[James_H._Harlow]_Electric_Power_Transformer_Engin(BookSee.org)
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2<br />
2 VL<br />
Q0<br />
* X<br />
VLa VS * VL<br />
*<br />
2 2<br />
( P * X) ( V Q * X)<br />
0<br />
2 P0<br />
* X<br />
VLr VS * VL<br />
*<br />
2 2<br />
( P * X) ( V Q * X)<br />
0<br />
L<br />
L<br />
0<br />
0<br />
2<br />
2<br />
(2.3.28)<br />
(2.3.29)<br />
V V* 2* sin <br />
/ 2<br />
(2.3.35)<br />
V V * cos / 2*<br />
3<br />
(2.3.36)<br />
<br />
and with I S = I L = I, the part of the current that is transferred to the exciting winding becomes<br />
2.3.5 Types of Phase-Shifting <strong>Transformer</strong>s<br />
L<br />
(2.3.30)<br />
2.3.5.1 General Aspects<br />
The general principle to obtain a phase shift is based on the connection of a segment of one phase with<br />
another phase. To obtain a 90˚ additional voltage V, the use of delta-connected winding offers the<br />
simplest solution. Figure 2.3.8 shows a possible arrangement and is used to introduce a few basic<br />
definitions. The secondary winding of phase V 2 – V 3 is split up into two halves and is connected in series<br />
with phase V 1 . By designing this winding as a regulating winding and using on-load tap changers (OLTC),<br />
V and the phase-shift angle can be changed under load. The phasor diagram has been plotted for noload<br />
conditions, i.e., without considering the voltage drop in the unit. It also should be noted that the<br />
currents in the two halves of the series winding are not in phase. This is different from normal power<br />
transformers and has consequences with respect to the internal stray field.<br />
From the connection diagram (Figure 2.3.8a), the following equations can be derived:<br />
From the phasor diagram (Figure 2.3.8b) follows (V S1 = V L1 = V):<br />
S<br />
I S1<br />
V 30<br />
FIGURE 2.3.8 Single core symmetrical PST.<br />
P<br />
* X<br />
arctan<br />
( P * X) ( V Q * X)<br />
,V 1<br />
V 10<br />
V 20<br />
V,<br />
<br />
0<br />
0<br />
2 2<br />
<br />
L<br />
0<br />
2<br />
V S1 = V 10 + (V 1 /2) (2.3.31)<br />
V L1 = V 10 –(V 1 /2) (2.3.32)<br />
V 1 = V S1 – V L1 (2.3.33)<br />
V V* cos <br />
/ <br />
0<br />
2<br />
L<br />
I L1<br />
V L1<br />
V S1<br />
V 10<br />
,V 1<br />
I L1<br />
I S1<br />
=<br />
I ,<br />
V 30<br />
V 20<br />
a) b)<br />
(2.3.34)<br />
The throughput power can be calculated from<br />
I<br />
<br />
V<br />
2<br />
* I* cos <br />
/ 2<br />
I* * sin <br />
/ 2<br />
V<br />
3<br />
<br />
P 3* V * I<br />
SYS<br />
and the rated design power, which determines the size of the PST, becomes<br />
P 3* V* I P * 2* sin <br />
/ 2<br />
T<br />
(2.3.37)<br />
(2.3.38)<br />
(2.3.39)<br />
A third kind of power (P ) is the power that is transferred into the secondary circuit. This power is<br />
different from P T because a part of the primary current is compensated between the two parts of the<br />
series winding itself. In two-core designs (see Equation 2.3.33), this power determines also the necessary<br />
breaking capability of the OLTC.<br />
1<br />
P <br />
V <br />
* I <br />
* P SYS<br />
* sin <br />
(2.3.40)<br />
3<br />
In addition to the transferred power, the phase-shift angle is also important. A phase-shift angle of<br />
20˚ means that the PST has to be designed for 34.8% of the throughput power, and an angle of 40˚ would<br />
require 68.4%. In this respect, it has to be considered that the effective phase-shift angle under load is<br />
smaller than the no-load phase-shift angle. In the optimum case when the load power factor is close to<br />
1, a PST impedance of 15% would reduce the load phase-shift angle by 8.5˚ (Equations 2.3.14 and 2.3.16).<br />
In practice, various solutions are possible to design a PST. The major factors influencing the choice are:<br />
• Throughput power and phase-shift angle requirement<br />
• Rated voltage<br />
• Short-circuit capability of the connected systems<br />
• Shipping limitations<br />
• Load tap-changer performance specification<br />
In addition, preferences of a manufacturer as to the type of transformer (core or shell) or type of windings<br />
and other design characteristics may also play a role. Depending on the rating, single- or two-core designs<br />
are used. Two-core designs may require either a one-tank or a two-tank design.<br />
2.3.5.2 Single-Core Design<br />
Symmetrical conditions are obtained with the design outlined in Figure 2.3.8a. Figure 2.3.9a and Figure<br />
2.3.9b show the general connection diagrams with more details of the regulating circuit.<br />
The advantage of the single-core design is simplicity and economy. But there are also a number of<br />
disadvantages. The OLTCs are connected to the system and directly exposed to all overvoltages and<br />
through faults. The voltage per OLTC step and the current are determined by the specification and do<br />
not always permit an optimal economical choice of the OLTC. The short-circuit impedance of the PST<br />
varies between a maximum and zero. Therefore, it can not be planned that the PST will contribute to<br />
the limitation of fault currents in the system.<br />
SYS<br />
© 2004 by CRC Press LLC<br />
© 2004 by CRC Press LLC