Unformatted text preview: Stability
l The ability of the power system to remain in synchronism
and maintain the state of equilibrium following a
disturbing force
u Steadystate stability: analysis of small and slow disturbances
n u gradual power changes Transient stability: analysis of large and sudden disturbances
n faults, outage of a line, sudden application or removal of load Power Systems I Generator Dynamic Model
l Under normal conditions, the relative position of the rotor
axis and the stator magnetic field axis is fixed
u
u u the angle between the two is the power angle or torque angle, d
during a disturbance, the rotor will accelerate or decelerate w.r.t.
the rotating stator field
acceleration or deceleration causes a change in the power angle Pe
Pe
Te =
=
w e 2p (60 Hz ) Pm
= Tm
w rotor Taccelation = DT = Tm  Te
d 2q m
J
= DT = Tm  Te q m = w ms t + d m
2
dt
Power Systems I w rotor poles
=
2
w ms Generator Dynamic Model
dq m
dd m
d 2q m d 2d m
wm =
= w ms +
am =
=
2
dt
dt
dt
dt 2
d 2q m
d 2d m
J
=J
= Tm  Te
2
2
dt
dt
d 2d m
Jw m
= w mTm  w mTe = Pm  Pe
2
dt
2 WKE
2
1
1
WKE = 2 Jw m = 2 Mw m
M=
= Jw m
wm
w m » w ms 2 WKE
®M »
= Jw ms
w ms Power Systems I Generator Dynamic Model
d 2d m
= Pm  Pe
M
2
dt
poles
d = de =
dm ®
2
p d 2d
p 2 WKE
M2=
2
2 w ms
dt
2 WKE d 2d
= Pm  Pe
2
w s dt
Power Systems I 2 p dd
M 2 = Pm  Pe
2
dt
d 2d
2 WKE d 2d
=
2
w s dt 2
dt 2 WKE d 2d Pm Pe
®
=
2
w s S B dt
SB SB Generator Dynamic Model
2 WKE d 2d
= Pm ( pu )  Pe ( pu )
2
w s S B dt
WKE kinetic energy in MJ at rated speed
=
=H
SB
machine power rating in MVA
2 H d 2d
= Pm ( pu )  Pe ( pu )
2
w s dt
H d 2d
®
= Pm ( pu )  Pe ( pu )
2
p f dt
H d 2d
®
= Pm ( pu )  Pe ( pu )
2
180 f dt
Power Systems I (radians )
(degrees) Synchronous Machine Model E Pmax Xd¢ Pe VT
Pm Round E ¢ = E ¢ Ðd
Rotor
Machine VG = VG Ð0°
Model
B= 1 ¢
Xd 0 Pe0 d
d0 p/2 p power angle curve E ¢ VG
Pe = E ¢ VG B cos(d  90°) =
sin d = Pmax sin d
¢
Xd Power Systems I The Swing Equation
H d 2d
= Pm  Pe
2
p f 0 dt Dynamic Generator Model Pe = Pmax sin d Synchronous Machine Model H d 2d
= Pm  Pmax sin d
2
p f 0 dt
Pm Pe H
p f0 E
ws Power Systems I Forming the Swing Equation Xd¢
VT ...
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 Fall '11
 THOMASBALDWIN
 Energy, Magnetic Field, Electric motor

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