10 – three phase theory

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


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.


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.



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.



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.



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.


N

Neutral

A

B

C

Phase Winding


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.


A

B

C

Phase Winding


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:


A

B

C

VL

VL

VL

VPh

IL

IL

IL

IPh

IPh IPh

I = I phL



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:


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


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:


V = V phL

A

B

C

VL

VL

VL

IL

IL

IL

IPh

IPh

IPh

VPh

VPh

VPh

3I = I orI 3 = I

LphphL



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:


I V 3 = S

I V 3 = Q

I V 3 = P

LLApparent

LLReactive

LLReal

sin

cos


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.



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.


RPh

VPh

IPh


Three Phase Wye Connected Loads


RPh

A

B

C

VL

VL

VL

VPh

IL

IL

IPh

IPhIPh

RPh R P

h

IL


Three Phase Delta Connected Loads


A

B

C

VL

VL

VL

IL

IL

IL

IPh

IPh

IPh

VPh

VPh

VPh R PhRPh

RPh


Three Phase Calculation Example


Given: Supply VPH = 120v

freq. = 60Hz

Load RPH = 10Ω

Find: Load IPH

VL

IL

R PhRPh

RPh


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.


PhPh

RPh

Supply VPH = 120v Load RPH = 10Ω

IPh Load

IL

VL

vvPh

VL

VSupplyY 846.20731203

vph

VL

VLoad 846.207


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.


RPhVPh Load = 207.846v

Iph Load

Load RPH = 10Ω

Av

R

VInCalculatioPhaseSingleLoad

Loadph

LoadphLoadph 785.20

10

846.207

AAII LoadphL 001.363785.203


Practice Exercises


R PhRPh

RPh

1. Given: Vph 120v (Supply) freq. = 60Hz RPh = 12

Find: Preal = IL = VL =


Practice Exercises


2. Given: Vph 208v (Supply) freq. = 60Hz RPh = 100

Find: Preal = IL =

RPh

RPh R P

h


Practice Exercises


3. Given: VL = 480v f = 60Hz RPh Load = 20Ω

Find: IPH Load =VPH SupplyIL =Preal =

RPh

RPh R P

h

10 – three phase theory

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