1
Problem Set #6 Power-flow solutions, Gauss-Seidel Method, and Newton-Raphson
Method
6-1
(Keyhani Lecture)
Using Gauss elimination and back substitution, solve
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
=
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
3
2
1
14
2
5
2
12
4
0
3
10
3
2
1
x
x
x
6-2
(Keyhani Lecture)
Use Newton-Raphson to find one solution to the polynomial equation
f
(
x
)=
y
, where
y
=0
and
f
(
x
)=3
x
3
+4
x
2
+5
x
+6. Start with
x
(0)=1.0 and continue until
ε
<
−
−
−
)
1
(
)
1
(
)
(
i
x
i
x
i
x
(6.1)
is satisfied, where
ε
=0.001.
6-3
(Keyhani Lecture)
Use Newton-Raphson to find a solution to
⎥
⎦
⎤
⎢
⎣
⎡
=
⎥
⎦
⎤
⎢
⎣
⎡
+
5
.
0
2
.
1
)
cos(
2
1
2
1
x
x
e
x
x
where
x
1
and
x
2
are in radians.
a)
Start with
x
1
(0)=1.0 and
x
2
(0)=0.5 and continue until Equation (6.1) is satisfied
with
ε
=0.005.
b)
Show that Newton-Raphson diverges for the example if
x
1
(0)=1.0 and
x
2
(0)=2.0.
6-4
(Grainger and Stevenson, Jr. Chapter 8, Prob 8.10)

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