FUNDAMENTAL FREQUENCY STABILITY AND HARMONIC ANALYSIS
A method, apparatus and computer readable medium for estimating a frequency of an electrical signal are disclosed. The method comprises taking a number of samples of an electrical signal throughout a main sampling window; dividing the number of samples taken throughout the main sampling window into a plurality of groups of consecutive samples, each group of consecutive samples forming a subwindow, wherein each subwindow includes a minimum number of the number of samples required to provide a required level of accuracy for estimating the fundamental frequency of the electrical signal; estimating, for each subwindow, the fundamental frequency of the electrical signal based on the group of consecutive samples of the respective subwindow; and determining if the fundamental frequency is stable throughout the main window by comparing the estimated fundamental frequency of each subwindow.
1 . A method for estimating a frequency of an electrical signal, the method comprising:
taking a number of samples of an electrical signal throughout a main sampling window;
dividing the number of samples taken throughout the main sampling window into a plurality of groups of consecutive samples, each group of consecutive samples forming a subwindow, wherein each subwindow includes a minimum number of the number of samples required to provide a required level of accuracy for estimating the fundamental frequency of the electrical signal;
estimating, for each subwindow, the fundamental frequency of the electrical signal based on the group of consecutive samples of the respective subwindow; and
determining if the fundamental frequency is stable throughout the main window by comparing the estimated fundamental frequency of each subwindow.
2 . The method according to claim 1 , further comprising determining a size of a main sampling window in terms of a number of samples prior to taking the number of samples.
3 . The method according to claim 1 , further comprising estimating the fundamental frequency over the main window if the fundamental frequency is determined to be stable throughout the main window.
4 . The method according to claim 1 , further comprising performing harmonic analysis on the number of samples if the fundamental frequency is determined to be stable.
5 . The method according to claim 1 , further comprising determining a total harmonic distortion associated with the number of samples and re-sampling the electrical signal if the total harmonic distortion exceeds a threshold.
6 . The method according to claim 1 , wherein the fundamental frequency is estimated using a maximum frequency point method.
7 . The method according to claim 6 , wherein the fundamental frequency is estimated using the maximum frequency point method in accordance with the following equations:
Max[ A (1)]=Max√{square root over ( a 1 2 ( F 1 )+ b 1 2 ( F 1 ))}{square root over ( a 1 2 ( F 1 )+ b 1 2 ( F 1 ))}
Wherein Max [A(1)] is the maximum magnitude value of fundamental frequency, F1 is the estimated fundamental frequency, and a1 and b1 are the fundamental discrete Fourier coefficients defined by:
a
1
=
1
N
T
∑
i
=
0
N
-
1
2
T
e
T
1
S
(
)
cos
(
2
π
F
1
T
e
)
,
and
b
1
=
1
N
T
∑
i
=
0
N
-
1
2
T
e
T
1
S
(
)
sin
(
2
π
F
1
T
e
)
Wherein T e is the sampling period, N is the total number of samples, N T is the total number of periods, i is the reference of a sample, and S(i) is a sample of the signal.
8 . The method according to claim 3 , wherein the fundamental frequency is estimated over the main window by using the maximum frequency point method with a starting frequency equal to the average frequency over all the sub-windows.
9 . The method according to claim 1 , wherein each subwindow comprises approximately 700 samples.
10 . The method according to claim 1 , wherein the main window comprises at least 1200 samples.
11 . The method according to claim 1 , wherein the main window comprises approximately 5000 samples.
12 . Apparatus for estimating a frequency of an electrical signal, the
apparatus arranged to:
take a number of samples of an electrical signal throughout a main sampling window;
divide the number of samples taken throughout the main sampling window into a plurality of groups of consecutive samples, each group of consecutive samples forming a subwindow, wherein each subwindow includes a minimum number of the number of samples required to provide a required level of accuracy for estimating the fundamental frequency of the electrical signal;
estimate, for each subwindow, the fundamental frequency of the electrical signal based on the group of consecutive samples of the respective subwindow; and
determine if the fundamental frequency is stable throughout the main window by comparing the estimated fundamental frequency of each subwindow
13 . The apparatus according to claim 12 , wherein the apparatus is an electricity meter.
14 . The apparatus according to claim 13 , wherein the electricity meter further comprises:
a sensor arranged to take the samples;
a memory arranged to store the one or more samples and store a computer program for implementing the method; and
a processor arranged to perform the method in accordance with the stored samples and the computer program.
15 . A computer readable medium comprising computer readable code operable, in use, to instruct a computer to:
take a number of samples of an electrical signal throughout a main sampling window;
divide the number of samples taken throughout the main sampling window into a plurality of groups of consecutive samples, each group of consecutive samples forming a subwindow, wherein each subwindow includes a minimum number of the number of samples required to provide a required level of accuracy for estimating the fundamental frequency of the electrical signal;
estimate, for each subwindow, the fundamental frequency of the electrical signal based on the group of consecutive samples of the respective subwindow; and
determine if the fundamental frequency is stable throughout the main window by comparing the estimated fundamental frequency of each subwindow.