An analytical solution to the economic dispatch problem

This letter treats the basic problem of economic operation of power systems and presents a mathematical derivation that proves that the classic economic dispatch (ED) problem, with quadratic-convex cost functions, can be solved analytically, i.e., without any approximations or need for numerical iterative optimization algorithms. Duality theory is employed to determine both the exact primal and exact dual solutions. All this requires, at most, are 2n function evaluations. It is stated, therefore, that the use of an ED model as an optimization-based electricity auction does not cause any conflict of interest.