Stability Analysis
Stability AnalysisS. MeikandasivamStability - DefinitionA
dynamic phenomenon in a power system is, as said above, initiated
by a disturbance in the system. Such a disturbance could as an
example be that a line impedance is changed due to an external
cause. The behaviour of the system after this disturbance depends
of course on a how large this disturbance is. A small disturbance
results usually in small transients in the system that are quickly
damped out, while a larger disturbance will excite larger
oscillations.
The IEEE/CIGRE Joint Task Force on stability terms and
conditions have proposed the following definition in 2004:
Power System stability is the ability of an electric power
system, for a given initial operating condition, to regain a state
of operating equilibrium after being subjected to a physical
disturbance, with most system variables bounded, so that
practically the entire system remains intact.Classification
From Prabha KundurSwing Equations
POWER ANGLE RELATIONSHIP IN A SMIB SYSTEMPower flow equation in
Salient pole model:
Steady state stability limit, which is defined as the maximum
power that can be transmitted in steady state without loss of
synchronism,TRANSIENT STABILITYTransient stability is the ability
of the system to remain stable under large disturbances like short
circuits, line outages, generation or load loss etc. Transient
stability analysis deals with actual solution of the nonlinear
differential equations describing the dynamics of the machines and
their controls and interfacing it with the algebraic equations
describing the interconnections through the transmission
network.Since the disturbance is large, linearized analysis of the
swing equation (which describes the rotor dynamics) is not
possible. Further, the fault may cause structural changes in the
network, because of which the power angle curve prior to fault,
during the fault and post fault may be different.Due to these
reasons, a general stability criteria for transient stability
cannot be established. Stability can be established, for a given
fault, by actual solution of the swing equation.The time taken for
the fault to be cleared (by the circuit breakers) is called the
clearing time.Critical clearing time is the maximum time available
for clearing the fault, before the system loses stability.EQUAL-
AREA CRITERIONTransient stability assessment of an SMIB system is
possible without resorting to actual solution of the swing
equation, by a method known as equalarea criterion.In a SMIB
system, if the system is unstable after a fault is cleared, (t)
increases indefinitely with time, till the machine loses
synchronism. In contrast, in a stable system, (t) reaches a maximum
and then starts reducing as shown in Figure.
The integral gives the area under the Pa curve. A SMIB system is
stable, if the area under the Pa curve, becomes zero at some value
of . This means that the accelerating (positive) area under Pa
curve, must equal the decelerating (negative) area under Pa curve.
SUDDEN CHANGE IN MECHANICAL INPUT
Under steady state/initial condn.Pm = PePmo, delo , ws at point
a.
Sudden increase in input power Pm1Accr. Power Increases, Del
increases, andPe electrical power Increases.
The area A1, during acceleration is given by
At b, even though the accelerating power is zero, the rotor is
running above synchronous speed.Hence, and Pe increase beyond b,
wherein Pe < Pm1 and the rotor is subjected to deceleration. The
rotor decelerates and speed starts dropping, till at point d, the
machine reaches synchronous speed and = max. The area A2, during
deceleration is given by
By equal area criterion A1 = A2. The rotor would then oscillate
between 0 and max at its natural frequency. However, damping forces
will reduce subsequent swings and the machine finally settles down
to the new steady state value 1 (at point b). Stability can be
maintained only if area A2 at least equal to A1, can be located
above Pm1. The limiting case is shown in Fig.5.9, where A2 is just
equal to A1.
13, 90, 131, 19, 136, 14, 24, 59, 38, 191, 79, 181, 61, 202,
248, 165, 133, 157, 46, 185, 183, 250,257, 20, 108
