Harmonic content determination apparatus

• US 5,559,689 A
• Filed: 08/08/1994
• Issued: 09/24/1996
• Est. Priority Date: 08/08/1994
• Status: Expired due to Fees

• Current Assignee: Sundstrand Corporation (Raytheon Technologies Corporation d/b/a RTX)
• Original Assignee: Sundstrand Corporation (Raytheon Technologies Corporation d/b/a RTX)
• Inventors: Kirchberg, Maurice, Cook, Alec
• Primary Examiner(s): Wong, Peter S.
• Assistant Examiner(s): Krishnan, Aditya
• Application Number:
  US08/287,326
• Time in Patent Office: 778 Days
• Field of Search: 363/37, 363/41, 363/78, 363/79, 363/95, 363/98, 363/132, 363/137, 364/483, 364/726, 318/800, 318/801, 318/802, 318/811
• US Class Current: 363/95
• CPC Class Codes: G01R 23/00 Arrangements for measuring frequencies; Arrangements for analysing frequency spectra
• CPC Class Codes: G01R 25/00 Arrangements for measuring phase angle between a voltage and a current or between voltages or currents

Abstract

An apparatus for determining a frequency component of a signal exploits the aliasing effect by sampling the signal at the frequency of the component (or an integer multiple thereof) to produce first and second sets of samples at the sampling frequency. Corresponding samples of the first and second sets of samples are separated in phase by substantially 90°. The apparatus vectorially determines the magnitude and phase of the frequency component of the signal from the first and second sets of samples.

Claims

1. An apparatus for determining a frequency component of a signal comprising:

sampling means for sampling the signal at a sampling frequency, wherein the sampling means produces first and second sets of samples at the sampling frequency, and wherein corresponding samples of the first and second sets of samples are separated in phase by substantially 90°

; and

,

frequency component determining means for determining the frequency component of the signal from the first and second sets of samples.

2. The apparatus of claim 1 wherein the frequency component determining means comprises phase and magnitude determining means for determining phase and magnitude of the frequency component from the first and second sets of samples.

3. The apparatus of claim 2 wherein the phase and magnitude determining means comprises first sample summing means for summing the first set of samples to determine a first sum, second sample summing means for summing the second set of samples to determine a second sum, and means for determining the magnitude and phase of the frequency component based upon the first and second sums.

4. The apparatus of claim 3 wherein the phase and magnitude determining means comprises magnitude determining means for determining the magnitude of the frequency component according to the following equation:

##EQU7## where mag is the magnitude of the frequency component, a is based upon the first sum, and b is based upon the second sum, and wherein the phase and magnitude determining means further comprises phase determining means for determining the phase of the frequency component according to the following equation;

##EQU8## where pha is the phase of the frequency component, a is based upon the first sum, and b is based upon the second sum.

5. The apparatus of claim 2 wherein the phase and magnitude determining means comprises magnitude determining means for determining the magnitude of the frequency component according to the following equation:

##EQU9## where mag is the magnitude of the frequency component, a is a normalized value relating to the first set of samples, and b is a normalized value relating to the second set of samples, and wherein the phase and magnitude determining means further comprises phase determining means for determining the phase of the frequency component according to the following equation;

##EQU10## where pha is the phase of the frequency component, a is a normalized value relating to the first set of samples, and b is a normalized value relating to the second set of samples.

6. An apparatus for determining a first harmonic component of a signal, wherein the signal has a fundamental frequency f, wherein the first harmonic component has a frequency n₁ f, wherein n₁ is an integer, wherein the signal has a second harmonic component, wherein the second harmonic component has a frequency n₂ f, and wherein n₂ is an integer multiple of n₁, the apparatus comprising:

sampling means for sampling the signal at a sampling frequency n₃ f, wherein the sampling means produces first and second sets of samples at the sampling frequency n₃ f, wherein n₃ is an integer multiple of n₁, and wherein corresponding samples in the first and second sets of samples are separated in phase by substantially 90°

; and

,

harmonic component determining means for determining the first harmonic component from the first and second sets of samples.

7. The apparatus of claim 6 wherein the harmonic component determining means comprises phase and magnitude determining means for determining phase and magnitude of the first harmonic component based upon the first and second sets of samples.

8. The apparatus of claim 7 wherein the phase and magnitude determining means comprises first sample summing means for summing samples of the first set of samples related to the frequency n₁ f to determine a first sum, second sample summing means for summing samples of the first set of samples related to the frequency n₂ f to determine a second sum, third sample summing means for summing samples of the second set of samples related to the frequency n₁ f to determine a third sum, fourth sample summing means for summing samples of the second set of samples related to the frequency n₂ f to determine a fourth sum, and means for determining the magnitude and phase of the first harmonic component based upon the first, second, third, and fourth sums.

9. The apparatus of claim 8 wherein the phase and magnitude determining means comprises magnitude determining means for determining the magnitude of the first harmonic component according to the following equation:

##EQU11## where mag_n1 is the magnitude of the first harmonic component, a is related to the first sum less the second sum, and b is related to the third sum less the fourth sum, and wherein the phase and magnitude determining means further comprises phase determining means for determining the phase of the first harmonic component according to the following equation;

##EQU12## where pha_n1 is the phase of the first harmonic component, a is related to the first sum less the second sum, and b is related to the third sum less the fourth sum.

10. The apparatus of claim 7 wherein the phase and magnitude determining means comprises magnitude determining means for determining the magnitude of the first harmonic component according to the following equation:

##EQU13## where mag_n1 is the magnitude of the first harmonic component, a is an average of the samples in the first set of samples related to the frequency n₁ f less an average of the samples in the first set of samples related to the frequency n₂ f, and b is an average of the samples in the second set of samples related to the frequency n₁ f less an average of the samples in the second set of samples related to the frequency n₂ f, and wherein the phase and magnitude determining means further comprises phase determining means for determining the phase of the first harmonic component according to the following equation;

##EQU14## where pha_n1 is the phase of the first harmonic component, a is an average of the samples in the first set of samples related to the frequency n₁ f less an average of the samples in the first set of samples related to the frequency n₂ f, and b is an average of the samples in the second set of samples related to the frequency n₁ f less an average of the samples in the second set of samples related to the frequency n₂ f.

11. The apparatus of claim 6 wherein n₃ is an integer multiple of n₂ and wherein n₂ and n₃ are unequal.

12. An inverter system comprising:

an inverter having a DC receiving means for receiving input DC power and AC providing means for providing output AC power having a fundamental frequency f;

harmonic determining means connected to the inverter for sampling a signal of the inverter at a sampling frequency n₂ f to produce first and second sets of samples and for determining a harmonic of the fundamental frequency f from the first and second sets of samples, wherein the harmonic has a frequency n₁ f, wherein corresponding samples in the first and second sets of samples are separated in phase by substantially 90°

, wherein n₂ is an integer greater than n₁, and wherein the frequency n₂ f is another harmonic of the fundamental frequency f; and

,

controlling means connected to the inverter and to the harmonic determining means for controlling the inverter so as to suppress the harmonic having the frequency n₁ f.

13. The apparatus of claim 12 wherein the harmonic determining means determines phase and magnitude of the harmonic having the frequency n₁ f from the first and second sets of samples.

14. The apparatus of claim 13 wherein the harmonic determining means sums the samples of the first set of samples related to the frequency n₁ f to determine a first sum, sums the samples of the first set of samples related to a frequency of a harmonic which is an integer multiple of the harmonic having frequency n₁ f to determine a second sum, sums the samples of the second set of samples related to the frequency n₁ f to determine a third sum, sums the samples of the second set of samples related to the frequency of the harmonic which is an integer multiple of the harmonic having frequency n₁ f to determine a fourth sum, and determines the magnitude and phase of the harmonic having the frequency n₁ f based upon the first, second, third, and fourth sums.

15. The apparatus of claim 14 wherein the harmonic determining means determines the magnitude of the harmonic having the frequency n₁ f according to the following equation:

##EQU15## where mag_n1 is the magnitude of the harmonic having the frequency n₁ f, a is related to the first sum less the second sum, and b is related to the third sum less the fourth sum, and determines the phase of the harmonic having the frequency n₁ f according to the following equation;

##EQU16## where pha_n1 is the phase of the harmonic having the frequency n₁ f, a is related to the first sum less the second sum, and b is related to the third sum less the fourth sum.

16. The apparatus of claim 13 wherein the harmonic determining means determines the magnitude of the harmonic having the frequency n₁ f according to the following equation:

##EQU17## where mag_n1 is the magnitude of the harmonic having the frequency n₁ f, a is an average of the samples in the first set of samples related to the frequency n₁ f less an average of the samples in the first set of samples related to a harmonic which is an integer multiple of the harmonic having the frequency n₁ f, and b is an average of the samples in the second set of samples related to the frequency n₁ f less an average of the samples in the second set of samples related to the harmonic which is an integer multiple of the harmonic having the frequency n₁ f, and wherein the harmonic determining means further determines the phase of the harmonic having the frequency n₁ f according to the following equation;

##EQU18## where pha_n1 is the magnitude of the harmonic having the frequency n₁ f, a is an average of the samples in the first set of samples related to the frequency n₁ f less an average of the samples in the first set of samples related to the harmonic which is an integer multiple of the harmonic having the frequency n₁ f, and b is an average of the samples in the second set of samples related to the frequency nf less an average of the samples in the second set of samples related to the harmonic which is an integer multiple of the harmonic having the n₁ f.

17. An inverter system comprising:

an inverter having a DC receiving means for receiving input DC power and AC providing means for providing output AC power having a fundamental frequency f;

harmonic determining means connected to the inverter for sampling a signal of the inverter at a sampling frequency to produce first and second sets of samples and for determining a harmonic of the fundamental frequency f from the first and second sets of samples, wherein the harmonic has a frequency n₁ f, and,

controlling means connected to the inverter and to the harmonic determining means for controlling the inverter so as to suppress the harmonic having the frequency n₁ f.

18. The apparatus of claim 17 wherein the harmonic determining means comprises phase and magnitude determining means for determining phase and magnitude of the harmonic having the frequency n₁ f from the first and second sets of samples.

19. The apparatus of claim 18 wherein the phase and magnitude determining means comprises first sample summing means for summing the samples of the first set of samples related to the frequency n₁ f to determine a first sum, second sample summing means for summing the samples of the first set of samples related to a frequency n₂ f to determine a second sum, wherein n₂ is an integer multiple of n₁, third sample summing means for summing the samples of the second set of samples related to the frequency n₁ f to determine a third sum, fourth sample summing means for summing the samples of the second set of samples related to the frequency n₂ f to determine a fourth sum, and means for determining the magnitude and phase of the harmonic having the frequency n₁ f based upon the first, second, third, and fourth sums.

20. The apparatus of claim 19 wherein the phase and magnitude determining means comprises magnitude determining means for determining the magnitude of the harmonic having the frequency n₁ f according to the following equation:

##EQU19## where mag_n1 is the magnitude of the harmonic having the frequency n₁ f, a is related to the first sum less the second sum, and b is related to the third sum less the fourth sum, and wherein the phase and magnitude determining means further comprises phase determining means for determining the phase of the harmonic having the frequency n₁ f according to the following equation;

##EQU20## pha_n1 is the phase of the harmonic having the frequency n₁ f, a is related to the first sum less the second sum, and b is related to the third sum less the fourth sum.

21. The apparatus of claim 18 wherein n₂ is an integer multiple of n₁, wherein the phase and magnitude determining means comprises magnitude determining means for determining the magnitude of the harmonic having the frequency n₁ f according to the following equation:

##EQU21## where mag_n1 is the magnitude of the harmonic having the frequency n₁ f, a is an average of the samples in the first set of samples related to the frequency n₁ f less an average of the samples in the first set of samples related to a frequency n₂ f, and b is an average of the samples in the second set of samples related to the frequency n₁ f less an average of the samples in the second set of samples related to the frequency n₂ f, and wherein the phase and magnitude determining means further comprises phase determining means for determining the phase of the harmonic having the frequency n₁ f according to the following equation;

##EQU22## where pha_n1 is the phase of the harmonic having the frequency n₁ f, a is an average of the samples in the first set of samples related to the frequency n₁ f less an average of the samples in the first set of samples related to the frequency n₂ f, and b is an average of the samples in the second set of samples related to the frequency n₁ f less an average of the samples in the second set of samples related to the frequency n₂ f.

22. A method for determining a component in a signal, wherein the signal has a fundamental frequency f, and wherein the component has a frequency n₁ f which is substantially an integer multiple of the fundamental frequency f, the method comprising to following steps:

sampling the signal at a sampling frequency to produce first and second sets of samples, wherein corresponding samples in the first and second sets of samples are separated in phase by substantially 90°

; and

,

determining the component from the first and second sets of samples.

23. The method of claim 22 wherein the step of sampling the signal comprises the step of determining phase and magnitude of the component from the first and second sets of samples.

24. The method of claim 23 wherein a frequency n₂ f is substantially an integer multiple of the frequency n₁ f, wherein the step of determining phase and magnitude comprises the steps of summing samples of the first set of samples related to the frequency n₁ f to determine a first sum, summing samples of the first set of samples related to the frequency n₂ f to determine a second sum, summing samples of the second set of samples related to the frequency n₁ f to determine a third sum, summing samples of the second set of samples related to the frequency n₂ f to determine a fourth sum, and determining the magnitude and phase of the component based upon the first, second, third, and fourth sums.

25. The method of claim 24 wherein the step of determining phase and magnitude comprises the further steps of determining the magnitude of the component according to the following equation:

##EQU23## where mag is the magnitude of the component, a is related to the first sum less the second sum, and b is related to the third sum less the fourth sum, and determining the phase of the component according to the following equation;

##EQU24## where pha is the phase of the component, a is related to the first sum less the second sum, and b is related to the third sum less the fourth sum.

26. The method of claim 23 wherein a frequency n₂ f is substantially an integer multiple of the frequency n₁ f, wherein the step of determining phase and magnitude comprises the further steps of determining the magnitude of the component according to the following equation:

##EQU25## where mag is the magnitude of the component, a is an average of the samples in the first set of samples related to the frequency n₁ f less an average of the samples in the first set of samples related to the frequency n₂ f, and b is an average of the samples in the second set of samples related to the frequency n₁ f less an average of the samples in the second set of samples related to the frequency n₂ f, and determining the phase of the component according to the following equation;

##EQU26## where pha is the phase of the component, a is an average of the samples in the first set of samples related to the frequency n₁ f less an average of the samples in the first set of samples related to the frequency n₂ f, and b is an average of the samples in the second set of samples related to the frequency n₁ f less an average of the samples in the second set of samples related to the frequency n₂ f.