Spline stochastic dynamic programming for multiple reservoir system operation optimization

The thesis examines spline stochastic dynamic programming (spline SDP) for multireservoir system operation optimization. For a continuous-state SDP, the future value function (FVF) can be approximated when solving the control problem at the discrete points of the state-space by a backward moving algorithm. Spline SDP uses tensor-product multidimensional piecewise cubic polynomials to approximate the FVF. Cubic splines maintain first and second degree continuity throughout the domain, enabling the use of efficient Newton-type nonlinear optimizing algorithms to solve the control problem.; Spline SDP was tested in idealized settings, including a sequence of related multireservoir problems of different dimension (two to five reservoirs) for quadratic and piecewise linear objectives. It was also tested in a realistic setting, the Shasta-Trinity system (two reservoirs in parallel and five hydropower plants, with common water and power demands), for several objectives involving energy value and penalties on shortages. For smooth or fairly well-behaved objective functions the performance of spline SDP is clearly superior to that of the traditional SDP that uses a multidimensional linear approximation of the FVF. For piecewise linear objectives its performance is not inferior to that of the multilinear SDP. The spline SDP's advantage tends to grow with the dimension of the problem. Its progress in the solution of a problem can be effectively monitored by the convexity checker developed here, enabling one to identify instances when problems arise.; The SDP-generated operating policies in the Shasta-Trinity model were tested using two simulation approaches: (1) the interpolated policy model, which uses the SDP policy tables to estimate the best reservoir releases by interpolation for the current state of the system, and (2) the implicit policy model, which uses the SDP future value function (FVF) to optimize the releases in each period. The implicit policy simulation was superior to the interpolated policy simulation. This suggests it is more meaningful to use the derived SDP's future value function, rather than policy tables as has generally been done. The value of using hydrologic state variables with different objective functions is considered.