THREE PHASE POWER Generation Transportation Consumption

THREE PHASE GENERATION

AB C A Expressions relative to ground 3G A B C Between terminals

THREE PHASE GENERATION 3G A B C Between terminals C B A 

THREE PHASE GENERATION Advantage of three phase Smooth flow of energy to load Consider resistive loadInstantaneous power P(t) Add to zero

THREE PHASE GENERATION

Smooth transfer of power Smooth operation of motor Each phase carries 1/3 of the total power delivered to the load 3G A B C How to connect to transmission lines

A’ B’ C’ THREE PHASE GENERATION 3G A B C 3T Three transmission lines Three generators (ABC) Terminal board For the generators chose: Identical generators and

THREE PHASE GENERATION A’ B’ C’ 3G A B C Three generators (ABC) “DELTA” connected A’ B’ C’ A B C 3T

THREE PHASE GENERATION A’ B’ C’ A B C Three generators (ABC) “DELTA” connected G A B C G G A’ B’ C’ 3T C A B

THREE PHASE GENERATION Phase diagram for DELTA connected generators G A B C G G A’ B’ C’ C A B  Voltages are across pairs of transmission lines Simple Voltage of generators

THREE PHASE GENERATION A’ B’ C’ 3G A B C Three generators (ABC) “STAR” connected A’ B’ C’ A B C 3T Ground Neutral

THREE PHASE GENERATION Three generators (ABC) “STAR” connected A B C G G G A’ B’ C’ 3T C A B A’ B’ C’ A B C Ground Neutral

THREE PHASE GENERATION Phase diagram for STAR connected generators A B C G G G A’ B’ C’ C A B  Recall the generator phase diagram We will start with the voltage between lines A and B

THREE PHASE GENERATION A B A’ B’ A B A B G G A’ B’ Change order of indices Change sign in front of supply Phasor “Addition” (- = flip direction by 180 o ) Back to phasor diagram for generators

THREE PHASE GENERATION  Original Diagram for AA’ and BB’  30 o 120 o

THREE PHASE GENERATION For  30 o 

THREE PHASE GENERATION Phase diagram for STAR connected generators A B C G G G A’ B’ C’ C A B  Recall the generator phase diagram 120 o Phase diagram Line to line voltages have 120 degree phase difference  What about amplitude of the voltages

THREE PHASE GENERATION 30 o The length of the red vector related to the length of the two black vectors 30 o

THREE PHASE GENERATION Phase diagram for STAR connected generators A B C G G G A’ B’ C’ C A B  Recall the generator phase diagram 120 o Phase diagram 

THREE PHASE TERMINOLOGY Phase Current: Current through a single generator G G Phase Voltage: Voltage across a single generator

THREE PHASE ROTATION CONVENTION  ABC ABC ABC …  ABC ABC ABC … ABC Motor turns clockwise ACB Motor turns counter clockwise

THREE PHASE TERMINOLOGY Line current: Current in a single line feeding a load 3G A B C 3T Line voltage: Voltage between the lines carrying the power

PHASE-LINE RELATIONSHIP For the STAR connected generators A B C G G G C A B

PHASE LINE RELATIONSHIP G A B C G G A’ B’ C’ C A B For the Delta connected generators Phasor current done in class

THREE PHASE TRANSFORMER NA p NA s ApAp NB p NB s NC p NC s A p’ BpBp CpCp B p’ C p’ AsAs A s’ BsBs B s’ CsCs C s’ How do you connect the primary coils together and separately the secondary coils together

THREE PHASE TRANSFORMER Star Star

THREE PHASE TRANSFORMER Star Delta

THREE PHASE TRANSFORMER Delta Star

THREE PHASE TRANSFORMER Delta Delta

THREE PHASE LOADS A B C Three phase load 3 Transformer 3G 3T 3Z Step up or step down 3 Tran sfor mer 3Z What does the three phase load look like? Voltages, currents, power, …..

THREE PHASE LOADS 3Z Made up of three impedances Usually three identical values Can be connected in STAR or DELTA DELTA Transformation expression

USE OF TRANSFORMATION EXPRESSION IN THREE PHASE LOADS DELTA Transmission line impedance Now two impedances are in series

THREE PHASE LOADS 3Z Load can be connected in STAR or DELTA A B C 3G Generators can be connected in STAR or DELTA 4 possible configurations Delta --- Delta Delta --- Wye (Star) Wye (Star) --- Delta Wye (Star) --- Wye (Star)

THREE PHASE LOADS 3Z Delta Connected DELTA A B C A B C Line currents Line to line voltages Phase currents Balanced three phase load

THREE PHASE LOADS 3Z Delta Connected: Consider node “A” A B C A B C Line to line voltages Flip Since load is only resistive

THREE PHASE LOADS Delta Connected: Consider node “A” A B C 30 o Result Leads by 30 degrees

THREE PHASE LOADS Delta Connected: Consider node “A” Per phase power A B C Power Factor (PF) For purely resistive load Power Factor = 1.0 Total power: Note:  is the phase angle of the load impedance. It may or may not be the phase angle between the line voltage and line current. For complex load: Phase angle

THREE PHASE LOADS Delta Connected: Consider node “A” Per phase power A B C Total power: Note: Phase voltage and phase current may be difficult to measure. For example inside a motor. However line voltage and line current can always be measured Phase angle of load (Can be measured)

THREE PHASE LOADS 3Z Wye (Star) Connected STAR A B C A B C Balanced three phase load N

THREE PHASE LOADS STAR A B C N Analysis flip

THREE PHASE LOADS Lags by 30 degrees 30 o STAR

THREE PHASE LOADS Star Connected: Per phase power Power Factor (PF) For purely resistive load Power Factor = 1.0 Total power: Note:  is the phase angle of the load impedance. It may or may not be the phase angle between the line voltage and line current. For complex load: Phase angle A B C N

THREE PHASE LOADS Star Connected: Per phase power Power factor (PF) A B C N Consider phase for point A and neutral and Per phase power Total power: Same as for Delta load

THREE PHASE LOADS SUMMARY 3Z Load can be connected in STAR or DELTA A B C 3G Generators can be connected in STAR or DELTA Real Power Reactive Power Apparent Power