  For many nonlinear control systems, the chosen equilibrium determines both
the steady-state efficiency and the dynamic performance. This paper addresses
the issue of obtaining an optimal equilibrium in terms of some steady-state
operation criteria for a Lur'e-type system and such an equilibrium can also
guarantee a sufficiently large stability region in the dynamic domain such that
the system can tolerate some given disturbance. For this purpose, a set of
computationally tractable algebraic constraints, which can properly represent
the stability certificate under the optimization framework, are proposed. The
existing methods formulate the dynamic performance under the optimization
framework by discretizing the differential-algebraic equations, which are
computationally intractable for large-scale Lur'e systems like power grids.
Dissimilarly, the introduced approach first constructs the stability region
based on quadratic Lyapunov functions. Then, a novel method is proposed to
project the stability region onto the feasible domain of the optimization
problem such that the stability certificate can be incorporated into the
optimization framework easily. In the transient stability-constrained optimal
power flow (TSCOPF) problem of power systems, researchers look for a
steady-state operating point with the minimum generation costs that can
maintain system stability under some given transient disturbances. The proposed
approach is applied to develop a scalable TSCOPF framework for power systems.
The TSCOPF model is tested on the IEEE 118-Bus power system.
