Experiment 3
Single Phase Transformer (II)
Objectives
•
•
•
To determine the polarity of single phase transformer windings.
To determine the internal resistance of single phase transformer windings.
To determine the efficiency and voltage regulation of a single phase transformer.
Windings Polarity Test (Dot Convention)
Introduction
The dots appearing at the primary winding in Figure 3.1 indicate the polarity of the voltage and current
on the secondary winding of the transformer. The relationship is as follows:
1. If the primary voltage is positive at the dotted end of the winding with respect to the undotted end,
then the secondary voltage will be positive at the dotted end also. Voltage polarities are the same
with respect to the dots on each side of the core
2. If the primary current of the transformer flows into the dotted end of the primary winding, the
secondary current will flow out of the dotted end of the secondary winding.
Figure 3.1: Schematic diagram for a single phase transformer.
Procedures
Using the lab equipments shown in Figure 3.2, do the following:
1. Connect the circuit shown in Figure 3.3.
2. Read the voltages of Voltmeter (1) and (2). Record that below. If
additive, otherwise if
then, the polarity is subtractive.
V1 [V]
V2 [V]
then, the polarity is
The polarity of tested transformer
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Experiment 3
Single Phase Transformer (II)
Figure 3.2: Real photo of lab equipments needed for the experiment 3.
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Experiment 3
Single Phase Transformer (II)
a
b
0‐430V‐5A
220V‐8A
0‐240V‐8A
0‐430V‐5A
220V‐10A
0‐240V‐10A
0‐225V‐1A
0
a
1
b
0
1
0
0
0
DL 1013M2
KY
L1 L2 L3 N
1
0
0
0
100%
L1 L2 L3
L1 L2 L3
L+ L‐
L+ L‐
Figure 3.3.a: Polarity test wiring diagram.
Figure 3.3.b: Polarity test schematic circuit.
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Experiment 3
Single Phase Transformer (II)
DC Test
Introduction
The internal resistance of each winding in a transformer is measured using a small dc current to avoid
causes a current
to flow throw the transformer
thermal and inductive effects. If a voltage
windings, then
Internal Resistor = R X =
Vdc
I dc
(3.1)
Procedures
Using the lab equipments shown in Figure 3.2, do the following:
1. Connect the high voltage side of the transformer to a dc power source as shown in Figure 3.4.
2. Adjust the voltage source such that you measure 0.2A and 0.4A in the windings. Record the voltage
adjusted in Table 3.1.
3. Repeat the previous steps to measure the resistance of the low voltage winding.
Winding
Ammeter Reading [A]
High voltage side
220V
Low voltage side
2 x 115V (series)
0.2
0.4
0.5
0.7
Voltmeter Reading [V]
RX [Ω]
Table 3.1: DC test readings
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Experiment 3
Single Phase Transformer (II)
Figure 3.4.a: DC test wiring diagram
Figure 3.4.b: DC test schematic circuit
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Experiment 3
Single Phase Transformer (II)
Load Test
Introduction
In the transformer load test the primary winding is connected to the supply voltage and various load
levels are applied on the secondary winding. The with-load actual transformer efficiency ( ηactual ) can be
determined mathematically from experimental readings as
ηactual =
Pout
.100%
Pin
(3.2)
where Pout = {V.I *} . If the load is purely resistive, then
Pout = V2 .I2
(3.3)
Note that in practice the output power would be measured. The theoretical on-load transformer
efficiency can be predicted from the transformer equivalent circuit using the following equation
ηactual =
Pout
Pout
.100%
+ Pcu + Piron
(3.4)
Transformer iron core losses Piron and copper losses PCu are defined as
Piron =
Pcu =
V1
2
Rm
(3.5)
2
I'2 .R1
(3.6)
where I'2 = I 2 / a . The maximum transformer efficiency occurs when the variable losses (dependent
upon the current drawn) equal the fixed losses (independent of the current drawn)
Piron = Pcu
(3.7)
For detail about the proof, refer to Appendix 3.1. Because a real transformer has series impedance
within it, the output voltage of a transformer varies with load even of the input voltage remains constant.
With-load voltage regulation (VR) is a quantity that compares the output voltage at no load with the
output voltage at certain load. It is defined by the equation
VR actual =
V2 (no-load) - V2 (with-load)
V2 (with-load)
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.100%
(3.8)
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Experiment 3
Single Phase Transformer (II)
Procedures
Using the lab equipments shown in Figure 3.2, do the following:
1. Connect a resistive load to the series combination of the 115V terminals of the tested transformer as
shown in Figure 3.5.
2. Calculate the value of the protection resistance that is inserted in the circuit shown in Figure 3.5.
3. Adjust the primary voltage to 220V, and keep it constant during the test.
4. Slowly increase the load current by decreasing the ohmic value of the resistive load, and then
complete Table 3.2.
I1 primary
current[A]
1.7
P1-input
power[W]
V2 – load
voltage[V]
I2 – load
current[A]
P2 – output
power[W]
η
Voltage
Regulation
1.4
1.1
0.9
0.5
Table 3.2: Load test results
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Experiment 3
Single Phase Transformer (II)
a
b
0‐430V‐5A
220V‐8A
0‐240V‐8A
0‐430V‐5A
220V‐10A
0‐240V‐10A
0‐225V‐1A
0
a
1
b
1
0
0
0
0
DL 1013M2
KY
L1 L2 L3 N
0
115
0
L1 L2 L3
0
160
0
0
100%
L1 L2 L3
0
1
L+ L‐
L+ L‐
115
220
Transformer
Resistive
Load
Protector
Figure 3.5.a: Load test wiring diagram
Figure 3.5.b: Load test schematic circuit
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Experiment 3
Single Phase Transformer (II)
Appendix 3.1
The transformer efficiency can be written as
η=
V 2 I 2 cos θ
V 2 I 2 cos θ + Piron + Pcu
(3.9)
to find out the maximum efficiency when the load power factor and secondary voltage are constants, the
first time derivative of efficiency is taken to the secondary current as
∂η
=0
∂I 2
(3.10)
thus,
∂η
∂
=
∂I 2 ∂I 2
⎡
⎤
V 2 I 2 cos θ
⎢
⎥
2
⎣V 2 I 2 cos θ + I 2 R 02 + Piron ⎦
(3.11)
where R 02 = Req referred to the secondary. Equation (3.11) can be re-written as
∂η V 2 cos θ (V 2 I 2 cos θ + Piron + I 22 R 02 ) −V 2 I 2 (V 2 I 2 cos θ + 2I 2 R 02 )
=
∂I 2
(V 2 I 2 cos θ + Piron + I 22 R 02 ) 2
(3.12)
thus, when equation (3.10) is applied, the following expression is obtained
V 2 cos θ (V 2 I 2 cos θ + Piron + I 22 R 02 ) −V 2 I 2 (V 2 I 2 cos θ + 2I 2 R 02 ) = 0
(3.14)
Piron = I 22 R 02 = Pcu
(3.15)
and then
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