TRANSFORMER
- Ideal Transformer
a=E1
E2
=N1
N2
=I2
I1
→ turns ratio
E1=−N1
dϕ
dt
|
E
|
=4.44 f N A core Bmax
S1=E1I1
¿=
(
a E2
)
(
I2
a
)
¿
=E2I2
¿=S2
- Non-ideal transformer
percent reg .=¿V2NL∨−¿V2F L∨¿
¿V2F L∨¿×100¿¿
percent reg .=¿V1/a∨−¿V2∨¿
|
V2
|
×100 → prat . ¿
η=output power
input power =P2
P1
η=P1−Plosses
P1
=P2
P2+Plosses
Isc=Poc
Voc
Typeequation here .
Per unit: Select
VB
and
SB
. After,
ZB=
(
VB
)
2
SB
IB=VB
ZB
Determine base:
Vbase 1
Vbase 2
=N1
N2
Conversion
Zp. u . new=Zact ual
Zbasenew
=Zp. u . old Zbasenew
Zbasenew
Zp. u . new=Zp . u . old
(
Vbaseold
Vbasenew
)
2
(
Sbasenew
Sbaseold
)
>> To convert back to actual values
just multiply the per unit values by
their per unit base.
- Three Phase Per Unit: Pick
SB
3ϕ
; Pick
different voltage (line to line);
Calculate impedance base
ZB=¿¿ ¿
Calculate the current base,
IB
IB
3ϕ=SB
3ϕ
√
3VB, ≪¿=IB
1ϕ¿
-Short Line (
l<50 miles
)
Z=
(
r+jωL
)
l=R+jX
Ss
(
3ϕ
)
=3VsIs
¿
SL
(
3ϕ
)
=Ss
(
3ϕ
)
−SR(3ϕ)
SL
(
3ϕ
)
=PL
(
3ϕ
)
+j QL(3ϕ)
PL
(
3ϕ
)
=3
|
IR
|
2R , QL
(
3ϕ
)
=3
|
IR
|
2X
η=PR
(
3ϕ
)
Ps
(
3ϕ
)
VR=¿VR NL∨−¿VRF L∨¿
¿VRF L∨¿×100¿¿
- Medium Line
(50<l<150 miles )
Z=
(
r+jωL
)
lY =
(
g+jωC
)
l
- Long Line
(l>150 miles)
γ=
√
YZ=α+jβ
V
(
x
)
=VRcosh
(
γx
)
+IR
√
Z
Ysinh (γx)
I
(
x
)
=IRcosh
(
γx
)
+VR
Zc
sinh (γx)
