| The cyclical demand for electricity over a course of a day requires utility company to plan for power generation on an hourly basis for up to a week at a time. The corresponding problem is called classical unit commitment problem, which can be formulated as an optimization problem. Due to a very large number of decision and state variables of the problem, the unit commitment problem is considered a large-scale optimization problem, which involves scheduling of generators over a set of time periods to satisfy demand constraints and operating constraints to minimize the total cost. A typical unit commitment system contains 10 to 100 generating units. Each generating unit may have minimum up-time and minimum down-time, ramping constraints and other special constraints varying from system to system. This is categorized as a non-linear, mixed integer dynamic programming or/and NP-hard combinatorial problem. Ad hoc methods have been historically used to produce generator scheduling. However systematic techniques have been sought because an optimal schedule could potentially yield a large cost saving even if the improvement is in a small percentage. Due to the characteristics of the problem, separating the static and dynamic aspects of the problem can behandled by an appropriate decomposition scheme. It enables the whole problem to be solved by solving only optimization problems with reasonable sizes, homogeneous, and well known structures. This is in contrast to the popular attempts to solving the problem via the dual side which often result in sub-optimality. Such methods employ heuristics to modify dual solutions usually approximated from the decomposed sub-problems to achieve primal feasible solutions. Our methodology is to attack the problem via its primal side. The strategy used is to take advantage of the special characteristics of the problem. Employing a customized sub-problem optimizer, the solution to each sub-problem is global and exact even if it consumes dramatically less time than other methods. Coordination of the sub-problems' exact solutions is then performed with some heuristics applied to obtain optimal or near optimal solutions. The test results using realistic data demonstrate the advantages of the proposed approach. |
