three phase power generation transportation consumption
TRANSCRIPT
THREE PHASE POWER
GenerationTransportationConsumption
THREE PHASE GENERATION
THREE PHASE GENERATION
A B C A𝑉 𝐴=𝑉 ′𝑝𝑐𝑜𝑠 (𝜔𝑡 )
𝑉 𝐵=𝑉 ′𝑝 𝑐𝑜𝑠 (𝜔𝑡−120𝑜 )
𝑉 𝐶=𝑉 ′𝑝 𝑐𝑜𝑠 (𝜔𝑡−240𝑜 )
Expressions relative to ground
3G
A
B
C
𝑉 𝐴𝐵=𝑉 𝑝𝑐𝑜𝑠 (𝜔𝑡 )𝑉 𝐵𝐶=𝑉 𝑝𝑐𝑜𝑠 (𝜔𝑡−120𝑜 )𝑉 𝐶𝐴=𝑉 𝑝𝑐𝑜𝑠 (𝜔𝑡−240𝑜 )
Between terminals
THREE PHASE GENERATION
3G
A
B
C
𝑉 𝐴𝐵=𝑉 𝑝𝑐𝑜𝑠 (𝜔𝑡 )𝑉 𝐵𝐶=𝑉 𝑝𝑐𝑜𝑠 (𝜔𝑡−120𝑜 )𝑉 𝐶𝐴=𝑉 𝑝𝑐𝑜𝑠 (𝜔𝑡−240𝑜 )
Between terminals
C
B
A
THREE PHASE GENERATION
Advantage of three phase Smooth flow of energy to load
Consider resistive load Instantaneous power P(t)
R
tV
R
tV
R
tVtP CABCAB )()()()(
222
𝑉 𝐴𝐵=𝑉 𝑝𝑐𝑜𝑠 (𝜔𝑡 )𝑉 𝐵𝐶=𝑉 𝑝𝑐𝑜𝑠 (𝜔𝑡−120𝑜 )𝑉 𝐶𝐴=𝑉 𝑝𝑐𝑜𝑠 (𝜔𝑡−240𝑜 )
))240(2cos())120(2cos()2cos(22
3)(
22oopp ttt
R
V
R
VtP
Add to zero
THREE PHASE GENERATION
))240(2cos())120(2cos()2cos(22
3)(
22oopp ttt
R
V
R
VtP
0
constant2
3)(
2
R
VtP p
THREE PHASE GENERATION
constant2
3)(
2
R
VtP p
Smooth transfer of powerSmooth 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
C3T
Three transmission lines
Three generators (ABC)
Terminal board
For the generators chose: ''' CCBBAA VVV 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
GAB
C
G
GA’
B’
C’ 3T
C
A
B
THREE PHASE GENERATION
Phase diagram for DELTA connected generators
GAB
C
G
GA’
B’
C’
C
A
B
CAV~
ABV~
BCV
ABV~
BCV
CAV~
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
GroundNeutral
THREE PHASE GENERATION
Three generators (ABC) “STAR” connected
A
B
C
GG
GA’ B’ C’
3T
C
A
B
A’
B’
C’
A
B
C
GroundNeutral
THREE PHASE GENERATION
Phase diagram for STAR connected generators
AB
C
GG
GA’ B’ C’
C
A
B
ACV~
BAV~
CBV
'
~AAV
'
~BBV
'
~CCV
'
~AAV
'
~BBV
'
~CCV
Recall the generator phase diagram
We will start with the voltage between lines A and B
THREE PHASE GENERATION
AB
A’ B’
A
BBAV~
'
~AAV
AB GG
A’ B’
'
~AAV'
~BBV
AABBBA VVV ''
~~~
''
~~~AABBBA VVV
Change order of indices
Change sign in front of supply
Phasor “Addition” (- = flip direction by 180o)
Back to phasor diagram for generators
THREE PHASE GENERATION
''
~~~AABBBA VVV
'
~AAV
'
~BBV
Original Diagram for AA’ and BB’
'
~AAV
'
~BBV
'
~AAV
'
~BBV
BAV~
30o120o
THREE PHASE GENERATION
For ACV~ For CBV
'
~BBV
'
~CCV
'
~AAV
'
~CCV
''
~~~CCAAAC VVV
'
~AAV '
~CCV
ACV~ 30o
30o
''
~~~BBCCCB VVV
CBV
'
~BBV
'
~CCV
THREE PHASE GENERATION
Phase diagram for STAR connected generators
AB
C
GG
GA’ B’ C’
C
A
B
ACV~
BAV~
CBV
'
~AAV
'
~BBV
'
~CCV
'
~AAV
'
~BBV
'
~CCV
Recall the generator phase diagram
120o
120o
120o
BAV~
ACV~
CBV
Phase diagram
Line to line voltages have 120 degree phase difference
What about amplitude of the voltages
THREE PHASE GENERATION
'
~AAV
'
~BBV
BAV~
30o
''' CCBBAA VVV
BAV~ The length of the red
vector related to the length of the two black vectors
'
~AAV
'
~BBV
30o'2
3AAV
'2
3BBV
'3~
AABA VV
THREE PHASE GENERATION
Phase diagram for STAR connected generators
AB
C
GG
GA’ B’ C’
C
A
B
ACV~
BAV~
CBV
'
~AAV
'
~BBV
'
~CCV
'
~AAV
'
~BBV
'
~CCV
Recall the generator phase diagram
120o
120o
120o
BAV~
ACV~
CBV
Phase diagram
'3~
AABA VV
'3~
AAAC VV
'3~
AACB VV
''' CCBBAA VVV
THREE PHASE TERMINOLOGY
Phase Current: Current through a single generator
GI
~G
V~
Phase Voltage: Voltage across a single generator
THREE PHASE ROTATION CONVENTION
ABV~
BCV
CAV~
ABC ABC ABC …
'
~AAV
'BBV
'
~CCV
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
LI~
Line voltage: Voltage between the lines carrying the power
LV~
PHASE-LINE RELATIONSHIP
For the STAR connected generators
AB
C
GG
G
C
A
B
ACV~
BAV~
CBV
'
~AAV
'
~BBV
'
~CCV
VVL 3~
V~
I~
IIL~~
PHASE LINE RELATIONSHIP
GAB
C
G
GA’
B’
C’
C
A
B
CAV~
ABV~
V~
VVL ~I~
IIL~
3~
For the Delta connected generators
Phasor current done in class
THREE PHASE TRANSFORMER
NAp NAs
Ap
NBp NBs
NCp NCs
Ap’
Bp
Cp
Bp’
Cp’
As
As’
Bs
Bs’
Cs
Cs’
How do you connect the primary coils together and separately the secondary coils together
THREE PHASE TRANSFORMER
NAp NAs
Ap
NBp NBs
NCp NCs
Ap’
Bp
Cp
Bp’
Cp’
As
As’
Bs
Bs’
Cs
Cs’
Star ----- Star
THREE PHASE TRANSFORMER
NAp NAs
Ap
NBp NBs
NCp NCs
Ap’
Bp
Cp
Bp’
Cp’
As
As’
Bs
Bs’
Cs
Cs’
Star ----- Delta
THREE PHASE TRANSFORMER
NAp NAs
Ap
NBp NBs
NCp NCs
Ap’
Bp
Cp
Bp’
Cp’
As
As’
Bs
Bs’
Cs
Cs’
Delta ----- Star
THREE PHASE TRANSFORMER
NAp NAs
Ap
NBp NBs
NCp NCs
Ap’
Bp
Cp
Bp’
Cp’
As
As’
Bs
Bs’
Cs
Cs’
Delta ----- Delta
THREE PHASE LOADS
A
B
C
Three phase load
3 Transforme
r3G 3T 3Z
Step up or step down
3 Transformer
3Z What does the three phase load look like?Voltages, currents, power, …..
THREE PHASE LOADS
3ZMade up of three impedances
Usually three identical values
Can be connected in STAR or DELTA
Z
ZZ
DELTA
YZ
yZZ 3
YZ YZTransformation
expression
USE OF TRANSFORMATION EXPRESSION IN THREE PHASE
LOADS
Z
ZZ
DELTA
YZ
3Z
ZY
YZ YZLZ
Transmission line impedance
LZ
LZ
LZLZ
LZ
Now two impedances are in series
3
~~~
ZZZ L
THREE PHASE LOADS
3Z
Load can be connected in STAR or DELTA
A
B
C3G
Generators can be connected in STAR or DELTA
4 possible configurations
Delta --- DeltaDelta --- Wye (Star)
Wye (Star) --- DeltaWye (Star) --- Wye (Star)
THREE PHASE LOADS
3Z Delta Connected
DELTA
A
B
C
A
BC
AI~
AI~
CI~
BI~
BI~
CI~
Line currents
ABI~
R CAI~
R
R
BCI~
ABV~
CAV~
BCV~
Line to line voltages
Phase currents
Balanced three phase load
CABCAB VVV~~~
o0 o120 o240
THREE PHASE LOADS
3ZDelta Connected: Consider node “A”
A
B
C
A
BC
AI~
AI~
BI~
CI~
ABI~
R CAI~
R
ABV~
CAV~
BCV~
Line to line voltages
CABCAB VVV~~~
o0 o120 o240
ACABA III~~~
CAABA III~~~
Flip
Since load is only resistive
ABAB IV~
with phasein ~
THREE PHASE LOADS
Delta Connected: Consider node “A”
A
BC
AI~
ABI~
R CAI~
R CAABA III~~~
ABAB IV~
with phasein ~
ABV~
ABI~
CAI~
BCI~
ABV~
CAI~
AI~
30o
3
~~ A
AB
II
Result
Leads by 30 degrees AI~
R
VI ABAB
~~
THREE PHASE LOADSDelta Connected: Consider node “A”
Per phase power
A
BC
AI~
CI~
BI~
ABI~
R CAI~
R
R
BCI~
)cos( IVP
Power Factor (PF)
For purely resistive load Power Factor = 1.0
Total power: )cos(333 IVPP
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: jXRZL ~Phase angle )(
R
Xatn
THREE PHASE LOADSDelta Connected: Consider node “A”
Per phase power
A
BC
AI~
CI~
BI~
ABI~
R CAI~
R
R
BCI~
)cos( IVP
Total power:
)cos(333 IVPP
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
)cos(3
333 L
L
IVPP
)cos(333 LLIVPP
Phase angle of load (Can be measured)
THREE PHASE LOADS
3Z Wye (Star) Connected
STAR
A
B
C
A
B C
AI~
AI~
CI~
BI~
BI~
CI~
jXRZL
LZ
ABV~
CAV~
BCV~
Balanced three phase load
CABCAB VVV~~~
o0 o120 o240
LZLZ
NABV
~
CAV~
BCV~
ANV~
BNV~
CNV~
THREE PHASE LOADS
STARA
B C
AI~
CI~
BI~
LZ
LZLZ
NABV
~
CAV~
BCV~
ANV~
BNV~
CNV~
NBANAB VVV~~~
Analysis
BNANAB VVV~~~
flip
CNV~
BNV~
ANV~
BNV~
ANV~
BNV~
ABV~
THREE PHASE LOADS
CNV~
BNV~
ANV~
BNV~
ANV~
BNV~
ABV~
3
~~ AB
AN
VV
Lags by 30 degrees ABV~
ANV~
ABV~
30o
STAR
THREE PHASE LOADS
Star Connected:Per phase power
)cos( IVP
Power Factor (PF)
For purely resistive load Power Factor = 1.0
Total power: )cos(333 IVPP
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: jXRZL ~Phase angle )(
R
Xatn
A
B C
AI~
CI~
BI~
LZ
LZLZ
N
THREE PHASE LOADS
Star Connected:Per phase power
)cos( IVP
Power factor (PF)
A
B C
AI~
CI~
BI~
LZ
LZLZ
N
ANVV~~
Consider phase for point A and neutral
LII~~ and
3
~~ AB
AN
VV and
)cos(3
LL IV
P Per phase power
)cos(333 LLIVPP Total power: Same as for Delta load
THREE PHASE LOADS SUMMARY
3Z
Load can be connected in STAR or DELTA
A
B
C3G
Generators can be connected in STAR or DELTA
Real Power Reactive Power Apparent Power
)cos(33 IVP
)cos(33 LLIVP
)sin(33 IVQ
)sin(33 LLIVQ
22 QPS
IVS 3
LLIVS 3