A STABILITY THEORY FOR CONSTRAINED DYNAMIC-SYSTEMS WITH APPLICATIONS TO ELECTRIC-POWER SYSTEMS

This paper develops a stability theory for constrained dynamic systems which are defined as dynamic systems whose state trajectories are res tricted to a particular set within the state space called the feasible operating region, Many physical systems may be modeled as constrained dynamic systems because certain variables or functions of variables a re often required to remain within acceptable ranges, A restricted sta bility region for constrained systems is defined as the set of points whose trajectories start and remain within the feasible operating regi on for all t greater than or equal to 0. The stability analysis is res tricted to this region as trajectories hitting the boundary are infeas ible and considered to be unstable, We also define the restricted asym ptotic stability region ol restricted domain of attraction as the set of points whose trajectories start and remain within the feasible oper ating region for all t greater than or equal to 0 and converge to the stable equilibrium point as t --> infinity. In [4]-[6], Venkatasubrama nian et nl, characterized the stability boundary for differential-alge braic-equation (DAE) systems which are dynamic systems with algebraic equality constraints, In [8], we used their results and some results f rom bifurcation theory to show that for DAE systems, parts of the stab ility boundary are formed by trajectories that are tangent to the boun dary of the solution sheet on which the algebraic equations have a uni que solution, In this paper, using similar techniques as contained in [4], we develop stability results for systems that are constrained to remain within a subset of the state space (i.e., the feasible operatin g region), This modeling framework is particularly useful for represen ting systems with inequality constraints, Also, for systems with equal ity constraints, we can develop an approximate model that is arbitrari ly close to the original system, The main theoretical result of this p aper is a characterization of the boundary of the restricted asymptoti c stability region (i.e., quasistability boundary), Specifically, me s how that the quasistability boundary includes trajectories that are ta ngent to the boundary of the feasible operating region, Our primary ap plication of these results is analyzing electric power system stabilit y following the occurrence of a network fault, We assume that the elec tric power protection system operates to clear the fault condition but that the post-fault trajectories should remain within the feasible op erating region of the new system configuration, A computational proced ure was developed in [8] to estimate the critical clearing time for a network fault based on the tangent trajectory results, This method is also extended in this paper to include the more general constrained dy namic system representation, An example is then included to illustrate the use of this computational method in estimating the critical clear ing time for a network fault.