Real‐time forecasting and daily operation of a multireservoir system during floods by linear quadratic Gaussian control

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Abstract
The problem of short‐term (daily) operation of a multireservoir system during floods is examined. The problem is how to use all available real‐time information to solve the “tactical” problem of regulating reservoirs to minimize the expected value of flood damage during a relatively short operating horizon and to do so consistently with the long‐term operating strategy. A state‐space mathematical model is presented for short‐term forecasting of river flows and description of the dynamics of a multireservoir system. The model includes reduced‐order state‐space unit hydrographs to forecast storm runoff from effective rainfall and state‐space representations of linear flood routing. The optimization problem is solved in the framework of discrete‐time linear quadratic Gaussian (LQG) control. LQG control is a computationally efficient and flexible method of solving the large‐dimensional optimization problems associated with the solution of the tactical problem of short‐term operation of reservoirs. For application of the LQG control methodology the system must be represented in state‐space form with quadratic cost functions subject to linear equality constraints given by the state transition equations. The scheme was found to be suitable for operation under moderate flood conditions when capacity constraints are not likely to become binding. The methodology has been applied and tested in a real‐world case.