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  • CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAMLevel 3 Line H: Install Electrical Equipment

    LEARNING GUIDE H-2INSTALL TRANSFORMERS

    H-2

  • ForewordThe Industry Training Authority (ITA) is pleased to release this major update of learning resources to support the delivery of the BC Electrician Apprenticeship Program. It was made possible by the dedicated efforts of the Electrical Articulation Committee of BC (EAC).

    The EAC is a working group of electrical instructors from institutions across the province and is one of the key stakeholder groups that supports and strengthens industry training in BC. It was the driving force behind the update of the Electrician Apprenticeship Program Learning Guides, supplying the specialized expertise required to incorporate technological, procedural and industry-driven changes. The EAC plays an important role in the provinces post-secondary public institutions. As discipline specialists the committees members share information and engage in discussions of curriculum matters, particularly those affecting student mobility.

    ITA would also like to acknowledge the Construction Industry Training Organization (CITO) which provides direction for improving industry training in the construction sector. CITO is responsible for organizing industry and instructor representatives within BC to consult and provide changes related to the BC Construction Electrician Training Program.

    We are grateful to EAC for their contributions to the ongoing development of BC Construction Electrician Training Program Learning Guides (materials whose ownership and copyright are maintained by the Province of British Columbia through ITA).

    Industry Training AuthorityJanuary 2011

    DisclaimerThe materials in these Learning Guides are for use by students and instructional staff and have been compiled from sources believed to be reliable and to represent best current opinions on these subjects. These manuals are intended to serve as a starting point for good practices and may not specify all minimum legal standards. No warranty, guarantee or representation is made by the British Columbia Electrical Articulation Committee, the British Columbia Industry Training Authority or the Queens Printer of British Columbia as to the accuracy or sufficiency of the information contained in these publications. These manuals are intended to provide basic guidelines for electrical trade practices. Do not assume, therefore, that all necessary warnings and safety precautionary measures are contained in this module and that other or additional measures may not be required.

  • Acknowledgements and CopyrightCopyright 2011, 2014 Industry Training Authority

    All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or digital, without written permission from Industry Training Authority (ITA). Reproducing passages from this publication by photographic, electrostatic, mechanical, or digital means without permission is an infringement of copyright law.

    The issuing/publishing body is: Crown Publications, Queens Printer, Ministry of Citizens Services

    The Industry Training Authority of British Columbia would like to acknowledge the Electrical Articulation Committee and Open School BC, the Ministry of Education, as well as the following individuals and organizations for their contributions in updating the Electrician Apprenticeship Program Learning Guides:

    Electrical Articulation Committee (EAC) Curriculum SubcommitteePeter Poeschek (Thompson Rivers University)Ken Holland (Camosun College)Alain Lavoie (College of New Caledonia)Don Gillingham (North Island University)Jim Gamble (Okanagan College)John Todrick (University of the Fraser Valley) Ted Simmons (British Columbia Institute of Technology)

    Members of the Curriculum Subcommittee have assumed roles as writers, reviewers, and subject matter experts throughout the development and revision of materials for the Electrician Apprenticeship Program.

    Open School BCOpen School BC provided project management and design expertise in updating the Electrician Apprenticeship Program print materials:

    Adrian Hill, Project ManagerEleanor Liddy, Director/SupervisorBeverly Carstensen, Dennis Evans, Laurie Lozoway, Production Technician (print layout, graphics)Christine Ramkeesoon, Graphics Media CoordinatorKeith Learmonth, EditorMargaret Kernaghan, Graphic Artist

    Publishing Services, Queens PrinterSherry Brown, Director of QP Publishing Services

    Intellectual Property Program Ilona Ugro, Copyright Officer, Ministry of Citizens Services, Province of British Columbia

    To order copies of any of the Electrician Apprenticeship Program Learning Guide, please contact us:

    Crown Publications, Queens PrinterPO Box 9452 Stn Prov Govt563 Superior Street 2nd FlrVictoria, BC V8W 9V7Phone: 250-387-6409Toll Free: 1-800-663-6105Fax: 250-387-1120Email: [email protected] Website: www.crownpub.bc.ca

    Version 1Corrected, January 2017 Corrected, March 2016 Corrected, September 2015 Revised, April 2014 Corrected, January 2014 New, October 2012

  • CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3 5

    LEVEL 3, LEARNING GUIDE H-2:

    INSTALL TRANSFORMERSLearning Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

    Learning Task 1: Describe the construction and features of three-phase transformers . . . . . . 9Self-Test 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

    Learning Task 2: Describe the connections of three-phase transformer banks . . . . . . . . . . 15Self-Test 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

    Learning Task 3: Calculate voltage, current and kVA values for three-phase transformer banks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69Self-Test 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

    Learning Task 4: Describe common connections for autotransformers in three-phase circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89Self-Test 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

    Learning Task 5: Calculate voltage, current and kVA values for three-phase autotransformer circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99Self-Test 5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .108

    Learning Task 6: Describe instrument transformer connections in three-phase circuits . . . .111Self-Test 6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .121

    Learning Task 7: Calculate instrument-transformer ratings and meter readings in three-phase circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .123Self-Test 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .130

    Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .131

  • 6 CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3

  • LEARNING ObjECTIVES H-2

    CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3 7

    Learning Objectives The learner will be able to connect and maintain three-phase transformers.

    The learner will be able to describe three-phase applications of autotransformers.

    The learner will be able to describe three-phase applications of instruments transformers.

    The learner will be able to determine installation requirements for three-phase transformers.

    Activities Read and study the topics of Learning Guide I-2: Install Transformers.

    Complete Self-Tests 1 through 7. Check your answers with the Answer Key provided at the end of this Learning Guide.

    Resources

    You are encouraged to obtain the following text to provide supplemental learning information:

    Alternating Current Fundamentals by John R. Duff and Stephen L. Herman; Delmar Publishers Inc.

    Delmars Standard Textbook of Electricity, 5th Revised Edition by Stephen Herman. Cengage Learning.

  • 8 CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3

    BC Trades Moduleswww.bctradesmodules.ca

    We want your feedback! Please go the BC Trades Modules website to enter comments about specific section(s) that require correction or modification. All submissions will be reviewed and considered for inclusion in the next revision.

    SAFETY ADVISORYBe advised that references to the Workers Compensation Board of British Columbia safety regulations contained within these materials do not/may not reflect the most recent Occupational Health and Safety Regulation. The current Standards and Regulation in BC can be obtained at the following website: http://www.worksafebc.com.

    Please note that it is always the responsibility of any person using these materials to inform him/herself about the Occupational Health and Safety Regulation pertaining to his/her area of work.

    Industry Training Authority January 2011

  • CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3 9

    Learning Task 1:

    Describe the construction and features of three-phase transformersThree-phase power is transformed from one voltage level to another using a three-phase transformer or a bank of single-phase transformers. When the transformer bank is used, the windings of each phase are on separate cores. See Figure 1.

    Figure 1A three-phase transformer bank

    Figure 2A three-phase transformer

    In a three-phase transformer, the high-voltage and low-voltage windings for each phase are wound on the same leg of the transformer.

  • LEARNING TASk 1 H-2

    10 CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3

    Construction of three-phase transformersFigure 3 shows the core of a simple three-phase transformer. Notice that the core has three legs (the vertical sections). The primary and secondary windings of any one phase are wound on each leg of the core.

    Figure 3Three-phase transformer core

    At any instant, the flux in any one leg of the transformer equals the phasor sum of the flux in the other two legs.

    Remember that for any given load on the transformer, the resultant flux in any leg is determined by the counter emf it must produce in the primary winding. It is not determined by the load current.

    Figure 4 shows the three phase voltages at four instants during a cycle. It also shows the core flux that results from these voltages.

    Three-phase transformer connectionsThe windings of a three-phase transformer or transformer bank are generally connected in one of two configurations: wye or delta.

    A wye connection is made as shown in Figure 5 by connecting the three similarly labelled ends of the windings to form a common point called the star point or neutral.

    A delta connection is made as shown in Figure 6 by connecting:

    The oppositely labelled winding ends of the first and second transformer

    The oppositely labelled winding ends of the second and third transformer

    The oppositely labelled winding ends of the third and first transformers

    Since it is possible to connect both the high- and low-side windings in either of these two configurations, there are four different transformer configurations:

    Wye-to-wye

    Delta-to-delta

    Wye-to-delta

    Delta-to-wye

  • LEARNING TASk 1 H-2

    CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3 11

    In these names, the first word represents the configuration of the primary winding and the second word represents the configuration of the secondary winding.

    Figure 4Core flux in a three-phase transformer core

  • LEARNING TASk 1 H-2

    12 CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3

    Figure 5Wye-connected transformer windings

    Figure 6Delta-connected transformer windings

    Advantages of a single three-phase transformerA single three-phase transformer has the following advantages:

    A three-phase transformer has slightly higher operating efficiency than three single-phase transformers connected in a bank.

  • LEARNING TASk 1 H-2

    CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3 13

    A three-phase transformer weighs less and requires less space than three single-phase transformers.

    A single three-phase transformer costs less than the three single-phase transformers.

    A three-phase transformer is easier to install because the transformer is less complex. The interconnections between the phases are already complete when the unit is shipped.

    Advantages of a bank of three single-phase transformersThe advantages that three single-phase transformers have over one three-phase transformer all relate to breakdown. Since modern transformers are very reliable, these advantages are somewhat limited.

    A bank of three single-phase transformers may be operated at a reduced kVA capacity with one unit down for repair in some cases. Since all phases of a three-phase transformer are wound on a single core, this is not possible with a three-phase unit.

    A bank of three single-phase transformers is simpler than a three-phase transformer. Therefore, if one phase needs repair, the single-phase transformer is less expensive to repair than the three-phase unit.

    The cost of a spare single-phase transformer is less than that of a spare three-phase transformer.

    Now do Self-Test 1 and check your answers.

  • LEARNING TASk 1 H-2

    14 CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3

    Self-Test 1

    1. List four advantages that a single, three-phase transformer has over a bank of single-phase transformers.

    2. List three advantages that a bank of single-phase transformers has over a single three-phase transformer.

    3. List the two common configurations in which the windings of a three-phase transformer may be connected.

    Go to the Answer Key at the end of the Learning Guide to check your answers.

  • CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3 15

    Learning Task 2:

    Describe the connections of three-phase transformer banksThere are four fundamental connections used for three-phase transformers (or banks). These are:

    Wye-wye connection

    Delta-delta connection

    Wye-delta connection

    Delta-wye connection

    In this Learning Task, you will also look at some special delta connections. These are:

    Four-wire delta connection

    Open-delta connection

    Wye-wye connectionThe wye-to-wye transformer connection is used mainly when transforming from one high voltage to another. The ability to ground the neutral point reduces the potential stress on the insulation. This means that less insulation can be used in the transformer.

    Constructing voltage diagrams for three-phase transformersFigure 1 shows the four standard voltage diagrams for three-phase transformers as specified by the Canadian Standards Association (CSA). Note that the diagrams are not marked with primary and secondary but rather with high side and low side. These standards ensure that all CSA-approved three-phase transformers have a consistent phase displacement between the high and low sides.

    The phase displacement is defined as the angle between the voltage VAN of the high side and VAN of the low side, where N is the neutral point of the diagram. Neutral refers to a point such that the voltages between it and each of the phase conductors are equally spaced in magnitude and phase angle. On the delta diagram, VAN is indicated by the dashed line.

    Wye-to-wye connections and delta-to-delta connections must always have a phase displacement of 0. It is physically possible to connect single-phase transformers in a three-phase bank so that the phase displacement is 180. However, avoid this, as it will not permit the bank to be connected in parallel to a standard wye-to-wye, or delta-to-delta, three-phase transformer. This is covered in detail later in this Learning Task.

  • LEARNING TASk 2 H-2

    16 CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3

    Figure 1Standard voltage diagrams for three-phase transformers

    Wye-to-delta connections and delta-to-wye connections must always have a phase displacement of 30, with the high side leading the low side for a standard ABC phase rotation. If the phase rotation is reversed to ACB, then the high side lags the low side by 30. Again, it is possible to connect single-phase transformers in a three-phase bank so that they produce other phase displacements, but you should avoid this, as it will not permit the bank to be connected in parallel to a standard wye-to-delta or delta-to-wye three-phase transformer.

    There are only three rules for reproducing standard transformer diagrams. You can use the diagrams produced to ensure that proper connections are made on the transformers.

    Rule 1The phasors represent instantaneous directions of the induced voltages in the windings. This means the primary phasor represents the counter emf, which is 180 out of phase with the primary applied voltage.

    Numbering is used in place of arrowheads. It is conventional to show induced voltage phasors for transformers with the tail of the arrow at the lower subscripted terminal and the head of the arrow at the higher subscripted terminal. For example, H1 and X1 represent the tail of the phasors and H2 and X2 represent the head of the phasors.

    Rule 2The high-voltage phasor VAN is always drawn at 30 to the horizontal and the high-voltage phasor VAB is always drawn at 60 to the horizontal. This corresponds to the 30 phase displacement that exists between the line and phase voltages in a three-phase system. When making the diagrams, always draw the high-side diagram first, whether it is for a step-up or step-down application.

  • LEARNING TASk 2 H-2

    CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3 17

    Figure 2Phasors representing induced voltages

    Rule 3For wye-to-wye and delta-to-delta connections the phase displacement from the high to low side must be 0. For wye-to-delta and delta-to-wye connections the phase displacement from high side to low side must be 30 with the high side leading.

    Constructing a voltage diagram for a wye-to-wye connected transformer bank

    1. Draw the first phasor (VAN) of the high side at 30 to the horizontal with H1 at the lower end and H2 at the upper end, as in Figure 3.

    Figure 3First high-side phasor drawn at 30 to the horizontal

    2. Draw the other two high-side phasors equally spaced 120 apart from each other and from the first phasor. Connect the H2 points together to form the wye point as shown in Figure 4.

    Figure 4Complete voltage diagram of high-side wye

  • LEARNING TASk 2 H-2

    18 CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3

    3. Since the low-side induced voltages are in phase with the high-side induced voltages, draw the low-side phasors parallel to the high-side phasors as in Figure 5. Notice that the X2 points are all connected together to form a wye point.

    Figure 5Voltage diagram of wye-to-wye connection

    4. Connect the H1 terminal of the first high-side phasor drawn to phase A; connect the next lagging one to phase B; and connect the other to phase C as shown in Figure 6. Label the X1 terminals of the phasors on the low side A, B or C according to which of the high-side phasors they are in phase with.

    5. The phasors represent the induced voltages in the transformer windings. The phasor with its H1 terminal connected to phase A is called the A phase transformer. Likewise for the other two phases.

    Figure 6Phase connections shown on a wye-to-wye voltage diagram

    Drawing a wiring diagram from the voltage diagramNormally a voltage diagram does not show all the individual H1, H2, X1 and X2 terminals of each transformer. Also, the phase terminals are not identified as A, B and C. Instead:

    On the high side, the phase A terminal is labelled H1, the phase B terminal, H2, and the phase C terminal, H3 as shown in Figure 1.

    On the low side, the phase A terminal is labelled X1, the phase B terminal, X2, and the phase C terminal, X3.

  • LEARNING TASk 2 H-2

    CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3 19

    This is also the way the terminals are labelled on a unit three-phase transformer. If present, the neutral points are labelled H0 for the high side and X0 for the low side. With the voltage diagram completed properly and the terminal information added, you can use the transformer voltage diagram to create a wiring diagram for the transformers.

    The voltage diagrams are independent of the individual transformer polarities. That is, it does not matter whether the transformers used in the bank are additive polarity, subtractive polarity, or some mixture of the two. The terminals that connect to a given point depend only on their subscript identification.

    1. Usually you arrange the transformer diagrams so that the phase A transformer is on the right-hand side when viewed from its high side and the phase B transformer is next to it, followed by the phase C transformer on the left. See Figure 7.

    Figure 7Three-phase bank of additive-polarity transformers

    2. Whether the transformer has additive or subtractive polarity, always put the H1 terminal of each transformer on the right-hand side when viewed from its high side.

    3. Now transfer information from the voltage diagram in Figure 6: Each transformers H2 terminals connect to form the high-side wye point.

    The H1 terminal of each phases transformer connects to its corresponding phase line.

  • LEARNING TASk 2 H-2

    20 CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3

    Figure 8 shows this information transferred.

    Figure 8Wye, high-side connections

    The X2 terminals of each transformer connect together to form the low-side wye point.

    The X1 terminal of each phases transformer connects to its corresponding phase line.

    Figure 9 shows the completed wiring diagram.

    Figure 9Three-phase, wye-to-wye bank of additive-polarity transformers

    Figure 10 shows a completed wiring diagram for a three-phase bank of subtractive-polarity transformers. It does not matter which polarity the transformers are, they will still have the same connections with respect to the terminal markings. All the H2 terminals still connect together and all the X2 terminals still connect together. As well, all the H1 and X1 terminals of each phases transformers still connect to their corresponding phases.

  • LEARNING TASk 2 H-2

    CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3 21

    H1 H2

    X1 X2

    A

    ABCN

    B C

    H1 H1H2 H2

    X1 X1X2X2

    NABC

    Figure 10Three-phase, wye-to-wye bank of subtractive-polarity transformers

    Figure 11 shows a three-phase bank of transformers with mixed polarities.

    H1 H2

    X2X1

    A

    ABCN

    NABC

    B C

    Subtractive Additive Subtractive

    H1 H1H2 H2

    X1 X1X2X2

    Figure 11Three-phase, wye-to-wye bank of mixed-polarity transformers

    For a step-down application from a wye high side to a wye low side: Connect the transformers so that the primary circuit connects to the high windings and the secondary circuit connects to the low windings.

    For a step-up application from a wye low side to a wye high side: Connect the transformers so that the primary circuit connects to the low windings and the secondary circuit connects to the high windings.

  • LEARNING TASk 2 H-2

    22 CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3

    Voltage relationships for the wye-to-wye transformer bank The line-to-line voltage-transformation ratio is exactly the same as the individual

    transformers turns ratio for a wye-to-wye connection.

    The voltage ratings of the transformers primary and secondaries must be equal to the corresponding line voltages divided by 3.

    If both high-side and low-side connections are made correctly, the line-to-line voltages on the secondary side should read 3 times the secondary phase voltage.

    Wrong connectionsConsider what happens if the connections to the X1 and X2 terminals of transformer B in Figure 9 are accidentally reversed as shown in Figure 12.

    Figure 12Incorrect low-side connection on the B-phase transformer

  • LEARNING TASk 2 H-2

    CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3 23

    The voltage diagram for this incorrect bank connection would look like the one shown in Figure13.

    H1

    H2

    H2

    H2

    H1 H1

    X1

    X2

    X1 X1

    B phase

    B

    CA

    A C

    A phase

    C phase

    X2

    X2B

    Figure 13Voltage diagram for the incorrect circuit shown in Figure 12

    For an incorrect low-side connection on the B-phase transformer:

    The phase angle between the two phase voltages VAN and VCN is the proper 120.

    The line-to-line voltage measured between lines A and C is still 3 times the phase voltage.

    However, the phase angle between the two phase voltages VAN and VBN (or between phase voltages VBN and VCN) is only 60.

    Therefore, the line voltages between lines A and B and between B and C equal the phase voltage. If the incorrect connections were made on transformer A or C instead of B, a similar imbalance of phase angles and line voltages would occur. The same incorrect line voltages and phase angles occur if the same mistake happens on the high side of one of the transformers rather than on the low side.

    Single-phase loads are unaffected by this incorrect connection. Three-phase loads such as motors are adversely affected. Also, the neutral wire might be overloaded.

    After the wye-to-wye transformer connections are made and before the load is applied, test the line voltages for balance. All line-to-line voltages should be equal to 3 times the phase voltage.

    180 phase shiftAs mentioned earlier, you can connect the transformers so that the voltage and phase relationships on the secondary are truly three-phase but there is a primary to secondary phase shift of 180. Figure 14 shows one way of connecting the transformers to do this.

  • LEARNING TASk 2 H-2

    24 CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3

    Figure 14Transformer bank connected for a 180 phase shift

    Figure 15 shows the voltage diagram for this three-phase bank connection. Notice the voltage VAN on the low side is 180 out of phase with VAN on the high side.

    Figure 15Voltage diagram for a wye-to-wye 180 phase shift

    Loads connected to this transformer bank would work perfectly well and the phase sequence would be the same as that for the 0 phase shift. However, you should avoid this connection because it is not possible to parallel another three-phase transformer with this bank. The CSA standard specifies that three-phase transformers connected wye-to-wye have a 0 phase shift.

    Delta-delta connectionThe delta-to-delta connection is used mainly in the medium voltage range where a neutral point is not required for the operation of loads.

  • LEARNING TASk 2 H-2

    CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3 25

    Constructing a voltage diagram To construct a voltage diagram for a delta-to-delta connected transformer, do the following:

    1. Draw the first phasor of the high side (VAB) at 60 to the horizontal with H1 at the lower end and H2 at the upper end. See Figure 16(a).

    Figure 16First high-side phasor drawn at 60 to the horizontal

    Notice the dotted line. This represents the voltage VAN. As mentioned earlier, the phase displacement is the angle between VAN of the high side and VAN of the low side. Since there is no physical point on the delta connection that meets the definition of neutral, this voltage VAN is shown as a dotted line. Its sole purpose is to show the phase displacement between the high and low side of the three-phase transformer. On the high side it is drawn at 30 to the horizontal.

    2. Draw the second high-side phasor 120 behind the first phasor with its H1 terminal connected to the H2 terminal of the first phasor as in Figure 16(b).

    3. Draw the third high-side phasor 120 behind the second phasor with its H1 terminal connected to the H2 terminal of the second phasor and its H2 terminal connected to the H1 terminal of the first phasor. See Figure 16(c). This completes the high-side delta connection.

    4. Since the low-side induced voltages are in phase with the high-side induced voltages, draw the low-side phasors parallel to the high-side phasors of the same transformer. See Figure17.

    Figure 17Voltage diagram of a delta-to-delta connection

  • LEARNING TASk 2 H-2

    26 CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3

    Notice that the X1 terminals are at the same relative ends of the low-voltage phasors as the H1 terminals are on the high-voltage phasors.

    5. The H1 terminal of the first high-side phasor drawn connects to line A, the next lagging one connects to line B, and the final one connects to line C, as shown in Figure 18. Identify the low-side phasor that is in phase with the high-side phasor connected to line A. Label its X1 terminal as line A. Similarly, label the low-side terminals for lines B and C.

    Figure 18Phase connections shown on a delta-to-delta voltage diagram

    6. The phasors represent induced voltages in the transformer windings. The phasor with its H1 terminal connected to line A is called the A-phase transformer. Likewise for the other two phases.

    Drawing a wiring diagram from the voltage diagramThe voltage diagram does not normally show the individual H1, H2, X1 and X2 terminals of each transformer and the phase terminals are not identified as A, B and C. These markings are to help you draw a proper wiring diagram for the transformers.

    The voltage diagrams are independent of the individual transformer polarities. Again, it does not matter whether the transformers used in the bank are additive polarity, subtractive polarity or some mixture of the two. The terminals that connect to a given point depend only on their subscript identification.

    1. As usual, arrange the individual transformers in the bank with the A-phase transformer on the right and the C-phase transformer on the left when viewed from the high side. Put the H1 terminal of each transformer on the right-hand side when viewed from its high side. See Figure 19.

  • LEARNING TASk 2 H-2

    CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3 27

    X1X2

    A B

    H1 H2 H1 H1

    C

    H2H2

    X1X2 X2 X1

    Figure 19Three-phase bank of additive-polarity transformers

    2. Now transfer information from the high side of the voltage diagram in Figure 18:

    The H2 terminal of the A-phase transformer connects to the H1 terminal of the B-phase transformer.

    The H2 terminal of the B-phase transformer connects to the H1 terminal of the C-phase transformer.

    To complete the high-side delta, the H2 terminal of the C-phase transformer connects to the H1 terminal of the A-phase transformer.

    Connect each of the H1 terminals to its corresponding line as shown in Figure 20.

    Figure 20Delta high-side connections

  • LEARNING TASk 2 H-2

    28 CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3

    3. Next transfer the information from the low side of Figure 18 to the wiring diagram:

    The X2 terminal of the A-phase transformer and the X1 terminal of the B-phase transformer connect together and to line B.

    The X2 terminal of the B-phase transformer and the X1 terminal of the C-phase transformer connect together and to line C.

    To complete the low side delta, the X2 terminal of the C-phase transformer and the X1 terminal of the A-phase transformer connect together and to line A.

    Connect each of the X1 terminals to its corresponding line as shown in Figure 21.

    Figure 21Three-phase, delta-to-delta bank of additive-polarity transformers

    Figure 22 shows a wiring diagram for a three-phase bank of subtractive-polarity transformers connected delta-to-delta. Figure 23 shows a three-phase bank of transformers with mixed polarities. No matter which polarity the transformers are, they have the same connections with respect to the terminal markings.

    For a step-down application from a delta high side to a delta low side, the transformers have the primary circuit connected to the high windings and the secondary circuit connected to the low windings.

    For a step-up application from a delta low side to a delta high side, the transformers have the primary connected to the low windings and the secondary connected to the high windings.

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    Figure 22Three-phase, delta-to-delta bank of subtractive-polarity transformers

    Figure 23Three-phase, delta-to-delta bank of mixed-polarity transformers

    Voltage relationships for the delta-to-delta transformer bankFor a delta-to-delta connection, the line-to-line voltage-transformation ratio is exactly the same as the individual transformers ratios. The voltage ratings of the transformers primary and secondaries must be equal to the corresponding line voltages.

    In a delta connection the two ends of any phase winding are connected directly across the lines. Therefore:

    The line voltage in the delta connection equals the phase voltage.

    The voltage rating of each transformer winding is equal to the line voltage.

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    For this reason, a different type of voltmeter test must be performed on a secondary delta connection to determine if all the connections are properly made. This test is referred to as the mesh or delta-closure test.

    To perform a mesh or delta-closure test, install a voltmeter in place of the final secondary delta connection as shown in Figure 24. Always do this test on the secondary side. It detects improper connections in either the primary or the secondary circuit.

    Figure 24Mesh or delta-closure test

    In theory, if the connections are all made correctly, the closure voltage should be zero volts. In practice, this is not the case. Third harmonic voltages created by the transformer core cause the voltmeter to read a voltage higher than zero, but less than line voltage. If a mistake is made in the transformer connections, the voltmeter reads double the line-voltage value.

    To see why these two voltages occur in the two different situations, examine the secondary voltage diagram of a correctly connected transformer and then of an incorrectly connected transformer. Figure 25 shows the diagram of a correctly connected transformer with a voltmeter connected across the final connection.

    Follow the voltage rises around the delta from one side of the voltmeter to the other. Note that the last phasor returns to the starting point. This indicates a difference between start and finish of zero volts. Calculate the voltage between the tail of the first phasor and the head of the last phasor by adding the three voltage rises:

    V V V V

    V V

    T A phase B phase C phase= + +

    = + +240 60 240 60 2 440 180

    0 0

    V

    V

    =

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    Figure 25Secondary voltage diagram of a correctly connected transformer bank

    Figure 26 is the diagram of an incorrectly connected transformer with secondary leads of the C phase transformer connected backward. This means that the secondary voltage of this phase is 180 out of phase from what it should be. Once again a voltmeter is placed across the final connection.

    Follow the voltage rises around the delta from one side of the voltmeter to the other. Note that the last phasor does not return to the starting point. This indicates a difference between start and finish of twice the phase voltage. Once again, the voltage between the tail of the first phasor and the head of the last phasor can be calculated by adding the three voltage rises:

    V V V V

    V V

    T A phase B phase C phase= + +

    = + +240 60 240 60 2 440 0

    480 0

    V

    V

    =

    Figure 26Secondary voltage diagram of an incorrectly connected transformer bank

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    If the incorrect connections are made on the primary rather than the secondary, the same 180 phase shift occurs and the voltmeter still reads 480 V. If there is an incorrect connection and you make the last connection before doing a voltmeter test, it can result in a disastrous short circuit across 480 V.

    Always do this voltmeter test before making the secondary closure connection.

    Whether the incorrect connection is made on the primary or the secondary, always correct it before you replace the voltmeter by the final connection.

    180 phase shiftIt is possible to connect the transformers so that the voltage and phase relationships on the secondary are truly three-phase but there is a primary to secondary phase shift of 180. Figure27 shows one way of doing this.

    Figure 28 shows the voltage diagram for this three-phase connection. Notice that the voltage VAN on the low side is 180 out of phase with VAN on the high side. Loads connected to this transformer bank would work perfectly well and the phase sequence would be the same as that for the 0 phase shift.

    Avoid this connection, because you must not parallel a three-phase transformer with this bank.

    The CSA specifies that three-phase transformers connected delta-to-delta must have a 0 phase shift.

    Figure 27Transformer bank connected for a 180 phase shift

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    Figure 28Voltage diagram for a delta-to-delta 180 phase shift

    Wye-delta connectionThe wye-to-delta transformer connection is commonly used to transform electrical energy from high voltages to medium voltages where a neutral is not required to supply single-phase loads. The voltage diagram to use for a wye-to-delta, step-down transformer bank is the one shown in Figure 29. This ensures a phase displacement of 30 with the high side leading the low side. This diagram is also used for delta-to-wye, step-up connections.

    Figure 29Voltage diagram for a wye-to-delta, step-down transformer bank and for a delta-to-wye, step-up transformer bank

    The voltage diagram to use for a wye-to-delta, step-up transformer bank is the one shown in Figure 30. Again, this ensures a phase displacement of 30 with the high side leading the low side. This diagram is also used for delta-to-wye, step-down connections.

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    Figure 30Voltage diagram for a wye-to-delta step-up transformer bank and for a delta-to-wye, step-down transformer bank

    Using the proper diagram for the required application ensures that the banks have the proper phase displacement to be paralleled with other wye-to-delta or delta-to-wye, three-phase transformers.

    Constructing these diagrams is not difficult if you remember to construct the high-voltage diagram first. This is true whether it is step-up or step-down. Then, apply the three rules discussed previously.

    Drawing voltage diagrams Wye-to-delta, step-down transformer bank

    1. Draw the first phasor (VAN) of the high-side wye at 30 to the horizontal with H1 at the lower end and H2 at the upper end as in Figure 31(a).

    Figure 31Voltage diagram of a wye high-side connection

    2. Draw the other two high-side phasors so that all three are equally spaced 120 apart. Connect the H2 points together to form the wye point as shown in Figure 31(b).

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    3. Since the low-side induced voltages are in phase with the high-side induced voltages, draw the low-side phasors parallel to the high-side phasors of the same transformer:

    Connect the X2 terminal of the A-phase, low-voltage phasor to the X1 terminal of the B-phase, low-voltage phasor.

    Connect the X2 terminal of the B-phase, low-voltage phasor to the X1 terminal of the C-phase, low-voltage phasor.

    To complete the delta, connect the X2 terminal of the C-phase, low-voltage phasor to the X1 terminal of the A-phase, low-voltage phasor. See Figure 32.

    Figure 32Voltage diagram of a wye-to-delta, step-down connection

    4. The phasor with its H1 terminal connected to line A is called the A-phase transformer. Likewise for the other two phases. Label the X1 terminal of the low-side phasor from the A-phase transformer as line A on the low side. Do the same for phases B and C.

    Wye-to-delta, step-up transformer

    1. It is important to draw the high side first even if the high side is the secondary. Since the high side is a delta connection, draw the first phasor VAB at 60 to the horizontal with H1 at the lower end and H2 at the upper end as in Figure 33(a).

    Figure 33Voltage diagram of delta high-side connection

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    2. Draw the second high-side phasor 120 behind the first phasor, with its H1 terminal connected to the H2 terminal of the first phasor as in Figure 33(b).

    3. Draw the third high-side phasor 120 behind the second phasor, with its H1 terminal connected to the H2 terminal of the second phasor. To complete the high-side delta connection, connect its H2 terminal to the H1 terminal of the first phasor as shown in Figure 33(c).

    4. Since the low-side induced voltages are in phase with the high-side induced voltages, draw the low-side phasors parallel to the high-side phasors of the same transformer. To ensure the proper phase displacement of 30, you will have to connect the X1 terminals of the low-side phasors to form the neutral or wye point. See Figure 34.

    5. Connect the H1 terminal of the first high-side phasor drawn to line A. Connect the next lagging one to line B and the third one to line C as shown in Figure 34.

    6. For this diagram, the way you select which X2 terminal to label as line A on the secondary is a little different. To ensure the correct phase displacement of 30 between the high side and low side, with the high side leading, connect:

    Line A to the X2 terminal of the C-phase transformer

    Line B to the X2 terminal of the A-phase transformer

    Line C to the X2 terminal of the B-phase transformer

    Figure 34Voltage diagram of a wye-to-delta, step-up connection

    Wye-to-delta, step-down transformer bankThe voltage diagram does not normally show the individual H1, H2, X1 and X2 terminals of each transformer. Also, the line terminals are not usually identified as A, B and C. These markings are just to help you draw a proper wiring diagram for the transformers.

    Voltage diagrams do not depend on individual transformer polarities. It does not matter whether the transformers used in the bank are additive polarity, subtractive polarity or some mixture of the two. The terminals that connect to a given point depend only on their subscript identification. Figure 35 shows a three-phase bank of additive-polarity transformers.

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    CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3 37

    1. As usual, arrange individual transformers in the bank with the A-phase transformer on the right and the C-phase transformer on the left when viewed from the high side.

    2. Always put the H1 terminal of each transformer on the right-hand side when viewed from its high side.

    X1X2

    A B

    H1 H2 H1 H1

    C

    H2H2

    X1X2 X2 X1

    Figure 35Three-phase bank of additive-polarity transformers

    3. Now, transfer information from the voltage diagram in Figure 32. In Figure 32, the H2 terminals of the transformers connect together to form the high-side wye point. The remaining H1 terminals connect to their corresponding phase lines. Figure 36 shows this information transferred.

    Figure 36Wye high-side connections

    4. Next, transfer the information from the low side of Figure 32 to the wiring diagram. In Figure 32, the X2 terminal of the A-phase transformer and the X1 terminal of the B-phase transformer connect together and to line B. The X2 terminal of the B-phase transformer and the X1 terminal of the C-phase transformer connect together and to line C. To complete the delta connection, the X2 terminal of the C-phase transformer and the X1 terminal of the A phase transformer connect together and to line A. Figure 37 shows this information transferred and the completed transformer bank connections.

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    38 CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3

    X2

    ABCN

    ABC

    X1X2 X2X1X1

    H1 H1 H1 H2H2H2

    A B C

    Figure 37Three-phase, wye-to-delta, step-down transformer bank using additive-polarity transformers

    Figure 38 shows a completed wiring diagram for a wye-to-delta, step-down transformer bank using subtractive-polarity transformers.

    H1

    A

    ABCN

    ABC

    H1 H1H2 H2 H2

    X2 X2 X2X1X1X1

    B C

    Figure 38Three-phase, step-down bank of subtractive-polarity transformers

    Figure 39 shows a completed wiring diagram for a wye-to-delta, step-down transformer bank using mixed-polarity transformers. Again, it does not matter which polarity the transformers are, they will still have the same connections with respect to the terminal markings.

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    CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3 39

    H1 H2

    X2X1

    A

    ABCN

    ABC

    B C

    Subtractive Additive Subtractive

    H1 H1H2 H2

    X1 X1X2X2

    Figure 39Three-phase, step-down bank of mixed-polarity transformers

    Wye-to-delta, step-up transformer bank

    1. Transfer information from the voltage diagram in Figure 34. In Figure 34, the X1 terminals of each of the transformers are connected together to form the low side neutral or wye point. The X2 terminal of the C-phase transformer connects to line A. The X2 terminal of the A-phase transformer connects to line B. The X2 terminal of the B-phase transformer connects to line C.

    Figure 40Wye low-side connections

    2. Next, transfer the information from the high side of Figure 34 to the wiring diagram. In Figure 34, the H2 terminal of the A-phase transformer and the H1 terminal of the B-phase transformer connect together and to line B. The H2 terminal of the B-phase transformer and the H1 terminal of the C-phase transformer connect together and to line C. To complete the delta connection, the H2 terminal of the C-phase transformer and the H1 terminal of the A-phase transformer connect together and to line A. See Figure 41 for the completed transformer-bank connections.

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    Figure 41Three-phase, wye-to-delta, step-up transformer bank using additive-polarity transformers

    Figure 42 shows a completed wiring diagram for a wye-to-delta, step-up transformer bank using subtractive-polarity transformers.

    H1H2

    X1X2

    H1H2 H1H2A

    ABCN

    ABC

    BC

    X1X2 X1X2

    Figure 42Wye-to-delta, step-up transformer bank using subtractive-polarity transformers

    Figure 43 shows a completed wiring diagram for a wye-to-delta, step-up transformer bank using mixed transformer polarities. It does not matter which polarity the transformers are, they still have the same connections with respect to the terminal markings.

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    CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3 41

    H1H2

    X1X2

    A

    ABCN

    ABC

    BC

    X1X2 X1 X2

    H1H2 H1H2

    Figure 43Wye-to-delta, step-up transformer bank using transformers of mixed polarities

    Voltage relationships for the wye-to-delta transformer bankFor a wye-to-delta connection:

    The line-to-line voltage ratio is equal to the individual transformer turn-ratio times 3 .

    The voltage ratings of the transformers primary windings must be equal to the primary line voltage divided by 3 .

    The voltage ratings of the transformers secondary windings must be equal to the secondary line voltage.

    To determine if both the primary and secondary connections are correct, do the mesh or delta-closure test on the secondary delta before making the final connection. Figure 44 shows the voltmeter placed in the secondary circuit to make this test on a wye-to-delta, step-down application.

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    Figure 44Delta closure test on a wye-to-delta, step-down application

    Delta-to-wye connectionThe delta-to-wye, three-phase transformer connection is the most popular connection used to supply low-voltage distribution systems. The reasons are:

    It can supply both single-phase and three-phase loads.

    It is easily grounded at the neutral point and this limits the voltage to ground available during a ground fault on any line conductor.

    In the past, many low-voltage, three-phase loads were supplied by ungrounded, delta-connected secondaries. In those systems, induced transient overvoltages often caused insulations to break down. Today, new installations are usually supplied by grounded, wye-connected secondaries.

    Delta-to-wye, step-down bankThe voltage diagram to use for a delta-to-wye, step-down transformer bank is shown in Figure45. This ensures a phase displacement of 30, with the high side leading the low side.

    Figure 45Voltage diagram for a delta-to-wye, step-down transformer bank

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    CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3 43

    Delta-to-wye, step-up bankThe voltage diagram to use for a delta-to-wye, step-up transformer bank is the one shown in Figure 46. Again this ensures a phase displacement of 30 where the high side leads the low side.

    Figure 46Voltage diagram for a delta-to-wye, step-up transformer bank

    Using the proper diagram for the required application ensures that the banks will have the proper phase displacement to be paralleled with other wye-to-delta and delta-to-wye, three-phase transformers.

    Constructing voltage diagramsFor a delta-to-wye, step-down transformer bank

    1. Since the high side is a delta connection, draw the first phasor VAB at 60 to the horizontal. Have H1 at the lower end and H2 at the upper end as in Figure 47(a).

    Figure 47Voltage diagram for a delta high side

    2. Draw the second high-side phasor 120 behind the first phasor with its H1 terminal connected to the H2 terminal of the first phasor as in Figure 47(b).

    3. Draw the third high-side phasor 120 behind the second phasor. Connect its H1 terminal to the H2 terminal of the second phasor. Now, connect its H2 terminal to the H1 terminal of the first phasor to complete the high-side delta connection. See Figure 47(c).

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    4. Since the low-side induced voltages are in phase with the high-side induced voltages, draw the low-side phasors parallel to the high-side phasors of the same transformer. To ensure the proper phase displacement of 30, connect the X1 terminals of the low-side phasors together to form the neutral or wye point. See Figure 48.

    Figure 48Voltage diagram of a delta-to-wye, step-down connection

    5. Connect the H1 terminal of the first high-side phasor drawn to line A. Connect the next lagging one to line B, and the third one to line C as shown in Figure 48.

    6. The way you select which X2 terminal will be labelled as line A on the secondary is a little different for this diagram. Choose it so that there is a 30 phase shift between the high and low side with the high side leading.

    7. Connect line A to the X2 terminal of the C-phase transformer; connect line B to the X2 terminal of the A-phase transformer; connect line C to the X2 terminal of the B-phase transformer.

    For a delta-to-wye, step-up transformer bank

    1. Draw the first phasor (VAN) of the high-side wye at 30 to the horizontal. Have H1 at the lower end and H2 at the upper end as in Figure 49(a).

    2. Draw the other two high-side phasors equally spaced 120 apart from each other and from the first phasor. Connect the H2 points to form the wye point as shown in Figure 49(b).

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    Figure 49Voltage diagram for a wye high side

    3. Since the low-side induced voltages are in phase with the high-side induced voltages, draw the low-side phasors parallel to the high-side phasors of the same transformer.

    4. Connect the X2 terminal of the A-phase, low-voltage phasor to the X1 terminal of the B-phase, low-voltage phasor. Connect the X2 terminal of the B-phase, low-voltage phasor to the X1 terminal of the C-phase, low-voltage phasor. To complete the delta, connect the X2 terminal of the C-phase, low-voltage phasor to the X1 terminal of the A-phase, low-voltage phasor. See Figure 50.

    Figure 50Voltage diagram of a delta-to-wye, step-up connection

    5. Label the phasor with its H1 terminal connected to line A as the A-phase transformer. Likewise for the other two phases.

    6. Label the X1 terminal of the low-side phasor from the A-phase transformer as line A on the low side. Follow the same procedure for phases B and C.

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    Drawing wiring diagramsFor a delta-to-wye, step-down transformer bankThe voltage diagram does not normally show the individual H1, H2, X1 and X2 terminals of each transformer and the line terminals are not identified as A, B and C. These markings are simply to help you draw a proper wiring diagram.

    The voltage diagrams are independent of the individual transformer polarities. It does not matter whether the transformers used in the bank are additive polarity, subtractive polarity or some mixture of the two. The terminals that connect to a given point depend only upon their subscript identification.

    1. Arrange the individual transformers in the bank with the A-phase transformer on the right and the C-phase transformer on the left when viewed from the high side. Put the H1 terminal of each transformer on the right-hand side when viewed from its high side. See Figure 51.

    X1X2

    A B

    H1 H2 H1 H1

    C

    H2H2

    X1X2 X2 X1

    Figure 51Three-phase bank of additive-polarity transformers

    2. Now transfer information from the voltage diagram in Figure 48:

    Connect the H2 terminal of the A-phase transformer and the H1 terminal of the B-phase transformer together and to line B.

    Connect the H2 terminal of the B-phase transformer and the H1 terminal of the C-phase transformer together and to line C.

    To complete the delta connection, connect the H2 terminal of the C-phase transformer and the H1 terminal of the A-phase transformer together and to line A.

    Figure 52 shows this information transferred.

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    Figure 52Delta high-side connections

    3. Next, transfer the information from the low side of Figure 48 to the wiring diagram:

    Connect the X1 terminals of each of the transformers together to form the low-side neutral or wye point.

    Connect the X2 terminal of the C-phase transformer to line A.

    Connect the X2 terminal of the A-phase transformer to line B.

    Connect the X2 terminal of the B-phase transformer to line C.

    Figure 53 shows the completed transformer bank connections.

    Figure 53Three-phase, delta-to-wye, step-down transformer bank using additive-polarity transformers

    Figure 54 shows a completed wiring diagram for a delta-to-wye, step-down transformer bank using subtractive-polarity transformers. Figure 55 shows a completed wiring diagram for a delta-to-wye, step-down transformer bank using a mixture of transformer polarities. It does not matter which polarity the transformers are, they still have the same connections with respect to the terminal markings.

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    Figure 54Delta-to-wye, step-down transformer bank using subtractive-polarity transformers

    Figure 55Delta-to-wye, step-down transformer bank using transformers of mixed polarities

    For a delta-to-wye, step-up transformer bank

    1. Transfer information from the voltage diagram in Figure 50. In Figure 50, the H2 terminals of each of the transformers are connected together to form the high-side wye point and the H1 terminal of each transformer is connected to its corresponding phase line. Figure 56 shows this information transferred.

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    Figure 56Wye high-side connections

    2. Next, transfer the information from the low side of Figure 50 to the wiring diagram:

    Connect the X2 terminal of the A-phase transformer and the X1 terminal of the B-phase transformer together and to line B.

    Connect the X2 terminal of the B-phase transformer and X1 terminal of the C-phase transformer together and to line C.

    To complete the delta connection, connect the X2 terminal of the C-phase transformer and the X1 terminal of the A-phase transformer together and to line A.

    See Figure 57 for the completed transformer bank connections.

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    Figure 57Three-phase, delta-to-wye, step-up transformer bank using additive-polarity transformers

    Figure 58 shows a completed wiring diagram for a delta-to-wye, step-up transformer bank using subtractive-polarity transformers. Figure 59 shows a completed wiring diagram for a delta-to-wye, step-up transformer bank using mixed-polarity transformers. Again it does not matter which polarity the transformers are, they still have the same connections with respect to the terminal markings.

    Figure 58Three-phase, delta-to-wye, step-up transformer bank using subtractive-polarity transformers

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    Figure 59Three-phase, delta-to-wye, step-up transformer bank using transformers with a mixture of polarities

    Voltage relationships for the delta-to-wye transformer bank The line-to-line voltage transformation ratio for a delta-to-wye connection is equal to the

    individual transformer ratio divided by 3.

    The voltage ratings of the transformers secondary windings must equal the secondary line voltage divided by 3 because they are connected in wye.

    The voltage ratings of the transformers primary windings must be equal to the primary line voltage because they are connected in delta.

    Since the secondary is connected in wye, you must test the three line-to-line voltages with a voltmeter. Each of the line-to-line voltages should be the same and equal to 3 times the phase voltage of each secondary. Figure 60 shows three voltmeters connected to measure these three voltages in a delta-to-wye, step-down application.

    If their readings are incorrect, then you must check the primary and secondary connections, and correct them before any load is connected.

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    Figure 60Checking the secondary line-to-line voltages to determine if all primary and secondary connections have been made correctly

    Special four-wire delta connectionOne disadvantage of the three-phase, delta-connected secondary is that it is not grounded and therefore is not suitable for supplying single-phase lighting loads. Section 30 of the Canadian Electrical Code (CEC) requires that:

    If a system incorporates a neutral (as does a 120/240 V single-phase distribution), it must be grounded.

    Screw-shells of lampholders in luminaires must be connected to the identified conductor.

    To connect these loads to a delta-connected secondary, the system must be grounded. The three-phase, four-wire, delta secondary is one way to do this. Figure 61 shows a diagram of this circuit.

    The secondary winding of one of the transformers is centre-tapped. This centre tap is grounded, which grounds the whole secondary system. The single-phase loads on the system connect across this transformer.

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    A B

    C

    Figure 61Three-phase, four-wire, delta-connected secondary

    Figure 62Unequal phase-to-ground voltages in a four-wire, delta-connected system

    The voltage between one line terminal and the grounded neutral is higher than the voltage between either of the other two line terminals and the grounded neutral (identified conductor). The three voltages to ground are:

    E V

    E V

    E E E

    V

    BN

    CN

    AN AB BN

    =

    =

    = +

    =

    120 120

    120 60

    240

    +

    =

    0 120 120

    208 30

    V

    V

    Figure 62 shows these voltages for a four-wire, 240 V, delta-connected system. (Note that the term neutral is loosely applied here. The grounded conductor is a neutral only to the single-phase system. To the three-phase system it is simply a grounded or identified conductor.)

    The line with the higher voltage to ground is referred to as the high leg and has the following CEC requirements:

    The high leg must be the A-phase conductor.

    Where a panelboard is supplied from a four-wire, delta-connected system, the grounded conductor ... shall be located in a compartment provided for single-phase connections and the phase conductor having the higher voltage-to-ground shall be suitably barriered from that compartment.

    This is to help prevent the higher voltage accidentally being applied across a lower voltage load. (For example, applying 208 V across a 120 V load.)

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    The voltage between the high leg and ground is always 3

    2 times the line-to-line voltage.

    For example, in this case:

    32

    240 208 =V V

    Also, the voltage between each of the other two lines and ground is 1/2 times the line-to-line voltage. For example, in this case:

    12

    240 120 =V V

    When you size transformers for this kind of bank, you must be aware that the transformer with the centre tap supplies only 2/3 of the current to the single-phase load. The other 1/3 must be carried by each of the other two transformers.

    When transformers of different kVA ratings are used in this type of bank, the maximum safe bank rating is three times the kVA rating of the smallest unit.

    Open-delta connectionAn open delta is created when one of the three transformer windings is removed from the delta connection. The open-delta connection has the following useful applications:

    To temporarily supply three-phase power when one transformer in a three-phase bank fails and is being repaired or replaced.

    To initially supply a system that is expected to expand in the future.

    To supply loads where the majority of the load is single-phase and only a small amount of three-phase power is required.

    Figure 63 shows a diagram of an open-delta transformer bank where both the primary and secondary windings are connected in open delta.

    Figure 63Open-delta, open-delta transformer bank connection

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    Figure 64 shows a phasor representation of the induced voltages. Note that, even though the C-phase transformer is not present, the same three line-to-line voltages still exist on the secondary. This means that the open-delta bank is capable of supplying energy to three-phase loads.

    Figure 64Phasor representation of the open-delta connection

    kVA capacity of an open-delta transformer bankThere is a limit to how much current a transformer can supply before its windings overheat. For a single-phase transformer this maximum current is determined by dividing the kVA rating by the rated voltage of the winding.

    Example 1: Figure 65 shows a balanced, 240 V, three-phase load supplied by a delta-connected secondary of a transformer bank. The bank consists of three single-phase transformers, each rated at 3 kVA with a secondary-voltage rating of 240 V.

    21.65

    21.65

    21.65

    Figure 65Delta secondary supplying a balanced, three-phase load

    The maximum current each of the windings can supply without overheating is:

    I VA V

    A

    P =

    =

    3000 240

    12 5.

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    56 CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3

    If each phase winding is capable of supplying 12.5 A, then at full load the line current is:

    I A

    A

    L =

    =

    3 12 5

    21 65

    .

    .

    The maximum three-phase load the bank is capable of supplying is:

    kVA E I

    V A

    kVA

    MAX L L=

    =

    =

    3 1000

    3 240 21 65 1000

    9

    .

    Example 2: Figure 66 shows the same transformer bank with one transformer removed. For simplicity, the load it supplies is a purely resistive, balanced, three-phase load. In this way, we can ignore the phase displacement between voltage and current caused by any reactance in the load.

    Figure 66Open-delta source supplying a balanced, purely resistive, three-phase load

    Notice that two of the phase windings are now in series with two of the lines. This means the maximum line current is now limited to the maximum phase current of the winding (12.5 A).

    If the line current is to be limited to a maximum of 12.5 A, then the current in each phase of the balanced delta load must be limited to:

    I A

    A

    P =

    =

    12 5 3

    7 22

    .

    .

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    CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3 57

    It might seem that this open-delta bank could supply 2/3 of the power of a complete bank to a balanced three-phase load. But this is not the case. The total apparent power this open-delta bank can supply to a balanced, three-phase load is:

    kVA E I

    V A

    kVA

    MAX L L=

    =

    =

    3 1000

    3 240 12 5 1000

    5 2

    .

    .

    Comparing Examples 1 and 2, note that 5.2 kVA = 57.7% of 9 kVA1. An open-delta transformer bank can supply only 57.7% as much power to a balanced three-phase load as a closed-delta bank can. This also corresponds to only 86.6% of the combined capacity of the two transformers in the open-delta bank.

    Line current in an open-delta secondary circuitApplying Kirchhoffs current law in Figure 66 at the junction of the two transformer windings with line B, it looks at first as though the current in line B cannot be 12.5 A when the currents in line A and line C are also 12.5 A. However, you must remember that these three currents are not in phase.

    Figure 67 shows that, to satisfy Kirchhoffs voltage law, the source-voltage rises must equal the load-voltage drops. The three voltages are 120 out of phase with each other.

    Figure 67Source-voltage rises equal load-voltage drops

    In Figure 68 the currents are added to the phasor diagram. Because the loads are balanced and purely resistive, the currents have equal magnitude and are in phase with the applied voltages. If the loads were not purely resistive but still balanced, there would be an equal phase displacement between each applied voltage and its corresponding phase current. The diagram in Figure 68 would then be swivelled because the currents are out of phase (lagging) with the phase voltages.

    1 Note that 57.7% = 1 3

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    58 CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3

    Figure 68Load phase currents caused by voltages across the loads

    Figure 69 shows the line currents being calculated by applying Kirchhoffs current law to each of the corner points in the delta. Notice that the line currents are equal in magnitude, but they are out of phase with each other by 120.

    Figure 69Line currents

    Figure 70 shows the addition of the three currents at the junction (in Figure 66) where the two transformer windings intersect with line B.

    These current phasors form a complete loop back to the point where the first one started. This shows that, at this junction, the sum of the three currents is 0 A. This satisfies Kirchhoffs current law and proves that the current in line B is 12.5 A.

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    CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3 59

    Figure 70Addition of all three line currents

    Open-wye, open-delta transformer bankFigure 71 shows the diagram of a transformer bank connected in open wye, open delta. The primary is connected in open wye, and the secondary is connected in open delta.

    H1 H2

    X1X2

    H1 H2

    X1X2

    BA

    N

    CBA

    AB

    Figure 71Open-wye, open-delta, step-down transformer bank connection

    This connection is used in rural areas where most of the load is single-phase. In areas like this the supply authority may only run two phase conductors and a neutral. This connection also allows the supply of small three-phase loads. Figure 72 shows the voltage phasor diagram for this connection.

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    60 CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3

    Figure 72Phasor diagram of an open-wye, open-delta, step-down connection

    Now do Self-Test 2 and check your answers.

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    CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3 61

    Self-Test 2

    1. How are the high-voltage and low-voltage terminals of a three-phase transformer normally marked?

    2. What is meant by phase displacement between the high and low sides of a three-phase transformer?

    3. What is meant by the term neutral point?

    4. What is the standard phase displacement for wye-to-wye and delta-to-delta transformer connections?

    5. What is the standard phase displacement for wye-to-delta and delta-to-wye transformer connections?

    6. Which voltages do the phasors in voltage diagrams represent?

    7. Which part of the phasor do the terminal markings H1 and X1 represent: the head or the tail?

    8. In voltage diagrams for three-phase transformers, in what position is the high-side voltage VAN always drawn?

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    62 CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3

    9. Why is the low-side phasor for any transformer always drawn parallel to the high-side phasor for the same transformer?

    10. Where is the A-phase transformer normally located in a transformer bank when viewed from the high side?

    11. Can an additive-polarity transformer be used in a bank with two subtractive-polarity transformers to make up a three-phase bank?

    12. Can a subtractive-polarity transformer be used in a bank with two additive-polarity transformers to make up a three-phase bank?

    13. Before connecting the load, what test should you perform on the secondary of a three-phase transformer bank with a wye-connected secondary?

    14. If a voltmeter test on the secondary of a wye-to-wye connected transformer shows VAB = 208V, VBC = 120 V and VCA = 120 V, what is indicated?

    15. For a step-down application, would the primary lines connect to H1, H2 and H3 or to X1, X2 and X3?

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    CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3 63

    Delta-delta connections16. What is the standard phase displacement for a delta-to-delta transformer connection?

    17. On voltage diagrams for three-phase delta transformers, in what position is the high-side voltage phasor VAB always drawn?

    18. Why is the low-side phasor for any transformer always drawn parallel to the high-side phasor for that transformer?

    19. In a transformer bank, where is the A-phase transformer normally located when viewed from the high side?

    20. Can an additive-polarity transformer be used with two subtractive-polarity transformers to make up a three-phase, delta-to-delta bank?

    21. Can a subtractive-polarity transformer be used with two additive-polarity transformers to make up a three-phase, delta-to-delta bank?

    22. What test must be performed on the secondary of a three-phase transformer bank with a delta-connected secondary?

    23. The phase voltage on the delta-connected secondary of a three-phase transformer bank is 240 V. The test in Question 22 gives a reading of 73 V. Is it safe to remove the meter and install the final connection?

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    64 CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3

    24. What is the most likely cause of the 73 V measurement in Question 23?

    25. For a delta-to-delta, step-up application, do the primary lines connect to H1, H2 and H3, or to X1, X2 and X3?

    Wye-delta connections26. What is the standard phase displacement for a wye-to-delta transformer connection? Which

    side leads?

    27. In voltage diagrams for three-phase transformers, at what position is the high-side voltage phasor VAB always drawn?

    28. Why is the low-side phasor for any transformer always drawn parallel to the high-side phasor for the same transformer?

    29. Where is the A-phase transformer normally located in a transformer bank viewed from the high side?

    30. Can an additive-polarity transformer be used with two subtractive-polarity transformers to make up a three-phase, wye-to-delta bank?

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    CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3 65

    31. Can a subtractive-polarity transformer be used with two additive-polarity transformers to make up a three-phase, wye-to-delta bank?

    32. What test must be performed on the secondary of a three-phase transformer bank with a delta-connected secondary?

    33. The phase voltage on the delta-connected secondary of a three-phase transformer bank is 480 V. The test in Question 32 gives a reading of 960 V. Is it safe to remove the meter and install the final connection?

    34. If you use the same voltage diagram for a wye-to-delta, step-up application as for a wye-to-delta, step-down application, are you still conforming to the CSA standards for three-phase transformers?

    Delta-wye connections35. What is the standard phase displacement for a delta-to-wye transformer connection? Which

    side leads?

    36. On voltage diagrams for three-phase, delta transformers, at what position is the high-side voltage phasor VAB drawn?

    37. Why is the low-side phasor of a transformer always drawn parallel to the high-side phasor for that transformer?

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    66 CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3

    38. In a transformer bank viewed from the high side, where is the A-phase transformer normally located?

    39. Can an additive-polarity transformer be used with two subtractive-polarity transformers to make up a delta-to-wye, three-phase bank?

    40. Can a subtractive-polarity transformer be used with two additive-polarity transformers to make up a delta-to-wye, three-phase bank?

    41. What test must be performed on the secondary of a three-phase transformer bank with a wye-connected secondary?

    42. What is the relationship between the primary line voltage and the primary transformer-winding voltage in a delta-to-wye, step-down transformer bank?

    43. What is the relationship between the secondary line voltage and the secondary transformer-winding voltage in delta-to-wye, step-down transformer bank?

    44. Can the same voltage diagram be used for a delta-to-wye, step-up application as for a delta-to-wye, step-down application and still conform to the CSA standards for three-phase transformers?

    Special delta connections45. A three-phase, four-wire, delta-connected system is to be used for supplying both three-phase

    motor loads and single-phase lighting loads. Where do you normally attach the ground?

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    CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3 67

    46. If the line-to-line voltage on the delta system is 480 V, what will the voltages be between the following points?

    a. line A to ground

    b. line B to ground

    c. line C to ground

    47. Which phase does the CEC specify as the high leg?

    48. Does the CEC permit this high leg to be in the compartment of a panelboard used to supply single-phase loads? Explain.

    49. The transformer with the centre tap supplies all of the current to the single-phase load. The other two transformers supply only their share of the balanced three-phase load.

    a. True

    b. False

    50. List three applications where an open-delta transformer connection is commonly used.

    Go to the Answer Key at the end of the Learning Guide to check your answers.

  • 68 CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3

  • CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3 69

    Learning Task 3:

    Calculate voltage, current and kVA values for three-phase transformer banksYou previously learned that for single-phase transformers:

    VA VAIN OUT=

    and

    NN

    EE

    II

    P

    S

    P

    S

    S

    P

    = =

    where

    NP = number of primary turns NS = number of secondary turns EP = primary voltage ES = secondary voltage IS = secondary current IP = primary current

    Wye-to-wye transformer bank calculationsWhen a wye-to-wye transformer connection is used, the following applies:

    The line-to-line voltage ratio equals the individual single-phase-transformer voltage ratio.

    However, the primary and secondary line voltages are 3 times higher than the respective primary and secondary transformer winding voltages.

    This means the voltage ratings on the transformer windings need only be 57.7% of the line voltage.

    Because of this reduction in insulation stress, this transformer connection is often used to connect high-voltage (over 100 000 V) transmission systems with unequal voltages.

    Since the transformer windings are in series with the lines, the line currents and their respective phase currents are equal. The primary-to-secondary current ratio equals the reciprocal of the primary-to-secondary voltage ratio. (Note: 3

    1 is the reciprocal of 1

    3.)

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    70 CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3

    Example 1: Figure 1 shows a 13.2 kV 347/600 V wye-to-wye transformer bank. If each transformer is rated at 100 kVA and the bank is operating at its rated three-phase load, calculate the following:

    a. voltage rating of each primary winding

    b. voltage rating of each secondary winding

    c. turns ratio of each transformer

    d. line-to-line voltage ratio

    e. total three-phase capacity of the bank

    f. secondary line current

    g. secondary phase current

    h. primary phase current

    i. primary line current

    Figure 1Wye-to-wye step-down transformer bank

    Solution:a. Since the primary windings are connected in wye across the lines, the rating of each

    primary winding is:

    13200 3 7621V V=

    b. Since the secondary windings are connected in wye across the lines, the rating of each secondary winding is:

    600 3 346 4V V= .

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    CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3 71

    c. Calculate the turns ratio by dividing the primary transformer voltage by the secondary transformer voltage:

    7621 V V to 1346 4 22. =

    d. Calculate the line-to-line voltage ratio by dividing the primary line voltage by the secondary line voltage:

    13.2 kV V to 1600 22=

    e. The total, balanced, three-phase capacity of this bank is:

    3 100 300 =kVA kVA

    f. Calculate the secondary line current at full load by using the equation

    VA E I

    IVA

    E

    VAV

    A

    L L

    LL

    =

    =

    =

    =

    3

    3

    3000003 600

    288 7

    .

    .

    g. Calculate the secondary phase current at full load using the equation

    VA E I

    IVA

    E

    VAV

    A

    P P

    PP

    =

    =

    =

    =

    3

    3

    3000003 346 4

    288 7

    .

    .

    .

    Note that this calculation is unnecessary because, for a wye connection, IL = IP.

    h. Calculate the primary phase current at full load using the equation

    VA E I

    IVA

    E

    VAV

    A

    P P

    PP

    =

    =

    =

    =

    3

    3

    3000003 7621

    13 12

    .

    .

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    72 CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3

    i. The primary line current (13.12 A) equals the primary phase current because the phase windings are connected in wye.

    Delta-to-delta transformer bank calculationsWhen a delta-to-delta transformer connection is used:

    The line-to-line voltage ratio equals the individual single-phase transformer voltage ratio.

    In this case each transformer winding is connected directly across the lines.

    Therefore, the primary and secondary line-to-line voltages equal the respective primary and secondary transformer winding voltages.

    Two phase windings connect to each line.

    This means that for balanced three-phase loads, the line current equals 3 times the phase (winding) current.

    The primary-to-secondary, line-to-line or phase-to-phase current ratio equals the reciprocal of the primary-to-secondary voltage ratio.

    Example 2: Figure 2 shows a 4160 V 480 V delta-to-delta transformer bank. If each transformer is rated at 200 kVA and the bank is operating at its rated three-phase capacity, calculate the following:

    a. voltage rating of each primary winding

    b. voltage rating of each secondary winding

    c. turns ratio of each transformer

    d. line-to-line voltage ratio

    e. total three-phase capacity of the bank

    f. secondary line current

    g. secondary phase current

    h. primary phase current

    i. primary line current

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    CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3 73

    Figure 2Delta-to-delta, step-down transformer bank

    Solution:a. Since the primary windings are connected in delta directly across the lines, the voltage

    rating of each primary winding must equal the primary line-to-line voltage = 4160 V.

    b. Since the secondary windings are connected in delta directly across the lines, the voltage rating of each secondary winding must equal the secondary line-to-line voltage = 480 V.

    c. The turns ratio may be calculated by dividing the primary transformer voltage by the secondary transformer voltage:

    4160 8 67 1V 480 V to= .

    d. Since both the primary and secondary windings are connected directly across the lines, the line-to-line ratio must equal the turns ratio of each transformer = 8.67 to 1.

    e. The total, balanced, three-phase capacity of this bank equals:

    3 200 600 =kVA kVA

    f. Calculate the secondary line current at full load using the equation

    VA E I

    IVAE

    L L

    LL

    =

    =

    =

    =

    3

    3

    480

    .

    600 000 VA3 V

    721.7 A

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    74 CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3

    g. Calculate the secondary phase current at full load using the equation

    VA E I

    IVA

    E

    VAV

    A

    P P

    PP

    =

    =

    =

    =

    3

    3

    600 0003 480

    416 7

    .

    .

    h. Calculate the primary phase current at full load using the equation

    VA E I

    IPVA

    E

    A

    P P

    P

    =

    =

    =

    =

    3

    3

    6000003 4160

    48 08

    .

    .

    i. Calculate the primary line current at full load using the equation

    VA E I

    IVA

    E

    VAV

    A

    L L

    LL

    =

    =

    =

    =

    3

    3

    6000003 4160

    83 27

    .

    .

    Wye-to-delta transformer bank calculationsWhen a wye-to-delta transformer connection is used:

    The line-to-line voltage ratio is 3 times the individual single-phase transformer-voltage ratio.

    The primary line-to-line voltage is also 3 times higher than the primary-winding voltage because it is wye connected.

    The secondary line-to-line voltage is equal to the secondary-winding voltage because it is delta connected.

    Since the primary windings are wye-connected, the primary phase current is equal to the primary line current.

    On the delta secondary, two windings connect to each line. This means that, for balanced

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    three-phase loads, the secondary line current is 3 times the secondary phase (winding) current.

    The primary-to-secondary, phase-to-phase current ratio is equal to the reciprocal of the single-phase, transformer-voltage ratio.

    The primary-to-secondary, line-to-line current ratio is equal to the reciprocal of the line-to-line voltage ratio.

    Caution: If the neutral is connected on the primary side of this bank, the bank attempts to balance any load imbalance that might be present on the wye-connected primary bus. This could result in damage to the transformer or the neutral conductor.

    Example 3: Figure 3 shows a 13.2 kV 240 V wye-to-delta transformer bank. If each transformer is rated at 125 kVA and the bank is operating at its rated three-phase load, calculate the following:

    a. voltage rating of each primary winding

    b. voltage rating of each secondary winding

    c. turns ratio of each transformer

    d. line-to-line voltage ratio

    e. total three-phase capacity of the bank

    f. secondary line current

    g. secondary phase current

    h. primary phase current

    i. primary line current

    Solution:a. Since the primary windings are connected in wye across the lines, the rating of each

    primary winding must be:

    13 2 3 7 62. .kV kV=

    b. The secondary windings are connected in delta directly across the lines. Therefore, the voltage rating of each secondary winding must equal the secondary line-to-line voltage = 240 V.

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    76 CONSTRUCTION ELECTRICIAN APPRENTICESHIP PROGRAM: LEVEL 3

    Figure 3Wye-to-delta, step-down transformer bank

    c. Calculate the turns ratio by dividing the primary transformer phase voltage by the secondary phase voltage:

    7620 240 31 75 1V V to= .

    d. The primary line voltage is 3 times the primary winding voltage. Therefore, the line-to-line voltage ratio must equal the transformer voltage ratio times 3.

    31.75 3 to 1 = 55