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lecture19 - Stability l The ability of the power system to...

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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 Steady-state 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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