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 gradual power changes faults, outage of a line, sudden application or removal of load u Transient stability: analysis of large and sudden disturbances
n 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 ) Taccelation = DT = Tm  Te Pm = Tm w rotor w rotor poles = 2 w ms d 2q m J = DT = Tm  Te q m = w ms t + d m 2 dt
Power Systems I 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 M 2 = 2 2 w ms dt 2 WKE d 2d = Pm  Pe 2 w s dt
Power Systems I p d 2d M 2 = Pm  Pe 2 dt 2 WKE d 2d d 2d = 2 2 w s dt 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
Xd VT
Pm
Round E = E d Rotor Machine VG = VG 0 Model B= 1 Pmax Pe E Pe0 Xd 0 d0 power angle curve p/2 p d Power Systems I E VG Pe = E VG B cos(d  90) = sin d = Pmax sin d Xd The Swing Equation
H d 2d = Pm  Pe 2 p f 0 dt Pe = Pmax sin d
Dynamic Generator Model Synchronous Machine Model
Forming the Swing Equation H d 2d = Pm  Pmax sin d 2 p f 0 dt
Pm H p f0
Power Systems I Pe E
ws Xd VT ...
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 Spring '11
 THOMASBALDWIN
 Energy, Magnetic Field, Electric motor

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