Exploiting Soft Constraints within Decomposition and Coordination Methods for Sub-hourly Unit Commitment

Abstract

Unit commitment (UC) is an important problem\nsolved on a daily basis within a strict time limit. While hourly UC problems\nare currently considered, they may not be flexible enough with the fast-changing\ndemand and the increased penetration of intermittent renewables. Sub-hourly UC\nis therefore recommended. This, however, will significantly increase problem\ncomplexity even under the deterministic setting, and current methods may not be\nable to obtain good solutions within the time limit. In this paper, deterministic\nsub-hourly UC is considered, with the innovative exploitation of soft\nconstraints – constraints that do not need to be strictly satisfied, but with\npredetermined penalty coefficients for their violations. The key idea is the\n“surrogate optimization” concept that ensures multiplier convergence within “surrogate”\nLagrangian relaxation as long as the “surrogate optimality condition” is\nsatisfied without the need to optimally solve the “relaxed problem.” Consequently,\nsubproblems can still be formed and optimized when soft constraints are not\nrelaxed, leading to a drastically reduced number of multipliers and improved\nperformance. To further enhance the method, a parallel version is developed.\nTesting results on the Polish system demonstrate the effectiveness and\nrobustness of both the sequential and parallel versions at finding high-quality\nsolutions within the time limit.