Optimal scheduling of thermal generating units

Scheduling the operation of thermal generating units involves the selection of units to be placed in operation and the allocation of the load among them- These two decisions must be taken so as to minimize the sum of tile startup, banking, and expected riming costs subject to the demand, spinning-reserve, and minimum down-time and up-time constraints and, sometimes, to the following two additional limitations: a unit should not be started up more than once a day; and no more than two units of the same plant should be started up simultaneously. This optimization problem is formulated in this paper as a mixed-integer nonlinear programming problem. Then, by following the Bender's approach, the problem is partitioned into a nonlinear and a pure-integer nonlinear programming problem- The First problem, which represents the economic dispatch problem, is not solved here. The second problem, usually called the unit commitment problem, is solved by a variational method and a branch-and-bound algorithm. Numerical results obtained for a network of ten generating units are presented.