US 11,144,023 B1Granted

Method for PMU data recovery using an improved cubic spline interpolation and singular value decomposition

AssigneeNorth China Electric Power University

InventorsHao Liu, Tianshu Bi, Zhiwei Yang

Life of this patent

Estimating the term…

Abstract

A data recovery method framework is described, in which the data is classified as either ambient or disturbance data, and recovered by different methods to achieve good performance efficiently. An approach based on decision tree is described for identifying ambient and disturbance data. Then, an improved cubic spline interpolation based on the priority allocation strategy is described for ambient data loss, which can quickly and accurately recover ambient data. Simultaneously, a disturbance data recovery method based on singular value decomposition is described. It can achieve disturbance data recovery accurately by a single channel of measurement.

Claims1

Dependent claims

A method for improving a data quality of a phasor measurement unit including a processor and a memory, the method comprising:

obtaining, using an interface of the phasor measurement unit, a plurality of datasets Ci including a plurality of data points from a power network;
dividing, using the processor, each dataset Ci into ambient data or disturbance data using a binary classification model stored on the memory and configured to perform the following steps:
providing (S1) all the datasets Ci as inputs to a decision tree;
calculating (S2) gain ratios of features (ai, bi), and selecting a largest dataset Ci for comparison with a threshold ε, wherein:
the gain ratio is defined as follows:
g
⁡
(
T
,
a
,
q
i
)
=
G
⁡
(
T
,
a
,
q
i
)
I
⁢
V
⁡
(
a
)
I
⁢
V
⁡
(
a
)
=
-
∑
β
∈
{
-
,
+
}
⁢

T
q
i
β


T

⁢
log
2
⁢

T
q
i
β


T

where IV(a) is an intrinsic value;
for each dataset Ci, ai is a variance, bi is an extreme value difference and qi is a diving point;
and G(T, a, qi) is information gain of qi which is computed as follows:
G
⁡
(
T
,
a
,
q
i
)
=
H
⁡
(
T
)
-

T
q
i
-


T

⁢
H
⁡
(
T
q
i
-
)
⁢

T
q
i
+


T

⁢
H
⁡
(
T
q
i
+
)
where |T| represents the number of groups, |Tqi−|/|T| is a weight of the groups in which ai≤qi, and |Tqi+|/|T| represents a weight of the groups where ai>qi;
if the gain ratio is less than the threshold ε, the decision tree is a single node tree and a state of all the datasets is the state of a majority;
and
if the gain ratio is not less than the threshold ε, g(T, a, qa) is the largest dataset Ci;
comparing (S3) ai with qa, and placing datasets Ci with ai≤qa in a class for ambient data, and placing remaining datasets Ci in a class for disturbance data;
and
repeating steps S1-S3 recursively until all datasets in each class are in the same state, or a maximum gain ratio is less than the threshold ε;
restoring missing data from the class of ambient data by:
determining a number E and a type of data points missing, wherein the number E represents a number of missing data points;
implementing a priority allocation strategy based on the number E and the type of data points missing;
determining an improved cubic spline interpolation function that satisfies an extreme value difference constraint and a missing data, wherein S(t) is the cubic spline interpolation function of ƒ(t) on node t0, t1, . . . , xn as written below:
S
⁡
(
t
)
=
M
i
⁢
(
t
i
+
1
-
t
)
3
6
⁢
h
i
+
M
i
+
1
⁢
(
t
-
t
i
)
3
6
⁢
h
i
+
(
X
i
h
i
-
M
i
6
⁢
h
i
⁢
)
⁢
(
t
i
+
1
-
t
)
+
(
X
i
+
1
h
i
-
M
i
+
1
6
⁢
h
i
)
⁢
(
t
-
t
i
)
where Mi=S″(ti), wherein:
on each subinterval [tk, tk+1] (k=1, 2, . . . , n−1), S(t) is a polynomial no more than three times, and s(ti)=Xi;
in interval [ti, ti+1], the second derivative of S(t) is expressed as:
S
″
⁡
(
t
)
=
M
i
⁢
t
i
+
1
-
t
h
i
+
M
i
+
1
⁢
t
-
t
i
h
i
where hi=ti+1−ti;
and
two consecutive integrations of S″(t) provide:
S
′
⁡
(
t
)
=
-
M
i
⁢
(
t
i
+
1
-
t
)
2
2
⁢
h
i
+
M
i
+
1
⁢
(
t
-
t
i
)
2
2
⁢
h
i
+
X
i
+
1
-
X
i
h
i
-
M
i
+
1
-
M
i
6
⁢
h
i
;
and
restoring the missing data using the cubic spline interpolation function and known data;
restoring missing data from the class of disturbance data by:
determining an amount of data N and a number of rows of a track matrix L according to an actual data loss position;
constructing a trajectory matrix and performing singular value decomposition to extract all characteristic components by mapping a one-dimensional time series X to a trajectory matrix Y of a high-dimensional space as follows:
X
=
[
X
t
1
,
X
t
2
,
…
⁢
,
X
t
N
]
→
Y
=
[
Y
1
,
Y
2
,
…
⁢
⁢
Y
K
]
Y
z
=
[
X
z
,
X
z
+
1
,
…
⁢
,
X
z
+
L
-
1
]
T
,
z
=
1
,
2
,
…
⁢
,
K
Y
=
[
X
t
1
X
t
2
…
X
t
m
…
X
t
n
…
X
t
K
X
t
2
X
t
3
…
X
t
m
+
1
…
X
t
n
+
1
…
X
t
K
+
1
⋮
⋮
⋮
⋮
⋮
⋮
⋮
⋮
X
t
L
X
t
L
+
1
…
X
t
m
-
1
+
L
…
X
t
n
-
1
+
L
…
X
t
N
]
where the matrix Y is a Hankel matrix which has equal elements Yij on anti-diagonals i+j=const;
subscript L is a number of matrix rows, which measure the dimension of the matrix Y, and K is a number of matrix columns, K=N−L+1;
reconstructing an original sequence using an optimal characteristic component, wherein the original sequence X decomposition is reconstructed into a sum X(1) of k sequences [X(1), X(2), . . . , X(k)], where:
X
(
k
)
=
[
X
t
1
(
k
)
,
X
t
2
(
k
)
,
…
⁢
,
X
t
N
-
1
(
k
)
,
X
t
N
(
k
)
]
X
⁡
(
1
)
↔
[
X
t
1
(
1
)
X
t
2
(
1
)
…
X
t
N
-
1
(
1
)
X
t
N
(
1
)
X
t
1
(
2
)
X
t
2
(
2
)
…
X
t
N
-
1
(
2
)
X
t
N
(
2
)
⋮
⋮
⋮
⋮
⋮
X
t
1
(
k
)
X
t
2
(
k
)
…
X
t
N
-
1
(
k
)
X
t
N
(
k
)
]
replacing a missing data Xlost by a corresponding position value of the reconstructed sequence X(1);
providing the missing data to the phasor measurement unit to support power system dynamic monitoring, power system state estimation, parameter identification, and/or closed-loop control.

619 more elements

Dependencies are inferred from the claim text.

Facts

Application: 17/157,709Filed 25 Jan 2021 · continuation
Priority: 7 Aug 2020
Granted: 12 Oct 2021
Term ends: Not estimatedThe source records don’t support an estimate.

Classification16 codes

G01R 19/2506
Using digital measurement techniques: arrangements for conditioning or analysing measured signals, e.g. for indicating peak values ; Details…
G05B 19/042
Program control other than numerical control, i.e. in sequence controllers or logic controllers: using digital processors
H02J 13/12
Circuit arrangements for providing remote monitoring or remote control of equipment in a power distribution network: monitoring network…
G01R 19/2513
Using digital measurement techniques: arrangements for monitoring electric power systems, e.g. power lines or loads; Logging

Family

PCT/CN2020/107979Parent of this continuation · filed 7 Aug 2020
Application17/015,798Parent of this continuation · filed 9 Sep 2020
US 10,983,492 B1Parent of this continuation
US 11,144,023 B1This patent

From the US filing history. Foreign family members aren’t listed.

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Citations

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Abstract

A method for improving a data quality of a phasor measurement unit including a processor and a memory, the method comprising:

obtaining, using an interface of the phasor measurement unit, a plurality of datasets Ci including a plurality of data points from a power network;
dividing, using the processor, each dataset Ci into ambient data or disturbance data using a binary classification model stored on the memory and configured to perform the following steps:
providing (S1) all the datasets Ci as inputs to a decision tree;
calculating (S2) gain ratios of features (ai, bi), and selecting a largest dataset Ci for comparison with a threshold ε, wherein:
the gain ratio is defined as follows:
g
⁡
(
T
,
a
,
q
i
)
=
G
⁡
(
T
,
a
,
q
i
)
I
⁢
V
⁡
(
a
)
I
⁢
V
⁡
(
a
)
=
-
∑
β
∈
{
-
,
+
}
⁢

T
q
i
β


T

⁢
log
2
⁢

T
q
i
β


T

where IV(a) is an intrinsic value;
for each dataset Ci, ai is a variance, bi is an extreme value difference and qi is a diving point;
and G(T, a, qi) is information gain of qi which is computed as follows:
G
⁡
(
T
,
a
,
q
i
)
=
H
⁡
(
T
)
-

T
q
i
-


T

⁢
H
⁡
(
T
q
i
-
)
⁢

T
q
i
+


T

⁢
H
⁡
(
T
q
i
+
)
where |T| represents the number of groups, |Tqi−|/|T| is a weight of the groups in which ai≤qi, and |Tqi+|/|T| represents a weight of the groups where ai>qi;
if the gain ratio is less than the threshold ε, the decision tree is a single node tree and a state of all the datasets is the state of a majority;
and
if the gain ratio is not less than the threshold ε, g(T, a, qa) is the largest dataset Ci;
comparing (S3) ai with qa, and placing datasets Ci with ai≤qa in a class for ambient data, and placing remaining datasets Ci in a class for disturbance data;
and
repeating steps S1-S3 recursively until all datasets in each class are in the same state, or a maximum gain ratio is less than the threshold ε;
restoring missing data from the class of ambient data by:
determining a number E and a type of data points missing, wherein the number E represents a number of missing data points;
implementing a priority allocation strategy based on the number E and the type of data points missing;
determining an improved cubic spline interpolation function that satisfies an extreme value difference constraint and a missing data, wherein S(t) is the cubic spline interpolation function of ƒ(t) on node t0, t1, . . . , xn as written below:
S
⁡
(
t
)
=
M
i
⁢
(
t
i
+
1
-
t
)
3
6
⁢
h
i
+
M
i
+
1
⁢
(
t
-
t
i
)
3
6
⁢
h
i
+
(
X
i
h
i
-
M
i
6
⁢
h
i
⁢
)
⁢
(
t
i
+
1
-
t
)
+
(
X
i
+
1
h
i
-
M
i
+
1
6
⁢
h
i
)
⁢
(
t
-
t
i
)
where Mi=S″(ti), wherein:
on each subinterval [tk, tk+1] (k=1, 2, . . . , n−1), S(t) is a polynomial no more than three times, and s(ti)=Xi;
in interval [ti, ti+1], the second derivative of S(t) is expressed as:
S
″
⁡
(
t
)
=
M
i
⁢
t
i
+
1
-
t
h
i
+
M
i
+
1
⁢
t
-
t
i
h
i
where hi=ti+1−ti;
and
two consecutive integrations of S″(t) provide:
S
′
⁡
(
t
)
=
-
M
i
⁢
(
t
i
+
1
-
t
)
2
2
⁢
h
i
+
M
i
+
1
⁢
(
t
-
t
i
)
2
2
⁢
h
i
+
X
i
+
1
-
X
i
h
i
-
M
i
+
1
-
M
i
6
⁢
h
i
;
and
restoring the missing data using the cubic spline interpolation function and known data;
restoring missing data from the class of disturbance data by:
determining an amount of data N and a number of rows of a track matrix L according to an actual data loss position;
constructing a trajectory matrix and performing singular value decomposition to extract all characteristic components by mapping a one-dimensional time series X to a trajectory matrix Y of a high-dimensional space as follows:
X
=
[
X
t
1
,
X
t
2
,
…
⁢
,
X
t
N
]
→
Y
=
[
Y
1
,
Y
2
,
…
⁢
⁢
Y
K
]
Y
z
=
[
X
z
,
X
z
+
1
,
…
⁢
,
X
z
+
L
-
1
]
T
,
z
=
1
,
2
,
…
⁢
,
K
Y
=
[
X
t
1
X
t
2
…
X
t
m
…
X
t
n
…
X
t
K
X
t
2
X
t
3
…
X
t
m
+
1
…
X
t
n
+
1
…
X
t
K
+
1
⋮
⋮
⋮
⋮
⋮
⋮
⋮
⋮
X
t
L
X
t
L
+
1
…
X
t
m
-
1
+
L
…
X
t
n
-
1
+
L
…
X
t
N
]
where the matrix Y is a Hankel matrix which has equal elements Yij on anti-diagonals i+j=const;
subscript L is a number of matrix rows, which measure the dimension of the matrix Y, and K is a number of matrix columns, K=N−L+1;
reconstructing an original sequence using an optimal characteristic component, wherein the original sequence X decomposition is reconstructed into a sum X(1) of k sequences [X(1), X(2), . . . , X(k)], where:
X
(
k
)
=
[
X
t
1
(
k
)
,
X
t
2
(
k
)
,
…
⁢
,
X
t
N
-
1
(
k
)
,
X
t
N
(
k
)
]
X
⁡
(
1
)
↔
[
X
t
1
(
1
)
X
t
2
(
1
)
…
X
t
N
-
1
(
1
)
X
t
N
(
1
)
X
t
1
(
2
)
X
t
2
(
2
)
…
X
t
N
-
1
(
2
)
X
t
N
(
2
)
⋮
⋮
⋮
⋮
⋮
X
t
1
(
k
)
X
t
2
(
k
)
…
X
t
N
-
1
(
k
)
X
t
N
(
k
)
]
replacing a missing data Xlost by a corresponding position value of the reconstructed sequence X(1);
providing the missing data to the phasor measurement unit to support power system dynamic monitoring, power system state estimation, parameter identification, and/or closed-loop control.

619 more elements

Facts

Application

17/157,709Filed 25 Jan 2021 · continuation

Priority

7 Aug 2020

Granted

12 Oct 2021

Term ends

Not estimatedThe source records don’t support an estimate.

Classification16 codes

G01R 19/2506
Using digital measurement techniques: arrangements for conditioning or analysing measured signals, e.g. for indicating peak values ; Details…
G05B 19/042
Program control other than numerical control, i.e. in sequence controllers or logic controllers: using digital processors
H02J 13/12
Circuit arrangements for providing remote monitoring or remote control of equipment in a power distribution network: monitoring network…
G01R 19/2513
Using digital measurement techniques: arrangements for monitoring electric power systems, e.g. power lines or loads; Logging