A NEW FORMULATION FOR THE STOCHASTIC-CONTROL OF SYSTEMS WITH BOUNDED STATE VARIABLES - AN APPLICATION TO A SINGLE RESERVOIR SYSTEM

A new formulation is presented for the analysis of reservoir systems s ynthesizing concepts from the traditional stochastic theory of reservo ir storage, moments analysis and reliability programming. The analysis is based on the development of the first and second moments for the s tochastic storage state variable. These expressions include terms for the failure probabilities (probabilities of spill or deficit) and cons ider the storage bounds explicitly. Using this analysis, expected valu es of the storage state, variances of storage, optimal release policie s and failure probabilities useful information in the context of reser voir operations and design, can be obtained from a nonlinear programmi ng solution. The solutions developed from studies of single reservoir operations on both an annual and monthly basis, compare favorably with those obtained from simulation. The presentation herein is directed t o both traditional reservoir storage theorists who are interested in t he design of a reservoir and modern reservoir analysts who are interes ted in the long term operation of reservoirs.