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EXPERIMENT Transformer Waveforms Steady-State Testing and Performance of Single-Phase Transformers Waveforms
OBJECTIVE
The voltage regulation and efficiency of a distribution system are affected by the electrical and magnetic characteristics of the transformers operating in the network. The design of such a distribution system must consider these effects. This experiment demonstrates the excitation current, magnetization current, AC saturation curve, and core-loss current of transformers. These are investigated at various load conditions. REFERENCES
- “Electric Machinery”, Fourth Edition, Fitzgerald, Kinglsey, and Umans, McGraw-Hill Book Company, 1983, Chapter 1.
- “Electromagnetic and Electromechanical Machines”, Matsch, Leander W., Intext Educational Publishers, 1972.
- “Electromechanical Devices for Energy Conversion and Control Systems”, Del Toro, Vincent, Prentice-Hall, Inc., 1968.
BACKGROUND INFORMATION
The basic theory of transformer operation is adequately explained in Reference 1. For our purposes here we will concentrate on the test methods and the experimental set- up of Figure 5. Figure 1 shows the traditionally accepted electrical equivalent circuit for a power transformer in steady-state. This particular equivalent circuit’s parameters are referred to side 1. All relevant impedances, voltages, and currents are shown in the figure.
Figure 1: Steady-state equivalent circuit for power transformer.
It is important to note that for a typical power transformer the ratio of the parallel combination of the common leg impedances to the total impedance of either winding will exceed 200. Algebraically, this can be described as
R^ jX
R c Xm
(^11)
Figure 2: Winding configuration of laboratory transformers.
5, resistor R 1 is used to measure the current I 1. Similarly, resistor R 3 in Figure 5 is
used to measure current I 2. It is not so easy to measure the currents I c and I m , but we
can derive a voltage signal that is in phase with I c. The no-load voltage across
terminals Y 1 and Y 2 is
dt
d
V Y Y NY
=^ φ
1 − 2 (2.9)
which corresponds to E 2 ′ from Figures 1 and 4. Thus, we have a voltage signal that is
in phase with I c. The resistor R 2 in Figure 5 provides an adjustable signal that is in
phase with I c , yet the resistor is large enough to prevent excessive loading of the circuit.
The requirement for an adjustable signal becomes clear as the experiment is performed. We now have access to signals representing three currents. It is seen from Figure 1 that
I 1 =^ Ic + Im + I 2 ′
and, clearly
I m =^ I 1 − Ic − I 2 ′
Thus, we have signals for the three terms on the right side of Eq. 2.11, which means we should be able to measure the unknown by some differential means. Figure 4 shows a voltage source equivalent for the system of Figure 5 and clearly indicates a synthesis of Eq. 2.11. Therefore, the voltage signal that remains after the sources interact is
representative of I m.
Figure 4: Voltage source equivalent of Eq. 2.11.
NOTE: The voltage signals used above are adequate for waveshape analysis and phase relationships. They are not accurate for magnitude comparisons and should not be used for this purpose.
SUGGESTED PROCEDURE
The transformers used for this experiment are rated 120V-120V, 0.6kVA. There are three of them on each set of wall shelves. The set of windings connected to the source side of the transformer are called primary windings, and those connected to the load are named secondary windings. To achieve a 600 volt-ampere rating, these two sets of main primary and secondary windings must be in parallel. The other two windings are information (instrumentation) windings and are not designed to support a load.
Figure 1 defines the currents that are referred to throughout the experiment.
1. Figure 5 shows the connections that are used to view i 1 , i c , i m , and φ m. The
first transformer is identical to the transformer being tested and is used to help prevent ground loops between the source and the instrumentation.
NOTE: The signal being observed as is a voltage from the 6V winding, but is
a signal that has the same waveform as i
i c
c.^ Also, the φ m signal is an integrated
voltage signal having the waveform of φ m.
2. Add a secondary resistive load by connecting the circuit of Figure 6 to the transformer load connection of Figure 5 and set input voltage to 120 V AC
maintain constant. Adjust R 3 to remove the load current i 2 from the oscilloscope
display. R 2 may also need to be readjusted slightly. Record the AC saturation
curve as the load current is varied between 0, 1.0, 1.5, 2.0 and 2.5 AMPS. Describe in the report the change in the peak-to-peak magnitude of flux as the load resistance is changed. For different primary voltages, describe the changes in the waveforms and curves
of i 1 , i c , i m , φ m and saturation as the load is varied. From this information,
comment on the transformer’s performance at different voltages.
3. Bypass the integrator by reconnecting the oscilloscope leads directly to terminals
and Y. Turn the calibration knob of the corresponding differential
amplifier fully counter-clockwise. This will prevent the amplifier from running over the maximum allowed range. Observe the relative magnitudes and phase angles of the terminal voltage and as the load resistance is varied. Magnitudes can be obtained directly from the meters on the panel. To obtain phase angle between signals displayed, use the MEASURE capability of the scope with selections of PERIOD and DELAY from the vertical menu. Determine the period of the voltage waveform because this signal is harmonic free.
Y 3 4
i 1
Without Cap Load current Voltage VT Current I 1 Phase VT to I (^1)
acitor
I 2 0.0A 1.0A 2.0A
r input. The lab presently does not contain the try an RL load type. ith Capa Load current Voltage VT Current I 1 Phase VT to I (^1)
Connect the large capacitor found on the shelf in parallel with the load resistor. Again observe the relative magnitudes and phase angles at the transforme proper inductor to W citor
I 2 0.0A 1.0A 2.0A
