values including zero-crossings,

said frequency deviation measurement apparatus comparing said measured frequency deviation with a plurality of threshold frequency deviation quantities so as to produce and feed each said respective electrical breaker signal to said circuit breaking means so that more energy-receiving means are disconnected by said circuit breaking means when the magnitude of said measured frequency deviation is at at least one higher level than when the magnitude of said measured frequency deviation is at at least one lower level,

whereby said at least some of said energy-receiving means are able to be shed and said power system apparatus is protectable.

9. Protectable electrical power system apparatus comprising

means for generating electrical energy having a frequency deviation, relative to a nominal system frequency, dependent upon an amount of energy demand on said generating means;

a plurality of electrical energy transmission line means for providing said energy demand to said generating means;

circuit breaker means connected to at least some of said plurality of transmission line means, each said circuit breaker means connecting one of said transmission line means to said generating means and being able to disconnect said one of said transmission line means when said each said circuit breaker means is tripped by a respective breaker signal; and

frequency deviation measurement apparatus being apparatus for measurement, relative to a reference frequency f, of frequency deviation Δ

f of frequency of a substantially single-frequency sinusoidal waveform having electrical values including zero-crossings and being provided to said frequency deviation measurement apparatus, said frequency deviation measurement apparatus comprising

means for generating triggering signals, each triggering signal being in response to a respective one of at least some of said zero-crossings of said waveform;

converting means being responsive to said waveform and to said each said triggering signal so that said converting means produces n digital representations, n being a whole number of at least 4, corresponding to n electrical values of said waveform occurring during a period 1/f of the reference frequency, one of said n digital representations corresponding to a timewise first one of said n electrical values, said first one value being located fΔ

t reference cycles relative to the zero-crossing nearest said each said triggering signal, Δ

t being a time interval; and

stored program computing means for receiving said n digital representations and computing a leakage coefficient of the discrete Fourier transform of said n digital representations and then computing the measured frequency deviation Δ

f from at least the leakage coefficient so that the frequency deviation so computed is substantially accurate in view of the number n and the quantity fΔ

t;

said frequency deviation measurement apparatus being coupled to said generating means so as to measure said generating means frequency deviation, said reference frequency f of said measurement apparatus being substantially equal to said nominal system frequency,

said frequency deviation measurement apparatus comparing said measured frequency deviation of said generating means with a plurality of threshold frequency deviation quantities so as to produce each said respective breaker signal to trip said circuit breaker means so that more of said transmission line means are disconnected by said circuit breaker means when the magnitude of said measured frequency deviation of said generating means is at at least one higher level than when the magnitude of said measured frequency deviation is at at least one lower level,

whereby said at least some of said plurality of transmission line means are able to be sequentially shed and said power system apparatus is protectable.

10. Protective apparatus for signalling excessive frequency deviation, from a standard frequency f, of an alternating current waveform having a fundamental frequency wave, said fundamental frequency wave having zero-crossings, said protective apparatus comprising

zero-crossing detector means for producing triggering pulses corresponding to at least some of said zero-crossings of said fundamental frequency wave;

analog-to-digital converter means responsive to said fundamental frequency wave and to each of said triggering pulses from said zero-crossing detector so that said converter produces a number n of binary values corresponding to the same number n of analog values of said fundamental frequency wave occurring after a zero-crossing and during a time period of a cycle of the standard frequency f, the converter acting so that a time interval being from each zero-crossing corresponding to a trigger pulse and the first analog value of said fundamental frequency wave converted to binary form in response to said trigger pulse is substantially the same for every trigger pulse; and

means for computing the discrete Fourier transform of said n binary values and then computing a leakage coefficient equal to the ratio of the amount of at least some of spuriously calculated frequency content other than at the standard frequency f divided by the magnitude of the calculated frequency component corresponding to the standard frequency f,

said computing means producing at least one electrical control signal when the magnitude of said ratio exceeds a threshold value,

whereby said apparatus produces said control signal and so signals excessive frequency deviation of the fundamental frequency wave from the standard frequency f suitable for electrical system protection purposes.

11. Apparatus for protecting an electrical power system having a system loading and having an alternating current power waveform having a fundamental frequency being influenceable by the system loading, said apparatus comprising

protective apparatus for signalling excessive frequency deviation, from a standard frequency f, of an alternating current waveform having a fundamental frequency wave, said fundamental frequency wave having zero-crossings, said protective apparatus for signalling excessive frequency deviation comprising

zero-crossing detector means for producing triggering pulses corresponding to at least some of said zero-crossings of said fundamental frequency wave;

analog-to-digital converter means responsive to said fundamental frequency wave and to each of said triggering pulses from said zero-crossing detector so that said converter produces a number n of binary values corresponding to the same number n of analog values of said fundamental frequency wave occurring after a zero-crossing and during a time period of a cycle of the standard frequency f, the converter acting so that a time interval being from each zero-crossing corresponding to a trigger pulse and the first analog value of said fundamental frequency wave converted to binary form in response to said trigger pulse is substantially the same for every trigger pulse; and

means for computing the discrete Fourier transform of said n binary values and then computing a leakage coefficient equal to the ratio of the amount of at least some of the spuriously calculated frequency content other than at the standard frequency f divided by the magnitude of the calculated frequency component corresponding to the standard frequency f,

said computing means producing at least one electrical control signal when the magnitude of said ratio exceeds a threshold value,

whereby said protective apparatus for signalling excessive frequency deviation produces said control signal and so signals excessive frequency deviation of the fundamental frequency wave from the standard frequency f suitable for electrical system protection purposes;

means for coupling said alternating current power waveform to said protective signalling apparatus, said coupling means including low-pass filter means for passing only a waveform being said fundamental frequency wave; and

means for changing the system loading in response to said at least one electrical control signal of said protective signalling apparatus so as to reduce the magnitude of the frequency deviation of the fundamental frequency wave from the standard frequency f.

12. Protecting apparatus as claimed in claim 11 wherein

protective signalling apparatus computing means compares said ratio with a plurality of threshold values and produces additional electrical control signals when the magnitude of said ratio exceeds each of said plurality of threshold values;

and

said means for changing the system loading is responsive to each of said additional electrical control signals so as to reduce the magnitude of the frequency deviation of the fundamental frequency wave from the standard frequency f.

13. Apparatus for measurement, relative to a reference frequency f, of frequency deviation Δ

f of the fundamental frequency of an electrical waveform provided to said apparatus, said frequency deviation measurement apparatus comprising;

filter means for passing substantially only the fundamental frequency waveform of said electrical waveform provided to said apparatus for frequency deviation measurement thereof, said fundamental frequency waveform having zero-crossings;

means for detecting said zero-crossings and generating a trigger signal corresponding to at least some of said zero-crossings;

means for sampling said fundamental frequency waveform at a rate equal to an integer multiple n of said reference frequency f, said multiple n being greater than or equal to 4, said sampling means being triggered by said zero-crossing detector means so as to obtain n analog samples of said fundamental frequency waveform, the first of said samples being located fΔ

t cycles relative to the nearest of said zero-crossings, where Δ

t is a time interval;

means for converting said n analog samples to n digital representations of said samples; and

stored program computing means for computing the leakage coefficient of the discrete Fourier transform of said n digital representations and then computing the measured frequency deviation Δ

f from the leakage coefficient in a manner corresponding to the value of said fΔ

t cycles.

14. In a method of measurement of frequency deviation Δ

f, of a substantially sinusoidal analog waveform having zero-crossings and electrical values, from a reference frequency f the steps of

electronically generating a triggering signal in response to one of said zero-crossings of said waveform;

electronically converting a number n of said electrical values of said sinusoidal analog waveform to digital representations by producing n said digital representations, n being greater than or equal to 4, corresponding to said number n of the electrical values of said waveform occurring during a period 1/f of the reference frequency subsequent to said one of said zero-crossings, one of said n digital representations corresponding to a timewise first one of said n electrical values, said first one value being located a fraction fΔ

t of one reference cycle relative to said one of said zero-crossings, said triggering signal initiating said converting step;

electronically computing a leakage coefficient of the discrete Fourier transform of said n digital representations; and

electronically computing the measured frequency deviation Δ

f from at least said leakage coefficient so that the frequency deviation so computed is substantially accurate in view of the number n and the fraction fΔ

t.

15. A method of repetitive measurement of frequency deviation Δ

f, of a substantially sinusoidal analog waveform having zero-crossings and electrical values, from a reference frequency f, said method comprising

successively repeating a second method comprising the steps of

A. electronically generating a triggering signal in response to one of said zero-crossings of said waveform;

B. electronically converting a number n of said electrical values of said sinusoidal analog waveform to digital representations by producing n said digital representations, n being greater than or equal to 4, corresponding to said number n of the electrical values of said waveform occurring during a period 1/f of the reference frequency subsequent to said one of said zero-crossings, one of said n digital representations corresponding to a timewise first one of said n electrical values, said first one value being located a fraction fΔ

t of one reference cycle relative to said one of said zero-crossings, said triggering signal initiating said converting step;

C. electronically computing a leakage coefficient of the discrete Fourier transform of said n digital representations; and

D. electronically computing the measured frequency deviation Δ

f from at least said leakage coefficient so that the frequency deviation so computed is substantially accurate in view of the number n and the fraction fΔ

t;

said second method being so successively repeated that said steps are performed in response to successive ones of at least some of said zero-crossings of said sinusoidal analog waveform thereby resulting in computing a succession of values of measured frequency deviation Δ

f.

16. A method of monitoring frequency deviation Δ

f, of a substantially sinusoidal analog waveform having zero-crossings and electrical values, from a reference frequency f, comprising

successively repeating a second method comprising the steps of

A. electronically generating a triggering signal in response to one of said zero-crossings of said waveform;

B. electronically converting a number n of said electrical values of said sinusoidal analog waveform to digital representations by producing n said digital representations, n being greater than or equal to 4, corresponding to said number n of the electrical values of said waveform occurring during a period 1/f of the reference frequency subsequent to said one of said zero-crossings, one of said n digital representations corresponding to a timewise first one of said n electrical values, said first one value being located a fraction fΔ

t of one reference cycle relative to said one of said zero-crossings, said triggering signal initiating said converting step;

C. electronically computing a leakage coefficient of the discrete Fourier transform of said n digital representations; and

D. electronically computing the measured frequency deviation Δ

f from at least said leakage coefficient so that the frequency deviation so computed is substantially accurate in view of the number n and the fraction fΔ

t;

said second method being so successively repeated that said steps are performed in response to successive ones of at least some of said zero-crossings of said sinusoidal analog waveform thereby resulting in computing a succession of values of measured frequency deviation Δ

f;

said frequency deviation monitoring method further comprising the steps of

electronically comparing each of said succession of values of measured frequency deviation Δ

f with a limit value of frequency deviation; and

electronically generating a monitor signal dependent upon whether said measured frequency deviation is higher or lower than said limit value.

17. In a method of monitoring over time an analog waveform having zero-crossings and electrical values the steps of

electronically sensing successive ones of at least some of said zero-crossings and in response to each of said successive ones electronically converting a respective group of n of said electrical values of said analog waveform to digital representations, said electrical values in each group having a spacing 1/(nf) and including an initial electrical value in each said group always being the same time interval Δ

t relative to its respective one of said at least some of said zero-crossings, f being a reference frequency and n being a whole number at least 4; and

electronically computing a leakage coefficient of the discrete Fourier transform of each group of n digital representations to produce a succession of computed leakage coefficient values,

whereby said leakage coefficient values are related to a frequency deviation Δ

f from said reference frequency f and said succession of leakage coefficient values effectively provides a monitoring of instantaneous frequency of said analog waveform.

18. The method of claim 17 wherein said method further comprises the steps of electronically comparing said succession of leakage coefficient values with at least one threshold value and generating a monitor signal dependent on the comparing of said leakage value to said threshold value.

19. Apparatus for monitoring over a period of time an analog waveform having zero-crossings and electrical values, the apparatus comprising

means for electronically sensing successive ones of at least some of said zero-crossings and in response to each of said successive ones electronically converting a respective group of n of said electrical values of said analog waveform to digital representations, said electrical values in each group having spacing 1/(nf) and including an initial electrical value in each said group always being the same time interval Δ

t relative to its respective one of at least some of said zero-crossings, f being a reference frequency and n being a whole number at least 4; and

means for electronically computing a leakage coefficient of the discrete Fourier transform of each group of n digital representations to produce a succession of computed leakage coefficient values,

whereby said leakage coefficient values are related to a frequency deviation Δ

f from said reference frequency f and said succession of leakage coefficient values effectively provides a monitoring of instantaneous frequency of said analog waveform.

20. Monitoring apparatus as claimed in claim 19 wherein

said apparatus further comprises means for electronically comparing said succession of leakage coefficient values with at least one threshold value and generating a monitor signal dependent on the comparison of said leakage value to said threshold value.

21. Apparatus for stabilizing the frequency of an analog waveform having zero-crossings and electrical values, the apparatus comprising

means for generating said analog waveform at and near a reference frequency f, the difference in the actual frequency of said generating means and the reference frequency f being a frequency deviation Δ

f;

means for affecting the generating means being connected to said generating means so as to adjust the actual frequency of said generating means to reduce the magnitude of the frequency deviation Δ

f in response to at least one error signal provided to said adjusting means; and

means for monitoring over a period of time said analog waveform, comprising

means for electronically sensing successive ones of at least some of said zero-crossings and in response to each of said successive ones electronically converting a respective group of n of said electrical values of said analog waveform to digital representations, said electrical values in each group having spacing 1/(nf) and including an initial electrical value in each said group always being the same time interval Δ

t relative to its respective one of at least some of said zero-crossings, f being the reference frequency and n being a whole number at least 4; and

means for electronically computing a leakage coefficient of the discrete Fourier transform of each group of n digital representations to produce a succession of computed leakage coefficient values, whereby said leakage coefficient values are related to said frequency deviation Δ

f from said reference frequency f and said succession of leakage coefficient values effectively provides a monitoring of instantaneous frequency of said analog waveform;

said monitoring means being coupled to said generating means for monitoring the analog waveform of said generating means, said succession of computed leakage coefficient values produced by said monitoring means being able to be used by said monitoring means to produce said at least one said error signal and said monitoring means being connected to said adjusting means so as to provide said error signal to said adjusting means,

whereby the frequency of said analog waveform is able to be stabilized.