Frequency estimation
Determining a property of an electrical signal at a node instant at the current instant (INSTC); determining a previous function indicative of a property of the signal at the node at a previous instant; determining an error function in a previous frequency estimation at the node at a previous instant; determining a first current function indicative of the property of the signal at the node at INSTC in accordance with the determined property, the previous function, and the error function; receiving, from another node, a second current function indicative of a property of an electrical signal at the at least one other node at INSTC; combining the first current function and the second current function to produce a current combined function (CCF) indicative of a property of the signal at the node at INSTC; and estimating a current frequency of the signal at the node in accordance with the CCF.
1. A method for estimating a frequency of an electrical signal at a node in an electrical system having a plurality of nodes, the method comprising:
determining, at a node of an electrical system having a plurality of nodes, at least one property of an electrical signal at the node at a current instant in time;
determining a previous function indicative of one or more properties of the electrical signal at the node at a previous instant in time;
determining a function of an error in a previous frequency estimation at the node at a previous instant in time;
determining a current function indicative of the one or more properties of the electrical signal at the node at the current instant in time in accordance with the at least one determined property of the electrical signal at the node at the current instant in time, the previous function indicative of the one or more properties of the electrical signal at the node at a previous instant in time, and the function of the error in the previous frequency estimation;
receiving, from at least one other node of the plurality of nodes, a current function indicative of one or more properties of an electrical signal at the at least one other node at the current instant in time;
combining the current function indicative of one or more properties of the electrical signal at the node and the current function indicative of one or more properties of the electrical signal at the at least one other node to produce a current combined function indicative of one or more properties of the electrical signal at the node at the current instant in time; and
estimating a current frequency of the electrical signal at the node in accordance with the current combined function.
2. The method according to claim 1 , wherein the one or more properties of the electrical signal that the previous and current functions are indicative of includes a frequency of the electrical signal.
3. The method according to claim 2 , wherein the one or more properties of the electrical signal that the previous and current functions are indicative of includes a phase associated with the electrical signal.
4. The method according to claim 1 , wherein the determined property of the electrical signal is a voltage, the method further comprising converting the three-phase electrical signal into a transform-domain, wherein the current function indicative of one or more properties of the electrical signal in the transform-domain.
5. The method according to claim 1 , wherein the function of an error in the previous estimated frequency is determined by multiplication of a calculated error in a previous estimated frequency by a weighting, wherein the weighting is indicative of a level of confidence in the calculated error.
6. The method according to claim 1 , wherein the function of an error is a function of a phase-only error.
7. The method according to claim 1 , wherein the combining is a linear combination process in the original or a transform domain.
8. The method according to claim 1 , further comprising:
after receiving the current function indicative of one or more properties of the electrical signal at the at least one other node, applying a node weighting factor to the received current function before performing the step of combining, wherein the node weighting factor is indicative of a confidence in the accuracy of the received current function.
9. The method according to 1 , wherein the current estimated frequency {circumflex over (f)} i (k) at the node i, is determined by:
f
^
i
(
k
)
=
1
2
πΔ
T
sin
-
1
(
funct
(
k
)
)
wherein ΔT is a sampling interval, and funct(k) is the current combined function at the current instant in time, k.
10. The method according to claim 1 , wherein the previous function indicative of one or more properties of the electrical signal at the node at a previous instant in time, the current function indicative of one or more properties of the electrical signal at the node at the current instant in time, and the function received from the at least one other node indicative of one or more properties of the electrical signal at the at least one other node at the current instant in time, each comprise:
a first function and a second function, wherein the first function utilizes the at least one determined property of the electrical signal, and the second function utilizes the complex conjugate of the at least one determined property of the signal; and
the step of combining comprises:
combining, at the node, the first function associated with the node with the first function associated with the at least one other node to produce a current combined first function; and
combining, at the node, the second function associated with the node with the second function associated with the at least one other node to produce a current combined second function; and
the step of estimating comprises estimating a current frequency of the at least one electrical characteristic at the node in accordance with the current combined first function and the current combined second function.
11. The method according to claim 10 , wherein the first function and the second function also utilize a function of a calculated error.
12. The method according to claim 10 , wherein the first function and the second function also utilize a function of the conjugate of a complex transform of the at least one determined property of the electrical signal at the node at the previous instant in time.
13. The method according to claim 10 , wherein the first function, h, at the current instant in time, k, is determined by:
h ( k )= h ( k−m )+μ p ( e ( k−m )) q ( v *( k−m ))
wherein m can take any integer value, h(k−m) is a previous first function, p(e(k−m)) is a function of a calculated error, μ is a weighting factor applied to the calculated error, and q(v*(k−m)) is a function of the conjugate of a complex transform of the at least one determined property of the electrical signal at the node at the previous instant in time.
14. The method according to claim 10 , wherein the second function, g, at the current instant in time, k, is determined by:
g ( k )= g ( k−m )+μ p ( e ( k−m )) q ( v ( k−m ))
wherein m can take any integer value, g(k−m) is a previous second function, p(e(k−m)) is a function of the calculated error, μ is a weighting factor applied to the calculated error at the previous instant in time, and q(v(k−m)) is a function of a complex transform of the at least one determined property of the electrical signal at the node at a previous instant in time.
15. The method according to claim 10 , wherein the current function indicative of the one or more properties of the electrical signal at the node at the current instant in time is determined in accordance with the following state space model:
State equation:
[
h
i
(
k
)
g
i
(
k
)
h
i
*
(
k
)
g
i
*
(
k
)
]
=
[
h
i
(
k
-
m
)
g
i
(
k
-
m
)
h
i
*
(
k
-
m
)
g
i
*
(
k
-
m
)
]
+
u
i
(
k
)
Observation equation for the node, i:
[
v
i
(
k
)
v
i
*
(
k
)
]
=
[
v
i
(
k
-
m
)
h
i
(
k
)
+
v
i
*
(
k
-
m
)
g
i
(
k
)
v
i
*
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k
-
m
)
h
i
*
(
k
)
+
v
i
(
k
-
m
)
g
i
*
(
k
)
]
+
n
i
(
k
)
Wherein h i (k−m) is the first function indicative of the one or more properties of the electrical signal at the node, i, at a previous instant in time, k−m, g i (k−m) is the second function indicative of the one or more properties of the electrical signal at the node at the previous instant in time, k−m, u i (k) and n i (k) are functions indicative of an error in the previous frequency estimation, and v i (k−m) is the determined property of the electrical signal at the previous instant in time, k−m, at the node, i.
16. The method according to claim 10 , wherein the current function indicative of the one or more properties of the electrical signal at the node, i, at the current instant in time is determined in accordance with the following state space model:
[
h
i
(
k
)
g
i
(
k
)
z
i
(
k
)
h
i
*
(
k
)
g
i
*
(
k
)
z
i
*
(
k
)
]
=
[
h
i
(
k
-
m
)
g
i
(
k
-
m
)
z
i
(
k
-
m
)
h
i
(
k
-
m
)
+
z
i
*
(
k
-
m
)
g
i
(
k
-
m
)
h
i
*
(
k
-
m
)
g
i
*
(
k
-
m
)
z
i
*
(
k
-
m
)
h
i
*
(
k
-
m
)
+
z
i
(
k
-
m
)
g
i
*
(
k
-
m
)
]
+
u
i
(
k
)
Observation equation for a node i:
[
v
i
(
k
)
v
i
*
(
k
)
]
=
[
z
i
(
k
)
z
i
*
(
k
)
]
+
n
i
(
k
)
Wherein h i (k−m) is the first function indicative of the one or more properties of the electrical signal at the node i at a previous instant in time, k−m, g i (k−m) is the second function indicative of the one or more properties of the electrical signal at the node at the previous instant in time, z i (k−m) is an estimation of the one or more properties of the electrical signal at the previous instant in time, k−m, u i (k) and n i (k) are functions indicative of an error in the previous frequency estimation, and v i (k−m) is the determined property of the electrical signal at the previous instant in time, k−m, at the node, i.
17. The method according to claim 1 , wherein the current function indicative of the one or more properties of the electrical signal at the node is also determined in accordance with a conjugate of the at least one determined property of the electrical signal.
18. An apparatus for estimating a frequency, the apparatus comprising:
a processing unit arranged to perform the method of claim 1 .
19. A system comprising:
a plurality of nodes, each node comprising a processing unit arranged to perform the method of claim 1 , wherein each node of the plurality of nodes is coupled to at least one other node of the plurality of nodes.
20. A non-transitory computer readable medium comprising computer readable code operable, in use, to instruct a computer to perform the method of claim 1 .