Methods and systems for measuring a rate of change of requency

US 20070136013A1
Filed: 12/09/2005
Published: 06/14/2007
Est. Priority Date: 12/09/2005
Status: Active Grant

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; and

calculating a rate of change of the calculated frequency based on the calculated frequency.

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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; and
  
  calculating a rate of change of the calculated frequency based on the calculated frequency.
- 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:
    - $\begin{matrix} E_{cs} (m) = \overline{X} (m) \cdot {\overline{X} (m - 1)}^{*}; \\ f_{cs} (m) = f + \frac{f}{π} \cdot a \tan (\frac{Im (E_{cs} (m))}{Re (E_{cs} (m))}); \end{matrix}$ 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:
    - $\begin{matrix} E_{cs} (m) = {\overline{X}}_{pos} (m) \cdot {{\overline{X}}_{pos} (m - 1)}^{*}; and \\ f_{cs} (m) = f + \frac{f}{π} \cdot a \tan (\frac{Im (E_{cs} (m))}{Re (E_{cs} (m))}); \end{matrix}$ and 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; and
  
  calculating a rate of change of the estimated frequency based on the estimated frequency.
- 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:
    - $\begin{matrix} E (m) = X_{pos} (m) \cdot {X_{pos} (m - 1)}^{*}; \\ f_{a} (m) = f + \frac{f}{π} \cdot a \tan (\frac{Im (E (m))}{Re (E (m))}); and \end{matrix}$ and 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

Granted Patent

US 7,328,114 B2
Time in Patent Office

Days
Field of Search
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 requency

First Claim

1 Assignment

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Abstract

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23 Claims

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Methods and systems for measuring a rate of change of requency

First Claim

1 Assignment

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Abstract

Citations

23 Claims

Specification

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Solutions

Use Cases

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