Methods and systems for measuring a rate of change of frequency

US 7,328,114 B2
Filed: 12/09/2005
Issued: 02/05/2008
Est. Priority Date: 12/09/2005
Status: Expired due to Fees

First Claim

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1. A method for measuring a rate of change of frequency, said method comprising:

estimating at least one phasor value;

estimating a frequency based on the estimated at least one phasor value;

compensating the estimated at least one phasor value based on the estimated frequency;

calculating a frequency based on the compensated at least one phasor value;

calculating a rate of change of the calculated frequency based on the calculated frequency; and

outputting a signal to an output device when the rate of change of the calculated frequency exceeds a pre-determined limit.

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Abstract

A method for measuring a rate of change of frequency includes estimating at least one phasor value, estimating a frequency based on the estimated at least one phasor value, compensating the estimated at least one phasor value based on the estimated frequency, calculating a frequency based on the compensated at least one phasor value, and calculating a rate of change of the calculated frequency based on the calculated frequency.

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23 Claims

1. A method for measuring a rate of change of frequency, said method comprising:
- estimating at least one phasor value;
  
  estimating a frequency based on the estimated at least one phasor value;
  
  compensating the estimated at least one phasor value based on the estimated frequency;
  
  calculating a frequency based on the compensated at least one phasor value;
  
  calculating a rate of change of the calculated frequency based on the calculated frequency; and
  
  outputting a signal to an output device when the rate of change of the calculated frequency exceeds a pre-determined limit.
- View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17)
- - 2. A method in accordance with claim 1 wherein estimating a frequency comprises estimating a frequency based on at least one rotational rate of the estimated at least one phasor value.
  - 3. A method in accordance with claim 1 wherein estimating a frequency based on at least one rotational rate comprises estimating a frequency based on at least one rotational rate of a positive sequence.
  - 4. A method in accordance with claim 1 wherein compensating the estimated at least one phasor value comprises computing at least one off-nominal phasor correction value based on the estimated frequency.
  - 5. A method in accordance with claim 1 wherein estimating at least one phasor value comprises estimating at least one phasor value using:
    - $\overline{X} (m) = \frac{\sqrt{2}}{N} \sum_{k = m \frac{N}{2} - \frac{N}{2}}^{m \frac{N}{2} + \frac{N}{2} - 1} x [(k + 1 / 2) \cdot Δ t] \cdot ⅇ^{- j (k - m \frac{N}{2} + 1 / 2) \frac{2 π}{N}};$ and wherein;
      
      m;
      
      Half cycle index.
  - 6. A method in accordance with claim 1 wherein estimating a frequency comprises estimating a frequency using:
    - $\begin{matrix} E_{cs} (m) = \overline{X} (m) \cdot {\overline{X} (m - 1)}^{*}; \\ f_{cs} (m) = f + \frac{f}{π} \cdot a \tan (\frac{Im (E_{cs} (m))}{Re (E_{cs} (m))}); \end{matrix}$ and wherein;
      
      f_cs;
      
      Coarse frequency estimate.
  - 7. A method in accordance with claim 1 wherein compensating the estimated at least one phasor value comprises compensating using:
    - $Δ f (m) = f_{cs} (m) - f; X (m) = [1 + \frac{1}{6} \cdot π^{2} + \frac{1}{4}) \cdot {(Δ f (m) / f)}^{2}] \cdot \overline{X (m)}; and - \frac{1}{2} \cdot Δ f (m) / f - \frac{1}{4} \cdot {(Δ f (m) / f)}^{2}] \cdot \overline{{X (m)}^{*}} .$
  - 8. A method in accordance with claim 1 wherein calculating a frequency comprises calculating a frequency using:
    - $\begin{matrix} E_{a} (m) = X (m) \cdot {X (m - 1)}^{*}; and \\ f_{a} (m) = f + \frac{f}{π} \cdot a \tan (\frac{Im (E_{a} (m))}{Re (E_{a} (m))}) . \end{matrix}$
  - 9. A method in accordance with claim 1 wherein calculating a rate of change comprise calculating a rate of change using:
    - $\frac{ⅆ f}{ⅆ t} = 2 f \cdot (f_{a} (m) - f_{a} (m - 1)) .$
  - 10. A method in accordance with claim 1 wherein estimating at least one phasor value comprises estimating at least one phasor value every half cycle.
  - 11. A method in accordance with claim 1 wherein estimating at least one phasor value comprises estimating at least one phasor value using:
    - $\begin{matrix} {\overline{X}}_{a} (m) = \frac{\sqrt{2}}{N} \sum_{k = m \frac{N}{2} - \frac{N}{2}}^{m \frac{N}{2} + \frac{N}{2} - 1} x_{a} [k + 1 / 2) \cdot Δ t] \cdot ⅇ^{- j \cdot (k - m \frac{N}{2} + 1 / 2) \frac{2 π}{N}}; \\ {\overline{X}}_{b} (m) = \frac{\sqrt{2}}{N} \sum_{k = m \frac{N}{2} - \frac{N}{2}}^{m \frac{N}{2} + \frac{N}{2} - 1} x_{b} [k + 1 / 2) \cdot Δ t] \cdot ⅇ^{- j \cdot (k - m \frac{N}{2} + 1 / 2) \frac{2 π}{N}}; \\ {\overline{X}}_{c} (m) = \frac{\sqrt{2}}{N} \sum_{k = m \frac{N}{2} - \frac{N}{2}}^{m \frac{N}{2} + \frac{N}{2} - 1} x_{c} [k + 1 / 2) \cdot Δ t] \cdot ⅇ^{- j \cdot (k - m \frac{N}{2} + 1 / 2) \frac{2 π}{N}}; and \end{matrix}$ wherein;
      
      m;
      
      Half cycle index.
  - 12. A method in accordance with claim 1 further comprising calculating positive and negative phasor estimates using:
    - $\begin{matrix} {\overline{X}}_{pos} (m) = \frac{1}{3} [{\overline{X}}_{a} (m) + a {\overline{X}}_{b} (m) + a^{2} {\overline{X}}_{c} (m)]; \\ {\overline{X}}_{neg} (m) = \frac{1}{3} [{\overline{X}}_{a} (m) + a^{2} {\overline{X}}_{b} (m) + a {\overline{X}}_{c} (m)]; and \\ wherein; a = ⅇ^{j \frac{2 π}{3}} . \end{matrix}$
  - 13. A method in accordance with claim 1 wherein estimating a frequency comprises estimating a frequency using:
    - $\begin{matrix} E_{cs} (m) = {\overline{X}}_{pos} (m) \cdot {{\overline{X}}_{pos} (m - 1)}^{*}; and \\ f_{cs} (m) = f + \frac{f}{π} \cdot a \tan (\frac{Im (E_{cs} (m))}{Re (E_{cs} (m))}); \end{matrix}$ wherein;
      
      f_cs;
      
      Coarse frequency estimate.
  - 14. A method in accordance with claim 1 wherein compensating the estimated at least one phasor value comprises compensating using:
    - $\begin{matrix} Δ f (m) = f_{cs} (m) - f; \\ X_{pos} (m) = [1 + \frac{1}{6} \cdot π^{2} + \frac{1}{4}) \cdot (Δ f (m) / f) \cdot {\overline{X}}_{pos} (m); and - \\ [\frac{1}{2} \cdot Δ f (m) / f - \frac{1}{4} \cdot {(Δ f (m) / f)}^{2}] \cdot {{\overline{X}}_{neg} (m)}^{*} . \end{matrix}$
  - 15. A method in accordance with claim 1 wherein calculating a frequency comprises calculating a frequency using:
    - $\begin{matrix} E_{a} (m) = X_{pos} (m) \cdot {X_{pos} (m - 1)}^{*}; and \\ f_{a} (m) = f + \frac{f}{π} \cdot a \tan (\frac{Im (E_{a} (m))}{Re (E_{a} (m))}) . \end{matrix}$
  - 16. A method in accordance with claim 1 wherein calculating a rate of change comprises calculating a rate of change using:
    - $\frac{ⅆ f}{ⅆ t} = 2 f \cdot (f_{a} (m) - f_{a} (m - 1)) .$
  - 17. A method in accordance with claim 4 wherein computing at least one off nominal phasor correction value based on the estimated frequency comprises computing at least one off-nominal phasor correction value using:
    - $\begin{matrix} C \approx 1 + (\frac{1}{6} \cdot π^{2} + \frac{1}{4}) \cdot {(Δ f / f)}^{2}; and \\ D \approx \frac{1}{2} \cdot Δ f / f - \frac{1}{4} \cdot {(Δ f / f)}^{2} . \end{matrix}$

18. A method for measuring a rate of change of frequency, said method comprising:
- estimating at least one phasor value;
  
  compensating the estimated at least one phasor value;
  
  calculating at least one positive sequence phasor value;
  
  estimating a frequency based on the calculated positive sequence phasor value;
  
  calculating a rate of change of the estimated frequency based on the estimated frequency; and
  
  outputting a signal to an output device when the rate of change of the estimated frequency exceeds a pre-determined limit.
- View Dependent Claims (19, 20, 21, 22, 23)
- - 19. A method in accordance with claim 18 wherein estimating at least one phasor value comprises estimating at least one phasor value using:
    - $\begin{matrix} {\overline{X}}_{a} (m) = \frac{\sqrt{2}}{N} \sum_{k = m \frac{N}{2} - \frac{N}{2}}^{m \frac{N}{2} + \frac{N}{2} - 1} x_{a} [(k + 1 / 2) \cdot Δ t] \cdot ⅇ^{- j \cdot (k - m \frac{N}{2} + 1 / 2) \frac{2 π}{N}}; \\ {\overline{X}}_{b} (m) = \frac{\sqrt{2}}{N} \sum_{k = m \frac{N}{2} - \frac{N}{2}}^{m \frac{N}{2} + \frac{N}{2} - 1} x_{b} [(k + 1 / 2) \cdot Δ t] \cdot ⅇ^{- j \cdot (k - m \frac{N}{2} + 1 / 2) \frac{2 π}{N}}; \\ {\overline{X}}_{c} (m) = \frac{\sqrt{2}}{N} \sum_{k = m \frac{N}{2} - \frac{N}{2}}^{m \frac{N}{2} + \frac{N}{2} - 1} x_{c} [(k + 1 / 2) \cdot Δ t] \cdot ⅇ^{- j \cdot (k - m \frac{N}{2} + 1 / 2) \frac{2 π}{N}}; and \end{matrix}$ wherein;
      
      m;
      
      Half cycle index.
  - 20. A method in accordance with claim 18 wherein compensating the estimated at least one phasor value comprises compensating the estimated at least one phasor value using:
    - $\begin{matrix} X_{a} (m) = {\overline{X}}_{a} (m) - j \cdot \frac{{{\overline{X}}_{a} (m)}^{*} + {{\overline{X}}_{a} (m - 1)}^{*}}{N \sin (\frac{2 π}{N})}; \\ X_{b} (m) = {\overline{X}}_{b} (m) - j \cdot \frac{{{\overline{X}}_{b} (m)}^{*} + {{\overline{X}}_{b} (m - 1)}^{*}}{N \sin (\frac{2 π}{N})}; and \\ X_{c} (m) = {\overline{X}}_{c} (m) - j \cdot \frac{{{\overline{X}}_{c} (m)}^{*} + {{\overline{X}}_{c} (m - 1)}^{*}}{N \sin (\frac{2 π}{N})} . \end{matrix}$
  - 21. A method in accordance with claim 18 wherein calculating at least one positive sequence phasor value comprises calculating the at least one positive sequence phasor value using:
    - $\begin{matrix} X_{pos} (m) = \frac{1}{3} [X_{a} (m) + {aX}_{b} (m) + a^{2} X_{c} (m)]; and \\ where, a = ⅇ^{j \frac{2 π}{3}} . \end{matrix}$
  - 22. A method in accordance with claim 18 wherein estimating a frequency based on the calculated positive sequence phasor value comprises estimating a frequency using:
    - $\begin{matrix} E (m) = X_{pos} (m) \cdot {X_{pos} (m - 1)}^{*}; \\ f_{a} (m) = f + \frac{f}{π} \cdot a \tan (\frac{Im (E (m))}{Re (E (m))}); and \end{matrix}$ wherein;
      
      f_α;
      
      Frequency estimate.
  - 23. A method in accordance with claim 18 wherein calculating a rate of change of the estimated frequency based on the estimated frequency comprises calculating a rate of change of the estimated frequency using:
    - $\frac{ⅆ f}{ⅆ t} = 2 f \cdot (f_{a} (m) - f_{a} (m - 1)) .$

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Current Assignee
General Electric Company
Original Assignee
General Electric Company
Inventors
Zhou, Rui, Premerlani, William
Primary Examiner(s)
Barlow; John
Assistant Examiner(s)
Bhat; Aditya S.

Application Number

US11/298,964
Publication Number

US 20070136013A1
Time in Patent Office

788 Days
Field of Search

702/75
US Class Current

702/75
CPC Class Codes

G01R 23/00 Arrangements for measuring ...

G01R 29/18 Indicating phase sequence; ...

Methods and systems for measuring a rate of change of frequency

First Claim

1 Assignment

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Abstract

60 Citations

23 Claims

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Methods and systems for measuring a rate of change of frequency

First Claim

1 Assignment

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0 Petitions

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Accused Products

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Abstract

60 Citations

23 Claims

Specification

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Use Cases

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Others