Stochastic optimization of a hydroelectric reservoir using piecewise polynomial approximations

We propose a method for optimizing a single hydro-electric reservoir using a piecewise polynomial approximation of the future value functions. Unlike previous methods based on splines, we avoid discretizing the inflow distribution. Instead, we carry out the expectation step of dynamic programming using an exact, easy-to-evaluate formula for the integral of a piecewise polynomial function. We then apply our method to solving a model which assumes a piecewise linear reward function of the energy produced, and takes into account the turbine head effects.