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  1. Power system model parameter values are becoming increasingly uncertain and time-varying. Therefore, it is important to determine the margin in parameter space between a given set of parameter values for which the system will recover from a particular fault, and the nearest parameter values for which it will not recover from that fault. This work presents an efficient method for computing parameter space recovery margins by exploiting the property that the trajectory becomes infinitely sensitive to small changes in parameter value along the operating point’s region of attraction boundary. Consequently, along this boundary the inverse sensitivity of the trajectory approaches zero. The method proceeds by varying parameter values so as to minimize the inverse sensitivity of the system trajectory. Recent results provide theoretical justification for the approach. The efficacy of the method is demonstrated using a modified IEEE 39-bus New England power system test case. 
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  2. The ability of a nonlinear system to recover from a large disturbance to a desired stable equilibrium point depends on system parameter values, which are often uncertain and time varying. A particular disturbance acting for a finite time can be modeled as an implicit map that takes a parameter value to its corresponding post disturbance initial condition in state space. The system recovers when the post-disturbance initial condition lies inside the region of attraction of the stable equilibrium point. Critical parameter values are defined to be parameter values whose corresponding post-disturbance initial condition lies on the boundary of the region of attraction. Computing such values is important in numerous applications because they represent the boundary between desirable and undesirable system behavior. Many realistic system models involve controller clipping limits and other forms of switching. Furthermore, these hybrid dynamics are closely linked to the ability of a system to recover from disturbances. The paper develops theory which underpins a novel algorithm for numerically computing critical parameter values for nonlinear systems with clipping limits and switching. For an almost generic class of vector fields with event-selected discontinuities, it is shown that the boundary of the region of attraction is equal to a union of the stable manifolds of the equilibria and periodic orbits it contains, and that this decomposition persists and the boundary varies continuously under small changes in parameter. 
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