Exploiting Soft Constraints within Decomposition and Coordination
Methods for Sub-hourly Unit Commitment
Abstract
Unit commitment (UC) is an important problem solved on a daily basis
within a strict time limit. While hourly UC problems are currently
considered, they may not be flexible enough with the fast-changing
demand and the increased penetration of intermittent renewables.
Sub-hourly UC is therefore recommended. This, however, will
significantly increase problem complexity even under the deterministic
setting, and current methods may not be able to obtain good solutions
within the time limit. In this paper, deterministic sub-hourly UC is
considered, with the innovative exploitation of soft constraints –
constraints that do not need to be strictly satisfied, but with
predetermined penalty coefficients for their violations. The key idea is
the “surrogate optimization” concept that ensures multiplier
convergence within “surrogate” Lagrangian relaxation as long as the
“surrogate optimality condition” is satisfied without the need to
optimally solve the “relaxed problem.” Consequently, subproblems can
still be formed and optimized when soft constraints are not relaxed,
leading to a drastically reduced number of multipliers and improved
performance. To further enhance the method, a parallel version is
developed. Testing results on the Polish system demonstrate the
effectiveness and robustness of both the sequential and parallel
versions at finding high-quality solutions within the time limit.