Combined heat and power (CHP) economic dispatch solved using Lagrangian relaxation with surrogate subgradient multiplier updates

This paper presents a flexible algorithm to solve the combined heat and power (CHP) economic dispatch problem. The CHP economic dispatch is solved in two levels known as the lower level and higher level. The higher level is the optimization of the surrogate dual function for the relaxed global constraints in which the surrogate subgradient is used to update the Lagrangian multipliers. Coherently, the lower levels are the optimization of the subproblems taking in count each of its local constraints. Flexibility for the choice of algorithm is given at the lower levels optimization techniques with the condition that the algorithm is able to improve its search at each iteration. It is also seen that simple step size rules such as the ‘square summable but not summable’ and ‘constant step size’ could be used easily and leads the method to convergence. In addition this paper illustrates the ear clipping method used to modify the common nonconvex feasible region of CHP benchmark problems to a convex region which subsequently enhances the search for an optimal solution. The algorithm is then justified through a numerical test on three benchmark CHP problem with a nonconvex feasible region. Results prove that the algorithm is reliable and could be easily implemented even on a much complex and nonconvex problems.