UNIT- V POWER SYSTEM STABILITY

EE 1352 POWER SYSTEM ANALYSIS

Questions and Answers

UNIT- V POWER SYSTEM STABILITY

What is power system stability?
The stability of an interconnected power system means is the ability of the power system is to return or regain to normal or stable operating condition after having been subjected to some form of disturbance.
How power system stability is classified?

What is rotor angle stability?
Rotor angle stability is the ability of interconnected synchronous machines of a power system to remain in synchronism.
What is steady state stability?
Steady state stability is defined as the ability of the power system to bring it to a stable condition or remain in synchronism after a small disturbance.
What is steady state stability limit?
The steady sate stability limit is the maximum power that can be transferred by a machine to receiving system without loss of synchronism
What is transient stability?
Transient stability is defined as the ability of the power system to bring it to a stable condition or remain in synchronism after a large disturbance.
What is transient stability limit?
The transient stability limit is the maximum power that can be transferred by a machine to a fault or a receiving system during a transient state without loss of synchronism.
Transient stability limit is always less than steady state stability limit

What is dynamic stability?
It is the ability of a power system to remain in synchronism after the initial swing (transient stability period) until the system has settled down to the new steady state equilibrium condition
What is voltage stability?
It is the ability of a power system to maintain steady acceptable voltages at all buses in the system under normal operating conditions and after being subjected to a disturbance.
State the causes of voltage instability.
A system enters a state of voltage instability when a disturbance, increase in load demand, or change in system condition causes a progressive and uncontrollable drop in voltage
The main factor causing instability is the inability of the power system to meet the demand for reactive power.
Write the power angle equation and draw the power angle curve.

P=(V_s V_r)/X_T sin⁡δ
Where, P – Real Power in watts
Vs – Sending end voltage; Vr- Receiving end voltage
XT - Total reactance between sending end receiving end
δ - Rotor angle.
Power angle curve


Write the expression for maximum power transfer.
P_max=(V_s V_r)/X_T
Write the swing equation for a SMIB (Single machine connected to an infinite bus bar) system.
H/πf (d^2 δ)/(dt^2 )=P_m-P_e
Since M in p.u=H/πf
M(d^2 δ)/(dt^2 )=P_m-P_e
Where H = inertia constant in MW/MVA
f = frequency in Hz
M = inertia constant in p.u


Define swing curve.
The swing curve is the plot or graph between the power angle δ and time t. From the nature of variations of δ the stability of a system for any disturbance can be determined.

In a 3 machine system having ratings G1, G2 and G3 and inertia constants M1, M2 and M3.What is the inertia constants M and H of the equivalent system.
M_eq=(M_1 G_1)/G_b +(M_2 G_2)/G_b +(M_3 G_3)/G_b

H_eq=(πfM_eq)/G_b
Where G1, G2, G3 – MVA rating of machines 1, 2, and 3
Gb = Base MVA or system MVA
State the assumptions made in stability studies.
Machines represents by classical model
The losses in the system are neglected (all resistance are neglected)
The voltage behind transient reactance is assumed to remain constant.
Controllers are not considered ( Shunt and series capacitor )
Effect of damper winding is neglected.
State Equal Area Criterion
The equal area criterion for stability states that the system is stable if the area under P – δ curve reduces to zero at some value of δ.
This is possible if the positive (accelerating) area under P – δ curve is equal to the negative (decelerating) area under P – δ curve for a finite change in δ. hence stability criterion is called equal area criterion.



Define critical clearing angle.
The critical clearing angleδ_cc, is the maximum allowable change in the power angle δ before clearing the fault, without loss of synchronism.
The time corresponding to this angle is called critical clearing time,t_cc.It can be defined as the maximum time delay that can be allowed to clear a fault without loss of synchronism.
List the methods of improving the transient stability limit of a power system.
Reduction in system transfer reactance
Increase of system voltage and use AVR
Use of high speed excitation systems
Use of high speed reclosing breakers
What are the numerical integration methods of power system stability?
Point by point method or step by step method
Euler method
Modified Euler method
Runge-Kutta method(R-K method)




What is power system stability?
The stability of an interconnected power system means is the ability of the power system is to return or regain to normal or stable operating condition after having been subjected to some form of disturbance.
How power system stability is classified?

What is rotor angle stability?
Rotor angle stability is the ability of interconnected synchronous machines of a power system to remain in synchronism.
What is steady state stability?
Steady state stability is defined as the ability of the power system to bring it to a stable condition or remain in synchronism after a small disturbance.
What is steady state stability limit?
The steady sate stability limit is the maximum power that can be transferred by a machine to receiving system without loss of synchronism
What is transient stability?
Transient stability is defined as the ability of the power system to bring it to a stable condition or remain in synchronism after a large disturbance.
What is transient stability limit?
The transient stability limit is the maximum power that can be transferred by a machine to a fault or a receiving system during a transient state without loss of synchronism.
Transient stability limit is always less than steady state stability limit

What is dynamic stability?
It is the ability of a power system to remain in synchronism after the initial swing (transient stability period) until the system has settled down to the new steady state equilibrium condition
What is voltage stability?
It is the ability of a power system to maintain steady acceptable voltages at all buses in the system under normal operating conditions and after being subjected to a disturbance.
State the causes of voltage instability.
A system enters a state of voltage instability when a disturbance, increase in load demand, or change in system condition causes a progressive and uncontrollable drop in voltage
The main factor causing instability is the inability of the power system to meet the demand for reactive power.
Write the power angle equation and draw the power angle curve.

P=(V_s V_r)/X_T sin⁡δ
Where, P – Real Power in watts
Vs – Sending end voltage; Vr- Receiving end voltage
XT - Total reactance between sending end receiving end
δ - Rotor angle.
Power angle curve


Write the expression for maximum power transfer.
P_max=(V_s V_r)/X_T
Write the swing equation for a SMIB (Single machine connected to an infinite bus bar) system.
H/πf (d^2 δ)/(dt^2 )=P_m-P_e
Since M in p.u=H/πf
M(d^2 δ)/(dt^2 )=P_m-P_e
Where H = inertia constant in MW/MVA
f = frequency in Hz
M = inertia constant in p.u


Define swing curve.
The swing curve is the plot or graph between the power angle δ and time t. From the nature of variations of δ the stability of a system for any disturbance can be determined.

In a 3 machine system having ratings G1, G2 and G3 and inertia constants M1, M2 and M3.What is the inertia constants M and H of the equivalent system.
M_eq=(M_1 G_1)/G_b +(M_2 G_2)/G_b +(M_3 G_3)/G_b

H_eq=(πfM_eq)/G_b
Where G1, G2, G3 – MVA rating of machines 1, 2, and 3
Gb = Base MVA or system MVA
State the assumptions made in stability studies.
Machines represents by classical model
The losses in the system are neglected (all resistance are neglected)
The voltage behind transient reactance is assumed to remain constant.
Controllers are not considered ( Shunt and series capacitor )
Effect of damper winding is neglected.
State Equal Area Criterion
The equal area criterion for stability states that the system is stable if the area under P – δ curve reduces to zero at some value of δ.
This is possible if the positive (accelerating) area under P – δ curve is equal to the negative (decelerating) area under P – δ curve for a finite change in δ. hence stability criterion is called equal area criterion.



Define critical clearing angle.
The critical clearing angleδ_cc, is the maximum allowable change in the power angle δ before clearing the fault, without loss of synchronism.
The time corresponding to this angle is called critical clearing time,t_cc.It can be defined as the maximum time delay that can be allowed to clear a fault without loss of synchronism.
List the methods of improving the transient stability limit of a power system.
Reduction in system transfer reactance
Increase of system voltage and use AVR
Use of high speed excitation systems
Use of high speed reclosing breakers
What are the numerical integration methods of power system stability?
Point by point method or step by step method
Euler method
Modified Euler method
Runge-Kutta method(R-K method)