# US 2013/0158901 A1 · Method and System for Detecting Unbalance in Power Grids

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- Number: US 2013/0158901 A1
- Document ID: US20130158901A1
- Status: Published application
- Kind: A1
- Application number: 13/329,720
- Filed: 2011-12-19
- Published: 2013-06-20
- Earliest claimed: 2011-12-19
- Inventors: Zafer Sahinoglu; Ming Sun; Koon Hoo Teo
- Web page: https://patentgrep.com/patent/US20130158901A1

## CPC

- G01R 29/16: Measuring asymmetry of polyphase networks
- H02J 3/381: {Dispersed generators}
- H02J 3/388: Arrangements for the handling of islanding, e.g. for disconnection or for avoiding the disconnection of power
- G01R: MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES (indicating correct tuning of resonant circuits H03J3/12)
- H02J: ELECTRIC POWER NETWORKS; CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY

## Abstract

A method for detecting unbalance in a 3-phase voltage signal includes sampling the signal over an observation widow to determine a set of observations, and detecting the unbalance of the signal based on a probability density function (pdf) of the set of observations.

## Claims

### Claim 1

A method for detecting unbalance in signal, wherein the signal is 3-phase voltage signal of a power grid, the method comprising:
sampling the signal over an observation window to determine a set of observations; and
detecting the unbalance of the signal based on a probability density function (pdf) of the set of observations.

### Claim 2 (depends on 1)

The method of claim 1, wherein the detecting further comprises:
determining the unbalance of the signal based on a joint pdf of the set of observations.

### Claim 3 (depends on 1)

The method of claim 1, wherein the detecting further comprises:
determining the unbalance of the signal based on a ratio of a joint pdf of the set of observations and a joint pdf of the signal without unbalance.

### Claim 4 (depends on 1)

The method of claim 1, wherein the signal is
va(n)=Va cos(nw+φa)+ea(n)
vb(n)=Vb cos(nw+φb)+eb(n)
vc(n)=Vc cos(nw+φc)+ec(n)
where n is an instant in time for i=a, b, c, Vi is an amplitude, φi is an initial phase angle of the phase i, w is an angular frequency of the power grid given by w=2πf/fs where f and fs are a grid frequency and a sampling frequency, respectively, e is additive noise, wherein the additive noise vector at time instant n is
e(n)=[ea(n),eb(n),ec(n)]T,
and T is a transpose operator.

### Claim 5 (depends on 4)

The method of claim 4, wherein the signal is represented by a vector
v(n)=vp(n)+vn(n)+v0(n)+e(n),
where vp(n), vn(n) and v0(n) represent a positive sequence, a negative sequence, and a zero sequence.

### Claim 6 (depends on 5)

The method of claim 5, further comprising:
transforming the signal to an αβ-reference frame signals using a Clark transformation matrix; and
determining the unbalance indicator based on the αβ-reference frame signals and an estimation of a frequency of the signal.

### Claim 7 (depends on 6)

The method of claim 6, wherein the Clarke transformation matrix is
T
=
2
3

[
1
-
1
2
-
1
2
0
3
2
-
3
2
]
,
and the αβ-reference frame signal is represented by
y

(
n
)
=
[
v
α

(
n
)
v
β

(
n
)
]
=
V
p

[
cos


θ
p

(
n
)
sin


θ
p

(
n
)
]
+
V
n

[
cos


θ
n

(
n
)
-
sin


θ
n

(
n
)
]
+
[
e
α

(
n
)
e
β

(
n
)
]
,
wherein Vi and θi(n) for i=p, n, 0 are an amplitude and a phase angle of each sequence, respectively.

### Claim 8 (depends on 6)

The method of claim 6, further comprising:
determining a statistical value using a general likelihood ratio test based on the αβ-reference frame signals and the frequency of the voltage signal; and
detecting the unbalance based on the statistical value.

### Claim 9 (depends on 8)

The method of claim 8, further comprising:
acquiring a data independent matrix A;
determining a block diagonal matrix G;
determining an estimate of a vector of unknowns; and
determining the statistical value based on the matrix A, the matrix G, and the vector of unknowns.

### Claim 10 (depends on 8)

The method of claim 8, further comprising:
determining the statistical value T(vt) according to
T

(
v
t
)
=
θ
^
1
T

A
T

(
A

(
G
T

G
)
-
1

A
T
)
-
1

A


θ
^
1
2

σ
2
/
3
,
wherein the matrix A is pre-determined according to A=[I4×4, O4×2], the matrix G is a block diagonal matrix which is a function of the fundamental frequency w, σ2 is the variance of noise and {circumflex over (θ)}1 is the estimate of the vector of unknowns.

### Claim 11 (depends on 1)

The method of claim 1, further comprising:
comparing the set of observation with a model of a balanced 3-phase voltage signal using a likelihood ratio test, wherein the set of observations represents the entire observation window.

### Claim 12

An unbalance detector, comprising:
an input terminal for acquiring a signal, wherein the signal is a 3-phase voltage;
a statistical model computation module for determining a joint pdf of a set of observations of the signal;
a processing unit for determining ratio of the joint pdf of the set of observations and a joint pdf of the signal without unbalance;
a comparison module for comparing the ratio with a threshold to determine an unbalance of the signal; and
an output terminal for signaling the unbalance of the signal.

### Claim 13 (depends on 12)

The detector of claim 12, wherein the ratio is determined as a statistical value T(vt) of a general likelihood ration test according to
T

(
v
t
)
=
θ
^
1
T

A
T

(
A

(
G
T

G
)
-
1

A
T
)
-
1

A


θ
^
1
2

σ
2
/
3
,
wherein the matrix A is pre-determined according to A=[I4×4, O4×2], the matrix G is a block diagonal matrix which is a function of the fundamental frequency w, σ2 is the variance of noise and {circumflex over (θ)}1 is the estimate of the vector of unknowns.

### Claim 14

A method for detecting unbalance in a signal, wherein the signal is 3-phase voltage, the method comprising:
determining a statistical value using a general likelihood ratio test based on a set of samples of the signal and a frequency of the signal; and
comparing the statistical value with a threshold to determine an unbalance of the signal, wherein the steps are performed by a processor.

### Claim 15 (depends on 16)

The method of claim 16, further comprising:
determining the threshold based on a probability of a false alarm.

### Claim 16 (depends on 17)

The method of claim 17, wherein the probability of the false alarm includes a probability of detecting unbalance in a balanced signal.

### Claim 17 (depends on 16)

The method of claim 16, further comprising:
determining an islanding condition based on the unbalance.