499 IEEE Transactions on Power Systems, Vol. 5, No. 2, May 1990

TRANSFORMER DESIGN IN THE UNDERGRADUATE POWER ENGINEERING LABORATORY

Ward T. Jewell Member, IEEE

Department of Electrical Engineering The Wichita State University

Wichita, Kansas

ABSTRACT

A power engineering laboratory experiment on transformer design is described in this paper. The experiment allows the student to proceed through the entire design process, including design and construction, and then modeling and analysis.

KEYWORDS: Power Engineering Education, Electric Power Transformers, Design, Modeling, Laboratory Prac- tice

INTRODUCTION

A complete design experience, in which the student designs, constructs, and tests a device, is difficult to provide in power system engineering classes. Two recent papers sponsored by the PES Power Engineering Education Committee describe experiments for undergraduate power engineering students in which the student designs a power system [l] and a distribution system [2] with the aid of computer software. While these are excellent experiments that this author intends to use in his classes, the student must rely on analysis and simulation to determine the performance of the design. The student must forego the "hands-on" experience of building the device, where much learning takes place.

Another paper [3] describes a detailed transformer analysis procedure suitable for classroom use, but again the students cannot actually build and test the transformers. A testing experiment is described in a fourth paper [4], in

89 SM 651-1 PWRS A paper recommended and approved by the IEEE Power Engineering Education Committee o f the IEEE Power Engineering Soc ie ty f o r presentation at the IEEE/PES 1989 Summer Meeting, Long Beach, California, July 9 - 14, 1989. Manuscript submitted February 1 , 1989; made ava i lab le for pr in t ing June 13, 1989.

which students do detailed harmonic testing on transformers, but no design is involved. Experiments on computer control of a dc generator and motor [5], and computer simulation of a power system [6], are described in other recent papers.

The design experiment described in this paper allows the student a complete design experience in a power engineering class. This experiment is part of an electric machinery class, a standard junior or senior level class offered in most electrical engineering programs. The experiment is scheduled early in the course, enhancing the students' interest in the course, and in power engineering. It is now the only design experiment in the course, although another experiment on the design and construction of a simple dc motor is being considered.

In the experiment the student designs, builds, and tests a single-phase transformer to specifications provided by the instructor. From initial test results, the transformer is redesigned, and the new design is tested. Standard open- and short-circuit tests are then performed to develop a circuit model for the transformer. The model is then used to predict the transformer's operation, and the predictions are compared with measured values from the lab. Although the initial design could be tested by computer simulation, the author believes that the two-stage design, construction, and redesign process is valuable to the student, and is realistic in that most new designs are first built as prototypes, then tested and redesigned.

The objectives of the experiment include learning:

1. Design process 2. Laboratory procedures 3. Modeling 4. Design and development as part of a team 5. Transformer operation

DESCRIPTION OFTHE EXF'ERIMENT

The experiment is performed over a period of four weeks. The theory needed for the experiment has already been presented in lectures when the experiment begins. Students work in groups of four.

0885-8950/90/0500-0499$01.00 Q 1990 IEEE

500

an Session 1 During the first design session, the transformer

1. Primary voltage rating Vp = 10 V. 2. Apparent power rating 10 VA. 3. Voltage ratio a = Vfl, = 0.8 -+ 10% 4. Full-load voltage regulation = 20% or less, from

nominala = 0.8. 5. High efficiency: should operate just below the

saturation region of the core. 6. The subscript "p" represents "primary" and "stt

means secondary.

specifications are presented

A toroidal iron core is provided to each group, and the magnetization curve (magnetizing intensity " H I vs. magnetic flux density "B") is provided for the core. A sample magnetization curve, supplied by the core manufacturer [q, is shown in Figure 1.

B (Kilogauss)

H (Oersteds)

Figure 1. Core Magnetization Curve.

The following information about the design is provided to the students as wek

From the magnetization curve, determine the minimum number of turns needed on the primary to avoid saturation at light loads. Then calculate the number of turns on the secondary. Determine how much wire you will need from the number of turns and the size of the core. From the wire table (shown here in Table I), determine the correct wire sue. Order the wire from the instructor. Wind the transformer. You may also want to consider different winding methods in your design.

With this information, the students begin the design and construction of the transformer.

The students must also design a test circuit and procedure that will allow them to measure the transformer's voltage ratio, voltage regulation, efficiency, and point of operation on the magnetization curve.

I I Gauge 1 Max. Amps for Temparature 80" C (AWG) for number of wire in a bundle I 1 I 2-5 I 6-15 I 16-30 I

Test Session 1 After one week, the students bring their transformers

and test procedures to the laboratory. There, they connect the circuit to a 10 V source and make the following measurements:

1. Primary and secondary voltage magnitudes, Vp and Vs, with the secondary open-circuited.

2. Vp and I, while varying Vp from 5 V to beyond saturation, with the secondary still open-circuited.

3. Primary and secondary voltages and currents, Yp, I,, L, and E, with a resistive load on the secondary that brings the transformer to full-load operation.

After completing the measurements, each student

1. Open-circuit (no-load) voltage ratio. 2. Full-load voltage regulation. 3. Full-load efficiency and plots. 4. Vp vs. Ip for varying Vp.

calculates:

Bsian Session II From the test results and calculations from the first

testing session, each group determines how close they have come to meeting the specifications. The transformer is then redesigned and rebuilt. The instructor is available to discuss the redesign.

The students must also design another test procedure to perform standard open- circuit and short-circuit tests on the transformer. They must also provide the equations needed to compute values for the circuit model shown in Figure 2.

Figure 2. Transformer Circuit Model.

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Test Session II During the second laboratory session, the no-load and

full-load tests performed in Testing session I are repeated on the new transformer design. The Vp vs. Ip test is also repeated if necessary. The short-circuit and open- circuit tests are then done, and the circuit model element values are calculated.

The circuit model is then used to estimate the full load operating condition of the transformer. These are then compared with those measured in the laboratory.

Final Repod A formal, typed report is required of each student.

Word processing software is available, and the students are encouraged to use it. They are asked to include the following in their reports.

1. Explain how you initially designed your transformer to meet each of the specifications.

2. Present the data recorded and the values calculated from the laboratory session I tests. Explain how and why your transformer did or did not meet the specifications.

3. Explain why and how you redesigned your transformer during the second design session.

4. Present the data recorded and the values calculated from the laboratory session I1 tests. Explain how your transformer did or did not meet the specifications.

5. Draw the transformer circuit model, and show the element values you calculated.

6. Use your circuit model to compute values of ,, L, and E at rated conditions (full load). Compare these with the values you measured.

7. If you could again redesign your transformer, what would you change?

The report is then graded on the following basis, which is provided to the students at the beginning of the experiment.

Technical accuracy 25% (Results should be complete, realistic and consistent.)

(Conclusions should be complete and consistent with results.)

Conclusions 25%

Readability 25% (Grammar and spelling should be correct and

understandable.) Organization 25%

(Report should follow a logical outline.)

EXAMPLE TRANSFORMER DESIGN AND TESTING

Desian Sessianl Faraday's law states that the voltage induced on a coil is

proportional to the number of turns of wire, N, in the coil and the time rate of change of magnetic flux, @ , through the coil:

If a voltage source v(t) is connected to the winding, then the flux is

@ = 'Jv(t)dt. N

For a sinusoidal voltage source, v(t) = d-2 vnns cos( o t ) ,

the flux will be

This can also be written in terms of flux density, B,

where A is the cross sectional area of the core. The maxi- mum flux density will occur when the sine term is 1,

The maximum flux density should be just below the saturation region, and can be read from the B-H curve for the core. Knowing Bmm, then, the minimum number of turns on the coil can be calculated:

The core whose magnetization curve is shown in Figure 1 has thickness 0.022 m and width 0.029 m. The cross-sectional area is then

A = 0.022 m x 0.029 m = 6.38 x lo4 m2 . The peak voltage for a 10 V RMS signal is

Vp = 4-2 x 10 V = 14.14 V. Choosing the operating point just below the knee of the magnetization curve gives

BmU = 10 kGauss = 1 T . Substituting these values into equation (1) results in a min- imum of

Np,min = 58.8 turns, or 59 turns on the primary winding. Most students then simply divide by the specified nominal turns ratio to obtain the number of turns on the secondary:

502

lo

g -

8 -

r -

6 -

5

The first transformer design therefore has 59 turns on the primary and 74 turns on the secondary. The length of the windings are then calculated from the transformer size:

Length of primary winding = 50 x ( 0.022 m + 0.022 m + 0.029 m + 0.029 m) = 6 m

Length of secondary winding = 74 x ( 0.022 m +

The windings are often placed on opposite sides of the toroid, because of the popular conceptual drawing used in many textbooks, shown in Figure 3.

0.022m + 0.029 m + 0.029 m) = 7.5 m .

\ Operating point

Figure 3. Simple Transformer.

Test Session I 1. When a 10 V source is applied to the primary of the

transformer described above with the secondary open-circuited, the secondary voltage is 12.4 V. This gives an open-circuit voltage ratio of

a=-- ;;:;; - 0.806 . 2. With the secondary still open, the voltage is varied

from 5 V to 12 V, and the primary current is measured. The results are shown in Table 11. The magnetization curve, a plot of the data in Table 11, is shown in Figure 4.

TABLE 11. Primary Current vs. Voltage

VP(V> 5.0 6.1 7.1 8.0 9.0

10.0 11.0 12.0

0.054 0.059

0.073 0.210

3. A resistive load is connected to the secondary. The primary voltage is set to 10 V, and the resistive

Primary voltage (V)

:: :

Figure 4. Primary Current versus Primary Voltage.

load is decreased until the transformer is at full load. Full load means that the primary current is

I ,=- - '' '* - 1.0 A , 10 v

or the secondary current is

1 'OVA - 0.8A . - 10/0.8 v The data is presented in Table 111. The phase angle

between primary voltage and current is measured with an oscilloscope. Because the load is resistive, the secondary phase angle is zero.

TABLE 111. Full Load Voltage and Current.

l p ( V ) &(A) & ( V ) & ( A ) 10.2 10' 0.947 1-54' 10.2 LO' 0.709 10'

The full load voltage ratio is

The voltage regulation, computed using the specified nominal turns ratio of 0.8, is

-- 10.2 = 0.25 = 25% . 0.8 10.2 vreg =

The input power to the transformer is Pp = VpIp COS = 9.62 W ,

and the output power is Ps = VsIs = 7.232 W ,

giving efficiency of

PS Efficiency = - = 0.752 = 75.2% . PP

I

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Besian S e s s W The initial transformer design met two of the

specifications: The open circuit turns ratio, which was 0.806, was within the specified range of 0.72 I a 5 0.88. And the curve of Figure 4 shows that the transformer is operating just below the knee of the magnetization curve for highest efficiency.

The transformer did not, however, meet the full load voltage ratio specification, nor did it meet the 20% limit on voltage regulation. At this point the student must realize that, in order to meet the design specifications, the transformer will have to be designed to operate with ahigher than nominal open-circuit voltage. The highest allowable open-circuit voltage is

10 0.72 Vs = - = 13.9 V .

The approximate number of secondary turns to produce this is

59 0.72 Ns = - = 81.9, or 82 turns .

Eight turns are added to the transformer secondary. Many students at this time also rewind the secondary on top of the primary winding to reduce leakage flux. Furthermore, some also realize that eight extra turns may not be the number that will give them exactly 13.9 V on the secondary, so they leave enough extra wire on the secondary to add 2 or 3 more turns during the lab session.

Test Session 2 When a 10 V source is applied to the primary of the redesigned transformer with the secondary open-circuited, the secondary voltage is 13.7 V. This gives an open-circuit voltage ratio of

When the transformer is operated at full load with primary voltage 10 V, the secondary voltage is 11.0. This gives a full load voltage ratio of

a=------- 11.0 v

The voltage regulation, again computed using the specified nominal turns ratio of 0.8, is now

11.0 -- = 0.136 = 13.6% . 0.8 11.0 Vreg =

The input power to the transformer is Pp = VpIp cos @ = 9.86 w ,

Ps = VSIS = 7.39 w , and the output power is

giving an efficiency of

Efficiency = = 0.749 = 74.9% . The voltage regulation is now within the specified range,

but the full load voltage ratio is still too high; it should be in the range of 0.72 I a 5 0.88. The number of primary turns, however, can again be increased because the open-circuit voltage ratio is still greater than 0.72.

Adding one more turn to the primary winding produces the results shown in Table IV. All values are now within the specified range except for full load voltage ratio, which should be 0.88 or less. Adding another turn to thesecondary to reduce this value causes the open-circuit voltage ratio to be less than 0.72.

PP

TABLE IV. Results of Final Transformer Test. Open circuit voltage ratio:

l!P( v ) 41s( v ) a 10.0 13.9 0.72

10.1 LO' 0.975 1-54' 11.3 10" 0.653 LO'

a Vreg PD(W) Ps(W) Efficiency 0.894 11.7% 9.80 7.38 75.3%

Transformer Modeling When the students are satisfied with their transformer

design and test results, they complete the experiment by doing standard open- and short- circuit tests on the transformer. Results of these for the example transformer, with both tests done on the primary side, are shown in Table V.

TABLE V. Short- and Open-circuit Test.

J!oc(V) Ioc(A) J!sc(V) M A ) 10.0 LOo 0.073 1-7.2' 2.09 10' 1.020 10'

Thevalues for the circuit model elements of Figure 2 can now be calculated.

- Y = 0.007 - j9.15 x 10- S Ec = 138ohms XM = 1,090ohms

Re+ jGq= -- 2*09 lo" - 2.05 ohms z = -= VSC LC 1.02/0" -

Be = 2.05 ohms x e s = 0

504

The zero value for Xes means there is negligible flux leakage in the transformer. This was expected because the core material has very high permeability. The Res value is simply the resistance of the winding conductors, a value that was not considered in the design. The relatively low values of R c and XM are explained by a very large hysteresis loop for the core, which produces high core losses, and explains the 75% efficiency.

Now the circuit model can be used to estimate the full load voltages and currents. Beginning with

y p = l0.lLO0 v , and using the open-circuit turns ratio of a = 0.72, and letting the secondary load resistance be 17 ohms, the value that gave full load in the laboratory, the following values are calculated from the circuit model.

5 = 0.961L- 0.5" - Vs = 11.5/0" - Is = 0.639/0" Comparing these with the Table 4 values taken in the

laboratory, the following errors in the circuit model results are calculated.

&,error = 1.8 %

- Vs error = - 2.1 % - Is error = 1.5 %

University in Wichita, Kansas since 1987. He teaches courses in electric machinery and power systems.

REFERENCES

1. R. Betancourt, W.V. Torre, "The Use of a Design Project as an Innovative and Practical Approach to the Teaching of Power Systems," JEEE Transactions on Power w, Vol. PWRS-4, No.1, February 1989, pp. 372-379.

2. W.H. Kersting, "A Method to Teach the Design and Operation of a Distribution System," SEEE T ransactions pn Power A- and Sy&m, Vol. PAS-103, No. 7,

3. M. Poloujadoff, R.D. Findlay, "A Procedure for Illustrating the Effect of Variation of Parameters on Optimal Transformer Design," IEEE Transactions on Power m, Vol. PWRS-1, No.4, November 1986, pp. 202-206.

4. E.B. Makram, R.L. Thompson, A.A. Girgis, "A New Laboratory Experiment for Transformer Modeling in the Presence of Harmonic Distortion using a Computer controlled Harmonic Generator," ZEEE T ransactions on Power m, Vol. PWRS- 3, No.4, November 1988, pp.

5 . A.J. Goetze, "Introducing Computers to the Undergraduate Machinery Laboratory - Computer Control of a DC Generator and Motor," JEEE

July 1984, pp. 1945-1952.

1857-1863.

ns on Power ADpaLatus and Systems , Vol.

6. A. Semlyen, H. Hamadanizadeh, "Computational

These errors show excellent agreement between the PAS-103, NO. 7, July 1984, pp. 1932-1937. circuit model and measured data.

CONCLUSIONS Experiments in Power Systems," IEEE Transxtions on Power A-s and Svstems , Vol. PAS-104, NO. 9, September 1985, pp. 2290-2295.

Magnetics, Components Division, BOX 391, Butler, PA, 16003-0391.

Upon completion of the experiment, the students have 7. Design Manus 1 featurinp Tape Wou nd C,o r e& been through the entire design process, from initial design and construction, through testing, redesign, modeling, and analysis. They have dealt with multiple specifications that can conflict, such as balancing efficiency in the use of materials with electrical efficiency. They have seen a number of trade-offs that can be made in the design process. They have learned specifically about transformer design and modeling. And they have learned some of the advantages and drawbacks of working with a team.

BIOGRAPHY

Ward T. Jewell (M) received a BSEE degree from Oklahoma State University in 1979, an MSEE degree from Michigan State University in 1980, and aPh.D. Degree from Oklahoma State University in 1986. From 1980-84 he was with the Power Systems Technology Program at Oak Ridge National Laboratory. His research interests are in the areas of photovoltnic power and power quality.

Dr. Jewell has been a member of the faculty of the Electrical Engineering Department at the Wichita State

DISCUSSION

ROBERT H. SAUNDERS, (Un ive r s i ty of C a l i f o r n i a , I r v i n e ) : The au tho r appea r s t o have c a r r i e d h i s s t u d e n t s through a s i g n i f i c a n t e x e r c i s e t h a t should g i v e them some i n s i g h t i n t o t h e v i c i s s i t u d e s of t r ans fo rmer f a b r i c a t i o n and test. However, i t does no t appear t o be a des ign expe r i ence i n a classical sense .

Classical des ign r e q u r e s t h a t t h e r e be a series of c o n s t r a i n t equa t ions of t h e form

f (x1 ,x2 ,x3 f . . . . . . . Xm) = y1 f (X1,X2,X3,. . . . . . .Xm) = y2 f(X1,X2,X3, ....... Xm) = ~3 f(XI,X2,X3 ,....... Xm) = yn . . . . . . . . . . . . .

where x . are independent v a r i a b l e s and yk are dependent v a r i a b d s . I f n>m, no s o l u t i o n is p o s s i b l e . I f n