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.
VALIDATION AND EXTENSION OF THE MATHEMATICAL EXPRESSION RESPONSE TYPE: APPLICATIONS OF SCHEMA THEORY TO AUTOMATIC SCORING AND ITEM GENERATION IN MATHEMATICS