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CHAPTER 11 Balanced Three - Phase Circuits CHAPTER CONTENTS 11.1 Balanced Three-Phase Voltages 11.2 Three-Phase Voltage Sources 11.3 Analysis of the Wye-Wye Circuit 11.4 Analysis of the Wye-Delta Circuit 11.5 Power Calculations in Balanced ThreePhase Circuits 11.6 Measuring Average Power in ThreePhase Circuits 11.1 Balanced Three-Phase Voltages (a) (b) Phasor diagrams of a balanced set of threephase voltages. (a) The abc (positive) sequence. (b) The acb (negative) sequence. 11.2 Three-Phase Voltage Sources The two basic connections of an ideal three-phase source. (a) A Y-connected source. (b) A ∆-connected source A model of a three-phase source with winding impedance: (a) A Y-connected source. (b) A ∆-connected source 11.3 Analysis of the Wye-Wye Circuit A three-phase Y-Y system Phasor diagrams showing the relationship between line-toline and line-toneutral voltages in a balanced system. (a)The abc sequence. (b)The acb sequence. 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. Phasor diagrams showing the relationship between line currents and phase currents in a ∆connected load. (a)The positive sequence. (b)The negative sequence. 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 TOTAL COMPLEX POWER IN A BALANCED THREEPHASE LOAD 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 circuit used to analyze the two-wattmeter method of measuring average power delivered to a balanced load. THE END