Download Open Circuit Test of a Single Phase Transformer jXm

Open Circuit Test of a Single Phase Transformer
The Open Circuit Test is used to determine the components (Rfe, Xm) used to model the
magnetic core effects in the practical transformer model. The test is typically performed by
applying rated voltage (Eoc) to the primary winding and measuring the resultant current (Ioc) and
power (Poc) while leaving the secondary winding open-circuited. Rated primary voltage is
utilized because the applied voltage determines the created flux and therefore the operating point
on the B-H curve which, in turn, determines the magnetization current, the eddy current losses,
and the hysteresis losses in the core.
Open-circuiting the secondary winding of the transformer results in no current flowing
through the series impedances that model the winding losses in the Approximate (Cantilever)
Equivalent Circuit. Thus, neglecting winding-impedances leg of the model, the equivalent
circuit simplifies to the following equivalent circuit. Since only the elements Rfe and Xm remain,
their values can be determined from the test data. The governing equations are shown below:
2
oc
Poc =
E
R fe
⇒
R fe =
E
Poc
Qoc =
E oc2
Xm
⇒
Xm =
E oc2
Qoc
Qoc = ( E oc I oc ) 2 − Poc
Ioc
2
oc
2
Eoc
Poc
Rfe
j Xm
Short Circuit Test of a Single Phase Transformer
The Short Circuit Test is used to determine the series winding components (Req, Xeq) in
the practical transformer model. The test is typically performed by applying the primary
winding voltage that results in rated secondary current under short-circuited conditions.
Warning – the applied primary voltage for the Short Circuit Test is typically much smaller
than the rated primary voltage. The test is performed at rated secondary current since it is the
current magnitude flowing in the windings that affects the winding losses and not the applied
primary voltage magnitude.
Short-circuiting the secondary winding of the transformer results in a majority of the
source current flowing through the short circuit instead of the magnetic core components (Rfe,
Xm). Thus, one may neglect the core components when under short-circuit conditions, resulting
in the following simplified Approximate (Cantilever) Equivalent Circuit:
:
Isc
jXeq
Req
Since only the elements Req and Xeq
remain, their values can be
determined from the test data. The
governing equations are shown
below:
Esc
Psc
Psc = I sc ⋅ Req
2
Q sc = I sc ⋅ X eq
2
⇒
Req =
⇒
Q sc = ( E sc I sc ) 2 − Psc
Psc
I sc
X eq =
2
Qsc
I sc
2
2
or
Z eq =
Z eq =
E sc
= Req + jX eq
I sc
Req + X eq
2
2
⇒
X eq =
Z eq
2
− Req
2
Base Values and Per-Unit/Percent Values
Transformer model characteristics are often provided by the manufacturer or expressed in
terms of per-unit (pu) impedances. Utilizing per-unit impedances allows for specification of the
model impedances independent of whether the primary winding is the high or the low voltage
winding. Thus, per-unit values provide for a general method of characterizing the transformer.
In general, a per-unit value is the ratio of an actual value compared to that of a base
value. In terms of transformers, based voltages, currents, and impedances are defined as follows:
Vbase = Vrated
I base = I rated =
S rated
Vrated
2
Z base =
Vrated Vrated
=
I rated
S rated
Note that, given the above set of definitions, the base voltages, currents, and impedances are
winding dependent (high/low voltage side).
Given these base definitions, the per-unit series winding impedances may be defined as:
Z pu =
Z eq
Z base
R pu =
X pu =
= R pu + jX pu
Req
Z base
X eq
Z base
such that Zeq, Req, and Xeq are referred to the same winding as the utilized base value.
Note that voltages and currents may also be defined in terms of per-unit values as follows:
V pu =
Vactual
Vbase
I pu =
I actual
I base
Winding Independence of PU Values (Example):
Given a 10kVA, 480-120V transformer with the following series winding impedances
that were determined by means of a short-circuit test applied with the high-voltage winding as
the primary winding and the low-voltage winding short-circuited:
Req = 0.8 Ω
X eq = 1.2 Ω
The per-unit impedances may be determined from the high-voltage side data as follows:
Z base =
480 2
= 23.04 Ω
10000
R pu =
0.8
= 0.03472
23.04
X pu =
1.2
= 0.05208
23.04
Z pu = 0.03472 + j 0.05208
But, what if the impedances were referred to the low-voltage side (i.e. – step-up
transformer operation) as follows:
ReqLV = ReqHV ' = a 2⋅ 0.8 = (120 480 ) ⋅ 0.8 = 0.05 Ω
2
X eqLV = X eqHV ' = a 2⋅ 1.2 = (120 480 ) ⋅ 1.2 = 0.075 Ω
2
The per-unit impedances may be determined from the low-voltage side data as follows:
Z base =
120 2
= 1.44 Ω
10000
R pu =
0.05
= 0.03472
1.44
X pu =
0.075
= 0.05208
1.44
Z pu = 0.03472 + j 0.05208
This is the same result as that obtained from the high-voltage side data. Thus, if the
manufacturer provides the impedance information in terms of per-unit values, the end user can
transform this back to impedances values as follows:
Req = R pu ⋅ Z base
X eq = X pu ⋅ Z base
provided that the appropriate based values are utilized for the transformer’s configuration.