A Method for Solving the Fuel Constrained Unit Commitment Problem

some utilities, contractual or other factors limit the amount of fuel available to certain units or plants. The addition of the fuel constraints severely complicates the unit commitment problem because they can affect how a constrained unit will be used. We therefore developed a method that integrates the fuel dispatch algorithm completely into the unit commitment methodology. The method devel¬ oped is based on Lagrangian relaxation approaches to the unit commitment problem. These methods solve the problem by adjoining the generation and reserve constraints onto the cost function using dual variables. The resulting problem is decom¬ posable into a sequence of single unit problems that can be solved efficiently by dynamic programming. The Lagrangian relaxation approach differs from the tradi¬ tional unit commitment methods in that it does not assume a strict priority ordering of the units. This priority ordering tends to limit the commit decisions in that it precludes certain startups/shutdowns of units solely due to the placement of the units in the priority ordering. Since the priority ordering is obtained heuristically, this can cause suboptimal solutions to be generated. The Lagrangian relaxation approach also has the advantage that most unit-related factors such as mini¬ mum up and down time, time-dependent startup cost and standby operation can be optimally included in the problem. Most important, for our purposes, Lagrangian relaxation allows the complete integration of the fuel dispatch with unit commitment. The optimization method distinguishes between three sets of dual variables in determining the solution, namely variables associated with: