power flow equation
TRANSCRIPT
-
7/28/2019 Power Flow Equation
1/16
POWER FLOWS
EQUATIONS for
ALTERNATOR & MOTOR
-
7/28/2019 Power Flow Equation
2/16
Fig A shows the circuit model of a phase cylindrical rotor
synchronous generator.Let, V = terminal voltage per phase,
Ef= excitation voltage per phase,
Ia
= armature current,
= phase angle between Efand V
The phasor diagram at lagging power factor is shown in
fig B.
The synchronous impedance is given by Zs = Ra +j XS =Zs
-
7/28/2019 Power Flow Equation
3/16
Fig. A Fig. B
-
7/28/2019 Power Flow Equation
4/16
Fig C shows the impedance
triangle.
Let the subscripts i, o, g and m
denote input, output, generator and
motor respectively.
By KVL in Fig. A,
S
a
ZZ
a
S
Z
X
R
R
X
1
1
tan90
tan
s
f
a
asf
Z
VEI
IZVE
Fig. C
-
7/28/2019 Power Flow Equation
5/16
Complex Power Output Of The Generator
Per Phase (Sog )
Zs
Z
s
Z
s
f
Z
s
f
ogog
Z
s
Z
s
f
og
Z
s
Z
s
f
og
Zs
f
s
f
aogogog
Z
VjZ
V
Z
VE
jZ
VE
jQP
Z
V
Z
VES
Z
V
Z
EVS
Z
VEV
Z
VEVVIjQPS
sincossincos
0
00
22
2
*
**
-
7/28/2019 Power Flow Equation
6/16
Real Power Output Of The Generator Per Phase
(Pog ) = Electrical Power Developed by the
Generator
RZ
V
Z
VEorP
RZ
V
Z
VEP
butR
Z
V
Z
VEP
ZZ
V
Z
VEP
S
Z
s
f
og
S
Z
s
f
og
ZZ
S
Z
s
f
og
s
ZZ
s
Z
s
f
og
2
2
2
2
2
2
2
sin
)(90cos
90cos
Rcossincecoscos
-
7/28/2019 Power Flow Equation
7/16
Reactive Power Output Of The Generator Per
Phase (Qog )
s22
s2
2
s2
2
s
2
Xcos
X)(90sin
90Xsin
Xsinsincesinsin
S
Z
s
fog
S
Z
s
f
og
ZZ
S
Z
s
f
og
s
ZZ
s
Z
s
f
og
Z
V
Z
VEQor
Z
V
Z
VEQ
but
Z
V
Z
VEQ
ZZV
ZVEQ
-
7/28/2019 Power Flow Equation
8/16
Complex Power Input Of The Generator
Per Phase (Sig )
Z
s
fZ
s
fZ
s
fZ
s
figig
Z
s
f
Z
s
f
ig
Z
s
Z
s
f
fig
Zs
f
f
s
f
fafigigig
Z
VEj
Z
VE
Z
Ej
Z
EjQP
Z
VE
Z
ES
Z
V
Z
EES
Z
VEE
Z
VEEIEjQPS
sincossincos
)(
0
22
2
**
*
-
7/28/2019 Power Flow Equation
9/16
Real Power Input Of The Generator Per
Phase (Pig)
-
7/28/2019 Power Flow Equation
10/16
Reactive Power Input Of The Generator
Per Phase (Qig )
-
7/28/2019 Power Flow Equation
11/16
Prove difference between input output must be equalto ohmic loss.
-
7/28/2019 Power Flow Equation
12/16
Maximum Power Output Of The Generator Per
Phase (Pog)(max)
-
7/28/2019 Power Flow Equation
13/16
-
7/28/2019 Power Flow Equation
14/16
Maximum Power Input Of The Generator Per
Phase (Pig)(max)
-
7/28/2019 Power Flow Equation
15/16
-
7/28/2019 Power Flow Equation
16/16
Power Flow Equations For A Generator With
Armature Resistance Neglected