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T 10.1

Transformers

by Prof. Guntram Schultz

1st Edition, April 2003

LEYBOLD DIDACTIC GMBH . Leyboldstrasse 1 . D-50354 Hrth . Phone (02233) 604-0 . Fax (02233) 604-222 . e-mail: [email protected]

by Leybold Didactic GmbH Printed in the Federal Republic of GermanyTechnical alterations reserved

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T 10.1 Contents

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Contents

1 Introduction 5

2 Safety Precautions and Measurement Notifications 7

2.1 Safety Precautions 7

2.2 Measurement Notices 7

3 Experiments with the Single-phase Transformer 9

3.1 Voltage and Current Transformation 10

3.2 Short-circuit Voltage and Sustained Short-circuit Current 11

3.3 Voltage Behavior with Resistive Load, Evaluating Efficiency 12

3.4 Voltage Behavior with Inductive or Capacitive Load 14

4 Experiments with the Single-phase Toroidal Core Transformer 17





5 Experiments with the Single-phase Autotransformer 25





6 Experiments with the Three-phase Transformer 33

6.1 Transformer in Yy0 Star-Star Circuit 34

6.2 Transformer in Dy5 Delta-Star Circuit 38

6.3 Transformer in Yd5 Star-Delta Circuit 41

6.4 Transformer in Yz5 Star-Zigzag Circuit 44

7 Experiments with the Scott Transformer 49

7.1 Transformer in a Scott Circuit 50

7.2 Transformer in a V Circuit 52

8 Practice Questions 55

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T 10.1 Introduction

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1 IntroductionOne of the essential advantages of alternating current, including three-phase current, over directcurrent lies therein that this form of electrical energy can be economically produced in large power

plants then transmitted over long distances at high voltages with relatively low losses and finallyconverted to a user-acceptable voltage level for the consumer. This is all made possible bytransformers. Transformers of all kinds that are built to handle power from less than a Watt to overa gigawatt. Three-phase transformers are used exclusively for large power requirements whilesmaller power requirements are often adequately served by single-phase designs. Single-phasetransformers will be examined first to illustrate just how transformers work.

The law of induction is fundamental to the way that a transformer works. This law states that avoltage will be induced in a coil that is exposed to a periodically changing magnetic field. Since atransformer is generally employed to connect two differing voltage levels, it is necessary to haveboth sides uniquely designated with indexes. Typically the side intended as the input is designatedthe primary side and labeled with the index 1. The side of the transformer to which the load is

connected is designated the secondary side and labeled with the index 2.According to the law of induction, if the number of turns in the windings are represented by N1 andN2 then the relationship between respective voltages for an ideal transformer will be:

1 1

2 2

V N

V N=

The voltage conversion ratio is the most important rating for a transformer.

If one disregards transformer losses, then the apparent power must be the same on both sides.This can be used to derive a ratio for the currents as follows:

1 2

2 1

I N

I N

=

The higher transmission voltage is made, the smaller the current will be for the same amount ofconducted power. This allows high-voltage lines to be utilized that have a smaller conductor crosssection which, in turn, is more economical.

In addition to a transformer's transformation ratio there are other factors which also determine theoperational behavior of a transformer. These are nominal apparent power, no-load current, short-circuit voltage, and efficiency.

The experiments to be performed here will use one transformer with a laminated core and anothertransformer which has a toroidal core, each of these will have two secondary windings. Theoperational behavior for both types will be similar; differences arise only in their short-circuitvoltages and no-load current.

Furthermore, a distinction must be made between the physical structure differences for "isolatingtransformers" and "autotransformers". Isolating transformers have absolutely no galvanic couplingbetween its windings whereas the autotransformer is formed by two, series-connected, parts of asingle winding. One portion of the winding, referred to as the common winding, is common to bothsides. The other portion of the winding, referred to as the auxiliary winding or series winding,together with the common winding forms the high voltage side.

Voltages can be transformed up or down with an autotransformer. Its overall potential power outputis referred to as its throughput rating. Its transfer from input to output winding is in part galvanicand part inductive. The greater the galvanic portion contributes to the amount of power transferred,the smaller the inductive portion will be. It is this inductive portion, also referred to as "nominalpower" that determines the physical size of the transformer. This means that the savings of copper

and iron, in comparison to a transformer with separate windings, becomes larger as the differencebetween input and output voltages becomes smaller. The experiments to be performed here willuse an autotransformer that has multiple taps.

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T 10.1 Introduction

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The distribution grid for electrical power primarily uses three-phase transformers. Like single-phasetransformers, these three-phase versions can also be wound as isolating transformers or asautotransformers. Even designs with three windings per phase are commonplace. Such

transformers allow, for example, one generator to simultaneously feed two different voltage levelsof a power grid.

A three-phase transformer can be envisioned as the interconnection of three single-phasetransformers. Though this allows various circuit configurations for primary and secondary sides tobe realized, one of these configurations will result in the optimal solution for the given application.For the star circuit, a voltage applied to a single winding is

NN

3

VV ' = ,

whereas for the delta circuit it is VN that is the nominal voltage. This means that the star circuit'soverhead for isolation is less, but does require conductors with larger cross-sections due to thehigher currents to be handled. Another configuration, primarily used for the low voltage side of

local transformers, is the zigzag circuit (a.k.a. interconnected star connection). It is formed by theseries connection of two different phases of the secondary windings.

Connection symbols are used for identify different circuit configurations. The letter "D" or "d" isused to identify a delta circuit, "Y" or "y" for a star circuit and "z" for a zigzag circuit. The capitalletter is used for the primary side and the lowercase letter for the secondary side. These lettercodes are followed by a code number that describes the lagging of phase-to-phase voltage on thelow-voltage side opposite the high-voltage side in multiples of 30 (comparable to the numbers onthe face of a clock). If the neutral point of a star or zigzag configured winding is brought out, thenthis is identified by the letter "N" or "n" (depending on transformer side). The most common circuitconfigurations are Yy0, Dy5, Yd5 and Yz5. Single-phase loads can only be connected to thetransformer when the neutral point is brought out.

The individual phase leg windings are differentiated with the letters "U", "V", and "W". A codenumber preceding these letters designates the winding's number (1: primary winding, 2 and, whenpresent, 3: for secondary windings). A further code number after the letter establishes the begin (1)and end (2) of the winding.

Whereas a transformer's connection symbol is virtually meaningless in symmetrical configurations,they are decisive for behavior where asymmetrical loads and faults are concerned.

The three-phase transformer used in these experiments possesses three separate windings perphase that can be interconnected freely. Behavior will be investigated for both symmetric as wellas asymmetric load conditions.

The so-called "Scott transformer" represents a special variation of the three-phase transformer. Itpermits the creation of a special circuit for producing two alternating voltages from a single three

phase system. The two AC voltages represent independent systems which exhibit a 90 phaseshift between them. Experiments will also be conducted with this type of transformer.

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T 10.1 Safety Precautions and Measurement Notifications

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2 Safety Precautions and Measurement Notifications

2.1 Safety PrecautionsVoltage-free metal components (e.g. housings) are to be connected with a PE ground conductoraccording to VDE regulations (Verband Deutscher Elektrotechniker, which translates to Associa-tion of German Electro-technical Engineers).

Power supply voltage is to be turned off when making any change to the experimental setup.

2.2 Measurement NotificationsThe power supply voltage to single-phase transformers under investigation is to be connected viaan isolating variable transformer (726 85) that provides an AC voltage in the range of 0 ... 260 V.For three-phase transformers, power supply voltage is to be provided via the three-phase variabletransformer (725 442 D) that has a voltage range of 0 ... 400 V.

Voltage and current measurements are to be made with RMS meters (727 10). Simple voltmetersand ammeters can also be used as an alternative. Notices about the proper measurement rangesare included in equipment lists for individual experiments. A measurement instrument capable ofproviding results within a tolerance range of 0.05% of measured value (or better) is recommendedfor investigations of voltage behavior in conjunction with resistive, capacitive and inductive loads.The unit configuration diagrams always show the RMS meter devices.

An oscilloscope (e.g. 575 211) is required in order to visualize the characteristic phase shifts thattake place between the high and low voltage sides of the three-phase transformer. This is to beconnected to the test object via an isolation amplifier (735 261). The details of utilizing the isolationamplifier and the oscilloscope are to be taken from their respective operating instructions.

It is recommended that transformers to be investigated are first loaded with nominal current for afew minutes before making measurements. This is done to ensure that they have reached theiroperating temperature so that reproducible results are achieved.

On the other hand, one should be careful not to place other devices (e.g. measuring instruments)directly above the test object or resistive loads. This is because of the heat dissipated by these testobjects and resistive loads.

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T 10.1 Experiments with the Single-phase Transformer

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3 Experiments with the Single-phase Transformer

Study Goals:

After carrying out the experiments, the student will be capable of: connecting a single-phase transformer and then demonstrating the significance of the terms"voltage transformation", "current transformation" and "no-load current" with appropriateexperimental circuits.

setting up a measurement circuit for determining short-circuit voltage and sustained short-circuit current and then be able to measure these values.

investigating a transformer's voltage behavior when it is connected to a resistive load anddetermining its efficiency as a function of the load.

investigating and interpreting a transformer's voltage behavior when it is connected to aninductive or capacitive load.

Equipment List:

1 single-phase transformer 733 97

1 variable transformer 0 ... 260 V / 4 A 726 85

1 resistive load 732 401 inductive load 732 421 capacitive load 732 41

1 set of 10 safety connectors, black 500 591 set of 10 safety connectors, green/yellow 500 5911 set of 32 safety experiment cables 500 8511 set of 10 safety experiment cables, green/yellow 500 852

1 power factor meter 727 123 RMS meters 727 10

as an alternative to the RMS meters:

2 voltmeters 0 ... 400 V1 ammeter 0 ... 1 A1 ammeter 0 ... 2.5 A

Fig. 3.1: Arrangement of Units for Single-phase Transformer Experiments

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3.1 Voltage and Current TransformationSet up the circuit as shown in Fig. 3.1.1.

Fig. 3.1.1: Circuit for Measuring Voltage Transformation in a Single-phase Transformer

The transformer to be investigated is to be operated with no-load for this. Turn on the circuit andselect the voltage V1 = 230 V on the variable transformer that powers the circuit. Measure the no-load current I0 of the test object and the voltage across each of the secondaries V2 and V3(between terminals 2.1 and 2.2, and 3.1 and 3.2, respectively).

Also measure voltage V23 between terminals 2.1 and 3.2, with the two secondary windingsconnected in series (by connecting terminal 2.2 with terminal 3.1).

Result: I0 = 0.18 A, V2 = 121 V, V3 = 121 V, V23 = 243 V

Reference the voltages V1, V2 and V3 to the turn counts N1, N2 and N3 of their respective windings:

Result: 1

1

0 564 VV

N.= , 2

2

0 565 VV

N.= , 3

3

0 565 VV

N.=

Formulate an equation for voltage transformation ratio from the above data:

Result:2

1 1

2

V

V

N

N= and

3

1 1

3

V

V

N

N=

Change the circuit to match Fig. 3.1.2 in order to determine the current transformation ratio:

Fig. 3.1.2: Circuit for Measuring Current Transformation in a Single-phase Transformer

Set the resistive load to a value of 100% and turn on the circuit. Again select the voltage 230 V onthe variable transformer that powers the circuit. Reduce the load's resistance value until rated

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current flows in the secondary side of the test object (see specifications on front plate). Measurethe corresponding current on the primary side.

Result: I1 = 0.72 A, I2 = 1.36 A

Reference the currents I1 and I2 to the turn counts N2 and N1 of their respective windings:

Result: =12

3 36 mAI

N. , =2

1

3 33 mAI

N.

Formulate an equation for current transformation ratio from the above data:

Result:

1

1 2

2

I

I

N

N

=

3.2 Short-circuit Voltage and Sustained Short-circuit CurrentThis experiment is intended to investigate the transformer's behavior when the secondary windingis shorted. Short-circuit voltage and sustained short-circuit current are also determined.

Set up the circuit as shown in Fig. 3.2.1.

Fig. 3.2.1: Circuit for Measuring Short-circuit Voltage

A transformer exhibits different values for short-circuit voltage depending upon whether one orboth of the secondary windings are loaded. The higher of these values results when both windingsare loaded.

The rated current for the primary side is required for this measurement. This was establishedduring the previous experiment. Beginning from zero, slowly increase the voltage of the variabletransformer until the current flowing in the primary side reaches its rated value; then read thecorresponding voltage Vsc.

Result: Vsc = 8.7 V

The value forVsc is the short-circuit voltage. When this is referenced to the corresponding nominalvoltage, then that is the relative short-circuit voltage vsc. This value is usually expressed as apercentage.

Determine the relative short-circuit voltage of the single-phase transformer under test:

Result: vsc = 3.8 %

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R/ % 100 90 80 70 60 50 40 30 20 15 10

I1 / A 0.24 0.24 0.25 0.26 0.28 0.34 0.41 0.54 0.58 0.70 0.94

cos 0.66 0.67 0.70 0.72 0.79 0.84 0.88 0.93 0.94 0.95 0.97

V2 / V 122 122 122 121 121 121 121 120 120 120 119

measu-red

I2 / A 0.19 0.20 0.23 0.27 0.34 0.47 0.63 0.92 1.00 1.22 1.66

P1 / W 36.4 37.0 40.3 43.1 50.9 65.79 83.0 115.5 125.4 153.0 209.7

P2 / W 23.2 24.4 28.1 32.7 41.1 56.9 76.2 110.4 120.0 146.4 197.5calcul-ated

/ % 63.6 66.0 69.7 75.9 80.9 86.6 91.9 95.6 95.7 95.7 94.2

Tab. 3.3.1: Voltage Behavior and Efficiency for a Resistively Loaded Single-phase Transformer

How large is the power factor when the transformer is loaded to its rated current value?

Result: The power factor is about 96 %.

Draw a single graph that contains the measured values for voltage V2 and efficiency as afunction of load current I2:

Fig. 3.3.2 Secondary voltage ( ) and

efficiency ( ) as a function of loadcurrent for a resistively loadedsingle-phase transformer.

Where does efficiency reach its maximum?

Result: With a resistive load, efficiency produces a very flat maximum. It lies in the range of

secondary currents between 1 and 1.3 A.

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Draw a single graph containing the measured voltage values for both measurement series.Represent these values as a function of the load current:

Fig. 3.4.2: Secondary voltage of a single-phasetransformer as a function of loadcurrent when inductively ( ) loadedand when capacitively ( ) loaded.

What characteristic differences does a transformer exhibit as load current is increased when it isconnected to a resistive, inductive, or capacitive load?

Result: When connected to a resistive or inductive load, secondary voltage decreases as loadcurrent increases. When connected to a capacitive load, secondary voltage increaseswith increasing load current.

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T 10.1 Single-phase Toroidal Core Transformer Experiments

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4 Experiments with the Single-phase Toroidal Core Transformer

Study Goals:

After carrying out the experiments, the student will be capable of: connecting a single-phase toroidal core transformer and then demonstrating the significanceof the terms "voltage transformation" and "current transformation" with appropriateexperimental circuits.



investigating and interpreting a transformer's voltage behavior when it is connected to aninductive or capacitive load.

Equipment List:

1 single-phase toroidal core transformer 733 98







Fig. 4.1: Arrangement of Units for Single-phase Toroidal Core Transformer Experiments

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Determine the relative short-circuit voltage of the single-phase toroidal core transformer under test:

Result: vsc = 2.4 %

Sustained short-circuit current is that current which flows after transient reaction has died out whennominal voltage is applied to the primary side. Since this has a very high value it cannot bemeasured directly. Therefore calculate its value from the secondary side's rated current and therelative short-circuit voltage with the help of the equation

2Nss

sc

100 %I

Iv

=

Determine the test object's sustained short-circuit current:

Result: Iss = 56.7 A

4.3 Voltage Behavior with Resistive Load, Evaluating EfficiencyChange the circuit to match Fig. 4.3.1.

Fig. 4.3.1 Circuit for Investigating Voltage Behavior with Resistive Load and for Evaluating Efficiency

Three separate resistors are to be connected in parallel to increase current handling capability.

First set the resistive load to a value of 100% and turn the circuit on. Set the variable transformerto maintain a voltage of 230 V.

Change the load according to the settings prescribed by Tab. 4.3.1. For each setting, measure thecorresponding values for secondary current and secondary voltage as well as the primary side's

values for effective powerP1 and power factor cos .After the measurements have been taken, calculate the effective power on the primary side withthe equation

1 1 1 cosP V I= ,

effective power on the secondary side with the equation

2 2 2P V I= ,

from the above results, derive a value for efficiency with

2

1

P

P = ,

and complete the table below. Be careful about the current handling capabilities of the secondarywinding!

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Fig. 4.4.2: Secondary voltage of a single-phasetoroidal core transformer as afunction of load current wheninductively ( ) loaded and whencapacitively ( ) loaded.

What characteristic differences does the transformer exhibit as load current is increased when it isconnected to a resistive, inductive, or capacitive load?

Result: Here too, secondary voltage decreases as load current increases if the load is resistiveor inductive but secondary voltage increases with increasing load current for acapacitive load. However, appropriate to the smaller relative short-circuit voltage es, thedependency on load is less.

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T 10.1 Single-phase Autotransformer Experiments

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5 Experiments with the Single-phase Autotransformer

Study Goals:

After carrying out the experiments, the student will be capable of: connecting a single-phase autotransformer and then demonstrating the significance of theterms "voltage transformation" and "current transformation" with appropriate experimentalcircuits.

determining the throughput rating and nominal power of an autotransformer from the dataprovided on its rating plate.



investigating and interpreting a transformer's voltage behavior when it is connected to an

inductive or capacitive load.Equipment List:

1 single-phase autotransformer 733 99







Fig. 5.1: Arrangement of Units for Single-phase Autotransformer Experiments

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5.3 Voltage Behavior with Resistive Load, Evaluating EfficiencyChange the circuit to match Fig. 5.3.1.

Fig. 5.3.1 Circuit for Investigating Voltage Behavior with Resistive Load and for Evaluating Efficiency

Three separate resistors are to be connected in parallel to increase current handling capability.

First set the resistive load to a value of 100% and turn the circuit on. Set the variable transformerto maintain a voltage of 230 V.

Change the load according to the settings prescribed by Tab. 5.3.1. For each setting, measure thecorresponding values for secondary current and secondary voltage as well as the primary side's

values for effective powerP1 and power factor cos .After the measurements have been taken, calculate the effective power on the primary side withthe equation

1 1 1 cosP V I= ,

effective power on the secondary side with the equation

2 2 2P V I= ,

from the above results, derive a value for efficiency with

2

1

P

P = ,

and complete the table below. Be careful about the current handling capabilities of individualtransformer windings!

R/ % 100 90 80 70 60 50 40 30 20 15 10 5

I1 / A 0.16 0.16 0.16 0.18 0.21 0.26 0.38 0.48 0.52 0.65 0.89 1.52

cos 0.88 0.89 0.91 0.91 0.93 0.94 0.96 0.97 0.97 0.98 0.99 0.99

V2 / V 115.3 115.3 115.2 115.2 114.7 114.5 114.4 114.3 114.3 114.0 113.2 111.5

measured

I2 / A 0.17 0.19 0.21 0.25 0.32 0.42 0.65 0.85 0.94 1.2 1.7 2.95

P1 / W 32.4 32.8 33.5 37.7 44.9 56.2 83.9 107.1 116.0 146.5 202.7 346.8

P2 / W 19.6 21.9 24.2 28.8 36.7 48.1 74.4 97.2 107.4 136.8 192.4 328.9calculated

/ % 60.5 66.9 72.2 76.4 81.7 85.6 88.6 90.7 92.6 93.4 95.0 95.0

Tab. 5.3.1: Voltage Behavior and Efficiency for a Resistively Loaded Single-phase Autotransformer

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Set the transformer powering the circuit for 230 V and maintain this value during the measurement.

First measure no-load voltage in the secondary side.

Take measurements for secondary current and secondary voltage with inductive loads set to the

values prescribed by Tab. 5.4.1. Turn off the circuit's supply voltage prior to making each changeto the inductive load. This is done to prevent large voltage surges when the secondary circuit isopened.

Lindiv. / H open 6 4.8 2.4 1.2 1 0.8

Ltotal / H open 2 1.6 0.8 0.4 0.33 0.27

I2 / A 0.00 0.16 0.20 0.40 0.81 0.98 1.25

V2 / V 115.3 115.2 115.1 115 114.8 114.6 114.4

Tab. 5.4.1: Voltage Behavior for an Inductively Loaded Single-phase Autotransformer

Replace the inductive load with a capacitive load and then repeat the above measurement seriesappropriately for values of capacitive load as specified in Tab. 5.4.2.

C/ F 0 2 4 8 12 16

I2 / A 0.00 0.08 0.15 0.30 0.45 0.60

V2 / V 115.3 115.4 115.5 115.5 115.6 115.7

Tab. 5.4.2: Voltage Behavior for a Capacitively Loaded Single-phase Autotransformer


Fig. 5.4.2: Secondary voltage of a single-phaseautotransformer as a function ofload current when inductively ( )loaded and when capacitively ( )loaded.

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T 10.1 Three-phase Transformer Experiments

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6 Experiments with the Three-phase Transformer

Study Goals:

After carrying out the experiments, the student will be capable of:

connecting a three-phase transformer in various types of circuits (connection symbols) andthen determining their respective values for voltage transformation, current transformation andno-load current.

investigating the behavior of the transformer when connected in various connection symbols tobalanced and unbalanced loads.

proving phase rotation between upper and lower voltage sides for individual connectionsymbols on the basis of appropriate test circuits.

The most frequently used connection symbols for three-phase transformers and their respective

voltage transformation ratios are presented in Tab. 6.1:

Schematic Symbol Phasor DiagramConnection

SymbolSide 1 Side 2 Side 1 Side 2

TranformationRatio

1

2

V

V

Yy01

2

N

N

Dy51

23

N

N

Yd5 1

2

3 N

N

Yz51

2

2

3

N

N

Tab. 6.1: Conventional connection symbols for three-phase transformers and their respective phase-to-phase transformation ratios. The dots in the schematic symbols indicate the respective winding'sline end.

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Equipment List:

1 three-phase transformer 733 90

1 3-phase voltage 400/2.5 A 725 442 D

1 softcase 42PU 400 V 725 572

1 resistive load 732 40


1 dual channel oscilloscope 303 575 2111 four channel isolation amplifier 735 261

3 RMS meters 727 10


2 voltmeters 0 ... 400 V2 ammeters 0 ... 1 A

6.1 Transformer in Yy0 Star-Star Circuit

Fig. 6.1.1: Arrangement of Units for Experiments with a Three-phase Transformer in a Yy0 Star-star Circuit

Set up the circuit as shown below, whereby only one secondary winding is needed:

Fig. 6.1.2: Circuit for Investigating the Three-phase Transformer in a Yy0 Star-star Circuit

On the three-phase 400 V / 2.5 A voltage supply select a phase-to-phase voltage of 400 V and turnon the circuit.

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An oscilloscope is needed to assess the phase rotation relationship between primary andsecondary sides of the transformer circuit used here. The oscilloscope is to be connected to thetest object by way of a isolation amplifier. Change the circuit to match Fig. 6.1.5 for this

assessment.

Fig. 6.1.5: Assessment of Phase Rotation between Primary and Secondary Voltages of a Three-phaseTransformer in a Yy0 Circuit

Ensure that the output of the three-phase 400 V / 2.5 A voltage supply has the correct (clockwise)phase sequence prior to beginning with the measurement. If available, you may wish to use thephase-sequence indicator PHASECOP 2 (727 300) for this purpose.

Connect the test object's primary voltage to isolation amplifier's channel A; the secondary voltageto channel B. These voltages are phase-to-phase voltages!

The voltage levels at the isolation amplifier's outputs are to be connected to the two oscilloscopeinputs so that they can be displayed simultaneously.

Apply nominal voltage to the test object's primary and simultaneously display the primary andsecondary voltages.

1

2

Fig. 6.1.6: Primary (1) and secondary (2) volt-age curves of a three-phase trans-former in a Yy0 circuit. (2.00 V/ DIV.,5 ms/ DIV.)

Determine the phase shift between the two voltages by the time delay between their zerocrossover points.

Result: The two voltages are in phase with each other. This corresponds to state "0" for theconnection symbol.

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6.2 Transformer in Dy5 Delta-Star Circuit

Fig. 6.2.1: Arrangement of Units for Experiments with a Three-phase Transformer in a Dy5 Delta-star Circuit

Set up the experimental circuit as shown below where, here too, only one secondary winding isneeded. Be careful to ensure that the line ends of windings are connected according to Tab. 6.1 !

Fig. 6.2.2: Circuit for Investigating the Three-phase Transformer in a Dy5 Delta-star Circuit


One after the other, measure the three no-load currents I01 through I03 on the primary side as wellas the phase-to-phase voltages between terminals 2U2-2V2, 2V2-2W2 and 2W2-2U2 on thesecondary side:

Result: I01 = 0.08 A, I02 = 0.07 A, I03 = 0.07 A,

V2U22V2 = 214 V, V2V22W2 = 214 V, V2W22U2 = 215 V

Calculate the connection symbol Dy5 transformation ratio from the measured voltages andcompare these to the value in Tab. 6.1 where the ratio is formulated on the basis of turn counts.When connected in delta, the primary winding has a turn count equal to N1 = 1330.

Result: 1U11V1

2U22V2

400 V1 85

216 V

V

V.== , =

=1

2

13301 85

7193.

N

N

The transformation ratio as measured for no-load conditions matches thetransformation ratio as derived from turn counts.

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Change the circuit to match Fig. 6.2.4 in order to investigate the transformer under single-leg loadconditions:

Fig. 6.2.4: Investigation of Three-phase Transformer under Single-leg Load Condition (Dy5 Circuit)

Change the value of load resistance (beginning with a value of 100 %) until rated current again

flows in the secondary side of the test object.Measure the three primary side currents Iprim1, Iprim2 and Iprim3 as well as the three star voltages onthe secondary side.

Result: I2 = I2N = 0.45 A, Iprim1 = 0.16 A, Iprim2 = 0.18 A, Iprim3 = 0.07 A,V2U12U2 = 120 V, V2V12V2 = 123 V, V2W12W2 = 123 V

The oscilloscope is used again here to assess the phase rotational relationship between primaryand secondary sides of the transformer circuit. Change the circuit to match Fig. 6.2.5 for thisassessment.

Fig. 6.2.5: Assessment of Phase Rotation between Primary and Secondary Voltages of a Three-phaseTransformer in a Dy5 Circuit




Apply nominal voltage to the test object's primary and simultaneously display the primary andsecondary voltages.

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Fig. 6.2.6: Primary (1) and secondary (2) volt-age curves of a three-phase trans-former in a Dy5 circuit. (2.00 V/ DIV.,

5 ms/ DIV.)


Result: The time delay between zero crossover points is 8.3 ms. At 50 Hz this corresponds to aphase shift of 150. This indicates that a vector group with code number 5 is actuallyimplemented.

6.3 Transformer in Yd5 Star-Delta Circuit

Fig. 6.3.1: Arrangement of Units for Experiments with a Three-phase Transformer in a Yd5 Star-delta Circuit

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Set up the experimental circuit as shown below where, here too, only one secondary winding isneeded.

Fig. 6.3.2: Circuit for Investigating the Three-phase Transformer in a Yd5 Star-delta Circuit

On the three-phase 400 V / 2.5 A voltage supply select a phase-to-phase voltage of 400 V and turn

on the circuit.One after the other, measure the three no-load currents I01 through I03 on the primary side as wellas the phase-to-phase voltages between terminals 2U2-2V2, 2V2-2W2 and 2W2-2U2 on thesecondary side:

Result: I01 = 0.08 A, I02 = 0.06 A, I03 = 0.08 A,V2U22V2 = 125 V, V2V22W2 = 124 V, V2W22U2 = 124 V

Calculate the connection symbol Yd5 transformation ratio from the measured voltages andcompare these to the value in Tab. 6.1 where the ratio is formulated on the basis of turn counts.Note that, when connected in a star configuration, the turn count for the primary winding has thevalue

11 768

3

NN = = .

Result: 1U11V1

2U22V2

400 V3 2

125 VV.

V== , =

== 11

2 2

3 13303 2

415N

N

N

N.

The transformation ratio as measured for no-load conditions matches thetransformation ratio as derived from turn counts.


Fig. 6.3.3: Determining Current Transformation Ratio for a Three-phase Transformer in a Yd5 Circuit

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Set the resistive load initially to a value of 100 % and turn on the circuit. Here again, the three-phase 400 V / 2.5 A voltage supply should be set to a nominal voltage of 400 V.

Reduce load resistance until rated current flows in the secondary side of the test object. Measure

the corresponding current on the primary side.

Result: I2 = I2N = 0.45 A, I1 = 0.16 A

Formulate the current transformation ratio from the above data and compare this to the valuewhich is calculated from Tab. 6.1:

Result: =21

2 8I

I. , =

== 11

2 2

3 13303 2

415N

N

N

N.

The current transformation ratio value resulting from the measurement is again only ofa qualitative significance since the small load presented to the transformer here isheavily influenced by no-load current.

In the following, the three-phase transformer's behavior is to be investigated under unbalancedload conditions.

First remove the connection between the test object's terminal 2W2 and the resistive load so that atwo-line load exists.

Change the value of load resistance (beginning with a value of 100 %) until rated current againflows in the secondary side of the test object.

Measure the three primary side currents Iprim1, Iprim2 and Iprim3 as well as the three leg voltages on

the secondary side.

Result: I2 = I2N = 0.45 A, Iprim1 = 0.06 A, Iprim2 = 0.19 A, Iprim3 = 0.16 A,V2U22V2 = 120 V, V2U22W2 = 124 V, V2V22W2 = 122 V

The oscilloscope is used again here to assess the phase rotational relationship between primaryand secondary sides of the transformer circuit. Change the circuit to match Fig. 6.3.4 for thisassessment.

Fig. 6.3.4: Assessment of Phase Rotation between Primary and Secondary Voltages of a Three-phaseTransformer in a Yd5 Circuit




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Set up the experimental circuit as shown below where both secondary windings are needed.

Fig. 6.4.2: Circuit for Investigating the Three-phase Transformer in a Yz5 Star-zigzag Circuit


One after the other, measure the three no-load currents I01 through I03 on the primary side as wellas the phase-to-phase voltages between terminals 2U2-2V2, 2V2-2W2 and 2W2-2U2 on thesecondary side:

Result: I01 = 0.08 A, I02 = 0.06 A, I03 = 0.08 A,V2U22V2 = 373 V, V2V22W2 = 370 V, V2W22U2 = 372 V

Calculate the connection symbol Yd5 transformation ratio from the measured voltages andcompare these to the value in Tab. 6.1 where the ratio is formulated on the basis of turn counts.Note again that, when connected in a star configuration, the turn count for the primary winding hasthe value

11 768

3

NN = = .

This type of circuit configuration requires that the secondary's turn count amounts to the sum ofturn counts for windings 2 and 3, i.e. the value

2 830N =

must be applied.

Result: 1U11V1

2U22V2

1 072V

V.= ,

==

1

2

15361 068

1433 8

2 N.

N

The transformation ratio as measured for no-load conditions matches (within thecontext of measurement accuracy) the transformation ratio as derived from turn counts.


Fig. 6.4.3: Determining Current Transformation Ratio for a Three-phase Transformer in a Yz5 Circuit

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An oscilloscope, which is connected to the test object by way of an isolation amplifier, is used hereto assess the phase rotational relationship between primary and secondary sides of thetransformer circuit. Change the circuit to match Fig. 6.4.5 for this assessment.

Fig. 6.4.5: Assessment of Phase Rotation between Primary and Secondary Voltages of a Three-phaseTransformer in a Yz5 Circuit




Apply nominal voltage to the test object's primary and simultaneously display the primary andsecondary voltage waveforms.

Fig. 6.4.6: Primary (1) and secondary (2) volt-

age waveforms for a three-phasetransformer in a Yz5 circuit.(2.00 V/ DIV., 5 ms/ DIV.)


Result: The time delay between zero crossover points is 8.3 ms. At 50 Hz this corresponds to aphase shift of 150. This indicates that a vector group with code number 5 is actuallyimplemented.

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T 10.1 Scott Transformer Experiments

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7 Experiments with the Scott Transformer

Study Goals:

After carrying out the experiments, the student will be capable of: connecting a transformer in a Scott circuit and then determining its respective voltagetransformations and no-load current.

investigating the behavior of a transformer in a Scott circuit with one and two phase loads onthe secondary side.

assessing the phase shift between the two independent voltage systems on the secondaryside with the aid of appropriate measurement circuitry.

operating the Scott transformer in a so-called "V circuit" as a three-phase transformer forbalanced loads.

Equipment List:

1 Scott transformer 733 93

1 3-phase voltage 400/2.5 A 725 442 D1 softcase 42PU 400 V 725 572

1 resistive load 732 40


1 dual channel oscilloscope 303 575 2111 four channel isolation amplifier 735 261

3 RMS meters 727 10

as an alternative to the RMS meters:2 voltmeters 0 ... 400 V2 ammeters 0 ... 1 A

Fig. 7.1: Arrangement of Units for Experiments with a Scott Transformer

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7.1 Transformer in a Scott CircuitSet up the experimental circuit shown below:

Fig. 7.1.1: Circuit for Investigating the Scott Transformer with No-load

On the three-phase 400 V / 2.5 A voltage supply select a phase-to-phase voltage of 400 V and turn

on the circuit.

One after the other, measure the three no-load currents I01 through I03 on the primary side as wellas the phase-to-phase voltages between terminals 2U1-2U2, 3V1-3V2, 2U1-2U3 and 3V1-3V3 onthe secondary side:

Result: I01 = 0.090 A, I02 = 0.094 A, I03 = 0.094 A,V2U12U2 = 248 V, V3V13V2 = 249 V, V2U12U3 = 124 V, V3V13V3 = 125 V

Formulate the Scott circuit's transformation ratio from the above voltage measurement values.

Result: =400 V

1 61248 V . and =400 V

3 23124 V .

In the following, the behavior of the transformer in a Scott circuit is investigated with one and twosingle-phase loads. To accomplish this, enhance the circuit to match Fig. 7.1.2.

Fig. 7.1.2: Circuit for Investigating the Scott Transformer under Load Conditions

Behavior when connected to a single-phase load will be investigated first. Change the value ofload resistance (beginning with a value of 100 %) until rated current flows in the secondary side ofthe test object.

Measure the three primary side currents Iprim1, Iprim2 and Iprim3 as well as the two secondary sidevoltages V2U12U2 and V3V13V2.

Result: I2 = I2N = 0.68 A , Iprim1 = 0.20 A, Iprim2 = 0.34 A, Iprim3 = 0.53 A,V2U12U2 = 232 V, V3V13V2 = 249 V

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What do you notice about the primary side currents and the voltage on the secondary winding thathas no load?

Result: The single phase load causes unbalanced currents on the primary side. The voltageacross the secondary winding that is not loaded is practically unaffected by the load onthe second winding.

Now change the circuit so that both secondary windings are loaded with their rated currents. Dothis by connecting the second single resistor in the resistive load to the output 2U1-2U2 of theScott transformer. Repeat the measurement made above.

Result: I2 = I2N = 0.68 A , Iprim1 = 0.53 A, Iprim2 = 0.53 A, Iprim3 = 0.53 A,V2U12U2 = 232 V, V3V13V2 = 233 V

What do you notice about the primary sided currents?

Result: The balanced current in the two secondary windings produce a symmetrical load in theScott transformer's primary side.

An oscilloscope is needed to assess the phase rotation relationship between the two secondaryvoltages of this transformer circuit. The oscilloscope is to be connected to the test object by way ofa isolation amplifier.

Change the circuit to match Fig. 7.1.3.

Fig. 7.1.3: Assessment of Phase Shift between the Two Voltage Systems on the Secondary Side of a ScottCircuit

Connect the test object's secondary voltage 1 (between terminals 2U1 and 2U2) to channel A onthe isolation amplifier; secondary voltage 2 (between terminals 3V1 and 3V2) to channel B.

As for the previous experiments, apply nominal voltage to the test object's primary side. Displaythe waveforms for the two secondary voltages simultaneously.

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Result: measured transformation ratio: 1U11U2

2U12U2

400 V1 60

250 V

V

V.==

transformation ratio per rating plate: =

400 V

1 73400 V 3 .

The secondary voltage measured for no-load conditions is somewhat higher than thatwhich is specified by the rating plate.


Fig. 7.2.2: Determining Current Transformation Ratio for a Transformer in a V Circuit

Set the resistive load initially to a value of 100 % and turn on the circuit. Here again, the three-phase 400 V / 2.5 A voltage supply should be set to a nominal voltage of 400 V.

Reduce load resistance until rated current flows in the secondary side of the test object. Measurethe corresponding current on the primary side. Perform measurements on the other two secondary

currents to ensure that a balanced load exists and then measure the three corresponding currentson the primary side.

Result: I2 = I2N = 0.68 A, Iprim1 = 0.48 A, Iprim2 = 0.46 A, Iprim3 = 0.47 A

Formulate the current transformation ratio for the transformer in its V circuit and compare this tothe reciprocal value of the voltage transformation ratio.

Result: = =12

0 4 7 A0 69

0 6 8 A.

I ..

I

The reciprocal value of the measured voltage transformation ratio is 0.63. Thedeviation is essentially the influence of no-load current that results in an increase ofcurrent on the transformer's primary side.

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T 10.1 Practice Questions

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8 Practice Questions

1) Why do both voltages of a single-phase transformer behave proportionally to their respective

turn counts while their current values are inversely proportional?The two sides of a transformer have power equilibrium (when losses are disregarded); i.e. theproduct of voltage and current must be the same for both sides.

2) How is short-circuit voltage defined for a transformer?

This term describes the voltage (at nominal frequency) across the primary side which isnecessary to produce rated current flow in the secondary side when the secondary winding isshorted.

3) What are the pros and cons of a large value for short-circuit voltage?

A transformer with a high value for short-circuit voltage (i.e. a relatively large short-circuitvoltage es) tends to limit current in the event of a short-circuit. This is advantageous. The

disadvantage is that, in normal operation, its secondary voltage is very dependent on loadcurrent.

4) Why is short-circuit voltage typically expressed as a relative value (based on nominalvoltage)?

This makes transformer short-circuit voltage values for different voltage levels easier tocompare.

5) What does the term "sustained short-circuit current" mean?

Sustained short-circuit current is that current which, in a steady state, flows in the primary sidewhen nominal voltage is applied to the primary side and the secondary winding is shorted.

6) What are the essential differences between transformers with a conventional core and thosewith a toroidal core?

No-load current is significantly smaller in the toroidal core transformer, as opposed to atransformer with a conventional core. This is because its design does not have an air gap. Italso exhibits a lower short-circuit voltage due to its smaller dispersion (leakage). Furthermore,windings can be wound on the entire core length of a toroidal transformer so that it makes anoverall savings in weight and volume possible.

7) What determines the efficiency of a transformer?

Efficiency is primarily a matter of how much losses are incurred in copper and iron.

8) What limits the amount of power that can be transferred over a transformer?

Winding currents increase with increasing power transfer. These increased currents result inincreased resistive losses (in the form of heat). When the load becomes too great, thetransformer will overheat and ultimately be destroyed.

9) What are the essential differences between autotransformers and transformers with separatewindings?

When the difference between primary and secondary voltage is not too great, then anautotransformer can be used to achieve significant savings in copper and iron. Thedisadvantage of an autotransformer is that it does not provide galvanic isolation betweenprimary and secondary windings. It may therefore never be used as a safety isolatingtransformer.

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T 10.1 Practice Questions

10) What is to be understood under the term "connector symbol" for a three-phase transformer?

The upper and lower voltage side windings of a three-phase transformer can each beconfigured in star (Y), in delta (D) or in zigzag (Z) circuits. The combination of two (one forprimary and one for secondary) of these configurations is considered to be a connectorsymbol. The configuration of the upper voltage winding is designated with a capital letter, thelower voltage winding is designated with a lowercase letter. The amount of phase shiftbetween the voltages of the upper and lower voltage sides is identified by a code digit thatrepresents a multiple of 30.

11) What is the meaning of so-called "winding points" on a schematic diagram?

Winding points mark the lead (starting) ends of windings that are located on one leg andcontinuously wound in a single direction. This information is important when, for example, it isdesirable to configure a particular vector group for three-phase transformers.

12) Why is it advantageous to connect the high voltage side's neutral point in a Yy0 circuit to the

neutral line of the supply grid?

If a single-phase load is placed on the transformer then the current for this leg of the primarywinding does not have to flow back through the other two (unloaded) legs. This return currentis handled by the neutral conductor.

13) What are the advantages of the delta connection; what advantages does the star connectionoffer?

Economic aspects pose the primary considerations for picking a particular circuit configuration.The star circuit is preferred for high voltages since less insulation is required than would be fora comparable delta circuit. On the other hand, the delta circuit is better where high currentsare involved because smaller copper cross-sections can be selected.

14) Where is the zigzag circuit used?

Transformers serving the low voltage grid must often handle heavily unbalanced loads. Thezigzag circuit equally supplies each leg of the low voltage winding as a distribution from twolegs. Transformer connected in this configuration can be fully loaded on one leg.

15) What must be observed when connecting two three-phase transformers in parallel?

Both transformers must exhibit the same connection symbol (vector group) and have at leastsimilar short-circuit voltage values. Furthermore, their nominal powers should not be toodivergent. Only then can an even distribution of the load across both units be guaranteed.

16) How can the phase shift between upper and lower voltage sides be measured?

One needs an oscilloscope with which the voltage waveform of one high voltage side phasecan simultaneously be displayed with its corresponding low voltage side phase. The time delaybetween zero crossover points will reveal the amount of phase shift.

17) What is the so-called "Scott circuit" used for?

The Scott circuit makes it possible to create two independent single-phase systems out of onethree-phase system. The phase shift between the two secondary voltages is 90.

18) What is the so-called "V circuit" used for in three-phase systems?

A V i it b i l t d ith l t i di l h id f th t f th t

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