Application of dynamic programming to optimisation of hydroelectric/steam power-system operation

The paper discusses the computational aspects in the application of dynamic programming to the schedule of generation among hydroelectric and steam units in a power system for minimum operating cost. An attractive feature of this method is its ability to handle restrictions upon problem variables, such as limits upon hydroelectric plant discharge and river elevation. A computation algorithm is presented. In order to avoid excessive computer requirements, an iterative method of solution is developed using a series of grids or meshes with increasingly smaller distances between its points. A coarse grid will cover the major portion of the available operating space. The next grid points are located around the optimum solution found with the previous grid. The convergence behaviour for a chosen example is numerically analyzed. It is found that the solution is almost unique with respect to the optimum cost of operation. The optimum trajectory itself is dependent upon the location of the first grid in the available space. In any series of iterations, a solution with an accuracy of practical value would require four or more iterations. Typical convergence behaviour of both the trajectory and the return function are demonstrated from computer experiments. The paper also discusses some aspects of the use of the method for online control purposes.