Vp
Zps =
Ip
Zsp is defined as the leakage impedance between secondary and primary winding measured in ohms on the secondary winding with the primary wind- ing short circuited. The value of Zsp is given by the following:
Zsp
= Vs
Is
5.4.4 Summary
The voltage, current, and impedance equations for the transformer can be rewritten as follows:
Vp I
= s
Np
= = N or
Vs Ip
V
Ns
⎛ Np ⎞
= V
and
⎛ N ⎞ ⎛ I ⎞
I = s I = I
p ⎜ ⎟ s
p ⎜ ⎟ s
⎜ ⎟ s
⎝Ns ⎠
Z = NVs
⎜ Np ⎟ ⎝N ⎠
= N 2 ⎛ Vs ⎞ = N 2 Z
(1/N )Is
⎜ ⎟ s p
⎝ Is ⎠
conversely,
Z = ⎛ 1 ⎞ Z
sp ⎜ ⎟ ps
⎝ ⎠
Generally, for power transformers the impedance is specified in a percentage rather than actual ohms. The percentage of impedance of a transformer can be expressed as
⎛Irated × Zps ⎞
Z % = ⎜ ⎟ × 100
ps ⎜
⎝
Vprated ⎟
= (voltage drop at rated voltage/rated voltage) × 100
The percentage of impedance can be expressed independently of the terminal voltages and is based on the kVA rating of the transformer. The equivalent circuit diagram of a transformer on a percentage basis is shown in Figure 5.7.
Ip%
Zps%
Is%
Vp% Vs%
FIGURE 5.7
Percentage equivalent circuit of transformer.
5.5 Transformer Polarity, Terminal Markings, and Connections
5.5.1 Single-Phase Transformers
Primary and secondary terminals of a single-phase transformer have the same polarity when the current enters the primary terminal and at the same time leaves the secondary terminal. Transformers are constructed with subtractive and additive polarities.
5.5.1.1 Subtractive Polarity
When the high-side lead, H1 and low-side lead, X1, are brought out on the same side of the transformer, the polarity is said to be subtractive, as shown in Figure 5.8a. If leads H1 and X1 are connected and the high side is energized with a given voltage, the resulting voltage, which appears across the H2 and X2 leads, will be less than the applied voltage (see Figure 5.8b). This is due to the fact that in this series connection the low-voltage winding opposes
~
H1 H2
V
X1 X2
X1 X2 H2 H1
(a) (b) (c)
FIGURE 5.8
(a) Subtractive polarity of single-phase transformer, (b) connection for polarity test, and
(c) resultant voltage across H1 and X1.