05-04-2012, 10:29 AM
EE532 Power System Dynamics and Transients
EE532 Power System Dynamics and Transients.ppt (Size: 407.5 KB / Downloads: 43)
Power System Stability
Modeling Assumptions
SLOWLY VARYING PHASOR
SLOWLY VARYING PHASOR
Classical model
The generator reactance X= Xd’
E’ is the phasor induced voltage
It is assumed that the magnitude
of E’ ‘freezes’ at the value
just prior to disturbance
The N- node network can be represented by the admittance matrix equation
I = Y V
The current injected into node ‘m’
Im = ∑Nm=1 Ymn Vn
The Complex power into node ‘m’ is
Sm=Vm (∑Nm=1 Ymn Vn)*
Let Vm=|Vm|/θm Vn=|Vn|/θn Ymn=|Ymn|/θmn
Starting with
Sm=Vm (∑Nm=1 Ymn Vn)*
Can show
Pm=Re(Sm)=|Vm| ∑nm=1 |Ymn| | Vn| cos (θm - θn - θmn )
Qm=Im(Sm)=|Vm| ∑nm=1 |Ymn| | Vn| sin (θm - θn - θmn )
Real Power
Pm=Re(Sm)=|Vm| ∑Nm=1 |Ymn| | Vn| cos (θm - θn - θmn )
Real power flow is controlled by voltage phase angles θm, θn…
For a line ( or generator with resistance and capacitance neglected, i.e., pure inductive reactance
|Vm|/θm Pmn Vn|/θn
Generator dynamics
Mechanical position
and speed
In steady state synchronous Machines run at synchronous speed
Insteady state synchronous Machines run at synchronous speed
Mechanical position
and speed
Mechanical position
and speed
Back to
Generator dynamics
A generator connected to an infinite bus through a line
Initially Pm=Pe
A generator connected to an infinite bus through a line
Initially Pm=Pe Suppose we increase Pm then speed increases
A generator connected to an infinite bus through a line
Initially Pm=Pe Suppose we increase Pm then speed increases
A generator connected to an infinite bus through a line
Initially Pm=Pe
Lecture 3
Qualitative Analysis
Examples of developing Swing Equations and Power Angle Curves
Equal Area Criterion of Stability