Electric Circuits Laboratory Experiment 4: Delta-Wye Transformation This experiment will allow the student to explore the following: β Delta-Wye (Pi-Tee) and Wye-Delta (Tee-Pi) Transformations Using Multisim Live Theory/Concepts: Delta-Wye (Pi-Tee) and Wye-Delta (Tee-Pi) Transformations The circuit configurations of wye and delta are shown in Figure 4. The names are derived from the shapes of the networks, as the wye appears similar to an inverted “Y” (or Tee), while the delta network is similar to the Greek letter “DELTA” or “β” (or Pi). The subscript notation used in this experiment is arrived at using R13 to indicate between terminals 1 and 3, while R20 is connected between terminals 2 and 0. Figure 4 The delta and wye are equivalent networks in that one can always be arrived at which exactly replace the other. For particular delta-wye pair to be equivalent, each must have the same resistance between any corresponding terminals. Let us consider the circuit of Figure 1 and call the total resistance between the terminals of 1 and 2 as Ra, and similarly, the total resistance from 1 to 3 can be called Rb, while the total resistance from 2 to 3 is called Rc. Then from the wye-circuit we see that, π π = π 10 + π 20 π π = π 10 + π 30 Experiment 4: Delta-Wye Transformation 1 Electric Circuits Laboratory π π = π 20 + π 30 In the case of the delta, π π′ = π 12 (π 13 + π 23 ) π 12 + π 23 + π 13 π π′ = π 13 (π 12 + π 23 ) π 12 + π 23 + π 13 π π′ = π 23 (π 12 + π 13 ) π 12 + π 23 + π 13 However, if the delta and wye circuits are exactly equivalent, then: π π = π π′ π π = π π′ π π = π π′ Or: π 10 + π 20 = π 12 (π 13 + π 23 ) π 12 + π 23 + π 13 π 10 + π 30 = π 13 (π 12 + π 23 ) π 12 + π 23 + π 13 π 20 + π 30 = π 23 (π 12 + π 13 ) π 12 + π 23 + π 13 Now if we subtract Equation 3 from Equation 2, the result will be: π 10 − π 20 = π 12 π 13 − π 12 π 23 π 12 + π 23 + π 13 Then if we add Equation 4 to Equation 2, we will have: π 10 = π 12 π 13 π 12 + π 23 + π 13 π 20 = π 12 π 23 π 12 + π 23 + π 13 Similarly, Experiment 4: Delta-Wye Transformation 2 Electric Circuits Laboratory π 30 = π 13 π 23 π 12 + π 23 + π 13 Equations 5, 6 and 7 allow us to compute the wye network which is equivalent to a given delta network. In much the same manner, Equations 1, 2 and 3 can be solved for R12, R23 and R13 in terms of R10, R20 and R30. π 12 = π 10 π 20 + π 10 π 30 + π 20 π 30 π 30 π 23 = π 10 π 20 + π 10 π 30 + π 20 π 30 π 10 π 13 = π 10 π 20 + π 10 π 30 + π 20 π 30 π 20 Equations of 8, 9 and 10 allow us to compute the delta which is equivalent to a given wye network. Objectives: At the end of the session, the students will be able to: 1. To become familiar with the three-terminal networks and the Delta-Wye transformation techniques. Materials and Equipment: • • • Personal computer with Windows 7 or 10 Multisim Live MS Excel and Word General Instructions: 1. Follow the general instructions and detailed procedures. 2. Your preliminary report should use Microsoft Word. The report should contain answers to questions, data asked in the procedures and screen captures of relevant visualization output. 3. The preliminary report should be submitted/uploaded on or before the designated deadlines. Refer to class policies on late submissions. Experiment 4: Delta-Wye Transformation 3 Electric Circuits Laboratory Detailed Procedures: ο© In this activity, you will substitute the original Delta (Pi) configuration for the Wye (Tee) configuration. This substitution will verify that the Delta-Wye (Pi-Tee) is valid. 1. Connect the circuit as shown in Figure 10. The network inside the broken line represents the Pi (or Delta) connection. Figure 10 2. Measure the currents I1 and I2 as shown in Figure 10 using a current probe and record the values in Table 3. 3. Measure the voltage drop using a voltage probe across the following terminals and record them in Table 3. a. 1 and 2 as E12 b. 1 and 3 as E13 c. 2 and 3 as E23 4. 5. Referring to the circuit shown in Figure 11, compute the values of Ra, Rb, and Rc which will make in Figure 11 the Wye (or Tee) equivalent of the Pi (or Delta) shown in Figure 10. Round-off the values of all resistors to the nearest whole number. Using the computed values in step 4, build and simulate the circuit in Figure 11. Experiment 4: Delta-Wye Transformation 4 Electric Circuits Laboratory Figure 11 6. Measure and record the currents I1 and I2 in Table 3. 7. Measure the voltage drop across the following terminals and record them in Table 3. a. 1 and 2 as E12 b. 1 and 3 as E13 c. 2 and 3 as E23 8. Compute the percent difference between each measured value obtained with the delta network and the corresponding value obtained with the wye. ο© %π πππ = |π«ππππ π½ππππ−πΎππ π½ππππ| ( π«ππππ π½ππππ+πΎππ π½ππππ ) π × πππ%% Table 3 I1 I2 E12 E13 E23 Values from Delta (or Pi) Connection (Fig. 10) Values from Wye (or Tee) Connection (Fig. 11) % Difference Additional Guide Questions / Exercises: Using Figure 12, simplify the network using Delta-Wye transformation and calculate the total resistance (RXY) and current (Is) of the circuit. Verify your theoretical calculations by simulating the circuit in Multisim Live. Show the details of your network transformation and measure the individual voltage drops across each resistor and the total current of the circuit. Experiment 4: Delta-Wye Transformation 5 Electric Circuits Laboratory Note: Vs = 10 V, R1 = 8.2 kο, R2 = 2.2 kο, R3 = 6.2 kο, R4 = 1 kο, and R5 = 5.6 kο Figure 12 References: 1. “Δ-Y and Y-Δ Conversions”. Accessed November 4, 2020. https://www.allaboutcircuits.com/textbook/direct-current/chpt-10/delta-y-and-yconversions/ Experiment 4: Delta-Wye Transformation 6 Electric Circuits Laboratory Experiment 4: Delta-Wye Transformation Issue Report / Suggestions for Improvement For Term: 1 SY: 2020-2021 Issue(s): Suggestions for Improvement: Reported by: ____________________ Experiment 4: Delta-Wye Transformation Date: ________________ 7 Electric Circuits Laboratory Document Revision Tracking Information Document Title: Experiment x: Title Created: date by name Filename: Acknowledgements: β Item 1 β Item 2 Modified: date by name Filename: Changes: β Item1 β Item2 Experiment 4: Delta-Wye Transformation 8
