1. EMLAB 1 11. Polyphase circuits

2. EMLAB 2 1. Three Phase Circuits Advantages of polyphase circuits 2. Three Phase Connections Basic configurations for three phase circuits 3. Source/Load Connections Delta-Wye connections 4. Power Relationships Study power delivered by three phase circuits 5. Power Factor Correction Improving power factor for three phase circuits Contents

3. EMLAB 3 11.1 Three phase circuits Instantaneous voltage

4. EMLAB 4 이행선 +-+- 1kW 100V (rms) Disadvantage of single phase two wire system 1.If the load increases to 2kW, P loss becomes 40W. 2.If each wire can sustain heat only to 5W power loss, the cross- section area should increase 4 times, whereby cost for copper wires increase 4 times. 100V (rms) +-+- 2kW 100V (rms)

5. EMLAB 5 이행선 5 +-+- 1kW 100V (rms) +-+- 1kW 100V (rms) 1.Although the power load increases to 2kW, P loss remains 10W. 2.With 2 times power load, only one copper wire is added. Single-phase 3 wire circuits

6. EMLAB 6 Advantage of three phase-four wire circuit +-+- 1kW +-+- 1.If power load increases to 3kW, the P loss for a wire is still 5W. 2.With three times larger power load, only one wires need to be added. +-+- 1kW

7. EMLAB 7 Three phase generator

8. EMLAB 8 Three phase electric motor 1.Power output of single phase circuit 2. Power output of three phase circuit

9. EMLAB 9 Three phase circuits Theorem For a balanced three phase circuit the instantaneous power is constant

10. EMLAB 10 Proof of Theorem For a balanced three phase circuit the instantaneous power is constant

11. EMLAB 11 Three-phase connections Positive sequence a-b-c Y-connected loads Delta connected loads

12. EMLAB 12 Line voltage, phase voltage Phase current : current that flows from a voltage source. Phase voltage : voltage drop across a voltage source. (current that flows in a transmission line.) (voltage difference between two lines.)

13. EMLAB 13 Source/load connections BALANCED Y-Y CONNECTION Positive sequence phase voltages Line voltages For this balanced circuit it is enough to analyze one phase

14. EMLAB 14 Y-connected source Phase voltage Line voltage In a balanced Y-Y connection, phase currents are equal to line currents.

15. EMLAB 15 Δ- connected source → Y-connected source Line voltage With Δ-connected sources, we can arbitrarily set the reference point and transform to Y-connected sources.

16. EMLAB 16 Example 11.2 For an abc sequence, balanced Y - Y three phase circuit Determine line currents and load voltages Because circuit is balanced data on any one phase is sufficient Chosen as reference Abc sequence

17. EMLAB 17 Example 11.4 Determine line currents and line voltages at the loads Source is Delta connected. Convert to equivalent Y Analyze one phase Determine the other phases using the balance

18. EMLAB 18 Delta-connected load Method 1: Solve directly Positive sequence phase voltages Method 2: We can also convert the delta connected load into a Y connected one. The same formulas derived for resistive circuits are applicable to impedances Line-phase current relationship

19. EMLAB 19 Subtract the first two then add to the third to get R a Replace in the third and solve for R 1 Δ- connected load → Y-connected load

20. EMLAB 20 Δ- connected load → Y-connected load

21. EMLAB 21 Example 11.4 Delta-connected load consists of 10-Ohm resistance in series with 20-mH inductance. Source is Y-connected, abc sequence, 120-V rms, 60Hz. Determine all line and phase currents Line-phase current relationship Alternatively, determine first the line currents and then the delta currents

22. EMLAB 22 Power relationships Line-phase current relationship Power factor angle - Impedance angle

23. EMLAB 23 Determine the magnitude of the line currents and the value of load impedance per phase in the delta Line-phase current relationship Example 11.5 Power factor angle - Impedance angle

24. EMLAB 24 For an abc sequence, balanced Y - Y three phase circuit Because circuit is balanced data on any one phase is sufficient Chosen as reference Abc sequence Determine real and reactive power per phase at the load and total real, reactive and complex power at the source P per_phase Q per_phase Example 11.6

25. EMLAB 25 Power factor correction Balanced load Low pf lagging Similar to single phase case. Use capacitors to increase the power factor Keep clear about total/phase power, line/phase voltages To use capacitors this value should be negative

26. EMLAB 26 Example 11.9

27. EMLAB