[James_H._Harlow]_Electric_Power_Transformer_Engin(BookSee.org)

jI 2 *X 2
jI 1 *X 1
V L * ,V
V S
V L
,V jI 1 *X 1
jI 2 *X 2
V S
V L * V L
VS retard
V L*
I L
*jX T
I L
*R T
V S advanced
I
I
PST
Z = 0
T 1:1
α (r)
α (a)
β
α∗ α∗ (
(r)
a)
Z = R T +jX T
V L I L
V S
I S
∆V
V L*
I L
V L
ϕ
b)
a) Advanced phase angle
V L * leads V S
b) Retard phase angle
V L *lags V S
V S
V L** V L*
c)
FIGURE 2.3.3 No-load voltage diagram of parallel systems.
a)
∆V, I* jX
α*(a)
β
∆V
Transmission Line, X
~ ~
I
V L*
V S , V L
FIGURE 2.3.5 On-load diagram of a PST.
V S V L* V L
V S + ∆V-I* jX-V L = 0
This is very important for the operation of a PST. Because the phase angle determines the voltage
across the PST, an increase of the load phase angle in a retard position would mean that the PST is
overexcited; therefore the retard-load phase-shift angle should be limited with the no-load angle.
The load angle b can be calculated from
for
V S = V L = V
henc e
∆V - I *jX = 0
zT
* cos g
Z
b = arc tan(
)
100 + z *sin g
T
Z
(2.3.16)
FIGURE 2.3.4 Connection of two systems.
The diagram is developed beginning at the load side, where voltage V L and current I L are known.
Adding the voltage drop, I*R T + I*jX T , to voltage V L results in voltage V L *, which is an internal, not
measurable, voltage of the PST. This voltage is turned either clockwise or counterclockwise, and as a
result the source voltages V S,retard or V S,advanced are obtained, which are necessary to produce voltage V L and
current I L at the load side. Angle determines the phase-shift at the no-load condition, either as retard
phase-shift angle (r) or as advanced phase-shift angle (a) . Under no load, the voltages V L and V L * are
identical, but under load, V L * is shifted by the load angle . As a result, the phase angles under load are
not the same as under no load. The advanced phase-shift angle is reduced to * (a) , whereas the retard
phase-shift angle is increased to * (r) . The advanced phase angle under load is given by
and the retard phase angle under load is given by
* (a) = (a) – (2.3.14)
* (r) = (r) + (2.3.15)
where all quantities are per unit (p.u.) and z T = transformer impedance.
In reality, the PST does not influence the voltages neither at the source nor at the load side because
it is presumed that the systems are stable and will not be influenced by the power flow. This means that
V S and V L coincide and V L* would be shifted by a* (a) to V L** (Figure 2.3.5c). As for developing the PST
load diagram, a certain load has been assumed. The advanced phase-shift angle is a measure of the
remaining available excess power.
2.3.4 Total Power Transfer
The voltages at the source side (V S ) and at the load side (V L ) are considered constant, i.e., not influenced
by the transferred power, and operating synchronously but not necessarily of the same value and phase
angle. To calculate the power flow it has been assumed that the voltages at source side (V S ) and load side
(V L ) and the impedance (Z) are known.
V S = V S *(cos g S + jsin g S ) (2.3.17)
V L = V L *(cos g L + jsin g L ) (2.3.18)
© 2004 by CRC Press LLC
© 2004 by CRC Press LLC