A need exists to optimally dispatch power generation to meet per-hour requirements on the power grid. This is a well documented and established problem called Unit Commitment (UC). It is commonly formulated as a Mixed Integer Linear Program (MILP), which utilizes intelligent solvers to produce a solution with speed and accuracy. The linear nature of MILP requires linear approximations of nonlinear constraints. This work introduces the Theory of Complementarity in order to remove integer variables, resulting in a continuous rather than a discontinuous solution space. This permits use of classical solution techniques, as well as nonlinear constraints, thereby increasing accuracy. A formulation is developed to demonstrate a proof of concept of the complementarity theory as used in UC. A subset of constraints will be used and the results will be compared against an MILP optimization, for 10-and 26-generator configurations. Similar trends in generator status and total cost are noted.

A need exists to optimally dispatch power generation to meet per-hour requirements on the power grid. This is a well documented and established problem called Unit Commitment (UC). It is commonly formulated as a Mixed Integer Linear Program (MILP), which utilizes intelligent solvers to produce a solution with speed and accuracy. The linear nature of MILP requires linear approximations of nonlinear constraints. This work introduces the Theory of Complementarity in order to remove integer variables, resulting in a continuous rather than a discontinuous solution space. This permits use of classical solution techniques, as well as nonlinear constraints, thereby increasing accuracy. A formulation is developed to demonstrate a proof of concept of the complementarity theory as used in UC. A subset of constraints will be used and the results will be compared against an MILP optimization, for 10-and 26-generator configurations. Similar trends in generator status and total cost are noted.