1. CHAPTER 11 Balanced Three - Phase Circuits

2. CHAPTER CONTENTS 11.1 Balanced Three-Phase Voltages 11.1 Balanced Three-Phase Voltages 11.2 Three-Phase Voltage Sources 11.2 Three-Phase Voltage Sources 11.3 Analysis of the Wye-Wye Circuit 11.3 Analysis of the Wye-Wye Circuit 11.4 Analysis of the Wye-Delta Circuit 11.4 Analysis of the Wye-Delta Circuit 11.5 Power Calculations in Balanced Three- Phase Circuits 11.5 Power Calculations in Balanced Three- Phase Circuits 11.6 Measuring Average Power in Three- Phase Circuits 11.6 Measuring Average Power in Three- Phase Circuits

3. 11.1 Balanced Three-Phase Voltages Phasor diagrams of a balanced set of three- phase voltages. (a) The abc (positive) sequence. (b) The acb (negative) sequence. (a) (b)

4. 11.2 Three-Phase Voltage Sources

5. The two basic connections of an ideal three-phase source. (a) A Y-connected source. (b) A ∆-connected source

6. A model of a three-phase source with winding impedance: (a) A Y-connected source. (b) A ∆-connected source

7. 11.3 Analysis of the Wye-Wye Circuit A three-phase Y-Y system

8. Phasor diagrams showing the relationship between line-to- line and line-to- neutral voltages in a balanced system. (a)The abc sequence. (b)The acb sequence.

9. 11.4 Analysis of the Wye-Delta Circuit A circuit used to establish the relationship between line currents and phase currents in a balanced ∆ load.

10. Phasor diagrams showing the relationship between line currents and phase currents in a ∆- connected load. (a)The positive sequence. (b)The negative sequence.

11. 11.5 Power Calculations in Balanced Three-Phase Circuits TOTAL REAL POWER IN A BALANCED THREE-PHASE LOAD TOTAL REACTIVE POWER IN A BALANCED THREE-PHASE LOAD

12. TOTAL COMPLEX POWER IN A BALANCED THREE- PHASE LOAD

13. 11.6 Measuring Average Power in Three-Phase Circuits A wattmeter measures the average power delivered to a load by using a current coil connected in series with the load and a potential coil connected in parallel with the load. A wattmeter measures the average power delivered to a load by using a current coil connected in series with the load and a potential coil connected in parallel with the load.

14. A circuit used to analyze the two-wattmeter method of measuring average power delivered to a balanced load.

15. THE END