An algorithm for the optimal scheduling of variable head hydro and thermal plants

The authors present an efficient and optimal method of scheduling thermal plants in coordination with fixed and variable hydro units. From the system model of the cost function, energy balance and water availability constraints, a set of coordination equations were derived from Kuhn-Tucker conditions of optimality. The equations when linearized were found to be partially separable. By neglecting the second order differentials of power losses the equations were made separable and this enabled the coordination equations to be reduced to two sets of equations and thus the Lagrange multiplier for the water availability constraints can be solved separately from unit generations instead of simultaneously. once the Lagrange multiplier of the reservoir constraint was determined the values of other variables were calculated by back substitutions. The reduction of the coordination equations reduced the size of the matrix to be inverted. Furthermore the matrix has a special structure that allowed its inverse to be computed directly and easily. Case studies with various systems were carried out to test the efficiency of the proposed algorithm and the detailed result of one test case is discussed