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Faculty of Engineering, Architecture and Science

Department of Electrical and Computer Engineering

Course Number EES 612

Course Title Electrical Machines and Actuators

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Faculty of Engineering, Architecture and Science

Department of Electrical and Computer Engineering

LAB INSTRUCTIONS

EES 612 – ELECTRICAL MACHINES AND ACTUATORS

EXPERIMENT # 1: SINGLE-PHASE TRANSFORMER

Introduction Transformers are widely applied in many electrical systems, small or large. A few of their most tangible areas of application include long-distance, bulk power transmission systems, medical and consumer electronic devices for level shifting and galvanic isolation, audio, video, and radio systems for impedance matching, and measurement devices for level shifting and galvanic isolation.

A typical single-phase transformer consists of two windings wound on a common (laminated) iron core. The windings are electrically isolated from each other and from the core, but are magnetically linked through the magnetic field within the core. The winding that is connected to the power source is commonly referred to as the primary winding, whereas the one connected to the load is called the secondary winding. In the ideal transformer, the voltage induced in each turn of a winding (whether primary or secondary) is the same as the voltage induced in any other turn of the same or the other winding. Hence, the ratio of the terminal voltages (or the so-called voltage ratio) is equal to the ratio of the windings number of turns (or the so-called turns ratio). In addition, the ideal transformer neither consumes nor generates power. Therefore, the ratio of the terminal currents equals the reciprocal of the voltage ratio (and turns ratio).

Even though well-designed large real transformers can closely approximate the ideal transformer, a real transformer often deviates from the ideal transformer, as follows:

The field created by a winding does not entirely stay within the core; some of it leaks off into air and, consequently, does not get linked by the other winding. The effect is that the voltage ratio in a real transformer is not exactly equal to the turns ratio.

The transformer draws a load-invariant current component, the exciting

current, from the source, due to the limited permeability of the core, and also

due to the energy losses of the core. The exciting current is harmonically

distorted, due to the hysteresis and the nonlinear relationship between the

magnetic field intensity andflux density in the core (remember the nonlinear B − H

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curves). The no-load exciting current produces the flux in the core. This

f lux in turn produces the hysteresis loss and the eddy current loss in the

core. These two losses are collectively called the core loss, P core.

In this experiment, the core losses of a transformer are evaluated through the open- circuit test at the rated voltage, whereas the copper losses are measured from the short-circuit test at the rated current. These, in turn, enable one to determine the parameters of the transformer’s equivalent circuit. Finally, a parameterized equivalent circuit enables the calculation of transformer’s efficiency and voltage regulation under different operating conditions.

Pre-Lab Assignment

P1- Calculate the rated currents of the low- and high-voltage sides of a 60 Hz, 120/60-V, 60 VA, single-phase transformer.

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P2- Draw the equivalent circuit of a single-phase transformer and explain how the core losses are almost invariant to the load (current). How do they depend on the terminal voltages of the transformer? Also, using the equivalent circuit explain how the copper losses depend on the load current.

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P3- A single-phase transformer drives a resistive load at some efficiency. Based on your answers to P2 above, explain how the efficiency will change if the supply voltage is reduced by 50%?

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P4 – The primary winding of a transformer is supplied by a sinusoidal voltage of Vs (rms) and frequency of fs . The flux density in the magnetic core is also sinusoidal function of time with a peak value of Bc . The core has a cross section area of Ac , and the winding has N turns.

P4a: Write an expression of Vs in terms of Bc, Ac, N and fs . Also provide an alternative expression in which Bc.Ac has been replaced by the flux in the core, Φc .

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P4b. The expressions you derived in P4a enable one to determine the number of turns of the windings as the design stage of a transformer. If the core does not saturate for maximum flux density B m , what should be the minimum turn N for the supply voltage V s ?

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P4c. Based on your answers to P4a and P4b, what is the risk involved in operating a transformer at an increased voltage? At a decreased frequency? If a particular application requires that a 60-Hz transformer be operated off a, for example, 50- Hz supply, how should the voltage be derated for proper operation?

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Lab Work

1. General safety note To prevent injury to persons or damage to equipment, the power source must be turned OFF prior to wiring up the circuit and making any subsequent changes. Ask your TA to check.

2. Equipment AC power supply module EMS 8821 (for energizing the transformer) Transformer module EMS 8341 (Nameplate rating 120/60 V, 60 VA) Resistance module EMS 8311 (for loading the transformer) Digital Multi-Meter (DMM) and its associated clamps

3. Experiments

E1: Open-Circuit Test

E1.1- With the AC power supply turned OFF, and the variac set at zero position (fully turned counterclockwise), connect the circuit of Figure E1. Note that, as Figure E1 indicates, in this test the low-voltage (60-V) winding is the one to be energized, while the high-voltage (120-V) winding is to be left open.

Figure E1: Circuit for the open-circuit test.

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E1.2- Place the ammeter clamp of the DMM around the wire that connects node 5 to node 6. Then, turn on the power supply and gradually turn the variac’s knob clockwise, until the voltmeter reads 60 V; this is the transformer’s rated low voltage. Record in Table E1 the current, power, and voltage readings of the DMM. Note that we have arbitrarily labeled the low-voltage side as side 1. Consequently, the high-voltage side will be regarded as side 2. Use the

measured voltages to calculate the turns ratio, = / .

Table E1: Meter readings under the open-circuit test. V1 (V) I1 (mA) P1 (W) V2 (V) a=V1/V2

60

E1.3- Turn off the power supply and turn the variac’s knob fully counterclockwise.

E2: Short-Circuit Test

E2.1- With the power supply turn off and the variac’s knob parked at zero position (that is, turned fully counter-clockwise), modify the circuit as shown in Figure E2. Note that, as Figure E2 indicates, in this test the high-voltage (120-V) winding is the one to be energized, while the low-voltage (60-V) winding is to be shorted.

Figure E2: Circuit for the short-circuit test.

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E2.2- Place the ammeter clamps of the DMM around the wire connecting the nodes 6 and 1. Turn on the power supply, and very slowly turn the variac’s knob clockwise until the ammeter reads 0.5 A; this is the rated current of the winding being energized (i.e., the high-voltage or 120-V winding). Record in Table E2 the current and power readings of the DMM.

Table E2: Meter readings under the short-circuit test.

I2 (mA) V2 (V) P2 (W)

500

E2.3- Turn off the power supply and turn the variac’s knob fully counterclockwise. E3: Voltage Regulation

E3.1- With the power supply turned off and the variac’s knob parked in zero position (turned fully counter-clockwise), modify the circuit as shown in Figure E3. Then, place the ammeter clamp of the DMM around the wire connecting node x to node y. The voltmeter shall be connected across the high-voltage terminals of the transformer, that is, to nodes 1 and 2. Note that we are to operate the transformer as a step-up transformer, since the load voltage will be higher than the source voltage.

Figure E3: Circuit for transformer loading and measurement of voltage regulation.

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E3.2- Switch on resistances 300Ω and 1200Ω to introduce an effective load resistance of 240Ω. At this load the transformer will provide the rated current of 0.5A (point five amperes) at rated voltage of 120V in the high voltage side. E3.3- Turn on the power supply and gradually turn the variac’s knob clockwise until the Voltmeter reads V2 =120V. Measure the load current I2 and the supply voltage, V1 (across nodes 5 and 9). Revcord the results in Table E3.3

Table E3.3: Meter readings for the high-voltage rated resistive load.

RL () Load Voltage V2 (V)

Source Voltage V1 (V)

240 120

E3.4- Change the load resistance according to Table E3.4, and record the results. Note that the first row of Table E3.4 reports the same result as Table E3.3. More

importantly, for each load resistance, the supply voltage 1 must be kept at the

same value as the one measured in E3.3 (see Table E3.3). Whenever needed, re-adjust the variac’s knob to ensure that 1 remains the same.

Table E3.4: Meter readings under different loads.

RL () Source Voltage

V1(V)

Load Voltage V2 (V)

Load Current I2 (mA)

240 Same as that in E3.3. Re-adjust if needed.

300 Same as that in E3.3. Re-adjust if needed.

400 Same as that in E3.3. Re-adjust if needed.

600 Same as that in E3.3. Re-adjust if needed.

1200 Same as that in E3.3. Re-adjust if needed.

∞ (all resistors off)

Same as that in E3.3. Re-adjust if needed.

0.0

E3.5- Turn off the power supply and park the variac’s knob at the zero position.

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Conclusions and Remarks:

C1- Using the results of E1 and E2, calculate and draw the equivalent circuit of the tested transformer, as referred to the high-voltage side (side 2). Also, for the rated operating conditions, determine , , and the efficiency of the transformer.

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C2- Suppose that the transformer derives at its high voltage side a 240Ω resistive Load at the rated voltage of 120V. Using the equivalent circuit found in part C1, calculate the required source voltage and compare it with the value measured in E3.3. Provide your reasons for discrepancies.

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C3- Suppose that the source voltage is the same as the voltage measured in E3.3. Using the equivalent circuit found in C1, calculate the load voltage for each of the load currents measured in E3.4. Complete the Table C3 below. In addition, plot on Graph C3 both the measured and calculated values of the load voltage, versus the corresponding values of the measured load current.

Table C3: Load voltage under different loads. Measured Load

Current from Table E3.4

I2 (mA)

Measured Source Voltage from

Table E3.4 V1(V)

Measured Load Voltage

from Table E3.4.

V2 (V)

Calculated Load Voltage

V2 (V)

Error (%)

0.0

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V2(V)

I2 (mA) --

Graph C3 : V2 vs I2

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