Experiment No. 3
Transformer Equivalent Circuit, Voltage Regulation, and Efficiency
Purpose
To determine the equivalent circuit of a transformer by the short-circuit test method and then use the
equivalent circuit to determine the voltage regulation and, also using the open-circuit test from last week,
the efficiency.
Discussion
Short-Circuit Test
It is possible to represent a transformer as an ordinary series electric circuit (neglecting the small, no-load
exciting current) that has three elements: (1) the equivalent resistance, (2) the equivalent leakage reactance,
and (3) the load.
The short-circuit test is an experimental method of determining the equivalent resistance, impedance, and
reactance of a transformer. In this test the windings are made to carry the rated currents without requiring
the transformer to deliver a load. This is done by shorting the secondary winding and increasing the primary
voltage from zero to that value which causes the rated current to flow. In this way, it is possible to simulate
the pattern of flux leakages in the primary and secondary because the latter depend upon the load currents
in the two windings.
From the data of watts, amperes, and volts obtained from this test, the values of equivalent resistance,
impedance, and reactance can then be calculated using the following equations:
𝑅𝑅𝑒𝑒 =
𝑍𝑍𝑒𝑒 =
𝑃𝑃𝑠𝑠𝑠𝑠
𝐼𝐼𝑠𝑠𝑠𝑠 2
𝐸𝐸𝑠𝑠𝑠𝑠
𝐼𝐼𝑠𝑠𝑠𝑠
𝑋𝑋𝑒𝑒 = �𝑍𝑍𝑒𝑒 2 − 𝑅𝑅𝑒𝑒 2
Where
Re = the equivalent resistance
Psc = the measured real power from the short circuit test
Isc = the measured current from the short circuit test (this should be the transformer’s rated current)
Esc = the measured voltage from the short circuit test (much smaller than the transformer’s rated voltage)
Ze = the equivalent impedance (the series combination of the equivalent resistance and reactance)
Xe = the equivalent reactance
1 |Page
ET-250 Industrial Electrical Machinery
Ver. 3.2
Experiment 3 - Equivalent Circuit, Voltage Regulation, and Efficiency
Voltage Regulation
Voltage regulation is a measure of merit for a transformer. However, it is often impractical, if not impossible,
to fully load a large transformer to determine its voltage regulation. This fact presents no problem if the short
circuit tests are available, or if they can be performed. From these tests it is possible to determine the
equivalent circuit with reference to either the primary or secondary winding. Taken from the secondary, the
resistive and reactive voltage drops can be calculated with rated current.
Looking at the secondary side, the no-load voltage can be calculated from:
𝐸𝐸𝑠𝑠 = 𝑉𝑉𝑠𝑠 + 𝐼𝐼𝑠𝑠 × 𝑍𝑍𝑒𝑒
Where
Vs = the rated secondary voltage (this is the full load voltage, VFL)
Es = the voltage required to provide rated secondary voltage (this is the no load voltage, VNL)
Is = the rated secondary current
Ze = the equivalent impedance on the secondary (the series combination of the equivalent resistance and
reactance)
Then, the voltage regulation (VR) can be calculated from:
𝑉𝑉𝑉𝑉 =
Voltage regulation is usually expressed in percent.
𝑉𝑉𝑁𝑁𝑁𝑁 − 𝑉𝑉𝐹𝐹𝐹𝐹
𝑉𝑉𝐹𝐹𝐹𝐹
Transformer Efficiency
Just like any other device, efficiency of a transformer can be defined as the output power divided by the
input power. Transformers are highly efficient devices. Most transformers have full load efficiency from 95%
to 98.5%. If the rated open-circuit and short-circuit losses are known, the efficiency (η) can be found from:
Where
𝜂𝜂 =
𝑃𝑃𝑂𝑂𝑂𝑂𝑂𝑂
𝑆𝑆𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 × 𝑝𝑝𝑝𝑝
=
𝑃𝑃𝑂𝑂𝑂𝑂𝑂𝑂 + 𝑃𝑃𝑂𝑂𝑂𝑂 + 𝑃𝑃𝑆𝑆𝑆𝑆 𝑆𝑆𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 × 𝑝𝑝𝑝𝑝 + 𝑃𝑃𝑂𝑂𝑂𝑂 + 𝑃𝑃𝑆𝑆𝑆𝑆
POut = is the real power output of the transformer in [W]
POC = the measured real power from the open-circuit test in [W]
PSC = the measured real power from the short-circuit test in [W]
Srated = the rated apparent power of the transformer in [VA]
pf = the power factor
2 |Page
ET-250 Industrial Electrical Machinery
Ver. 3.2
Experiment 3 - Equivalent Circuit, Voltage Regulation, and Efficiency
Apparatus Required
1.
2.
3.
4.
One Hampden ET-100 Transformer
One Fluke 435 II Power and Energy Analyzer
One fixed 120 volt AC power source
One variable 0-140 volt AC power source
Procedure
Short-Circuit Test
1. Calculate full load current for the primary and secondary of the experimental transformer. (Note: the
transformer rating is 140 VA, 240V-120V)
I primary =
I secondary =
mA
583.000
1.160
A
2. Connect the transformer primary (H1 and H5) to a variable voltage source and short the secondary (X1
to X7). Make sure to install a jumper from H3 to H4, and another from X4 to X5, to include all the
windings in the measurement. The setup us shown in Figure 1. Slowly adjust voltage from zero up
until the point where the ammeter indicates full load current. When you reach full load current,
record the voltage, current, real, apparent, and reactive power, and power factor on your
engineering note sheet and in Table 1. Using the information from the short circuit test, derive the
equivalent circuit parameters.
Calculated
Measured
Table 1. Short-Circuit Values
Short-Circuit Values
Voltage, Esc
Current, Isc
Real Power, Psc
Apparent Power, Ssc
Reactive Power, Qsc
Power factor, pf
Equivalent Resistance, Re
Equivalent Impedance, Ze
Equivalent Reactance, Xe
24.990
V
583.000
mA
14.30
W
14.60
VA
2.30
kVAr
0.98
Lead
42.100
kΩ
42.860
Ω
Ω
8.200
Question: On which side, primary or secondary, are these values taken?
Primary
3 |Page
ET-250 Industrial Electrical Machinery
Ver. 3.2
Experiment 3 - Equivalent Circuit, Voltage Regulation, and Efficiency
Figure 1. Short Circuit Configuration
Voltage Regulation
3. Using just the series equivalent circuit referred to the primary, calculate the voltage regulation for
the transformer at rated power and 0.8 lagging, unity, and 0.8 leading power factor.
Power Factor
0.8 lagging
unity
0.8 leading
E1 – Voltage on
the primary of
the Ideal
transformer
[V]
Voltage Drop
(𝑅𝑅𝑒𝑒 + 𝑗𝑗𝑋𝑋𝑒𝑒 ) × 𝐼𝐼⃗
240.00
25.010
240.00
25.010
240.00
25.010
[V]
∠
∠
∠
11.02
11.02
11.02
°
°
°
V1 – Voltage
magnitude on
the actual
transformer
primary
[V]
264.588
Voltage
Regulation
𝑉𝑉1 − 𝐸𝐸1
𝐸𝐸1
[%]
104.00%
264.588
104.00%
264.588
104.00%
Figure 2. Equivalent Circuit Referred to Primary
4 |Page
ET-250 Industrial Electrical Machinery
Ver. 3.2
Experiment 3 - Equivalent Circuit, Voltage Regulation, and Efficiency
4. Repeat step 6 with the series equivalent circuit referred to the secondary.
Power Factor
0.8 lagging
unity
0.8 leading
V2 – Voltage on
the secondary of
the actual
transformer
[V]
Voltage Drop
E2 – Voltage on
the ideal
transformer
secondary
(𝑅𝑅′𝑒𝑒 + 𝑗𝑗𝑋𝑋′𝑒𝑒 ) × 𝐼𝐼⃗
[V]
∠
∠
∠
°
°
°
[V]
Voltage
Regulation
𝐸𝐸2 − 𝑉𝑉2
𝑉𝑉2
[%]
0.000%
0.000%
0.000%
Figure 3. Equivalent Circuit Referred to Secondary
Efficiency
5. Using the cantilevered equivalent circuit referred to the primary calculate the efficiency of the
transformer at rated power and 0.8 lagging, unity, and 0.8 leading power factor.
5 |Page
ET-250 Industrial Electrical Machinery
Ver. 3.2
Experiment 3 - Equivalent Circuit, Voltage Regulation, and Efficiency
Figure 4. Cantilevered Equivalent Circuit Referred to the Primary
Questions
1. Include calculations for Re, Ze and Xe on the primary and then referred to the secondary.
6 |Page
ET-250 Industrial Electrical Machinery
Ver. 3.2