Single-Phase Transformers

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Brice Perkins
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1 Single-Phase Transformers Single-Phase Transformers Introdution Figure shows the transformer hemati symbol and the orresponding ommonly used Steinmetz model is shown in Figure. Therein, the model voltage and urrent phasors are defined as: V ˆ Î Vˆ ' Iˆ ' Î φ Primary side voltage (V) Primary side urrent (A) Referred seondary side voltage (V) Referred seondary side urrent (A) Magnetizing urrent (A) The model parameters are: Primary oil resistane (Ω) X l Primary oil leakage reatane (H) R Core loss resistane (Ω) X m Core magnetizing reatane (Ω) R ' Referred seondary oil resistane (Ω) X ' l Referred seondary oil leakage reatane (H) N N Transformer turns ratio R

2 Single-Phase Transformers Note that this Steinmetz model utilizes the seondary quantities referred to the primary whih are related to the physial quantities by N = () ˆ ' Vˆ N V Iˆ N ˆ ' = I () N R N = (3) ' R N X N l ' X l N = (4) Furthermore, this Steinmetz model has be augmented with a ore loss term R in parallel with X that approximately aounts for the hysteresis and eddy urrent losses in the ore. m Measuring Winding Resistane The resistane parameters R and R an be found by applying a d voltage to the respetive windings. For example, if a d voltage is applied to the primary winding, the indutors beome short iruits and the Steinmetz model predits the equivalent iruit shown in Figure 3. The primary resistane an then be determined by V R = DC (5) I DC The same predure an be used to find the seondary resistane R. Note that the turns ratio is needed to refer this resistane to the primary aording to (3). The turns ratio is usually given by the transformer manufaturer as the ratio of the rated primary voltage to the rated seondary voltage.

3 Single-Phase Transformers 3 Measuring Leakage Reatanes If the seondary of the transformer is short-iruited, the magnetizing urrent Î φ is negligible and the equivalent iruit an be approximated as shown in Figure 4. In this ase, the magnetizing impedane is assumed to be muh larger than the seondary resistane and seondary leakage reatane. This is typially a good assumption for pratial transformer designs. From the voltage, urrent, and power measurements, the magnitude and angle of the short-iruit impedane an be determined as VA = Vˆ Iˆ (6) Z Vˆ = (7) Iˆ Z P = os (8) VA From the imaginary part of this impedane, the sum of the primary and seondary leakage reatanes an be found. In partiular, X l X l ' = { Z } + Im (9) The individual leakage reatanes an be determined if it is assumed that X = l X l ' (0) Although it is possible to perform other tests on the transformer to determine a more exat relationship between X l and X l ', (0) is a good approximation.

4 Single-Phase Transformers 4 Measuring Magnetizing Reatane and Core Losses The next test involves open-iruiting the seondary winding and applying rated voltage to the primary winding. Under this ondition, the Steinmetz equivalent iruit (inluding the ore loss term) redues to that shown in Figure 5. From measured voltage, urrent, and power, the openiruit impedane an be found using VA = Vˆ Iˆ () Z Vˆ = () Iˆ Z P = os (3) S Using the measured open-iruit impedane as well as R and X l values from the previous tests, the ore admittane an be determined by Y = Z (4) ( R + jx ) l From this admittane, the magnetizing reatane and ore loss resistane an be found from X m = (5) Im { Y } R = (6) Re { Y }

5 Single-Phase Transformers 5 Laboratory Software Figure 6 shows a reen-shot of the program used for the single-phase transformer experiments. This program monitors the first two hannels of the meter box and displays their waveforms and measurements. Data an be logged by seleting the type of test and liking Add. The type of test an be seleted from the drop-down Test menu. When the DC Test is seleted (as shown in Figure 6), hannel will read d values. Due to analog offsets, the d voltage may have a small value before the measurement is taken (when the d voltage and urrent are zero). In this ase, the Zero DC Offset button an be liked to zero the meters. When a tests, suh as Short- Ciruit and Open-Ciruit, are seleted, the meter on hannel reads rms values.

6 Single-Phase Transformers 6 Laboratory Transformers Figure 7 shows the laboratory transformer and a orresponding eletrial onnetion diagram. The transformer has multiple primary and seondary windings whih may be onneted in series or parallel for different voltage ratings. Internally, the primary windings have been onneted in series and the seondary has been onneted in parallel yielding the ratings show in the table below. Laboratory transformer ratings. V ˆ = 40 V V ˆ = 0 V I ˆ = 4.7 A I ˆ = 8.33 A N From the voltage ratings, it an be seen that the turns ratio is =. The onnetion diagram N also shows the primary taps whih are aessible through the onnetors. As an be seen, primary taps at 0-V and 08-V are available using terminals H-H3 and H4 respetively. In low-power single-phase residential appliations, 0-V is a ommon voltage level. This is typially obtained by splitting a 40-V winding. Alternatively, 0-V an be obtained from the line-to-neutral voltage of a 08-V three-phase system. For these reasons, 0- V and 08-V tap settings are ommonly available on many 40-V transformers.

7 Single-Phase Transformers 7 Laboratory Work DC Resistane Test Connet the transformer as shown in Figure 8 using two-ondutor blak (B) and white (W) able. For this test, resistane from the load box will be plaed in series with the soure to limit the urrent. Note that all three phases of the load box are onneted in parallel using the additional jumper wires on the load box onnetor. The load box should be set to use two of the resistors in eah phase as shown in Figure 9. Turn on the load box fans. For this test, lik the "DC Test" tab in the software display. This test must be seleted for the meter to read urrent from a d soure! Swith on the soure panel iruit breaker and inrease the voltage until the d urrent is 4.7-A. Add the data to the log (you an also type "Primary" next to DC Test). Derease the voltage and swith off the iruit breaker. Move the transformer onnetions from the H and H5 terminals to the X-X3 and X-X4 terminals. Repeat the d resistane test for the seondary side. For this test, the voltage should be inreased until the d urrent is 8.33-A.

8 Single-Phase Transformers 8

9 Single-Phase Transformers 9 Short-Ciruit Test Using two phases of the AC soure panel and a resistane from the load panel, onnet the transformer as shown in Figure 0. Note that this is similar to the d resistane test, exept for the soure onnetions and the short-iruit wire on the transformer seondary side. The load box settings are also the same as before. Selet "Short-Ciruit" from the Test type in the software. Inrease the voltage applied to the primary until the rms primary urrent reahes 4.7- A. Log the voltage and urrent values by liking Add. Redue the voltage to zero and swith off the soure iruit breaker.

10 Single-Phase Transformers 0 Open-Ciruit Test The lab set-up for the open-iruit test is similar to that of the short-iruit test. To set-up for the open-iruit test, remove the short-iruit wire on the transformer seondary. Swith on the soure iruit breaker and inrease the voltage to 00%. This is near rated voltage for the transformer. Log the data values and note the primary urrent waveform. This is the transformer exiting urrent and has a non-linear shape due to transformer saturation. Print the waveform from the reen. Redue the voltage and swith off the soure iruit breaker. Transformer Load Test Connet the transformer to the three-phase soure and load as shown in Figure. For the first test, the load box settings from before (Figure 9) an be used. Swith on the soure iruit breaker and inrease the voltage to 00%. Log the primary and seondary data. Redue the voltage to zero and swith off the soure iruit breaker. Repeat the load test for the R-L and R-C load ases using the load box settings shown in Figures and 3 respetively. Clik Save to save the voltage, urrent, and power measurements from the transformer tests.

11 Single-Phase Transformers

12 Single-Phase Transformers

13 Single-Phase Transformers 3 Calulations. From the d resistane test, short-iruit test, and open-iruit test, alulate the Steinmetz model parameters R, X l, R ', X l ', R, and X m.. Using the transformer turns ratio, alulate the values of the referred load impedanes for eah of the three load tests (R, R-L, and R-C). The individual values of R, L, and C an be obtained from the Single- and Three-Phase Power Measurements experiment. Note the series and parallel ombinations used in this experiment to determine the atual values. 3. Using the transformer model and referred loads, ompute the voltages and urrents that orrespond to eah of the three load tests. Use the primary voltage from the load tests and ompute the primary urrent and power as well as the seondary voltage, urrent, and power. Compare these values to the measured values in a table along with perent errors.

VOLTAGE CONTROL WITH SHUNT CAPACITANCE ON RADIAL DISTRIBUTION LINE WITH HIGH R/X FACTOR. A Thesis by. Hong-Tuan Nguyen Vu

VOLTAGE CONTROL WITH SHUNT CAPACITANCE ON RADIAL DISTRIBUTION LINE WITH HIGH R/X FACTOR A Thesis by Hong-Tuan Nguyen Vu Eletrial Engineer, Polytehni University of HCMC, 1993 Submitted to the College of