Electrical Power Systems

276 Electrical Power Systems
Power System Stability
11.1 INTRODUCTION
11
Power system stability implies that its ability to return to normal or stable operation after
having been subjected to some form of disturbance. Instability means a condition denoting loss
of synchronism of synchronous machines or falling out of step. Therefore the state of equilibrium,
or stability of a power system commonly alludes to maintaining synchronous operation of the
system. In this chapter, we will focus on this aspect of stability whereby a loss of synchronism
will mean to render the system unstable. Three types of stability are of concern: Steady state,
dynamic and transient stability.
Steady state stability relates to the response of a synchronous machine to a gradually
increasing load. It is basically concerned with the determination of the upper limit of machine
loadings before losing synchronism, provided the loading is increased gradually. Dynamic
stability involves the response to small disturbances that occur on the system, producing
oscillations. The system is said to be dynamically stable if these oscillations do not acquire more
than certain amplitude and die out quickly. If these oscillations continuously grow in amplitude,
the system is dynamically unstable. The source of this type of instability is usually an
interconnection between control systems. Dynamic stability can be significantly improved
through the use of phase lead-lag power system stabilizers. The system’s response to the
disturbance may not become apparent for some 10 to 30 secs.
Transient stability involves the response to large disturbances, which may cause rather
large changes in rotor speeds, power angles, and power transfers. Transient stability is a fast
phenomenon usually evident within a few seconds.
Stability studies of power systems are carried out on a digital computer. In this chapter, we
present special cases to illustrate certain principle and basic concepts.
11.2 INERTIA CONSTANT AND THE SWING EQUATION
Inertia constant and the angular momentum play an important role in determining the transient
stability of a synchronous machine. The per unit inertia constant H in MJ/MVA is defined as the
kinetic energy stored in the rotating parts of the machine at synchronous speed per unit
megavoltampere (MVA) rating of the machine.
Rotor kinetic energy at synchronous speed is given as:
KE = 1
2
2
Jws-mech ´
10 6 –
MJ
...(11.1)