Symmetry breaking in MILP formulations for Unit Commitment problems

Abstract

Please cite this article as: Ricardo M. Lima, Augusto Q. Novais, Symmetry Breaking in MILP Formulations for Unit Commitment Problems, Computers and Chemical Engineering (2015), http://dx.doi.org/10. 1016/j.compchemeng.2015.11.004 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. • Symmetry issues are discussed in the context of UC formulations.• Three sets of SBC are proposed and analyzed.• Three well-known UC MILP models are used to implement the SBC.• The results presented are completely disruptive compared with the results presented in the literature.• The SBC derived have a clear advantage over general methods available in two MILP solvers. *HighlightsPage 2 of 43 show that problems that could not be solved to optimality within hours can be solved with a relatively small computational burden if the symmetry breaking constraints are assumed.The proposed symmetry breaking constraints are also compared with the symmetry breaking methods included in two MILP solvers, and the symmetry breaking constraints derived in this work have a distinct advantage over the methods in the MILP solvers.

Combining Lagrangian relaxation, benders decomposition, and the level bundle method in the stochastic hydrothermal unit‐commitment problem

“…In Equations (5) and (6), z h,u,t , u h,u,t and w h,u,t are, respectively, the start-up, shut-down and status decisions of hydropower plant h's generating unit u in time t. Additionally, TU H h and TD H h are, respectively, the minimum uptime and downtime of hydro plant h's units. The set H is the set of hydropower plants and set U h is the set of generating units of plant h. Constraint (7) aims at reducing the symmetry 26 of the hydro problem: unit u + 1 of plant h can only operate if unit u of the same plant is operating in time t. In Equation 7, U gr h,j is the set of generating units in the j group of similar units installed at plant h.…”

“…To account for possible load curtailments or excess of generation, we introduce the slack variables δ + b,t,s and δ − b,t,s , respectively. The nonnegativity requirement for these variables is enforced in Equation (26). The flow f l, t, s is given in Equation 27, where x l is line l's reactance, and θ b f l ð Þ,t,s and θ b t l ð Þ,t,s are line l's from and to buses, respectively.…”

Energy Storage System Analysis Review for Optimal Unit Commitment

“…LR is combined with a genetic algorithm (GA) to obtain satisfactory results for operational cost minimization UC problem in [64]. By implementing MILP, many UC problems involving ESSs have been solved with objective functions such as peak shaving [65], maximizing energy production by reducing curtailment [66], minimization of cost [67][68][69][70][71], minimization of emissions [72], and so on.…”

An Improved Mixed Integer Linear Programming Approach Based on Symmetry Diminishing for Unit Commitment of Hybrid Power System

“…The results demonstrated that their work is superior to the conventional method with the solution optimality and computation efficiency are improved a lot. Lima et al [6] made a comparison between the case with and without symmetry breaking constraints. The results of their study state that symmetry breaking constraints performance well in UC MILP models without having a significant impact on the size of the model.…”

“…Therefore, this paper presents an improved symmetry breaking approach, which is derived from Reference [1] to diminish symmetry in an efficient way. The UC MILP model comes from [7,8] is taken in this paper without considering ramping up and down constraints as these constraints may prevent the utilization of symmetry breaking constraints [6].…”