In conclusion, this paper focuses primarily on the power system dynamics, but the approach is general and can be applied to hybrid dynamical systems in a broader range of = +1) large-scale computations using the second-level adjoint sensitivity systems (2.-LASS) for obtaining all of the second-order sensitivities. The accuracy and the computational efficiency of the proposed approach are demonstrated in comparison with the forward sensitivity analysis approach. Moreover, our approach includes a consistent treatment of systems with switching, such as dc exciters, by deriving and implementing the adjoint jump conditions that arise from state-dependent and time-dependent switchings. This is an essential feature for use in optimization applications. The proposed approach is highly efficient for calculating sensitivities of larger systems and is consistent, within machine precision, with the function whose sensitivity we are seeking. In this paper, we investigate, implement, and test a discrete adjoint sensitivity approach whose computational effort is effectively independent of the number of sensitivity parameters. The existing approaches for sensitivity calculations, namely, finite-difference and forward sensitivity analysis, require a computational effort that increases linearly with the number of sensitivity parameters. It is a central component in preventive and corrective control applications. Sensitivity analysis is an important tool for describing power system dynamic behavior in response to parameter variations.
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