2. Three-Phase Power. 1 Prof. Mack Grady, TAMU
Description: 2. Three-Phase Power. 1 Prof. Mack Grady, TAMU Relay Conference Tutorial, Topic 2, March 31, 2015 Instantaneous power p(t) flowing into the box, Circuit in a box, four-wires For a balanced system, Combining terms, Trig. identity yields 2
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slide1. 2. Three-Phase Power. 1 Prof. Mack Grady, TAMU Relay Conference Tutorial, Topic 2, March 31, 2015 Instantaneous power p(t) flowing into the box, Circuit in a box, four-wires For a balanced system, Combining terms, Trig. identity yields<br>
slide2. 2 Prof. Mack Grady, TAMU Relay Conference Tutorial, Topic 2, March 31, 2015 then expanding yields cancel each other Instantaneous three-phase power is constant – thus, smooth running machines! 2. Three-Phase Power, cont. Letting x = (2ωt+δ+Θ) and expanding the time varying term,<br>
slide3. 3 Prof. Mack Grady, TAMU Relay Conference Tutorial, Topic 2, March 31, 2015 2. Three-Phase Power, cont. Analogous to a piston engine with an infinite number of cylinders Strong 120 Hz torque<br>
slide4. Prof. Mack Grady, TAMU Relay Conference Tutorial, Topic 2, March 31, 2015 4 2. Three-Phase Power, cont.<br>
slide5. Prof. Mack Grady, TAMU Relay Conference Tutorial, Topic 2, March 31, 2015 5 2. Three-Phase Power, cont. Balanced Three-Phase System<br>
slide6. Prof. Mack Grady, TAMU Relay Conference Tutorial, Topic 2, March 31, 2015 6 2. Three-Phase Power, cont. Line currents Ia, Ib, and Ic
Delta currents Iab, Ibc, and Ica Balanced Three-Phase System<br>
slide7. Prof. Mack Grady, TAMU Relay Conference Tutorial, Topic 2, March 31, 2015 7 Balanced three-phase systems, no matter if they are delta connected, wye connected, or a mix of wye and delta, are easier to solve if you follow these steps:
Convert the entire circuit to an equivalent wye with a grounded neutral.
Draw the one-line diagram for phase a, recognizing that phase a has one third of the P and Q.
Solve the one-line diagram for line-to-neutral voltages and line currents.
If needed, compute line-to-neutral voltages and line currents for phases b and c using the ±120° relationships.
If needed, compute line-to-line voltages and delta currents using the and ±30° relationships. 2. Three-Phase Power, cont.<br>
slide8. 8 Single-Phase Residence. 1kVA to the customer requires 4.17A in each of the two legs 7.2kV 30:1 single-phase transformer 4.17A on the 240V side corresponds to 0.14A on the 7.2kV side<br>
slide9. 9 1kVA to the customer corresponds to 1.20A in each of the three phases Most commercial buildings, like ENS, are served by a 12.47kV (line-to-line) to 480V (line-to-line) three-phase transformer, delta-connected on the 12.47kV side, and grounded-wye connected on the 480V side Most lighting in commercial buildings is 277V fluorescent – that’s the voltage behind the switchplate cover. 120V outlets are served by 480:120V step down transformers on each floor of the building, often located in utility closets in two diagonally-opposite corners of each floor.<br>
slide2. 2 Prof. Mack Grady, TAMU Relay Conference Tutorial, Topic 2, March 31, 2015 then expanding yields cancel each other Instantaneous three-phase power is constant – thus, smooth running machines! 2. Three-Phase Power, cont. Letting x = (2ωt+δ+Θ) and expanding the time varying term,<br>
slide3. 3 Prof. Mack Grady, TAMU Relay Conference Tutorial, Topic 2, March 31, 2015 2. Three-Phase Power, cont. Analogous to a piston engine with an infinite number of cylinders Strong 120 Hz torque<br>
slide4. Prof. Mack Grady, TAMU Relay Conference Tutorial, Topic 2, March 31, 2015 4 2. Three-Phase Power, cont.<br>
slide5. Prof. Mack Grady, TAMU Relay Conference Tutorial, Topic 2, March 31, 2015 5 2. Three-Phase Power, cont. Balanced Three-Phase System<br>
slide6. Prof. Mack Grady, TAMU Relay Conference Tutorial, Topic 2, March 31, 2015 6 2. Three-Phase Power, cont. Line currents Ia, Ib, and Ic
Delta currents Iab, Ibc, and Ica Balanced Three-Phase System<br>
slide7. Prof. Mack Grady, TAMU Relay Conference Tutorial, Topic 2, March 31, 2015 7 Balanced three-phase systems, no matter if they are delta connected, wye connected, or a mix of wye and delta, are easier to solve if you follow these steps:
Convert the entire circuit to an equivalent wye with a grounded neutral.
Draw the one-line diagram for phase a, recognizing that phase a has one third of the P and Q.
Solve the one-line diagram for line-to-neutral voltages and line currents.
If needed, compute line-to-neutral voltages and line currents for phases b and c using the ±120° relationships.
If needed, compute line-to-line voltages and delta currents using the and ±30° relationships. 2. Three-Phase Power, cont.<br>
slide8. 8 Single-Phase Residence. 1kVA to the customer requires 4.17A in each of the two legs 7.2kV 30:1 single-phase transformer 4.17A on the 240V side corresponds to 0.14A on the 7.2kV side<br>
slide9. 9 1kVA to the customer corresponds to 1.20A in each of the three phases Most commercial buildings, like ENS, are served by a 12.47kV (line-to-line) to 480V (line-to-line) three-phase transformer, delta-connected on the 12.47kV side, and grounded-wye connected on the 480V side Most lighting in commercial buildings is 277V fluorescent – that’s the voltage behind the switchplate cover. 120V outlets are served by 480:120V step down transformers on each floor of the building, often located in utility closets in two diagonally-opposite corners of each floor.<br>