考虑回水顶托影响的梯级库群日前调峰MILP模型
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摘要
水电日前调峰优化调度需要同时考虑电网、水库及机组多重约束,本质上属于复杂的多维、动态、非凸、非线性规划问题,将回水顶托影响考虑到模型当中进一步加剧了模型的求解难度。本文建立考虑回水顶托的梯级水库混合整数线性规划(MILP)96点调峰模型,通过将回水顶托水库中多个非线性约束聚合成单个四维超曲面约束的方式减少模型整体非线性约束个数,并采用SOS2约束对该模型进行线性化处理,最终实现模型高精度高效求解。以西南地区某梯级库群为工程背景,选取汛枯期4种典型日方案验证所提模型及算法的有效性,并分析考虑回水顶托的必要性。结果表明,所提模型较传统模型在提高精度的同时也显著提升了求解效率,并在各场景下均能达到较好的调峰效果,对水库精细化调度具有重要意义。
In order to realize day-ahead peak regulation of cascade hydropower stations, multiple constraints of power grids,reservoirs and the hydro units should be considered simultaneously. Essentially,the day-ahead peak regulation problem is a complex multi-dimensional,dynamic,non-convex and non-linear programming problem. After considering the impact of backwater,the difficulty of solving the problem increases significantly. This paper established a mixed integer linear programming(MILP) model for 96-period peak-shaving problem with considering the impact of backwater. In order to reduce the number of non-linear constraints,all the non-linear constraints are aggregated into a single four-dimensional hypersurface constraint,which is linearized by SOS2 constraints method. Taking a hydropower cascade system in Southwest China as an engineering background,four typical days in dry and wet seasons are selected to verify the effectiveness of the proposed model and analyze the necessity of considering backwater. The results show that the proposed model can consider both the accuracy and efficiency of the solution,and obtain better results in all scenarios,which is of great significance to the refined reservoir operation.
In order to realize day-ahead peak regulation of cascade hydropower stations, multiple constraints of power grids,reservoirs and the hydro units should be considered simultaneously. Essentially,the day-ahead peak regulation problem is a complex multi-dimensional,dynamic,non-convex and non-linear programming problem. After considering the impact of backwater,the difficulty of solving the problem increases significantly. This paper established a mixed integer linear programming(MILP) model for 96-period peak-shaving problem with considering the impact of backwater. In order to reduce the number of non-linear constraints,all the non-linear constraints are aggregated into a single four-dimensional hypersurface constraint,which is linearized by SOS2 constraints method. Taking a hydropower cascade system in Southwest China as an engineering background,four typical days in dry and wet seasons are selected to verify the effectiveness of the proposed model and analyze the necessity of considering backwater. The results show that the proposed model can consider both the accuracy and efficiency of the solution,and obtain better results in all scenarios,which is of great significance to the refined reservoir operation.
引文
[1]赖晓文，钟海旺，杨军峰，等.全网统筹电力电量平衡协调优化方法[J].电力系统自动化，2015,39(7):103-110.
[2]吕泉，王伟，韩水，等.基于调峰能力分析的电网弃风情况评估方法[J].电网技术，2013,37(7):1887-1894.
[3]白涛，黄强，畅建霞.基于可行搜索空问优化的电力市场下梯级水电站短期调峰运行研究[J].水力发电学报，2012,31(5):90-95.
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[5]王浩，王旭，雷晓辉，等.梯级水库群联合调度关键技术发展历程与展望[J].水利学报，2019,50(1):25-37.
[6]高耶，孙亚飞，赵静飞，等.水工程回水顶托对水位流量关系的影响[J].湖南水利水电，2016,203(3):56-58.
[7]曹辉，张继顺，董先勇，等.白鹤滩水电站受溪洛渡水电站回水顶托影响的分析[J].水力发电，2017,43(12):69-71,79.
[8]纪昌明，俞洪杰，阎晓冉，等.考虑后效性影响的梯级水库短期优化调度耦合模型研究[J].水利学报，2018,49(11):1345-1356.
[9]钟华，姜俊红.红旗水电站发电量受东乡水电站回水顶托的影响分析[J].广东水利水电，2013,207(6):19-21,40.
[10]程春田，武新宇，申建建，等.亿千瓦级时代中国水电调度问题及其进展[J].水利学报，2019,50(1):111-123.
[11]申建建，程春田，程雄，等.跨省送电梯级水电站群调峰调度两阶段搜索方法[J].中国电机工程学报，2014,34(28):4817-4826.
[12]申建建，程春田，曹瑞，等.大规模水电消纳和调峰调度关键问题及研究进展[J].电力系统自动化，2018,42(11):174-183.
[13]武新宇，程春田，李刚，等.水电站群长期典型日调峰电量最大模型研究[J].水利学报，2012,43(3):115-123.
[14] LI XIANG. Hydro unit commitment via mixed integer linear programming:A case study of the three gorges project,China[J]. Power Systems,IEEE Transactions on,2014,29(3):1232-1241.
[15] CATALAO J P S,MARIANO S J P S,MENDES V M F,et al. Scheduling of head-sensitive cascaded hydro systems:A nonlinear approach[J]. IEEE Transactions on Power Systems,2009,24(1):337-346.
[16] TEEGAVARAPU R S V,SIMONOVIC S P. Short-term operation model for coupled hydropower reservoirs[J].Journal of Water Resources Planning and Management,2000,126(2):98-106.
[17]贾江涛，翟桥柱，管晓宏，等.水库群水电站短期调度的整数规划方法[J].西安交通大学学报，2008,42(8):1006-1009.
[18] CHENG C,WANG J,WU X. Hydro unit commitment with a head-sensitive reservoir and multiple vibration zones using MILP[J]. IEEE Transactions on Power Systems,2016,31(6):4842-4852.
[19]苏承国，王沛霖，武新宇，等.考虑机组组合的梯级水电站短期调峰MILP模型[J].电网技术，2018,42(6):1883-1891.
[20] D’AMBROSIO Claudia,LODI Andrea,MARTELLO Silvano. Piecewise linear approximation of functions of two variables in MILP models[J]. Operations Research Letters,2010,38(1):39-46.
[21] CONE A J,ARROYO J M,CONTRERAS J,et al. Self-scheduling of a hydro producer in a pool-based electricity market[J]. IEEE Transactions on Power Systems,2002,17(4):1265-1272.
[22] TONG B,ZHAI Q,GUAN X. An MILP based formulation for short-term hydro generation scheduling with analysis of the linearization effects on solution feasibility[J]. IEEE Transactions on Power Systems,2013,28(4):3588-3599.
[23] ANDRES R S J,ANJOS M F,PASCAL C,et al. MILP formulations for generator maintenance scheduling in hydropower systems[J]. IEEE Transactions on Power Systems,2018,33(6):6171-6180.
[24]王嘉阳.西南干流梯级水电站群短期与实时精细化调度研究[D].大连：大连理工大学，2017.
[2]吕泉，王伟，韩水，等.基于调峰能力分析的电网弃风情况评估方法[J].电网技术，2013,37(7):1887-1894.
[3]白涛，黄强，畅建霞.基于可行搜索空问优化的电力市场下梯级水电站短期调峰运行研究[J].水力发电学报，2012,31(5):90-95.
[4]孙正运，裴哲义，夏清.减少水电弃水调峰损失的措施分析[J].水力发电学报，2003(4):1-7.
[5]王浩，王旭，雷晓辉，等.梯级水库群联合调度关键技术发展历程与展望[J].水利学报，2019,50(1):25-37.
[6]高耶，孙亚飞，赵静飞，等.水工程回水顶托对水位流量关系的影响[J].湖南水利水电，2016,203(3):56-58.
[7]曹辉，张继顺，董先勇，等.白鹤滩水电站受溪洛渡水电站回水顶托影响的分析[J].水力发电，2017,43(12):69-71,79.
[8]纪昌明，俞洪杰，阎晓冉，等.考虑后效性影响的梯级水库短期优化调度耦合模型研究[J].水利学报，2018,49(11):1345-1356.
[9]钟华，姜俊红.红旗水电站发电量受东乡水电站回水顶托的影响分析[J].广东水利水电，2013,207(6):19-21,40.
[10]程春田，武新宇，申建建，等.亿千瓦级时代中国水电调度问题及其进展[J].水利学报，2019,50(1):111-123.
[11]申建建，程春田，程雄，等.跨省送电梯级水电站群调峰调度两阶段搜索方法[J].中国电机工程学报，2014,34(28):4817-4826.
[12]申建建，程春田，曹瑞，等.大规模水电消纳和调峰调度关键问题及研究进展[J].电力系统自动化，2018,42(11):174-183.
[13]武新宇，程春田，李刚，等.水电站群长期典型日调峰电量最大模型研究[J].水利学报，2012,43(3):115-123.
[14] LI XIANG. Hydro unit commitment via mixed integer linear programming:A case study of the three gorges project,China[J]. Power Systems,IEEE Transactions on,2014,29(3):1232-1241.
[15] CATALAO J P S,MARIANO S J P S,MENDES V M F,et al. Scheduling of head-sensitive cascaded hydro systems:A nonlinear approach[J]. IEEE Transactions on Power Systems,2009,24(1):337-346.
[16] TEEGAVARAPU R S V,SIMONOVIC S P. Short-term operation model for coupled hydropower reservoirs[J].Journal of Water Resources Planning and Management,2000,126(2):98-106.
[17]贾江涛，翟桥柱，管晓宏，等.水库群水电站短期调度的整数规划方法[J].西安交通大学学报，2008,42(8):1006-1009.
[18] CHENG C,WANG J,WU X. Hydro unit commitment with a head-sensitive reservoir and multiple vibration zones using MILP[J]. IEEE Transactions on Power Systems,2016,31(6):4842-4852.
[19]苏承国，王沛霖，武新宇，等.考虑机组组合的梯级水电站短期调峰MILP模型[J].电网技术，2018,42(6):1883-1891.
[20] D’AMBROSIO Claudia,LODI Andrea,MARTELLO Silvano. Piecewise linear approximation of functions of two variables in MILP models[J]. Operations Research Letters,2010,38(1):39-46.
[21] CONE A J,ARROYO J M,CONTRERAS J,et al. Self-scheduling of a hydro producer in a pool-based electricity market[J]. IEEE Transactions on Power Systems,2002,17(4):1265-1272.
[22] TONG B,ZHAI Q,GUAN X. An MILP based formulation for short-term hydro generation scheduling with analysis of the linearization effects on solution feasibility[J]. IEEE Transactions on Power Systems,2013,28(4):3588-3599.
[23] ANDRES R S J,ANJOS M F,PASCAL C,et al. MILP formulations for generator maintenance scheduling in hydropower systems[J]. IEEE Transactions on Power Systems,2018,33(6):6171-6180.
[24]王嘉阳.西南干流梯级水电站群短期与实时精细化调度研究[D].大连：大连理工大学，2017.