Page 295 - Mathematical Models and Algorithms for Power System Optimization

Local Decoupling Control Method for Transient Stability of a Power System 287

In theoretical analysis and simulation calculations, the mathematical models selected are the
most simplified, and the control measures taken are also single, whereas some technical details
are ignored. In addition, the network used for calculation is also given after the equivalent
simplification of the actual system. But these simplifications and approximations do not affect
the conclusions and can make the issues discussed clearer and certain, which will be more
conducive to understanding and explaining the problem.
In this chapter, Section 8.2 provides the ideas of two stage local control via constructing a new
state space (local equilibrium state); Section 8.3 describes the concept for system stability
control via two stage local controls; Section 8.4 gives mathematical formulation and proof for
the first stage control criterion; Section 8.5 proves that the new constructed state space for the
second stage control criterion, which is observable and decoupled by a mathematical theory,
from which the new state space is topologically equivalent to the original system state space;
Section 8.6 expounds on the general simulation calculation process for two stage control;
Section 8.7 provides a numerical calculation model in simulation calculation for two stage
control; and Section 8.8 makes a simulating calculation for a small-scale example, by which the
correctness and effectiveness of the proposed mathematical theory and relevant criteria has
been verified.

8.2 Basic Ideas of Solving the Problem

8.2.1 Analysis of Two Scenarios in Power System Instability

There are two scenarios of stability loss in the power system:

(1) The local generator loses its synchronism with the system within the first swing period.
(2) The local generator does not lose its synchronism with the system within the first swing
period, but it loses synchronism in the following swing period as a result of the severe
oscillation of the system.

In the first scenario, the main reason is that a serious short circuit fault happened near the
generator without timely and effective control measures. Because of the short circuit, the local
generator only provides limited power (three-phase short circuit is zero power) for the
system, and at the beginning of the moment, due to the inertia, the input shaft power is almost
the same as that before the failure. Therefore, the power balance of the local generators is
destroyed, and the generator rotor will be quickly accelerated by the input shaft power from the
prime mover, thus increasing the relative angle between the local generator and the rest of the
system.

It is worth noting, however, that at the beginning of the first swing cycle of the system, the rest
of the system has not yet had a serious swing.