US 11,953,398 B2 · Quasi-static calculation method for lateral unbalanced force of transmission lines

Abstract

The present invention belongs to the technical field of disaster prevention and reduction of transmission lines, and provides a quasi-static calculation method for lateral unbalanced force of transmission lines. The present invention can quantify significant unbalanced force caused by a failed tower to an adjacent tower, thus to quantitatively evaluate cascading failure risk of transmission lines. The present invention does not need a lot of iteration, and can parametrically reveal influence of various factors on unbalanced force. The present invention quantifies influence of large deformation effect of a conducting wire on wind load, and at the same time, wind load of the conducting wire is corrected by the trapezoidal equivalent wind pressure proposed, which avoids wind load calculation error of the conducting wire caused by a relatively large vertical height difference, better reflects actual mechanical state of the lines, and optimizes existing wind load calculation method of transmission lines.

A quasi-static calculation method for lateral unbalanced force of transmission lines, comprising the following steps:

step 1:
determining mean wind-induced lateral unbalanced force
for a span conducting wire with an initial vertical height difference c0 at both ends, displacement components of one end in longitudinal direction (x-axis direction), vertical direction (y-axis direction) and lateral direction (z-axis direction) are respectively ΔX, ΔY and ΔZ, and a standard cubic equation with H1 as a variable is obtained:
H
1
3
+
(
E
⁢
A
⁢
q
2
⁢
L
2
2
⁢
4
⁢
H
0
2
-
E
⁢
A
⁡
(
Δ
⁢
Y
2
+
Δ
⁢
Z
2
+
2
⁢
L
⁢
Δ
⁢
X
+
2
⁢
c
0
⁢
Δ
⁢
Y
)
2
⁢
L
2
-
H
0
)
⁢
H
1
2
+
(
-
E
⁢
A
⁢
Δ
⁢
Z
⁢
λ
L
3
)
⁢
H
1
+
E
⁢
A
⁡
(
-
q
2
⁢
L
2
2
⁢
4
-
δ
2
⁢
L
3
)
=
0
(
1
)
δ
=
∫
0
L
(
(
∫
0
L
∫
0
x
2
(
f
¯
R
⁢
e
⁢
f
(
x
1
)
⁢
d
⁢
x
1
)
⁢
d
⁢
x
2
)
2
+
L
2
(
∫
0
x
f
¯
R
⁢
e
⁢
f
(
x
1
)
⁢
d
⁢
x
1
)
2
-
2
⁢
L
⁢
∫
0
L
∫
0
x
2
(
f
¯
R
⁢
e
⁢
f
(
x
1
)
⁢
d
⁢
x
1
)
⁢
d
⁢
x
2
·
∫
0
x
f
¯
R
⁢
e
⁢
f
(
x
1
)
⁢
d
⁢
x
1
)
⁢
dx
(
2
)
λ
=
∫
0
L
(
∫
0
L
∫
0
x
2
(
f
¯
R
⁢
e
⁢
f
(
x
1
)
⁢
d
⁢
x
1
)
⁢
d
⁢
x
2
-
L
⁢
∫
0
x
f
¯
R
⁢
e
⁢
f
(
x
1
)
⁢
d
⁢
x
1
)
⁢
dx
(
3
)
where:
H0 represents initial horizontal tension;
EA represents Young's modulus;
q represents weight per unit length of the span conducting wire;
L represents horizontal span;
both δ and λ represent constants related to mean wind pressure;
fRef(x) is a distribution function of the mean wind pressure along line direction;
and H1 represents horizontal tension of the span conducting wire under combined action of support displacement and mean wind, which can be obtained by solving formula (1) via a Cardan's formula;
further, the mean wind-induced lateral unbalanced force at both ends of the span conducting wire is obtained:
T
_
z
⁢
0
=
1
L
⁢
∫
0
L
∫
0
x
2
(
f
¯
R
⁢
e
⁢
f
(
x
1
)
⁢
dx
1
)
⁢
d
⁢
x
2
+
H
1
⁢
Δ
⁢
Z
L
(
4
)
T
_
z
⁢
1
=
1
L
⁢
∫
0
L
∫
0
x
2
(
f
¯
R
⁢
e
⁢
f
(
x
1
)
⁢
d
⁢
x
1
)
⁢
d
⁢
x
2
-
∫
0
x
f
¯
R
⁢
e
⁢
f
(
x
1
)
⁢
d
⁢
x
1
+
H
1
⁢
Δ
⁢
Z
L
(
5
)
where:
subscripts 0 and 1 respectively represent one side of the span conducting wire without support displacement and one side of the span conducting wire with support displacement, the same below;
step 2:
determining fluctuating wind-induced lateral unbalanced force
considering quasi-static background response only, the fluctuating wind-induced lateral unbalanced force at both ends of the span conducting wire is calculated by an influence line method:
T
z
⁢
0
(
t
)
=
L
n
⁢
∑
i
=
1
n
(
1
-
x
i
L
+
Δ
⁢
Z
L
⁢
φ
h
)
⁢
F
Ref
(
x
i
,
t
)
(
6
)
T
z
⁢
1
(
t
)
=
L
n
⁢
∑
i
=
1
n
(
x
i
L
-
Δ
⁢
Z
L
⁢
φ
h
)
z
⁢
1
ι
⁢
F
Ref
(
x
i
,
t
)
(
7
)
where:
FRef(xi,t) represents fluctuating wind load acting on each point of the span conducting wire;
n represents number of wind speed simulation points;
xi represents x-coordinate of the fluctuating wind load;
φh represents increment of horizontal tension caused by unit wind load, and the expression thereof is:
φ
h
=
1
-
x
1
/
L
H
1
⁢
∫
0
x
1
d
⁢
w
¯
d
⁢
x
⁢
d
⁢
x
-
x
1
/
L
H
1
⁢
∫
x
1
L
d
⁢
w
¯
d
⁢
x
⁢
dx
L
EA
-
q
⁢
∫
0
L
d
⁡
(
y
0
+
v
¯
)
d
⁢
x
⁢
(
2
⁢
x
-
L
)
⁢
d
⁢
x
2
⁢
H
1
2
+
∫
0
x
1
(
d
⁢
w
¯
d
⁢
x
)
2
⁢
d
⁢
x
+
∫
x
1
L
(
d
⁢
w
¯
d
⁢
x
)
2
⁢
d
⁢
x
H
1
-
Δ
⁢
Z
⁡
(
∫
0
x
1
d
⁢
w
¯
d
⁢
x
⁢
d
⁢
x
+
∫
x
1
L
d
⁢
w
¯
d
⁢
x
⁢
d
⁢
x
)
H
1
⁢
L
(
8
)
d
⁡
(
γ
0
+
v
¯
)
d
⁢
x
=
q
2
⁢
H
1
⁢
(
L
-
2
⁢
x
)
+
Δ
⁢
y
L
(
9
)
d
⁢
w
¯
d
⁢
x
=
1
H
1
⁢
L
⁢
∫
0
L
∫
0
x
2
(
f
¯
R
⁢
e
⁢
f
(
x
1
⁢
λ
⁢
1
⁢
x
1
)
⁢
d
⁢
x
2
-
1
H
1
⁢
∫
0
X
f
¯
R
⁢
e
⁢
f
(
x
1
)
⁢
λ1
⁢
x
1
+
Δ
⁢
Z
L
(
10
)
where:
y0, v and w respectively represent initial vertical displacement, vertical displacement under combined action of mean wind and support displacement, and lateral displacement caused by mean wind of the span conducting wire;
finally, total lateral reaction force is a sum of the mean wind-induced lateral unbalanced force and the fluctuating wind-induced lateral unbalanced force, the total lateral unbalanced force is obtained:
{circumflex over (T)}z0(t)=Tz0+Tz0(t) (11)
{circumflex over (T)}z1(t)=Tz1+Tz1(t) (12).

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Quasi-static calculation method for lateral unbalanced force of transmission lines

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Quasi-static calculation method for lateral unbalanced force of transmission lines

Life of this patent

Abstract

Claims2