EE 221 CIRCUITS II. Chapter 12 Three-Phase Circuit

Transcription

1 EE 221 CIRCUITS II Chapter 12 Three-Phase Circuit 1

2 THREE-PHASE CIRCUITS CHAPTER What is a Three-Phase Circuit? 12.2 Balanced Three-Phase Voltages 12.3 Balanced Three-Phase Connection 12.4 Power in a Balanced System 12.5 Unbalanced Three-Phase Systems 12.6 Application Residential Wiring 2

3 12.1 Advantages of Three-Phase Circuit? 1. Most of the electric power is generated and distributed in three-phase. 2. The instantaneous power in a three-phase system can be constant. 3. The amount of power generated by a three-phase generator is more economical than that of a singlephase generator 4. The amount of wire required for a three-phase system is less than that required for an equivalent singlephase system. 3

4 Schematic Diagram of a Power System

5 US Electric Energy Generation Mix

6 Thermal Power Plants

7 Nuclear Power Plant

8 Natural Gas Power Plants

9 Hydro Power Plants

10 Renewable Power Plants

11 12.2 Balanced Three-Phase Voltages A three-phase generator consists of a rotating magnet (in the rotor) surrounded by stationary windings (in the stator). A three-phase generator The generated voltages 11

12 12.1 Definition of a Three-Phase Circuit It is a system with a generator consisting of three sources having the same amplitude and frequency but out of phase with each other by 120. Three sources with 120 out of phase Four wired system 12

13 12.2 Balanced Three-Phase Voltages Two possible configurations: Three-phase voltage sources: (a) Y-connected ; (b) Δ-connected 13

14 12.2 Balance Three-Phase Voltages Balanced phase voltages are equal in magnitude and are out of phase with each other by 120. The phase sequence is the time order in which the voltages pass through their respective maximum values. a-b-c (or positive sequence) a-c-b (or negative sequence) A balanced load is one in which the phase impedances are equal in magnitude and in phase 14

15 12.2 Balance Three-Phase Voltages Example 1 Determine the phase sequence of the set of voltages. v v v an bn cn 200 cos( ωt + 10 ) 200 cos( ωt 230 ) 200 cos( ωt 110 ) 15

16 12.2 Balanced Three-Phase Voltages Solution: The voltages can be expressed in phasor form as V V V an bn cn V V V We notice that V an leads V cn by 120 and V cn in turn leads V bn by 120. Hence, we have an a-c-b sequence (or negative sequence). 16

17 12.3 Balanced Three-Phase Connection Four possible connections 1. Y-Y connection (Y-connected source with a Y-connected load) 2. Y-Δ connection (Y-connected source with a Δ-connected load) 3. Δ-Δ connection 4. Δ-Y connection 17

18 12.3 Balance Three-Phase Connection A balanced Y-Y system is a three-phase system with a balanced Y-connected source and a balanced Y- connected load. V L V V p L 3V p V, where V an ab V V bn bc V V cn ca I n a b c ( I + I + I ) 0 18

19 12.3 Balanced Three-Phase Connection Example 2: Obtain the line currents 19

20 12.3 Balanced Three-Phase Connection A balanced Y-Δ system is a three-phase system with a balanced Y-connected source and a balanced Δ- connected load. I L 3I p, where I L I a I b I c I p I AB I BC I CA 20

21 12.3 Balanced Three-Phase Connection Example 3: 21

22 12.3 Balanced Three-Phase Connection A balanced Δ-Δ system is a three-phase system with a balanced Δ -connected source and a balanced Δ -connected load. 22

23 12.3 Balance Three-Phase Connection Example 4: 23

24 12.3 Balanced Three-Phase Connection A balanced Δ-Y system is a three-phase system with a balanced y-connected source and a balanced y-connected load. 24

25 12.3 Balanced Three-Phase Connection Example 5: let Find the line currents 25

26 12.4 Power in a Balanced System P Q 3V I cos( θ ) 3V I cos( θ ) p 3V I sin( θ ) 3V I sin( θ ) p L L S 3 VpI 3V L I 26

27 12.3 Balanced Three-Phase Systems Example 6 Determine the total complex power at the source and at the load Ans At the source: S s ( j834.6) VA At the load: S L ( j1113) VA 27

28 12.3 BALANCED LOAD: EXAMPLE 7 28

29 12.5 Unbalanced Three-Phase Systems An unbalanced system is due to unbalanced voltage sources or an unbalanced load. I a V Z AN A, I b V Z BN B, I c V Z CN C, I n (I a + I b + I c ) The total power is not simply three times the power in one phase but the sum of the powers in the three phases. To calculate power in an unbalanced three-phase system requires that we find the power in each phase. 29

30 12.5 UNBALANCED THE-WIRE Y-CONNECTED CIRCUIT 30 Solve the problem again using nodal analysis.

31 12.5 UNBALANCED THE WIRE Δ CONNECTED CIRCUIT Calculate the line currents and total real and reactive power supplied by the source: 31 Rework the problem using a simpler method

32 12.4 Power in a unbalanced System Three Watt-Meter Method: P T P 1 +P 2 +P 3 Two Watt-Meter Method: P T P 1 +P 2 Special case: for a balanced load, the total reactive power may be computed From the readings of the two wattmeters: Q T 3 1 ( P 2 P ) 32

33 2-WATTMETER METHOD The unbalanced load is supplied by a balanced source such that Vab 2080 V with positive phase sequence. Calculate the reading of each wattmeter. 33 Verify the answer by computing the power consumed by each resistor

34 12.6 Application Residential Wiring A 120/240 household power system 34

35 12.6 Application Residential Wiring A typical wiring diagram of a room 35

36 12.6 Application Residential Wiring + 7,600 V - Single-phase three-wire residential wiring 36

37 12.6 Application Residential Wiring 37

38 UTILITY APPLICATION OF CAPACITORS FOR VOLTAGE REGULATION AND POWER TRANSFER Capacitors are placed in series with high Voltage transmission lines to improve voltage Regulation and power transfer capability Capacitor are also used in medium voltage power Distribution lines to regulate voltage and reduce power losses 38

39 ENERGY METER (KILO-WATT-HOUR METER) Old electro-mechanical meter records only energy consumed over a time period using mechanical dials. New smart meter records average power, reactive power, power factor, power demand, energy over a period of time, etc -Remote (wireless) reading -Remote turn ON and OFF -Communicates with the utility operator in near-continuous basis -Able to communicate with home appliances such as HVAC thermostat. 39