Download presentation
Presentation is loading. Please wait.
1
EET 103 Chapter 3 (Lecture 1) Three Phase System
2
INTRODUCTION TO THREE PHASE SYSTEM
In general, three phase systems are preferred over single phase systems for the transmission of the power system for many reasons, including the following Thinner conductors can be used to transmit the same kVA at the same voltage, which reduces the amount of copper required (typically about 25% less) and turn reduces construction and maintenance costs.
3
The lighter lines are easier to install and the supporting structures can be less massive and farther apart. In general, most larger motors are three phase because they are essentially self starting and do not require a special design or additional starting circuitry.
4
Three phase voltages A 3 phase generator basically consists of a rotating magnet (called the rotor) surrounded by a stationary winding (called the stator). Three separate windings or coils with terminals a - a’, b - b’ and c - c’ are physically placed 120o apart around the stator.
5
Generated Voltages The three phase generator can supply power to both single phase and three phase loads
6
The sinusoidal expression for each of the phase voltages
7
Phase expression In phase expression Where EM : peak value EA, EB and EC : rms value
8
The phasor diagram of the phase voltages
The effective value of each is determined by
9
If the voltage sources have the same amplitude and frequency ω and are out of the phase with each other by 120o, the voltages are said to be balanced. By rearranging the phasors as shown in figure below, so Where
10
Connection in Three Phase System
A 3 phase system is equivalent to three single phase circuit Two possible configurations in three phase system Y - connection (star connection) ∆ - connection (delta connection)
11
Three phase Voltages Source
Y-connected source ∆-connected source
12
Three phase Load Y - connected load ∆ - connected load
13
Generator and Load Connections
Each generator in a 3 phase system maybe either Y or D - connected and loads may be mixed on a power system. Z Z
14
Wye Connected Generator
Applying KVL around the indicated loop in figure above, we obtain
15
For line-to-line voltage VAB is given by
16
Phasor Diagram
17
The relationship between the magnitude of the line-to-line and line-to-neutral (phase) voltage is
The line voltages are shifted 300 with respect to the phase voltages. Phasor diagram of the line and phase voltage for the Y connection is shown below. VAB VAN VBC VBN VCA VCN Line-to-line voltages Phase voltages Rearrange
18
Delta Connected Generator
For line-to-line voltage VAB is given by
19
The relationship between the magnitude of the line and phase current is
The line currents are shifted 300 relative to the corresponding phase current. Phasor diagram of the line and phase current for the Y connection is shown below. IA IAB IBC IB ICA Line-to-line currents Phase currents IC
20
Phase sequence The phase sequence is the order in which the voltages in the individual phases peak. VA VB VC VA VC VB abc phase sequence acb phase sequence
21
EXAMPLE 3.1 Calculate the line currents in the three-wire Y - Y system as shown below.
22
Solution 3.1 Single Phase Equivalent Circuit
Phase ‘a’ equivalent circuit
24
EXAMPLE 3.2 A balanced delta connected load having an impedance 20 - j15 is connected to a delta connected, positive sequence generator having VAB = 3300 V. Calculate the phase currents of the load and the line currents.
25
Solution 3.2
26
Phase Currents
27
Line Currents
28
∆ - Connected Generator with a Y - Connected Load
29
EXAMPLE 3.3 A balanced Y - connected load with a phase impedance 40 + j25 is supplied by a balanced, positive-sequence Δ-connected source with a line voltage of 210V. Calculate the phase currents. Use VAB as reference.
30
Solution 3.3 the load impedance, ZY and the source voltage, VAB are
31
When the ∆ - connected source is transformed to a Y - connected source,
32
The line currents are
33
Summary of Relationships in Y and ∆ - connections
Y-connection ∆-connection Voltage magnitudes Current magnitudes Phase sequence VL leads Vφ by 30° IL lags Iφ by 30°
34
EET 103 Chapter 3 (Lecture 2) Three Phase System
35
Y - Connected Balanced Load
Power Y - Connected Balanced Load 22
36
The average power delivered to each phase
The total power to the balanced load is 23
37
The reactive power of each phase is
The total reactive power of the load is 23
38
The apparent power of each phase is
The total apparent power of the load is 24
39
The power factor of the system is
24
40
∆ - Connected Balanced Load
25
41
Average Power Reactive Power 26
42
Apparent Power Power Factor 27
43
EXAMPLE 3.4 Determine the total power (P), reactive power (Q) and complex power (S) at the source and at the load.
44
Single Phase Equivalent Circuit
Solution 3.4 Phase ‘a’ equivalent circuit Known quantities Vg =VAN= 1100 V ZY = 10 + j8 Zline = 5 - j2
45
Line / Phase Currents
46
Source & Load Power
47
EXAMPLE 3.5 A three phase motor can be regarded as a balanced Y - load. A three phase motor draws 5.6 kW when the line voltage is 220 V and the line current is 18.2 A. Determine the power factor of the motor Known Quantities PLoad = 5600 W VL = 220 V IL = 18.2 A
48
Solution 3.5 Power factor = cos |S| Q P
49
Example 3.6 For the Y - connected load in Figure find the average power to each phase and the total load determine the reactive power to each phase and the total reactive power find the apparent power to each phase and the total apparent power find the power factor of the load
50
Figure
51
Solution 3.6 a) The average power to each phase is Total load
52
b) The reactive power to each phase is
Total reactive power
53
c) The apparent power to each phase is
Total apparent power
54
d) The power factor
55
Volt-Amps-Reactive (VAR)
Power relationship - Phase quantities The power equations applied to Y-or D- load in a balanced 3-phase system are Real power Watts (W) Reactive power Volt-Amps-Reactive (VAR) Apparent power Volt-Amps (VA) q - angle between voltage and current in any phase of the load
56
Power relationship - Line quantities
The power equations applied to Y-or D- load in a balanced 3-phase system are Real power Reactive power Apparent power q - angle between phase voltage and phase current in any phase of the load
57
Since both the three phase source and the three phase load can be either Y or connected, we have 4 possible connections Y - Y connections (Y - connected source with Y - connected load) Y - connection (Y - connected source with - connected load) - connection ( - connected source with - connected load) - Y connection ( - connected source with Y - connected load)
58
1. Y connected generator / source with Y connected load
59
2. Y - D Connection A balanced Y - system consists of a balanced Y - connected source feeding a balanced - connected load Z/3 Z D - must consists of three equal impedances
60
3. ∆ - ∆ Connection A balanced ∆ - system consists of a balanced ∆ - connected source feeding a balanced - connected load Z Z
61
4. D - Y Connection A balanced - Y system consists of a balanced - connected source feeding a balanced Y - connected load Z/3 Z
62
Example 3.7 Each transmission line of the 3 wire, three phase system in Figure has an impedance of 15 Ω + j 20 Ω. The system delivers a total power of 160 kW at 12,000 V to a balanced three-phase load with a lagging power factor of 0.86. Determine the magnitude of the line voltage EAB of the generator. Find the power factor of the total load applied to the generator. What is the efficiency of the system?
63
Figure
64
And assigning , a lagging power factor results in
Solution 3.7 a. Vø (load) = PT (load) = 3 Vø Iø cos θ and Since θ = cos = 30.68o (lagging) And assigning , a lagging power factor results in
65
For each phase, the system will appear as shown in figure below.
Then
66
b. And And < 0.86 of load c.
67
Example 3.8 A 208V three phase power system is shown in Figure 1. It consists of an ideal 208V Y - connected three phase generator connected to a three phase transmission line to a Y - connected load. The transmission line has an impedance of j0.12W per phase and the load has an impedance of 12 + j9W per phase. For this simple system, find The magnitude of the line current IL The magnitude of the load’s line and phase voltages VLL and VfL The real, reactive and apparent powers consumed by the load The power factor of the load The real, reactive and apparent powers consumed by the transmission line The real, reactive and apparent powers supplied by the generator The generator’s power factor
68
Figure 1 0.06 i0.12 V Vcn=120-2400 Van=12000 208V Z=12+ i9 - Z
_ i0.12 V Van=12000 Vbn=120-1200 Vcn=120-2400 208V Figure 1
69
The magnitude of the line current IL
Solution 3.8 The magnitude of the line current IL So, the magnitude of the line current is thus 7.94 A
70
and the magnitude of the load’s line voltage is
(b) The magnitude of the load’s line and phase voltages VLL and VfL The phase voltage on the load is the voltage across one phase of the load. This voltage is the product of the phase impedance and the phase current of the load Therefore, the magnitude of the load’s phase voltage is and the magnitude of the load’s line voltage is
71
(c) The real power consumed by the load is
The reactive power consumed by the load is The apparent power consumed by the load is
72
(d) The load power factor is
(e) The current in the transmission line is or The impedance per phase of the line is Therefore, the real, reactive and apparent powers consumed in the line are
73
(f) The real and reactive powers supplied by the generator are the sum of the powers consumed by the line and the load The apparent power of the generator is the square root of the sum of the squares of the real and reactive powers
74
(g) From the power triangle, the power factor angle is
Therefore, the generator’s power factor is
75
A 208V three phase power system is shown in Figure 2
A 208V three phase power system is shown in Figure 2. It consists of an ideal 208V Y - connected three phase generator connected to a three phase transmission line to a - connected load. The transmission line has an impedance of j0.12W per phase and the load has an impedance of 12 + j9W per phase. For this simple system, find Assignment 3.1 The magnitude of the line current IL The magnitude of the load’s line and phase voltages VLL and VfL The real, reactive and apparent powers consumed by the load The power factor of the load The real, reactive and apparent powers consumed by the transmission line The real, reactive and apparent powers supplied by the generator The generator’s power factor
76
Figure 2
Similar presentations
