1
EE740 Final, Au04
Problem 1
(25 points)
Consider a 3-
φ
distribution feeder as shown below:
Load #1 is rated 133.3 kVar with power factor of 0.0 leading. Load #2 is rated 100 kW
with power factor of 0.6 lagging.
1)
Calculate the power factor at the load bus. (15 points)
2)
Describe the real power flow direction in the system. (5 points)
3)
Describe the reactive power flow direction in the system. (5 points)
Solution:
1) Load #1:
P
1
= 0,
Q
1
= -133.33 MVar.
Load #2:
P
2
= 100 kW, cos
θ
2
= 0.6,
3
.
133
)
6
.
0
sin(cos
6
.
0
100
1
2
=
=
−
Q
kVar
0
0
tan
tan
1
2
1
2
1
1
=
=
+
+
=
−
−
P
P
Q
Q
θ
pf = cos0 = 1
2) Real power flows from source to Load 2.
3) Reactive power flows from Load 1 to Bus and then to Load 2.
Problem 2
(45 points)
Consider the power system given below:
Given:
Z
G(1)
=
Z
G(2)
=
j
0.2 p.u.,
Z
G(0)
=
j
0.1 p.u.
Z
AB(1)
=
Z
AB(2)
=
j
0.3 p.u.,
Z
AB(0)
=
j
0.8 p.u.
Z
BC(1)
=
Z
BC(2)
=
j
0.3 p.u.,
Z
BC(0)
=
j
0.8 p.u.
Z
T(1)
=
Z
T(2)
=
Z
T(0)
=
j
0.1 p.u.
V
L
= 1.0
∠
-20.0
°
p.u.,
S
L
=
j
0.625 p.u.

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