Estimation of a waveform period
View Patent ↗Disclosed herein are systems and methods for estimating a period and frequency of a waveform. In one embodiment a system may comprise an input configured to receive a signal comprising a representation of the waveform. A period determination subsystem may calculate an estimated period of the signal based on a period determination function. An estimated period adjustment subsystem may determine an adjustment to the estimated period based on a result of the period determination function. A quality indicator subsystem configured to evaluate a measurement quality indictor function based on the estimated period, and to selectively update the period of the waveform based on the measurement quality indicator. A control action subsystem configured to implement a control action based on the period of the waveform.
1. A system configured to determine a period of a waveform, the system comprising:
an input configured to receive a signal comprising a representation of the waveform of a power delivery system;
a period determination subsystem configured to calculate an estimated period of the signal based on a period determination function;
an estimated period adjustment subsystem configured to determine an adjustment to the estimated period based on a result of the period determination function;
a quality indicator subsystem configured to:
determine a measurement quality indicator of the estimated period by evaluating a measurement quality indicator function based on the estimated period;
update a previously determined period of the waveform with the estimated period when the measurement quality indicator of the estimated period exceeds a threshold;
retain the previously determined period of the waveform when the measurement quality indicator is below the threshold; and
a control action subsystem configured to implement a control action on the power delivery system based on the updated estimated period of the waveform.
2. The system of claim 1 wherein the period determination subsystem is further configured to incorporate the adjustment into a subsequent estimated period.
3. The system of claim 2 , wherein the period determination subsystem and the estimated period adjustment subsystem are further configured to determine a plurality of adjustments to the estimated period.
4. The system of claim 1 , wherein the waveform represents one of an alternating current and an alternating voltage in an electric power distribution system and the control action comprises an adjustment to a load associated with the electric power distribution system.
5. The system of claim 1 , wherein the period determination subsystem is configured to calculate the estimated period based on a time shift in the period determination function that results in a zero value of an integrated product of the input and the derivative of the input at the time shift.
6. The system of claim 1 , wherein the period determination function comprises an integral of the product over a time shift.
7. The system of claim 1 , wherein the period determination function is represented as:
B ( t,T )=∫ t−T t x ( t−T )· x ′( t ) dt
T 0 ( t )= T for which B ( t,T ) is at zero.
8. The system of claim 7 , wherein the estimated period adjustment subsystem is configured to increase the estimated period when B(t, T) is positive and to decrease the estimated period when B (t, T) is negative.
9. The system of claim 1 , further comprising an interpolating subsystem configured to interpolate between a plurality of adjacent samples associated with the input signal to determine the estimated period.
10. The system of claim 1 , wherein the measurement quality indictor function comprises:
A
(
t
,
T
)
=
∫
t
-
T
t
x
(
t
)
·
x
(
t
-
T
)
dt
∫
t
-
2
T
t
x
(
t
)
·
x
(
t
)
dt
,
where T comprises the estimated period.
11. The systems of claim 1 , wherein the quality indicator subsystem is further configured to establish a variable gain to be applied to the signal comprising the representation of the waveform, the variable gain being proportional to the measurement quality indicator function.
12. A method for estimating a period of a waveform, the method comprising:
receiving a signal of a power delivery system comprising a representation of the waveform;
calculating an estimated period of the signal based on a period determination function;
determining an adjustment to the estimated period based on a result of the period determination function;
determine a measurement quality indicator of the estimated period by evaluating a measurement quality indictor function based on the estimated period;
updating a previously determined period of the input signal with the estimated period when the measurement quality indicator exceeds a threshold;
retaining the previously determined period of the waveform when the measurement quality indicator is below the threshold; and
performing a control action on the power delivery system based on the updated estimated period of the waveform.
13. The method of claim 12 further incorporating the adjustment into a subsequent estimated period.
14. The method of claim 13 , further comprising identifying the period by adding a plurality of adjustments to the estimated period.
15. The method of claim 12 , wherein waveform represents an alternating current in an electric power distribution system and the control action comprises adjusting a load associated with the electric power distribution system.
16. The method of claim 12 , wherein calculating the estimated period based on the period determination function comprises:
calculating a time shift that results in a zero value of an integrated product of the waveform and the derivative of the waveform at the time shift.
17. The method of claim 12 , wherein the period determination function comprises an integral of the product over a time shift.
18. The method of claim 12 , wherein the period determination function is represented as:
B ( t,T )=∫ t−T t x ( t−T )· x ′( t ) dt
T 0 ( t )= T for which B ( t,T ) is at zero.
19. The method of claim 18 , wherein the adjustment to the estimated period comprises:
increasing the estimated period when B (t, T) is positive; and
decreasing the estimated period when B(t, T) is negative.
20. The method of claim 12 , further comprising interpolating between a plurality of adjacent samples associated with the representation of the input signal to determine the estimated period.
21. The method of claim 12 , wherein the measurement quality indictor function comprises:
A
(
t
,
T
)
=
∫
t
-
T
t
x
(
t
)
·
x
(
t
-
T
)
dt
∫
t
-
2
T
t
x
(
t
)
·
x
(
t
)
dt
,
where T comprises the estimated period.
22. The method of claim 12 , further comprising:
establishing a variable gain based on the measurement quality indicator function; and
applying the variable gain the signal representing the waveform.
23. The method of claim 12 , further comprising implementing a low pass filter on the period determination function.
24. The system of claim 1 , wherein the control action subsystem is configured to reduce loads connected to the system by implementing the control action.
25. The method of claim 12 , wherein the measurement quality indicator is indicative of periodicity of the waveform.