Method for fast and accurately sensing power grid information based on nonlinear robust estimation
A method for sensing power grid information based on nonlinear robust estimation, may include: acquiring a phase voltage signal of actual power grid; obtaining a nonlinear state-space distorted power grid model based on the phase voltage signal of actual power grid and a virtual orthogonal signal of phase voltage signal; establishing an H∞ smoothing estimation performance indicator based on the nonlinear state-space distorted power grid model, converting an H∞ smoothing estimation problem into a generalized H 2 smoothing estimation problem according to the H∞ smoothing estimation performance indicator, and constructing an H∞ smoothing estimator; and obtaining an initial sensed amplitude value and an initial sensed phase value of power grid voltage signal by using the H∞ smoothing estimator, and performing zero-crossing point detection on the initial sensed amplitude and phase values of the power grid voltage signal to obtain sensed amplitude, frequency and phase values of a distorted voltage.
1 . A method for sensing power grid information based on nonlinear robust estimation, comprising:
acquiring a phase voltage signal of an actual power grid;
obtaining a nonlinear state-space distorted power grid model based on the phase voltage signal of the actual power grid and a virtual orthogonal signal of the phase voltage signal;
establishing an H∞ smoothing estimation performance indicator based on the nonlinear state-space distorted power grid model, converting an H∞ smoothing estimation problem into a generalized H 2 smoothing estimation problem according to the H∞ smoothing estimation performance indicator, and constructing an H∞ smoothing estimator;
obtaining an initial sensed amplitude value and an initial sensed phase value of a power grid voltage signal by using the H∞ smoothing estimator, and performing zero-crossing point detection on the initial sensed amplitude value and the initial sensed phase value of the power grid voltage signal to obtain sensed amplitude, frequency and phase values of a distorted voltage; and
based on the obtained sensed amplitude, frequency and phase values of the distorted voltage, controlling a phase difference between an output current in a current loop control of the grid-connected inverter and a grid-side fundamental voltage to be 0, to implement a grid connection under a unit power factor;
wherein,
the converting the H∞ smoothing estimation problem into the generalized H 2 smoothing estimation problem according to the H∞ smoothing estimation performance indicator and constructing the H∞ smoothing estimator specifically comprises:
(1) setting an H∞ indicator upper limit constant γ>0, a sampling moment i=k l =0, a state estimate initial value x̌ 0 =0, and a Riccati equation initial value P 0 =l, N being a specific time point:
C
2
=
[
C
T
F
T
L
T
]
T
Q
2
(
i
)
=
diag
{
I
,
-
γ
1
-
2
I
,
-
γ
2
I
}
y
˜
2
(
i
,
2
)
=
y
2
(
i
)
-
C
2
x
ˆ
(
i
,
2
)
y
˜
2
(
i
,
2
)
=
[
y
T
(
i
)
z
⌣
∅
T
(
i
|
i
)
z
⌣
T
(
i
|
i
+
l
)
]
T
,
and
wherein,
C
=
[
1
0
0
0
0
1
]
,
F represents a constant matrix of the nonlinear portion in the phase voltage model, and L represents a unit matrix; Q represents a diagonal matrix constructed based on diag{ } function, γ 1 represents a Lipschitz constant of a nonlinear portion in a phase voltage model; {tilde over (y)} 2 (i, 2) represents an observed estimation error, {circumflex over (x)}(i, 2) is a second-piece initial state value; y(i) is an observation sequence, ž Ø (i|i) is an estimation equation of the virtual output ž Ø ; ž(k l |k) is an estimator of the signal z(k), wherein k l =k−l, when let the sampling moment i=k l =0, it can be written as ž(i|i+l); i represents a first sampling moment, k represents a second sampling moment, l is a smoothing step number, and the superscript T represents transposed matrix;
calculating:
a second-piece output error variance R 2 (i, 2):
R
2
(
i
,
2
)
=
C
2
P
2
(
i
)
C
2
T
+
Q
2
(
i
)
,
(
13
)
wherein P 2 (i) represents a second-piece Riccati equation value;
a second-piece gain parameter K 2 (i):
K
2
(
i
)
=
A
P
2
(
i
)
C
2
T
R
2
-
1
(
i
,
2
)
,
(
14
)
wherein,
A
=
[
1
0
0
T
ω
¯
1
0
0
0
1
]
,
T represents a sampling period, and w represents a set initial power grid frequency;
a second-piece Riccati equation P 2 (i+1):
P
2
(
i
+
1
)
=
A
P
2
(
i
)
A
T
+
B
B
T
+
I
-
K
2
(
i
)
R
2
(
i
,
2
)
K
2
T
(
i
)
(
15
-
1
)
P
2
(
0
)
=
P
0
,
(
15
-
2
)
wherein,
B
=
[
-
T
0
0
]
;
and, a second-piece state estimation equation {circumflex over (x)}(i+1,2):
x
ˆ
(
i
+
1
,
2
)
=
A
x
ˆ
(
i
,
2
)
+
∅
(
x
⌣
(
i
|
i
)
)
+
K
2
(
i
)
y
˜
2
(
i
,
2
)
(
16
-
1
)
x
ˆ
(
0
,
2
)
=
x
⌣
0
;
(
16
-
2
)
wherein, Ø represents a nonlinear term;
(2) setting a first-piece initial state value {circumflex over (x)}(i, 1)={circumflex over (x)}(i, 2) and a first-piece Riccati equation initial value P 1 (i)=P 2 (i), and calculating:
a zeroth-piece output error variance R 0 (i):
R
0
(
i
)
=
C
P
1
(
i
)
C
T
+
I
,
(
17
)
a zeroth-piece state gain parameter K 0 (i):
K
0
(
i
)
=
F
P
1
(
i
)
C
T
R
0
-
1
(
i
)
,
(
18
)
and, an estimation error variance R Ø (i|i) of a virtual output ž Ø :
R
∅
(
i
|
i
)
=
F
P
1
(
i
)
F
T
-
γ
1
-
2
I
-
K
0
(
i
)
R
0
(
i
)
K
0
T
(
i
)
;
(
19
)
(3) if R 0 (i)>0 and R Ø (i|i)<0 are satisfied, calculating:
an estimation equation ž Ø (i|i) of the virtual output ž Ø :
z
⌣
∅
(
i
|
i
)
=
F
x
ˆ
(
i
,
1
)
+
K
0
(
i
)
y
˜
0
(
i
)
,
(
20
)
wherein, a zeroth-piece output estimation error {tilde over (y)} 0 (i) is:
y
~
0
(
i
)
=
y
(
i
)
-
C
x
^
(
i
,
1
)
further performing (4); or:
if R 0 (i)>0 and R Ø (i|i)<0 are not satisfied, resetting the value of γ, and performing (1);
(4) setting an initial value of a smoothing gain parameter to be
R
x
,
k
l
k
l
=
P
1
(
k
l
)
,
wherein P 1 (k l ) represents a Riccati equation obtained in an estimator design process,
C
1
=
[
C
T
F
T
]
T
Q
1
(
k
l
)
=
diag
{
I
,
-
γ
1
-
2
I
}
,
calculating:
a first-piece output error variance R 1 (k l , 1):
R
1
(
k
l
,
1
)
=
C
1
P
1
(
k
l
)
C
1
T
+
Q
1
(
k
l
)
,
(
21
)
and, a filtering estimation error variance R z (k l |k l ) of a signal to be estimated:
R
z
(
k
l
❘
k
l
)
=
LP
1
(
k
l
)
L
T
-
γ
2
I
-
K
z
(
k
l
)
R
1
(
k
l
,
1
)
K
z
T
(
k
l
)
,
(
22
)
wherein,
K
z
(
k
l
)
=
LP
1
(
k
l
)
C
1
T
R
1
-
1
(
k
l
,
1
)
if R z (k l |k l )<0, calculating an H∞ filtering estimate ž(k l |k l ):
z
⌣
(
k
l
❘
k
l
)
=
L
x
^
(
k
l
,
1
)
+
LR
x
,
k
l
k
l
C
1
T
R
1
-
1
(
k
l
,
1
)
y
~
1
(
k
l
,
1
)
,
(
23
)
wherein, a first-piece output estimation error {tilde over (y)} 1 (k l , 1) and an output signal y 1 (k l ) are as follows:
y
~
1
(
k
l
,
1
)
=
y
1
(
k
l
)
-
C
1
x
^
(
k
l
,
1
)
y
1
(
k
l
)
=
[
y
T
(
k
l
)
z
⌣
∅
T
(
k
l
❘
k
l
)
]
T
further performing (5); or:
if R z (k l |k l )<0 is not satisfied, resetting the value of γ, and performing (1);
(5) setting i=i+1, calculating R 1 (i, 1) according to (21), calculating:
a first-piece state gain parameter K 1 (i):
K
1
(
i
)
=
AP
1
(
i
)
C
1
T
R
1
-
1
(
i
,
1
)
,
(
24
)
a first-piece Riccati equation P 1 (i+1):
P
1
(
i
+
1
)
=
AP
1
(
i
)
A
T
+
BB
T
+
I
-
K
1
(
i
)
R
1
(
i
,
1
)
K
1
T
(
i
)
P
1
(
k
l
)
=
P
2
(
k
l
)
,
and
(
25
)
and, a first-piece state estimation equation {circumflex over (x)}(i+1,1):
x
^
(
i
+
1
,
1
)
=
A
x
^
(
i
,
1
)
+
∅
(
x
⌣
(
i
❘
i
)
)
+
K
1
(
i
)
y
~
1
(
i
,
1
)
x
^
(
k
l
,
1
)
=
x
^
(
k
l
,
2
)
,
(
26
)
calculating R 0 (i), K 0 (i), and R Ø (i|i) according to formulas (17) to (19), and
if R 0 (i)>0 and R Ø (i|i)<0, calculating ž Ø (i|i) according to formula (20), and performing (6); or
if R 0 (i)>0 and R Ø (i|i)<0 are not satisfied, resetting the value of γ, and performing (1);
(6) calculating the smoothing gain parameter
R
x
,
k
l
i
:
{
R
x
,
k
l
i
=
R
x
,
k
l
i
-
1
(
A
-
K
1
(
i
-
1
)
C
1
)
T
R
x
,
k
l
k
l
=
P
1
(
k
l
)
,
(
27
)
and, a smoothing estimation error variance R z (k l |i):
R
z
(
k
l
❘
i
)
=
LP
1
(
k
l
)
L
T
-
γ
2
I
-
K
z
(
k
l
)
R
1
(
k
l
,
1
)
K
z
T
(
k
l
)
-
∑
j
=
k
l
+
1
i
R
k
l
j
R
1
(
j
,
1
)
(
R
k
l
j
)
T
,
(
28
)
wherein,
R
k
l
j
=
LR
x
,
k
l
j
C
1
T
R
1
-
1
(
j
,
1
)
,
if R z (k l |i)<0, calculating an H∞ smoothing estimate ž(k l |i):
z
⌣
(
k
l
❘
i
)
=
z
^
(
k
l
❘
i
-
1
)
+
LR
x
,
k
l
i
C
1
T
R
1
-
1
(
i
,
1
)
y
~
1
(
i
,
1
)
;
(
29
)
or,
if R z (k l |i)<0 is not satisfied, resetting the value of γ, and performing (1);
(7) repeating (5) to (6) until i=k; and
(8) setting k=k+1, and repeating (1) to (7) until k=N, wherein N represents a termination moment of measurement or prediction.
2 . The method for sensing power grid information based on nonlinear robust estimation according to claim 1 , wherein the converting the H∞ smoothing estimation problem into the generalized H 2 smoothing estimation problem specifically comprises:
converting the H∞ smoothing estimation problem into the generalized H 2 smoothing estimation problem in a space mapping manner according to the H∞ smoothing estimation performance indicator.
3 . The method for sensing power grid information based on nonlinear robust estimation according to claim 1 , wherein the constructing the H∞ smoothing estimator specifically comprises:
performing processing by using an output reconstruction method according to the generalized H 2 smoothing estimation problem to construct the H∞ smoothing estimator.
4 . The method for sensing power grid information based on nonlinear robust estimation according to claim 1 , wherein the nonlinear state-space distorted power grid model is a Lipschitz nonlinear system model.
5 . The method for sensing power grid information based on nonlinear robust estimation according to claim 1 , wherein the H∞ smoothing estimator is a Riccati-equation-based recursive H∞ smoothing estimator.
6 . The method for sensing power grid information based on nonlinear robust estimation according to claim 1 , wherein the obtaining the initial sensed amplitude value and the initial sensed phase value of the power grid voltage signal by using the H∞ smoothing estimator and performing zero-crossing point detection on the initial sensed amplitude value and the initial sensed phase value of the power grid voltage signal to obtain sensed amplitude, frequency and phase values of the distorted voltage specifically comprises:
determining, according to whether adjacent signals are opposite in sign, whether zero is crossed; and using a first zero-crossing point as a frequency determining standard, and using an amplitude of a zero-crossing point as an amplitude in a first half of the period.
7 . The method for sensing power grid information based on nonlinear robust estimation according to claim 1 , wherein the obtaining the nonlinear state-space distorted power grid model based on the phase voltage signal of the actual power grid and the virtual orthogonal signal of the phase voltage signal specifically comprises:
the phase voltage signal v of the actual power grid and the virtual orthogonal signal u of the phase voltage signal are represented as sums of a series of harmonics, defined as:
{
v
=
∑
h
=
0
v
h
=
∑
h
=
0
V
h
cos
θ
h
=
∑
h
=
0
V
h
cos
(
h
ω
t
+
φ
h
)
u
=
∑
h
=
0
u
h
=
∑
h
=
0
V
h
sin
θ
h
=
∑
h
=
0
V
h
sin
(
h
ω
t
+
φ
h
)
,
(
1
)
wherein, h represents a harmonic component order, V h represents an amplitude of an h th harmonic component, θ h represents a phase angle of the h th harmonic component, φ h represents an initial phase angle of the h th harmonic component, ω represents an angular frequency of the actual power grid, t represents running time, v h represents an h th harmonic component of the phase voltage signal v of the power grid, and un represents an h th harmonic component of the virtual orthogonal signal u;
the h th harmonic components are represented as:
[
v
˙
h
u
˙
h
]
=
[
0
-
h
ω
h
ω
0
]
[
v
h
u
h
]
,
(
2
)
wherein, {dot over (v)} h represents a derivative of v h , and {dot over (u)} h represents a derivative of u h ; ω is an intermediate variable, and it is complex to estimate ω, so that Ω is set as a frequency parameter to be estimated, and the following equations are defined:
Ω
=
ω
2
ϖ
,
(
3
-
1
)
ψ
h
=
ϖ
ω
u
h
,
(
3
-
2
)
wherein, ψ h represents a corrected virtual orthogonal signal, and u h represents an actual virtual orthogonal signal;
then,
[
v
˙
h
ψ
˙
h
]
=
[
0
-
h
Ω
h
ϖ
0
]
[
v
h
ψ
h
]
,
(
4
)
wherein, ω represents a set initial power grid frequency, and a sign with “′” above represents a derivative of a variable;
a fundamental signal of a phase voltage is extracted, an orthogonal signal is constructed, and if a sampling period Tis short enough, the formula (4) is discretized as:
x
0
(
k
+
1
)
-
x
0
(
k
)
T
=
[
0
0
ω
_
0
]
x
0
(
k
)
+
[
0
-
1
0
0
]
x
0
(
k
)
Ω
+
w
0
(
k
)
,
(
5
)
wherein,
x
0
(
k
)
=
[
x
0
1
(
k
)
x
0
2
(
k
)
]
=
[
v
(
k
)
ψ
(
k
)
]
,
and w 0 (k) represents a hypothetical process noise;
if:
Ω
(
k
+
1
)
=
Ω
(
k
)
+
w
1
(
k
)
,
(
6
)
wherein, Ω(k+1) represents a frequency parameter estimated at a moment k+1, Ω(k) represents a frequency parameter estimated at a moment k, w 1 (k) represents a hypothetical process noise, and k represents the second sampling moment;
based on the formula (5) and the formula (6), a state equation is redescribed as:
[
x
1
(
k
+
1
)
x
2
(
k
+
1
)
x
3
(
k
+
1
)
]
=
[
1
0
0
T
ω
¯
1
0
0
0
1
]
[
x
1
(
k
)
x
2
(
k
)
x
3
(
k
)
]
+
[
-
T
0
0
]
x
2
(
k
)
x
3
(
k
)
+
w
(
k
)
,
(
7
)
wherein
x
(
k
)
=
[
x
1
(
k
)
x
2
(
k
)
x
3
(
k
)
]
=
[
v
(
k
)
ψ
(
k
)
Ω
(
k
)
]
,
and w(k) represents a hypothetical process noise;
further, a first observation equation is constructed:
y
x
1
(
k
)
=
[
1
0
0
]
x
(
k
)
+
v
1
(
k
)
,
(
8
)
wherein, yx 1 (k) represents an observed value, and v 1 (k) represents an observed noise;
if an ideal voltage signal is:
α
(
k
)
=
A
cos
(
2
π
w
kT
)
β
(
k
)
=
A
sin
(
2
π
w
kT
)
wherein, α(k) represents a cosine component of an ideal voltage signal at the moment k; and β(k) represents a sinusoidal component of the ideal voltage signal at the moment k;
then a second observation equation is:
y
x
2
(
k
)
=
a
tan
(
β
(
k
)
α
(
k
)
)
2
π
kT
=
[
0
0
1
]
x
(
k
)
+
v
2
(
k
)
,
(
9
)
wherein, yx 2 (k) represents an observed value, and v 2 (k) represents an observed noise;
based on the above discussion, the phase voltage model is represented as follows:
{
x
(
k
+
1
)
=
Ax
(
k
)
+
B
∅
(
x
(
k
)
)
+
w
(
k
)
y
(
k
)
=
Cx
(
k
)
+
v
(
k
)
z
(
k
)
=
Lx
(
k
)
x
(
0
)
=
x
0
,
(
10
)
wherein,
A
=
[
1
0
0
T
ω
¯
1
0
0
0
1
]
,
B
=
[
-
T
0
0
]
,
C
=
[
1
0
0
0
0
1
]
,
y
(
k
)
=
[
y
x
1
(
k
)
y
x
2
(
k
)
]
,
v
(
k
)
=
[
v
1
(
k
)
v
2
(
k
)
]
,
x 0 represents an initial state of x(k), L represents the unit matrix, and z(k) represents a signal to be sensed; and
Ø(x(k))=x 2 (k)x 3 (k) is a nonlinear term that satisfying the following Lipschitz condition:
∅
(
x
(
k
)
)
-
∅
(
x
ˆ
(
k
)
)
≤
γ
1
F
(
x
(
k
)
-
x
ˆ
(
k
)
)
,
(
11
)
wherein, γ 1 and F respectively represent a Lipschitz constant and the constant matrix, and {circumflex over (x)}(k) represents a state estimate of x(k).
8 . The method for sensing power grid information based on nonlinear robust estimation according to claim 1 , wherein the establishing the H∞ smoothing estimation performance indicator based on the nonlinear state-space distorted power grid model specifically comprises:
if the H∞ estimation performance indicator is a given scalar γ>0, a smoothing step number l≥0, and an observation sequence
{
y
(
i
)
}
i
=
0
k
,
seeking for an estimator ž(k l |k) (k l =k−l) satisfying the performance indicator for a signal z(k):
[
sup
(
x
0
,
w
,
v
)
≠
0
(
∑
k
=
0
N
z
⌣
(
k
l
|
k
)
-
z
(
k
)
2
x
0
-
x
⌣
0
P
0
-
1
2
+
∑
k
=
0
N
w
(
k
)
2
+
∑
k
=
0
N
v
(
k
)
2
)
]
<
γ
2
,
(
12
)
wherein, x̌ 0 and P 0 respectively represent the given state estimate initial value and a positive definite matrix; k represents the second sampling moment; x 0 represents the initial state value of the phase voltage model; w represents a process noise of the phase voltage model; v represents a measured noise of the phase voltage model; and N represents the termination moment of measurement.