Figure 2.33 gives the general Δ -Y transformation. (a) Show that the general transformation reduces to that given in Figure 2.16 for a balanced three-phase load. (b) Determine the impedances of the equivalent Y for the following Δ impedances: Z AB = j 10 , Z BC = j 20 , and Z CA = − j 25 Ω . Z AB = Z A Z B + Z B A C + Z C Z A Z C Z A = Z AB Z CA Z AB + Z BC + Z CA Z BC = Z A Z B + Z B A C + Z C Z A Z A Z B = Z AB Z BC Z AB + Z BC + Z CA Z CA = Z A Z B + Z B A C + Z C Z A Z B Z A = Z CA Z BC Z AB + Z BC + Z CA
Figure 2.33 gives the general Δ -Y transformation. (a) Show that the general transformation reduces to that given in Figure 2.16 for a balanced three-phase load. (b) Determine the impedances of the equivalent Y for the following Δ impedances: Z AB = j 10 , Z BC = j 20 , and Z CA = − j 25 Ω . Z AB = Z A Z B + Z B A C + Z C Z A Z C Z A = Z AB Z CA Z AB + Z BC + Z CA Z BC = Z A Z B + Z B A C + Z C Z A Z A Z B = Z AB Z BC Z AB + Z BC + Z CA Z CA = Z A Z B + Z B A C + Z C Z A Z B Z A = Z CA Z BC Z AB + Z BC + Z CA
Figure 2.33 gives the general
Δ
-Y transformation. (a) Show that the general transformation reduces to that given in Figure 2.16 for a balanced three-phase load. (b) Determine the impedances of the equivalent Y for the following
Δ
impedances:
Z
AB
=
j
10
,
Z
BC
=
j
20
, and
Z
CA
=
−
j
25
Ω
.
Z
AB
=
Z
A
Z
B
+
Z
B
A
C
+
Z
C
Z
A
Z
C
Z
A
=
Z
AB
Z
CA
Z
AB
+
Z
BC
+
Z
CA
Z
BC
=
Z
A
Z
B
+
Z
B
A
C
+
Z
C
Z
A
Z
A
Z
B
=
Z
AB
Z
BC
Z
AB
+
Z
BC
+
Z
CA
Z
CA
=
Z
A
Z
B
+
Z
B
A
C
+
Z
C
Z
A
Z
B
Z
A
=
Z
CA
Z
BC
Z
AB
+
Z
BC
+
Z
CA
4. For the periodic signal shown in Fig. 4;
a) Find the exponential Fourier Series for y(t).
b) Use Parseval's Theorem to compute the total power contained in the 4th harmonic and all higher
harmonics.
2+
y(t)
+
-2л
-л
0
2л
Зл
4л
Fig. 4
2. a) Find the Fourier transform of the signal
shown in Fig. 2 and express it in its most
compact form;
b) Find the value of the energy spectral
density at f=1/4.
0
-2
-1
-3.
Fig. 1
g(t)
3
1
2
t-
Fig 2
5. Consider a filter whose transfer function is: H(f) =
-12xfß
(a + jπ f ) ²
(a) show that the filter is non-causal for α = 3, p= -1;
(b) choose alternate values of α, ẞ that result in a causal filter, and demonstrate that your choice
valid.
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Power System Analysis and Design (MindTap Course ...Electrical EngineeringISBN:9781305632134Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. SarmaPublisher:Cengage Learning