Civil Engineering Reference
In-Depth Information
Water source (e.g. a dam)
with constant head h
1
Node 2 :
q
1
+
q
2
Q
2
=
0
Node 3 :
q
2
+
q
3
Q
3
=
0
1
Pipe 1:
h
1
+
h
2
+
r
1
q
1
q
1
=
0
1
Pipe 2 :
h
3
+
h
2
+
r
2
q
2
q
2
=
0
3
q
1
q
3
Pipe 3 :
h
1
+
h
3
+
r
3
q
3
q
3
=
0
q
2
2
Demand node
head: h
3
3
Demand node
2
Known terms:
h
1
and
D
i
,
L
i
,
i
(
i
=
1, 2 , 3
)
head: h
2
2
outgoing flow: Q
3
Unknowns:
flows
q
1
,
q
2
,
q
3
and heads
h
2
,
h
3
outgoing flow: Q
(a)
(b)
Slack bus
complex voltage V
1
Node 2:
P
2
=
V
2
V
1
G
21
cos
21
+
B
21
sin
21
(
) +
V
2
G
22
+
V
3
G
23
cos
23
+
B
23
sin
23
(
)
Q
2
=
V
2
V
1
G
21
sin
21
B
21
cos
21
)
+
V
2
B
22
)
+
V
3
G
23
sin
23
B
23
cos
23
(
(
(
)
1
Node 3:
P
3
=
V
3
V
1
G
31
cos
31
+
B
31
sin
31
)
+
V
2
G
32
cos
32
+
B
32
sin
32
)
+
V
3
G
33
(
(
1
3
complex voltage
V
1
and power
S
2
real power
P
3
and voltage magnitude
V
3
and line impedances
z
i
Generator
real power: P
3
voltage magnitude: |V
3
|
Known terms:
2
i
=
1, 2 , 3
(
)
3
Load bus
complex power:
S
2
= P
2
+ jQ
2
2
Unknowns: voltage magnitude
V
2
and phase angles
2
,
3
(c)
(d)
18.6
Elementary WSS (top) and (EPN) bottom, and the corresponding fl ow equations.
Search WWH ::
Custom Search