Developments in Stochastic Dynamic Programming for Reservoir Operation Optimization

Operation of reservoir systems represents a sequential stochastic decision problem. Stochastic dynamic programming (SDP) is a natural formulation of the problem for developing optimal decision rules, or the information needed to make optimal decisions. Pete Loucks was a pioneer in this area (Loucks 1968, Gablinger and Loucks 1970, and Loucks and Falkson 1970). The curse of dimensionality plagues dynamic programming models. Early efforts used composite representations of hydropower systems. More recent efforts use higher order approximations of the future value function and better use of hydrologic information. A better description of the joint distribution of flows and forecasts is provided by Sampling SDP (Kelman, et al. 1990; Faber and Stedinger 2001; Kim, et al. 2007; Eu, et al. 2011; Côté, et al. 2011). Ongoing work is described that uses Sampling SDP with a state-space corridor approximation of the future value function and radial-basis-functions for interpolation among nonequally spaced points.