[en] Sensitivity analysis is an important tool for describing power system dynamic behavior in response to parameter variations. It is a central component in preventive and corrective control applications. 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. 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 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. This is an essential feature for use in optimization applications. 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. The accuracy and the computational efficiency of the proposed approach are demonstrated in comparison with the forward sensitivity analysis approach. 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 fields.

[en] Highlights: • Addresses the problem water shortages and effect weather conditions on plant performance. • Presents the problem as a stochastic programming problem. • Uses an efficient new algorithm BONUS to solve the problem. • Provides real time optimization solutions for various scenarios. - Abstract: A stochastic optimization framework for water management in cooling-constrained power plants is proposed. The approach determines optimal set-points to maximize power output in the presence of uncertain weather conditions and water intake constraints. Weather uncertainty is quantified in the form of ensembles using the state-of-the-art numerical weather prediction model WRF. The framework enables the handling of first-principles black-box simulation models by using the reweighting scheme implemented in the BONUS solver. In addition, it enables the construction of empirical distributions from limited samples obtained from WRF. Using these computational capabilities, the effects of cooling constraints and weather conditions on generation capacity are investigated. In a pulverized coal power plant study it has been found that weather fluctuations make the maximum plant output vary in the range of 5–10% of the nominal capacity in intraday operations. In addition, it has been found that stochastic optimization can lead to daily capacity gains of as much as 245 MW h over current practice and enables more robust bidding procedures. It is demonstrated that reweighting schemes can enable real-time implementations