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Chapter 12 Three-Phase Circuits. Power Factor Correction A balanced three-phase circuit Medium Voltage Metal Enclosed Capacitor Banks.

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Presentation on theme: "Chapter 12 Three-Phase Circuits. Power Factor Correction A balanced three-phase circuit Medium Voltage Metal Enclosed Capacitor Banks."— Presentation transcript:

1 Chapter 12 Three-Phase Circuits

2 Power Factor Correction A balanced three-phase circuit Medium Voltage Metal Enclosed Capacitor Banks

3 Three-Phase Voltages (b) Balanced three-phase voltages (a)The three windings on a cylindrical drum used to obtain three-phase voltages

4 Three-Phase Voltages Generator with six terminals

5 Three-Phase Balanced Voltages Phase sequence or phase rotation is abc Positive Phase Sequence Phase sequence or phase rotation is acb Negative Phase Sequence neutral terminal

6 (a) Y-connected sources (b)  -connected sources Two Common Methods of Connection phase voltage

7 Phase and Line Voltages The line-to-line voltage V ab of the Y-connected source Similarly

8 The Y-to-Y Circuit A four-wire Y-to-Y circuit

9 The Y-to-Y Circuit (cont.) The average power delivered by the three-phase source to the three-phase load When Z A = Z B = Z C the load is said to be balanced Four - wire

10 The Y-to-Y Circuit(cont.) The average power delivered to the load is There is no current in the wire connecting the neutral node of the source to the neutral node of the load.

11 The Y-to-Y Circuit (cont.) A three-wire Y-to-Y circuit

12 Three - wire We need to solve for V Nn The Y-to-Y Circuit (cont.) Solve for V Nn

13 When the circuit is balanced i.e. Z A = Z B = Z C The Y-to-Y Circuit (cont.) The average power delivered to the load is

14 A three-wire Y-to-Y circuit with line impedances The Y-to-Y Circuit (cont.) Transmission lines

15 The Y-to-Y Circuit (cont.) The analysis of balanced Y-Y circuits is simpler than the analysis of unbalanced Y-Y circuits. V Nn = 0. It is not necessary to solve for V Nn. The line currents have equal magnitudes and differ in phase by 120 degree. Equal power is absorbed by each impedance. Per-phase equivalent circuit

16 Example S = ? Unbalanced 4-wire

17 Example (cont.) The total complex power delivered to the three-phase load is

18 Example S = ?Balanced 4-wire The total complex power delivered to the three-phase load is Also

19 Example S = ? Unbalanced 3-wire Determine V Nn

20 Example (cont.) The total complex power delivered to the three-phase load is

21 Example S = ?Balanced 3-wire The total complex power delivered to the three-phase load is

22 Example P Load = ? P Line = ? P Source = ? Balanced 3-wire per-phase equivalent circuit The phase voltage at the load is

23 Example (cont.) The power delivered by the source is The power delivered to the load is The power lost in the line is

24 The  -Connected Source and Load Total resistance around the loop Circulating current Unacceptable Therefore the  sources connection is seldom used in practice.

25 The  -Y and Y-  T ransformation

26 Example

27 The Y-  Circuits where

28 The Y-  Circuits (cont.) or

29 Example I P = ? I L = ? The  -connected load is balanced with The line currents are

30 The Balanced Three-Phase Circuits per-phase equivalent circuit Y-to-  circuit equivalent Y-to-Y circuit

31 Example I P = ?

32 Example (cont.) The voltages in the per-phase equivalent circuit are The line-to-line voltages are

33 Instantaneous and Average Power in BTP Circuits One advantage of three-phase power is the smooth flow of energy to the load. The instantaneous power

34 Instantaneous and Average Power in BTP Circuits The total average power delivered to the balanced Y-connected load is Phase A

35 Instantaneous and Average Power in BTP Circuits The total average power delivered to the balanced  -connected load is

36 Example P = ?

37 Two-Wattmeter Power Measurement cc = current coil vc = voltage coil W1 read W2 read For balanced load with abc phase sequence

38 Two-Wattmeter Power Measurement(cont.) To determine the power factor angle

39 Example P = ? line-to-line voltage = 220Vrms The phase voltage The line current and

40 Electrodynamic Wattmeter

41 Digital Power Meter VAR Meter pf Meter

42 Summary Three-Phase voltages The Y-to-Y Circuits The  -Connected Source and Load The Y-to-  Circuits Balanced Three-Phase Circuits Instantaneous and Average Power in Bal. 3  Load Two-Wattmeter Power Measurement


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