IEEE TRANSACTIONS ON EDUCATION, VOL. 46, NO. 3, AUGUST 2003 373

A Lecture on Autotransformers for PowerEngineering Students

Carlos A. Castro, Senior Member, IEEE,and Carlos A. F. Murari, Member, IEEE

Abstract—A lecture on autotransformers intended specificallyfor power engineering students is proposed in this paper. An orig-inal approach to introducing the equipment is shown, and impor-tant information that does not appear in most textbooks is providedand discussed. In particular, a strong connection between the theo-retical aspects and the engineer’s every day practice is emphasized.Simple laboratory experiments are also proposed to validate thetheoretical information.

Index Terms—Autotransformer, education, laboratory, powerengineering, voltage regulator.

I. INTRODUCTION

M ANY classic textbooks contain a section on autotrans-formers [1]–[6]. Autotransformers are important equip-

ment, because they are used as voltage regulators [5], as variableac voltage sources [5] (where a fixed input voltage can betransformed into a variable output voltage), and as a connectionbetween two transmission systems with different nominal volt-ages (e.g., 345/500 kV [2]), among other applications. However,the approach to the subject is rather simple in most texts. Thispaper proposes a new approach to introducing the equipment,providing the student with more practical information.

The basic principle of the autotransformer is presented. Then,a discussion based on its practical utilization is presented withcomments on its performance. Finally, some laboratory exper-iments are proposed to verify and complement the theoreticalmaterial.

II. THE PROPOSEDLECTURE

A. Introduction—Basic Principles of Autotransformers

A load is fed by a voltage source through an ideal transformer,as shown in Fig. 1.

The following relationships hold:

and

and are the magnitudes of voltage phasorsand ,respectively; and are the magnitudes of current phasors

and , respectively; and are the number of turns ofthe windings; is the transformer ratio; and is the trans-former’s nominal apparent power.

Manuscript received June 25, 2002; revised October 22, 2002.The authors are with the Power Systems Department, School of Electrical and

Computer Engineering, UNICAMP, 13081-970 Campinas, São Paulo, Brazil(e-mail: ccastro@ieee.org; murari@dsee.fee.unicamp.br).

Digital Object Identifier 10.1109/TE.2003.814592

Fig. 1. Ideal transformer.

Fig. 2. Ideal autotransformer.

The transformer windings can also be connected to each otherto form anautotransformer, as shown in Fig. 2. The connectionbetween the primary (voltage source side) and the secondary(load side) windings is additive; that is, the winding voltagesadd up. The windings can be connected in a subtractive way; thatis, the voltages oppose each other. The voltages and currents inboth windings are the same as in the transformer of Fig. 1. Theapparent power at the primary winding is given by

Since , the input power of the autotransformer isgreater than that of the transformer. The same windings areused for both the transformer and the autotransformer. Theapparent power at the secondary winding is

which is equal to in an ideal autotransformer. is trans-ferred from the primary to the secondary winding through themutual magnetic flux, and is directly transferred fromthe voltage source to the load via the electrical connection be-tween the windings. The first is usually referenced astrans-formed power, while the latter is referenced asconducted power.

0018-9359/03$17.00 © 2003 IEEE

374 IEEE TRANSACTIONS ON EDUCATION, VOL. 46, NO. 3, AUGUST 2003

Fig. 3. Load fed by voltage source through (a) a transformer or (b) anautotransformer.

The voltages and currents at the windings of the autotrans-former are the same as those of the transformer, as are the coreand copper losses. Since more power can be delivered to theload through the same equipment, the efficiency of the auto-transformer is greater than that of the transformer.

For a voltage at the primary winding of an autotrans-former, the resulting voltage at the secondary winding will be

. The loads of Figs. 1 and 2 are identical. To supplythe nominal voltage to the loads connected to the secondary,a lower voltage must be applied to the primary winding ofthe autotransformer. In this case, the magnetic flux in the coreand, consequently, the core losses will be less than that of thetransformer.

B. Observations on Practical Applications of Autotransformers

The analysis made in Section II-A, though theoreticallysound, may be misleading as far as practical applications ofautotransformers are concerned. The idea that a conventionaltransformer can be connected as an autotranformer and anefficiency gain is obtained is not always applicable in practice.Some situations that power engineers face in their everydaypractice will be discussed in this section.

Problem: A 110-V load must be fed by a fixed 220-Vsource. This situation is typical in industrial environments.

Situation 1: A 220/110-V transformer is available.Discussion: In this case, the load can be connected to the

voltage source through the transformer or through the autotrans-former, as shown in Fig. 3.

The first issue to be addressed is whether the load mustbe electrically isolated from the voltage source. If isolationis the case, only Fig. 3(a) applies. Otherwise, the connectionaccording to Fig. 3(b) can also be used. However, in this par-ticular case, there is no efficiency gain if the autotransformeris chosen, since a subtractive connection must be used. Theapparent power at the primary winding is

which is equal to the apparent power of the transformer. Notonly the efficiency but also the voltage regulation are the sameas that of the transformer. The connection of the windings asan autotransformer in this particular case does not result in any

Fig. 4. Load fed by voltage source through an autotransformer.

advantages as far as the system efficiency is concerned. Finally,for other ratios between load and source voltages, the connec-tion as an autotransformer may not be possible at all.

Situation 2: The most appropriate transformer or autotrans-former must be specified and purchased.

Discussion: Again, the first issue to be addressed iswhether the load must be electrically isolated from the voltagesource. If isolation is the case, only Fig. 3(a) applies. Otherwise,an autotransformer can be used, resulting in efficiency gain.

The autotransformer shown in Fig. 4(a) corresponds to takingonly the primary winding (220 V) of the transformer of Fig. 3(a).The secondary winding (110 V) is not necessary and is an ad-vantage, since this autotransformer requires less material thanthe one of Fig. 3. The voltage applied to the load comes froma tap positioned at the middle of the primary winding. Obvi-ously, the autotransformer’s nominal apparent power is equal to

.The autotransformer of Fig. 4(a) can be seen as shown in

Fig. 4(b), that is, two identical windings connected in an additiveway. The apparent power in the windings are

and

Since and , one obtains

The apparent power in the windings will determine theirdesign characteristics. Savings in material (conductors andcore) will result in less expensive equipment. Besides, anautotransformer used as shown in situation 2 is smaller, lighter,and cheaper than a transformer of the same rating [1].

C. Evaluation of the Proposed Approach

In conclusion of the previous discussion, a better way tojustify the utilization of an autotransformer, as opposed to atransformer, is that, for a certain load and a certain voltagesource, the autotransformer is smaller, lighter, more efficient,and less expensive than a transformer of the same rating. Thisjustification is the main contribution of this paper, since mosttextbooks show numerical examples in which a transformer isturned into an autotransformer and either the voltage source orthe load have its nominal voltages changed, an unreal situationfrom a practical standpoint. The student needs a clear view ofthe advantages of using the autotransformer for a given practical

CASTRO AND MURARI: A LECTURE ON AUTOTRANSFORMERS FOR POWER ENGINEERING STUDENTS 375

condition. The approach proposed in this paper is somewhatsimilar to the one in [7]. However, this paper differs from[7] in that it provides a more detailed student-driven analysisof the problem, including laboratory experiments oriented tovalidate the discussions. In addition, an important applicationof autotransformers in the power system area is described.

III. L ABORATORY EXPERIMENTS

In this section, a number of laboratory experiments are pro-posed in order to validate most of the discussions carried out inthis paper. These experiments include the calculation of equiv-alent circuits and performance assessment of transformers andautotransformers.

A. Equipment

The equipment used in the experiments was

• a variable voltage source (variac) to provide a fixed 220-Voutput voltage;

• a variable 110-V resistive load;• a 1-kVA transformer with four 110-V coils in each side,

as shown in Fig. 5, which can be conveniently connecteddepending on the primary and secondary voltages;

• voltmeters, ammeters, and wattmeters.

B. Connections

Four different transformer connections were used to feed the110-V load from the 220-V voltage source. Fig. 6 shows theseconnections, calledmodelshereafter.

Model 1 corresponds to the conventional transformer. Model2 is the subtractive autotransformer. Models 3 and 4 correspondto additive transformers. In model 3, only one leg of the trans-former’s core, along with its respective coils, are used. In model4, both legs and all coils are used.

C. Equivalent Circuits

The equivalent circuit of both the transformer and the auto-transformer is shown in Fig. 7 [4]. Shunt parametersand

represent, respectively, the core losses and magnetizationand are determined by the open-circuit test. Series parameters

and represent, respectively, the copper losses and fluxleakage and are determined by the short-circuit test. Both open-circuit and short-circuit tests were performed for all modelsshown in Fig. 6.

Fig. 8 shows the shunt parameters obtained for the fourmodels. The parameters are basically the same for all models.Smaller shunt parameters and, therefore, smaller excitationcurrents can be obtained in case an autotransformer is designedspecifically for this application, since a smaller core can beused.

Fig. 9 shows the series parameters obtained for the fourmodels. In this case, large variations can be observed bothin resistance and reactance. The additive autotransformers(models 3 and 4) have smaller parameters. In particular, theleakage reactance of model 3 is very small, since the windingsare on the same leg of the core and low flux leakage occurs.Additional protection measures must be taken in the case of

Fig. 5. Transformer used in the experiments.

Fig. 6. (a) Transformer. (b) Subtractive autotransformer. (c) Additiveautotransformer using one leg of the core. (d) Additive autotransformer usingtwo legs of the core.

Fig. 7. Equivalent circuit of a transformer.

autotransformers, since their low series parameters result inhigher currents during short-circuit situations.

D. Performance Evaluation

A performance evaluation for the models analyzed their ef-ficiencies and voltage regulation, as shown in Figs. 10 and 11,respectively.

The figures show that the additive autotransformers are moreefficient and provide better voltage regulation than the trans-former and the subtractive autotransformer, as expected.

E. Validation of the Equivalent Circuits

The equivalent circuit parameters were validated by usingthem to compute the load voltage as a function of the load cur-rent. Fig. 12 shows the comparison between computed and mea-

376 IEEE TRANSACTIONS ON EDUCATION, VOL. 46, NO. 3, AUGUST 2003

Fig. 8. Shunt parameters for the four models.

Fig. 9. Series parameters for the four models.

sured curves for models 1 and 3. The computed values closelyfollow the measured values for both models.

IV. V OLTAGE REGULATORS—AN IMPORTANT APPLICATION OF

AUTOTRANSFORMERSVOLTAGE REGULATORS

One of the most important applications of autotransformersis as voltage regulators. This equipment is used to control thevoltage magnitude at predetermined points of an electrical

system as special load buses or substation buses. A voltageregulator is an autotransformer with a transformer ratio close toone. Several tap positions in the winding allow the transformerratio to vary around one, for instance,10% in steps of 1%.The main characteristic of the voltage regulator is that itscopper losses increase as the transformer ratio moves awayfrom unity. Consider the voltage regulator shown in Fig. 13.

This voltage regulator has three tap positions (0,1, and 1).Position 0 corresponds to the nominal position, for which thetransformer ratio is equal to one. The regulator shown in Fig. 13

CASTRO AND MURARI: A LECTURE ON AUTOTRANSFORMERS FOR POWER ENGINEERING STUDENTS 377

Fig. 10. Efficiency versus load current curves.

Fig. 11. Load voltage versus load current curves.

is set as a step-down voltage regulator, since the tap position issuch that . The transformer ratio is

Considering that the winding has a resistance equal to, thecopper losses are given by

(1)

and are, respectively, the magnitudes of the currentsthrough the upper and lower parts of the winding. The first

term of the right-hand side of (1) corresponds to the losses atthe upper part of the winding. Similarly, the second term corre-sponds to the losses at the lower part. Considering thatand , after some manipulation, one obtains

(2)

According to (2), there are no copper losses when the tap isat the nominal position . In this case, the excitationcurrent flows through the winding, and copper losses do exist.However, for most practical high-voltage/high-power voltageregulators, the excitation current is usually neglected, since it

378 IEEE TRANSACTIONS ON EDUCATION, VOL. 46, NO. 3, AUGUST 2003

Fig. 12. Validation of the equivalent circuits.

Fig. 13. Voltage regulator.

is much smaller than the load current. As long as the tap po-sition is drifted away from the nominal position, the copperlosses increase. The same conclusion holds for step-up voltageregulators.

V. CONCLUSION

A new approach to teaching the principles of autotrans-formers and their main applications in power engineering waspresented in this paper. The approach will provide the studentswith more comprehensive information about the equipment. Inaddition, a strong connection between the theoretical aspectsand the engineer’s every day practice is emphasized. A number

of laboratory experiments were proposed as a complement tothe theoretical information.

REFERENCES

[1] A. R. Bergen and V. Vittal, Power Systems Analysis, 2nded. Englewood Cliffs, NJ: Prentice-Hall, 2000.

[2] J. J. Grainger and W. D. Stevenson,Power System Analysis. New York:McGraw-Hill, 1994.

[3] J. D. Glover and M. Sarma,Power System Analysis and De-sign. Boston, MA: PWS-Kent, 1989.

[4] A. E. Fitzgerald, C. Kingsley, and S. D. Umans,Electric Machinery, 5thed. New York: McGraw-Hill, 1990.

[5] D. Zorbas,Electric Machines. St. Paul, MN: West, 1989.[6] P. C. Sen,Principles of Electric Machines and Power Electronics, 2nd

ed. New York: Wiley, 1997.[7] Westinghouse Electric Co.,Electrical Transmission and Distribution

Reference Book, 4th ed. East Pittsburgh, PA: Westinghouse ElectricCo., 1964.

Carlos A. Castro (S’90–M’94–SM’00) received the B.S. and M.S. degreesfrom UNICAMP, São Paulo, Brazil, in 1982 and 1985, respectively, and thePh.D. degree from Arizona State University, Tempe, in 1993.

He has been with UNICAMP since 1983, where he is currently an AssociateProfessor.

Carlos A. F. Murari (M’90) received the B.S., M.S., and Ph.D. degrees fromUNICAMP, São Paulo, Brazil, in 1975, 1980, and 1986, respectively.

He has been with UNICAMP since 1976, where he is currently an AssociateProfessor.