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This paper addresses short-term scheduling of hydrothermal systems by using extended differential dynamic programming and mixed coordination. The problem is first decomposed into a thermal subproblem and a hydro subproblem by relaxing the supply-demand constraints. The thermal subproblem is solved analytically. The hydro subproblem is further decomposed into a set of smaller problems that can be solved in parallel. Extended differential dynamic programming and mixed coordination are used to solve the hydro subproblem. Two problems are tested and the results show that the new approach performs well under a simulated parallel processing environment, and high speedup is obtained. The method is then extended to handle unpredictable changes in natural inflow by utilizing the variational feedback nature of the control strategy. A quick estimate on the impact of an unpredictable change on total cost is also obtained. Numerical results show that estimates are accurate, and unpredictable change in natural inflow can be quickly and effectively handled.