Page 300 - Mathematical Models and Algorithms for Power System Optimization

292 Chapter 8

8.3.2 Basic Concept of the First Stage Control Criterion (Energy Equilibrium)

The major theoretical foundation for the first stage (energy equilibrium) control is an equal area
criterion.
The equal area criterion generally applies to the analysis of a simple single-machine infinite-
bus system only; however, in the initial stage of fault at part i of the system, the rest of the
system has not had severe swing yet, and the inertia constant T Ji of part i of the system is far less
X X
than the sum T Jj of the inertia constants of other parts, that is, T Ji ≪ T Jj . So in the initial
j6¼i j6¼i
stage of the fault, that is, the first stage energy equilibrium control stage, the relation of the
faulty part of system to the rest of the system could be temporarily taken as a simple
relation with a single-machine infinite-bus system. Therefore, as for the energy equilibrium
control in the first stage, the equal area criterion can be used for dynamic analysis for the
faulty part i of the system.
It is known from the equal area criterion that, when the maximum possible deceleration area is
less than the acceleration area, the system is in transient stability state, and the purpose
of the electric braking in the initial period of the fault is to heighten the power angle
characteristic curve and enlarge the deceleration area, so as to decrease the power angle swing
and avoid loss of synchronism in the first swing period. The optimal switch-off time for the
electric braking is discussed via Fig. 8.2. Simply stated, assume the postfault system will restore
to the prefault operation state, the brake is always switched on when removing the fault, and the
resistance is the same.

Fig. 8.2
Contrast of backswing potential energy zones for different brake switch-off time.

In Fig. 8.2A–C, the acceleration area S abcM is equal, that is, the fault scenarios are the same,
whereas the difference lies in the brake switch-off time.