CAJ | 학술논문

提出一种含四类 0-1 变量更为简洁-紧凑的机组组合混合整数线性规划(mixed-integer linear programming,MILP)模型,有效提高了求解效率.通过引入辅助变量表示冷启动状态,提出一种启动费用的线性表达,同时增强了MILP模型的简洁性和紧凑性;利用爬坡速度和最小运行时间限制,提出新的机组出力约束表达,极大地压缩了机组出力的可行域,进一步增强了紧凑性.更简洁的模型,提高了线性规划松弛的求解效率;更紧凑的模型,缩小了最优解的寻优空间,使线性规划松弛解更接近 MILP 最优解.对 10~1000 机 24时段系统计算的结果表明,所提模型在获得高质量解的同时,可提高求解效率数十倍,尤其适合于大规模系统.
제출일충함사류 0-1 변량경위간길-긴주적궤조조합혼합정수선성규화(mixed-integer linear programming,MILP)모형,유효제고료구해효솔.통과인입보조변량표시랭계동상태,제출일충계동비용적선성표체,동시증강료MILP모형적간길성화긴주성;이용파파속도화최소운행시간한제,제출신적궤조출력약속표체,겁대지압축료궤조출력적가행역,진일보증강료긴주성.경간길적모형,제고료선성규화송이적구해효솔;경긴주적모형,축소료최우해적심우공간,사선성규화송이해경접근 MILP 최우해.대 10~1000 궤 24시단계통계산적결과표명,소제모형재획득고질량해적동시,가제고구해효솔수십배,우기괄합우대규모계통.
Compared with the models for the unit commitment problem in literatures, this paper proposed a more compact and tighter mixed-integer linear programming (MILP) model using four sets of binary variables. The proposed model held higher solving efficiency. By introducing auxiliary variables to represent the cold start-up status, the start-up cost was formulated as a linear expression, which improved the compactness and tightness of the MILP model simultaneously. Using the ramp rate and minimum uptime limits, new expressions of generation limits were proposed as well, which could shrink the feasible region of the power output significantly with a much tighter model. The efficiency of solving linear programming relaxations of the proposed model is higher because of the more compact model. Its linear programming relaxed solution is nearer to the MILP optimal solution due to the tighter model, since the search space to find the optimal solution is reduced. The results of the systems which range in size from 10 to 1000 units during 24 periods indicate that the proposed model can obtain high-quality solutions. Moreover, the solving efficiency can be improved by dozens of times, especially for large-scale systems.