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

A Stability-constrained Optimization Framework for Lur'e Systems with Applications in Power Grids