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Presentation : IMS – Tech Managers Conference Author : IMS Staff Creation date : 08 March 2012 Classification : D3 Conservation : Page : 1 10 – Three Phase Theory Author : IMS Stafff Creation date : 5 Nov 2012 Classification : D3
10 – Three Phase Theory
Presentation : IMS – Tech Managers Conference Author : IMS Staff Creation date : 08 March 2012 Classification : D3 Conservation : Page : 2 10 – Three Phase Theory Author : IMS Stafff Creation date : 5 Nov 2012 Classification : D3
The intent of this presentation is to present enough information to provide the reader with a fundamental knowledge of Three Phase Alternating Current and to better understand basic Michelin system and equipment operations.
Presentation : IMS – Tech Managers Conference Author : IMS Staff Creation date : 08 March 2012 Classification : D3 Conservation : Page : 3 10 – Three Phase Theory Author : IMS Stafff Creation date : 5 Nov 2012 Classification : D3
Characteristics of Three Phase Systems
A three phase (3) system is a combination of three single phase (1) systems. In a 3 balanced system, the power comes from an AC generator that produces three separate but equal voltages, each of which is out of phase with the other voltages by 120(illustrated below). When any of the three voltages is at its maximum value (negative or positive), each of the other two voltages will be at 50 percent of their maximum value in the opposite direction. Although single phase circuits are widely used in electrical systems; most generation and distribution of alternating current is 3.
10 – Three Phase Theory
Presentation : IMS – Tech Managers Conference Author : IMS Staff Creation date : 08 March 2012 Classification : D3 Conservation : Page : 4 10 – Three Phase Theory Author : IMS Stafff Creation date : 5 Nov 2012 Classification : D3
Definitions
Single Phase System - System energized by a single alternating voltage.
Poly Phase System - System energized by two, three or more alternating voltages.
Three Phase System - System energized by three equal alternating voltages 120 apart.
Line Voltage (VL) - The voltage measured between terminals of an alternator, motor or branch circuit feeder wires.
Phase - Each winding of an alternator, of a motor, or of a branch circuit forming part of a load.
Phase Voltage (Vph) - The voltage measured across a phase of an alternator, motor or load.
10 – Three Phase Theory
Presentation : IMS – Tech Managers Conference Author : IMS Staff Creation date : 08 March 2012 Classification : D3 Conservation : Page : 5 10 – Three Phase Theory Author : IMS Stafff Creation date : 5 Nov 2012 Classification : D3
Advantages of a 3 phase system versus a single phase system
• 3 circuits require less weight of conductors than 1 circuits of the same power rating.
• 3 circuits permit flexibility in the choice of voltages.
• 3 circuits can be used for 1 loads.
• 3 equipment is smaller in size, lighter in weight, and more efficient than 1 machinery of the same rated capacity.
10 – Three Phase Theory
Presentation : IMS – Tech Managers Conference Author : IMS Staff Creation date : 08 March 2012 Classification : D3 Conservation : Page : 6 10 – Three Phase Theory Author : IMS Stafff Creation date : 5 Nov 2012 Classification : D3
The three phases of a 3 system may be connected in two ways.
In most industrial applications, the 3 phase generation is done by the power company and distributed through a power distribution system. The voltage is stepped down along the way and delivered to the facilities. The facility uses three phase transformers to supply the loads in the facility. The following representations are of the secondary windings of a 3 phase transformer not a standalone generator.
1. If the three common ends of each secondary phase winding are connected together at a common terminal marked N for neutral, then the other three ends become the A, B, and C 3 line conductors.
This system is Wye or Y-connected.
This configuration can be related as being connected in
series. Sometimes the neutral connection is grounded
and brought out to form a 3, 4-wire system.
10 – Three Phase Theory
N
Neutral
A
B
C
Phase Winding
Presentation : IMS – Tech Managers Conference Author : IMS Staff Creation date : 08 March 2012 Classification : D3 Conservation : Page : 7 10 – Three Phase Theory Author : IMS Stafff Creation date : 5 Nov 2012 Classification : D3
The three phases of a 3 system may be connected in two ways.
2. If the three phases are connected to form a closed loop, the system is delta or Δ-connected. This configuration can be related as being connected in parallel.
10 – Three Phase Theory
A
B
C
Phase Winding
Presentation : IMS – Tech Managers Conference Author : IMS Staff Creation date : 08 March 2012 Classification : D3 Conservation : Page : 8 10 – Three Phase Theory Author : IMS Stafff Creation date : 5 Nov 2012 Classification : D3
Three Phase Wye Relationships
Voltage Relationship in a Wye Configuration - Since the line voltage is connected across two windings and the phase voltage is only connected across one winding, the line voltage (VL) is much larger than the phase voltage (Vph). At first, you would think that the line voltage is twice as large as the phase voltage, this is not the case. The actual relationship is as follows:
Current Relationship in a Wye Configuration - Since
the line current does not split as it leaves the phase
winding, the line current (IL) is equal to the phase
current (Iph). The relationship is as follows:
10 – Three Phase Theory
A
B
C
VL
VL
VL
VPh
IL
IL
IL
IPh
IPh IPh
I = I phL
Presentation : IMS – Tech Managers Conference Author : IMS Staff Creation date : 08 March 2012 Classification : D3 Conservation : Page : 9 10 – Three Phase Theory Author : IMS Stafff Creation date : 5 Nov 2012 Classification : D3
Three Phase Wye Relationships
Power Relationship in a Wye Configuration - As discussed in AC concepts, there are three different power relationships for AC circuits. Real, reactive and apparent power still applies for three phase circuits. There are some minor differences as shown with the relationships below:
10 – Three Phase Theory
A
B
C
VL
VL
VL
VPh
IL
IL
IL
IPh
IPh IPhI V 3 = S
I V 3 = Q
I V 3 = P
LLApparent
LLReactive
LLReal
sin
cos
Presentation : IMS – Tech Managers Conference Author : IMS Staff Creation date : 08 March 2012 Classification : D3 Conservation : Page : 10 10 – Three Phase Theory Author : IMS Stafff Creation date : 5 Nov 2012 Classification : D3
Three Phase Delta Relationships
Voltage Relationship in a Delta Configuration - Since the line voltage is connected across one winding just as is the phase voltage, the line voltage (VL) is equal to the phase voltage (Vph). The actual relationship is as follows:
Current Relationship in a Delta Configuration - Since
the line current is a combination of current from two
windings and the phase current only comes from one
winding, the line current (IL) is much larger than the
phase current (Iph). At first, you would think that the
line current is twice as large as the phase current, this
is not the case. The actual relationship is as follows:
10 – Three Phase Theory
V = V phL
A
B
C
VL
VL
VL
IL
IL
IL
IPh
IPh
IPh
VPh
VPh
VPh
3I = I orI 3 = I
LphphL
Presentation : IMS – Tech Managers Conference Author : IMS Staff Creation date : 08 March 2012 Classification : D3 Conservation : Page : 11 10 – Three Phase Theory Author : IMS Stafff Creation date : 5 Nov 2012 Classification : D3
Three Phase Wye Relationships
Power Relationship in a Delta Configuration - As discussed in AC concepts, there are three different power relationships for AC circuits. Real, reactive and apparent power still applies for three phase circuits. There are some minor differences as shown with the relationships below:
10 – Three Phase Theory
I V 3 = S
I V 3 = Q
I V 3 = P
LLApparent
LLReactive
LLReal
sin
cos
Presentation : IMS – Tech Managers Conference Author : IMS Staff Creation date : 08 March 2012 Classification : D3 Conservation : Page : 12 10 – Three Phase Theory Author : IMS Stafff Creation date : 5 Nov 2012 Classification : D3
Three Phase Generation
The generation of 3 AC and the associated relationships has been discussed. We now need to talk about the 3 loads and their associated relationships. Remember, without a load connected to the supply, there will be no current flow. The voltage, current and power relationships that apply to the generation of 3 AC also applies to 3 loads. There are two different types of loads: balanced and unbalanced. We will only be discussing the balanced loads.
In actual industrial applications there are several different configurations for loads:
Resistive, Inductive and Capacitive, as well as, many combinations of each. To better understand the basic concepts for line and phase voltages and currents we will only use loads that are resistive.
Balanced 3 loads have identical resistances in each winding. The phase voltage Vph and the phase current Iph are the same for each winding.
10 – Three Phase Theory
Presentation : IMS – Tech Managers Conference Author : IMS Staff Creation date : 08 March 2012 Classification : D3 Conservation : Page : 13 10 – Three Phase Theory Author : IMS Stafff Creation date : 5 Nov 2012 Classification : D3
Three Phase Generation
Once the phase voltage of the load Vph and phase current of the load Iph are established, the circuit can be evaluated just as a single phase AC circuit. You can then evaluate the circuit just as we did in AC Theory.
10 – Three Phase Theory
RPh
VPh
IPh
Presentation : IMS – Tech Managers Conference Author : IMS Staff Creation date : 08 March 2012 Classification : D3 Conservation : Page : 14 10 – Three Phase Theory Author : IMS Stafff Creation date : 5 Nov 2012 Classification : D3
Three Phase Wye Connected Loads
10 – Three Phase Theory
RPh
A
B
C
VL
VL
VL
VPh
IL
IL
IPh
IPhIPh
RPh R P
h
IL
Presentation : IMS – Tech Managers Conference Author : IMS Staff Creation date : 08 March 2012 Classification : D3 Conservation : Page : 15 10 – Three Phase Theory Author : IMS Stafff Creation date : 5 Nov 2012 Classification : D3
Three Phase Delta Connected Loads
10 – Three Phase Theory
A
B
C
VL
VL
VL
IL
IL
IL
IPh
IPh
IPh
VPh
VPh
VPh R PhRPh
RPh
Presentation : IMS – Tech Managers Conference Author : IMS Staff Creation date : 08 March 2012 Classification : D3 Conservation : Page : 16 10 – Three Phase Theory Author : IMS Stafff Creation date : 5 Nov 2012 Classification : D3
Three Phase Calculation Example
10 – Three Phase Theory
Given: Supply VPH = 120v
freq. = 60Hz
Load RPH = 10Ω
Find: Load IPH
VL
IL
R PhRPh
RPh
Presentation : IMS – Tech Managers Conference Author : IMS Staff Creation date : 08 March 2012 Classification : D3 Conservation : Page : 17 10 – Three Phase Theory Author : IMS Stafff Creation date : 5 Nov 2012 Classification : D3
1. First label the given information on the circuit, then what you need to find.
2. Next do the Supply calculation for VL.
3. Then do the Load calculation for VPh.
10 – Three Phase Theory
PhPh
RPh
Supply VPH = 120v Load RPH = 10Ω
IPh Load
IL
VL
vvPh
VL
VSupplyY 846.20731203
vph
VL
VLoad 846.207
Presentation : IMS – Tech Managers Conference Author : IMS Staff Creation date : 08 March 2012 Classification : D3 Conservation : Page : 18 10 – Three Phase Theory Author : IMS Stafff Creation date : 5 Nov 2012 Classification : D3
4. Now we can draw a single phase circuit that represents only one phase of the 3 phase delta load.
5. Next do the single phase calculation.
6. Then do the IL calculation.
10 – Three Phase Theory
RPhVPh Load = 207.846v
Iph Load
Load RPH = 10Ω
Av
R
VInCalculatioPhaseSingleLoad
Loadph
LoadphLoadph 785.20
10
846.207
AAII LoadphL 001.363785.203
Presentation : IMS – Tech Managers Conference Author : IMS Staff Creation date : 08 March 2012 Classification : D3 Conservation : Page : 19 10 – Three Phase Theory Author : IMS Stafff Creation date : 5 Nov 2012 Classification : D3
Practice Exercises
10 – Three Phase Theory
R PhRPh
RPh
1. Given: Vph 120v (Supply) freq. = 60Hz RPh = 12
Find: Preal = IL = VL =
Presentation : IMS – Tech Managers Conference Author : IMS Staff Creation date : 08 March 2012 Classification : D3 Conservation : Page : 20 10 – Three Phase Theory Author : IMS Stafff Creation date : 5 Nov 2012 Classification : D3
Practice Exercises
10 – Three Phase Theory
2. Given: Vph 208v (Supply) freq. = 60Hz RPh = 100
Find: Preal = IL =
RPh
RPh R P
h
Presentation : IMS – Tech Managers Conference Author : IMS Staff Creation date : 08 March 2012 Classification : D3 Conservation : Page : 21 10 – Three Phase Theory Author : IMS Stafff Creation date : 5 Nov 2012 Classification : D3
Practice Exercises
10 – Three Phase Theory
3. Given: VL = 480v f = 60Hz RPh Load = 20Ω
Find: IPH Load =VPH SupplyIL =Preal =
RPh
RPh R P
h