# THREE PHASE CIRCUITS

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1 THREE PHASE CIRCUITS A. PREPARATION 1. Three Phase Voltages and Systems 2. The Determination of Phase Sequence 3. Blondel's Theorem and Its Consequences 4. References B. EXPERIMENT 1. Equipment List 2. Three Phase Power Supply 3. Balanced Three Phase Resistive Loads 4. Unbalanced Three Phase Resistive Loads 5. The Three Phase Transformer C. REPORT 1. Three Phase Power Supply 2. Balanced Three Phase Loads 3. Unbalanced Three Phase Loads 4. The Three Phase Transformer Three Phase Circuits - 1

2 1. Three Phase Voltages and Systems Three Phase Circuits - 2

3 Three Phase Circuits - 3

4 Three Phase Circuits - 4

5 Three Phase Circuits - 5

6 2. The Determination of Phase Sequence Three Phase Circuits - 6

7 Three Phase Circuits - 7

8 3 Blondel s Theorem and Its Consequences Three Phase Circuits - 8

9 Three Phase Circuits - 9

10 4 Chapman, Stephen J., Electric Machinery and Power System Fundamentals. McGraw Hill Three Phase Circuits - 10

11 B. EXPERIMENT - THREE PHASE CIRCUITS 1. Equipment List a. The standard instrument rack found at each station. b. Various current shunts and probes. c. One single-phase wattmeter. d. One three-phase transformer. e. One Phase Sequence Indicator (PSI). f. One rheostat module with two 50-Ω rheostats rated at 4.5 Amp each. g. Various power cords. 2. Three Phase Power Supply a. A schematic of the Phase Sequence Indicator (PSI) is provided on the next page. Plug this device into the Three Phase (3φ) wall power source using the 3-Phase Cord Set and determine the phase sequence (ABC or CBA) using the PSI. Be sure the switch is in the NORMAL position. Also, observe the Phase A and Phase B waveforms on the oscilloscope using two 10X Probes or the A/100 and B/100 test points with coaxial cables. Determine their phase relationship and the phase angle between them using the scope. Copy this display. Now repeat the above step for Phase A and Phase C and record the display. Next reverse the phase sequence by flipping the switch to REVERSE and observe the lamp pattern. Be sure and return the switch to the NORMAL position for the rest of the experiment. Finally, observe the voltage waveform for the Star Point (STAR) on the Phase Sequence Indicator on the scope and copy this display. b. Being fully aware of the potential for an electric shock, and therefore careful to shut off the 3-phase breaker each time the DMM connections are moved, accurately measure the rms values for the three line-to-line voltages and the three line-to-neutral voltages at your station using three DMMs. c. The "green" neutral wire on the 3-phase supply provides a return to ground. It is well and thoroughly grounded and will remain at Mother Earth potential as long as there is no IR voltage drop, i.e, as long as the neutral return current is zero. This is the case for perfectly balanced three phase voltage sources and perfectly Three Phase Circuits - 11

12 Input Phase CBA Input Phase ABC C Reverse A B A C Normal B Three Phase Circuits - 12

14 4. Unbalanced Three Phase Resistive Loads a. Now disconnect the Phase A and Phase B leads from the left rheostat. Connect a DMM to the left side of the left rheostat and adjust this rheostat until a resistance of 15 Ω is obtained. Measure and record both of the left rheostat resistances. Now reconnect the circuit as it was in Part B.3.c. above and show it to the instructor. When approved by the instructor, turn on 3φ power and record all DMM and wattmeter measurements. Turn off 3φ power when finished. b. Obtain a second Wattmeter and reconfigure the instrumentation to measure load power using the 2 wattmeter method. Configure the DMMs to measure the three load voltages relative to the rheostat Common Point (O). Show this set-up to the instructor. When approved, turn on 3φ power and record the measured powers and load voltages. Be sure that both Wattmeters read upscale. Turn off 3φ power when finished. c. Remove both Wattmeters from the circuit and reconnect the Neutral Return wire between the rheostat Common Point and the Neutral Point of the PSI. Reconfigure the DMMs to measure Phase A line current, Phase A load voltage, and Neutral Return line current. Turn on 3φ power and record all DMM measurements. Turn off 3φ power when finished. 5. The Three Phase Transformer Because this portion involves exposed power points, it is electrically the most dangerous procedure of the course. You will therefore power up only under the direct and continuous supervision of one of the faculty. NO EXCEPTIONS!! a. Using DMM voltage measurements, determine how to use the three individual transformers in the step-down direction and calculate the three step-down ratios. Parts b and c below operate in the step-down direction. b. Connect the high voltage primaries of the transformers to form a wye. The secondaries of the transformers are to be connected as a delta, but before closing the delta, you must determine that phasing is correct by measuring the voltage across the open delta to see that it is approximately zero. With Three Phase Circuits - 14

15 power off, close the delta through a rheostat set to 50 Ω. Turn the power back on and measure the voltage across the rheostat. If it still measures approximately zero, adjust the rheostat to minimum resistance and measure the 3 secondary line-to-line delta voltages. c. With the power off and the primaries still wye connected, open the delta and reverse the connections for one of the secondaries, but leave the delta open. Now turn power back on and measure and record the voltage across the open terminals in the delta. Note that it is large. With the power off, close the delta through a rheostat set to 50 Ω. Now measure the ring current in the 50 Ω rheostat by measuring the voltage across it. C. REPORT - THREE PHASE CIRCUITS 1. Three Phase Power Supply a. What is the phase sequence provided by the 3-phase wall supply in the laboratory. Assuming that the phase A voltage is the reference (0 phase shift), what are the measured phase angles for the phase B and C voltages? Did the Phase Sequence Indicator provide the same information that you deduced from oscilloscope observation? Also, discuss and explain the STAR point waveform you observed and recorded in part B.2.a. b. Make a table showing the three line-to-line voltages, their average, and their deviation from the average value. Make a second table showing the three lineto-neutral (phase) voltages, their average, and their deviation from average value. What is the ratio these two averages? Is it in agreement with theory? Considering the voltage deviations from average shown in the tables, do you think the laboratory supply is adequate for 3 phase circuit experiments? c. Comment on the Neutral Point (N) voltage you observed on scope. Does the Neutral Point appear to be well grounded to Mother Earth? 2. Balanced Three Phase Resistive Loads a. Based on data from part B.3.a, calculate the average value of load resistance and make a table showing the load resistances and their deviation from the average value. Did you present a nearly balanced load to the 3φ power supply? Three Phase Circuits - 15

16 The measured values of the load resistors inherently include the resistances of the banana plug cords if the measurements were made using the DMM as an ohmmeter. Comment on any effect these added resistances may have on the experiments of parts B.3.b and B.3.c. b. Make a table comparing expected and measured values of I A, V AO, P AO, and I ON for the results of part B.3.b. In calculating the expected values of I A, P AO, and I ON, use the 3 resistances measured in part B.3.a and the 3 phase voltages measured in part B.2.b and assume that the phase shift between the voltages is exactly 120 in the proper sequence (CBA or ABC). Comment on the deviations observed. Why is the assumption that total power (P T ) is equal to 3 P AO (P T = 3 P AO ) a reasonable assumption for a balance load with a neutral return line? c. Make a table comparing expected and measured values of I A, V AO, P AO, and V ON for the results of part B.3.c. In calculating the expected values of I A, P AO, and V ON, use the 3 resistances measured in part B.3.a and 3 phase voltages measured in part B.2.b and assume that the phase shift between the phase voltages is exactly 120 in the proper sequence (CBA). Comment on the deviations observed. Why is the assumption that P T = 3 P AO a reasonable assumption for a balance load with no neutral return line? d. Make a table comparing measured values of I A, V AO, and P AO made in part B.3.b and B.3.c. How should these values compare considering that the neutral return line was not used in part B.3.c? 3. Unbalanced Three Phase Resistive Loads a. Based on data from part B.4.a, calculate the average value of load resistance and make a table showing the load resistances and their deviation from the average value. Did you present an unbalanced load to the 3φ power supply? b. Make a table comparing expected and measured values of I A, V AO, P AO, and V ON for the results of part B.4.b. In calculating the expected values of I A, V AO, P AO, and V ON, use the 3 resistances measured in part B.4.a and the 3 phase voltages measured in part B.2.b and assume that the phase shift between the phase voltages is exactly 120 in the proper sequence (CBA or ABC). Comment on the Three Phase Circuits - 16

17 deviations observed. Now calculate the expected values of V BO and V CO and the corresponding expected values of P BO, and P CO. Obtain the total power P T as the sum of these powers. Compare this total power to the sum of the powers measured using 2 Wattmeters. Why is the assumption that P T = 3 P AO not reasonable for an unbalanced load with no neutral return line? For this circuit, it is clear that 3 Wattmeters could have been used to measure total power. Explain why total power can be measured using only 2 Wattmeters. c. Make a table comparing expected (calculated) and measured values of I A, V AO, P AO, and I ON for the results of part B.4.b. In calculating the expected values of I A, V AO, P AO, and I ON, use the resistances measured in part B.4.a and the phase voltages measured in part B.2.b and assume that the phase shift between the phase voltages is exactly 120 in the proper sequence (CBA or ABC). Comment on the deviations between measured and calculated values shown in the table. Calculate P AO, P BO, and P CO and obtain the total power P T as the sum of these powers. Why is the assumption that P T = 3 P AO not reasonable for an unbalanced load with a neutral return line? Obviously, 3 Wattmeters could be used to measure total power. Explain why total power cannot be measured using only 2 Wattmeters. d. Make a table comparing measured values of I A and V AO made in parts B.4.b and B.4.c. Also include the calculated values of P AO in this table. Include in the table the calculated values of P T for the unbalanced load with and without the Neutral Return line. Comment on the results shown in the table. 4. Three Phase Transformer a. In part B.5.a, what is the step-down ratio for each transformer? b In part B.5.b, what are the secondary line-to-line voltages? c In part B.5.c, what are the open delta voltage and ring current with one secondary phase wired backwards? Explain the last result with the aid of phasor algebra and a phasor diagram. Three Phase Circuits - 17

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