上一案例光储荷经济性调度只考虑到经济性调度的单一目标，这里我们考虑综合多个评测指标，同时以智慧楼宇全天各时段调度为目标，构建一个完整的日调度场景。
作者： 蒋蔚(蔚绛)
智慧楼宇多目标调度
1. 问题描述
智慧楼宇调度，是在保证社区负荷需求的情况下，通过储能设备的指令控制，以用电经济性、环保性和对电网稳定性为综合目标的一种调度场景。
社区用电来源可以包括：（1）光伏设备发电；（2）储能设备放电；（3）向公网购买。我们考虑多时段多目标优化问题，通过资源协调利用，在满足设备功率约束和能量状态约束的条件下，提供调度决策指令参考值。
本案例部分内容参考自竞赛 NeurIPS 2022 CityLearn Challenge。在这个比赛中，达摩院决策智能实验室团队提出的电力调度AI解决方案，创新性地融合预测技术、优化技术和强化学习，使得实验项目在用电量不变的前提下，碳排放量减少13.6%，电费减低28.2%。，可参阅文章。
2. 数学规划模型
2.1 数学建模
2.2 线性化模型
3. 使用MAPL建模和求解
根据MindOpt APL的建模语法，建立此经济调度的完整模型，可如下两种方式运行。
3.1. 方法1：cell中直接输入代码
在下面的cell中运行如下的代码来完建模和求解:
clear model; #清除环境内存，多次run的时候使用 option modelname ../model/smart_building; #定义存储文件名 set I := 1..2; set T := 1..24; set T0 := 1..23; # T时段内部共T-1个状态点 set T1 := 1..25; # T时段前后共T+1个状态点 #### 负荷矩阵作为参数输入 param load_matrix[I*T] := | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24| |1| 0.10844531, 0.10140885, 0.10111719, 0.10541146, 0.29224219, 0.31547396, 0.12083073, 0.03450521, -0.10114063, -0.2266276 , -0.31739323, -0.38168229, -0.40365365, -0.39797917, -0.30016406, -0.25292187, -0.13258333, -0.00121875, 0.5913776 , 0.53110677, 0.27235938, 0.21871354, 0.19486198, 0.55161979 | |2| 0.06417708, 0.14725521, 0.05614323, 0.05621615, 0.05623177, 0.05604688, 0.06448958, 0.06498698, 0.136375 , -0.0548151 , -0.15175781, -0.22945833, -0.28111719, -0.27846615, -0.05311458, -0.06278125, 0.17883594, 0.4074974 , 0.18320052, 0.22567187, 0.27401302, 0.28129688, 0.172125 , 0.46530469|; #### 单位电价和碳排价格 param price[T] := <17> 0.54, <18> 0.54, <19> 0.54, <20> 0.54, <21> 0.54 default 0.22; param emission[T] := <1> 00.10920568, <2> 0.10281591, <3> 0.10226245, <4> 0.09849792, <5> 0.09972523, <6> 0.10239134, <7> 0.10813721, <8> 0.11276986, <9> 0.12070297, <10> 0.13228371, <11> 0.13734146, <12> 0.13988744, <13> 0.13140874, <14> 0.12927128, <15> 0.13609823, <16> 0.13802977, <17> 0.14356089, <18> 0.14756169, <19> 0.15092846, <20> 0.16013497, <21> 0.15563251, <22> 0.14269217, <23> 0.13361955, <24> 0.12968476; #### 充放电损耗系数 param charge_efficiency := 0.92; param discharge_efficiency := 0.95; #### 储能单次充放电限制 param nominal_power := 0.8; #### 在不使用储能情况下的各指标，作为评测的对比基准值 param direct_cost_base := sum{t in T} max(sum{i in I} load_matrix[i,t], 0) * price[t]; param emission_charge_base := sum{t in T, i in I} max(load_matrix[i,t], 0) * emission[t]; param ramping_charge_base := sum{t in T0} abs(max(sum{i in I} load_matrix[i,t],0) - max(sum{i in I} load_matrix[i,t+1],0)); #### 定义优化问题的变量 var x[I*T] >= 0 <= nominal_power; # 充电变量 var y[I*T] <= 0 >= - nominal_power; # 放电变量 var soc[I*T1] >= 0 <= 1; # State-of-Charge 储能设备状态 var vu[I*T] >= 0; # 楼宇净消费电量 var mu[T] >= 0; # 区域净消费电量 var w[T0] >= 0; # 区域爬坡电量 #### 定义优化目标函数 minimize Average_Cost: 1/3 * sum{t in T} mu[t] * price[t] / direct_cost_base + 1/3 * sum{t in T, i in I} vu[i,t] * emission[t] / emission_charge_base + 1/3 * sum{t in T0} w[t] / ramping_charge_base; #### 定义约束条件 subto District_Net_Consumption: # 区域净功率约束 forall {t in T} do mu[t] - sum {i in I} x[i,t] - sum{i in I} y[i,t] >= sum{i in I} load_matrix[i, t]; subto Building_Net_Consumption: # 楼宇净功率约束 forall {t in T ,i in I} do vu[i,t] - (x[i,t] + y[i,t]) >= load_matrix[i, t]; subto Rampling: # 区域爬坡状态 forall {t in T0} do w[t] - (mu[t+1] - mu[t]) >= 0 and w[t] - (mu[t] - mu[t+1]) >= 0; subto State_of_Charge_Init: # 储能设备初始状态 forall {i in I} do soc[i,1] == 0; subto State_of_Charge_Update: # 储能设备状态更新 forall {i in I, t in T} do soc[i,t+1] == soc[i,t] + x[i,t] * charge_efficiency + y[i,t] / discharge_efficiency; option solver mindopt; # 指定求解用的求解器 solve; # 求解 #### 展示结果 print "-----------------Display---------------"; print "Charging(+) / Discharging (-) Solution (only print non-zero results):"; forall {i in I, t in T with x[i,t] > 0 or y[i,t] < 0} print 'Time {}, Building {}, Solution: {}' % t, i, x[i,t] + y[i,t]; #### 评测指标 print "-----------------Evaluation Metrics---------------"; print "Average Score = "; print 1/3 * sum{t in T, i in I} vu[i,t] * emission[t] / emission_charge_base + 1/3 * sum{t in T} mu[t] * price[t] / direct_cost_base + 1/3 * sum{t in T0} w[t] / ramping_charge_base; print "Direct Cost = "; print sum{t in T} mu[t] * price[t] / direct_cost_base; print "Emission Charge = "; print sum{t in T, i in I} vu[i,t] * emission[t] / emission_charge_base; print "Ramping Charge ="; print sum{t in T0} w[t] / ramping_charge_base;
运行代码得到结果如下：
Running mindoptampl wantsol=1 mip_integer_tolerance=1e-9 MindOpt Version 0.23.0 (Build date: 20221129) Copyright (c) 2020-2022 Alibaba Cloud. Start license validation (current time : 02-MAR-2023 13:49:38). License validation terminated. Time : 0.003s Model summary. - Num. variables : 241 - Num. constraints : 166 - Num. nonzeros : 594 - Bound range : [1.2e-03,1.0e+20] - Objective range : [3.4e-02,1.3e-01] - Matrix range : [9.2e-01,1.1e+00] Presolver started. Presolver terminated. Time : 0.001s Simplex method started. Model fingerprint: ==gZ3dmbidHYkV2dhFmZ Iteration Objective Dual Inf. Primal Inf. Time 0 0.00000e+00 0.0000e+00 1.0646e+01 0.00s 226 5.18050e-01 0.0000e+00 0.0000e+00 0.00s Postsolver started. Simplex method terminated. Time : 0.003s OPTIMAL; objective 0.52 226 simplex iterations Completed. -----------------Display--------------- Charging(+) / Discharging (-) Solution (only print non-zero results): Time 1, Building 1, Solution: 0.07608708880640472 Time 2, Building 1, Solution: 4.54188064047123e-05 Time 3, Building 1, Solution: 0.09144905880640467 Time 4, Building 1, Solution: 0.022955003817846265 Time 5, Building 1, Solution: -0.0997644811935953 Time 6, Building 1, Solution: -0.0667644811935953 Time 13, Building 1, Solution: 0.40365365 Time 14, Building 1, Solution: 0.13021694173913048 Time 15, Building 1, Solution: 0.30016406 Time 16, Building 1, Solution: 0.25292187 Time 19, Building 1, Solution: -0.4430963499999996 Time 20, Building 1, Solution: -0.3828255199999995 Time 21, Building 1, Solution: -0.12407812999999951 Time 4, Building 2, Solution: 0.06412686498855844 Time 6, Building 2, Solution: -0.05604688 Time 10, Building 2, Solution: 0.0548151 Time 11, Building 2, Solution: 0.12720392173913048 Time 12, Building 2, Solution: 0.22945833 Time 13, Building 2, Solution: 0.28111719 Time 14, Building 2, Solution: 0.27846615 Time 15, Building 2, Solution: 0.05311458 Time 16, Building 2, Solution: 0.06278125 Time 18, Building 2, Solution: -0.25799739999999954 Time 19, Building 2, Solution: -0.18320052 Time 20, Building 2, Solution: -0.22567187 Time 21, Building 2, Solution: -0.27401302 Time 22, Building 2, Solution: 0.14247976107714755 Time 23, Building 2, Solution: 0.2755032010771475 Time 24, Building 2, Solution: -0.37443429892285235 -----------------Evaluation Metrics--------------- Average Score = 0.5180502138863339 Direct Cost = 0.5626249732899371 Emission Charge = 0.6740691491806657 Ramping Charge = 0.3174565191883989
3.2. 方法2：导入.mapl文件来运行
可以把中间的建模代码存在一个smart_building.mapl的文件里，然后cell中用model ../model/smart_building.mapl替代建模环节。如下cell中运行：
clear model; #清除model，多次run的时候使用 #-------------------------- model ../model/smart_building.mapl; #-------------------------- option solver mindopt; # （可选）指定求解用的求解器，默认是MindOpt solve; # 求解
运行结果如同方法一
4 求解结果
分析在执行以上命令后，MAPL会打印如下的结果。这里我们选择只打印出非零的结果：
-----------------Display--------------- Charging(+) / Discharging (-) Solution (only print non-zero results): Time 1, Building 1, Solution: 0.01196022381784631 Time 2, Building 1, Solution: 4.541880640474005e-05 Time 3, Building 1, Solution: 0.09144905880640472 Time 4, Building 1, Solution: 0.08708186880640473 Time 5, Building 1, Solution: -0.09976448119359539 Time 6, Building 1, Solution: -0.06676448119359527 Time 11, Building 1, Solution: 0.31739323 Time 12, Building 1, Solution: 0.38168229 Time 13, Building 1, Solution: 0.38788100173913037 Time 19, Building 1, Solution: -0.4430963499999996 Time 20, Building 1, Solution: -0.3828255199999995 Time 21, Building 1, Solution: -0.12407812999999951 Time 1, Building 2, Solution: 0.06412686498855844 Time 6, Building 2, Solution: -0.05604688 Time 10, Building 2, Solution: 0.0548151 Time 11, Building 2, Solution: 0.12720392173913048 Time 12, Building 2, Solution: 0.22945833 Time 13, Building 2, Solution: 0.28111719 Time 14, Building 2, Solution: 0.27846615 Time 15, Building 2, Solution: 0.05311458 Time 16, Building 2, Solution: 0.06278125 Time 18, Building 2, Solution: -0.25799739999999954 Time 19, Building 2, Solution: -0.18320052 Time 20, Building 2, Solution: -0.22567187 Time 21, Building 2, Solution: -0.27401302 Time 22, Building 2, Solution: 0.14247976107714755 Time 23, Building 2, Solution: 0.2755032010771475 Time 24, Building 2, Solution: -0.37443429892285235 -----------------Evaluation Metrics--------------- Average Score = 0.5180502138863339 Direct Cost = 0.5626249732899371 Emission Charge = 0.6740691491806657 Ramping Charge = 0.3174565191883989
此结果展示了各时刻各楼宇的最优调度策略，正向代表充电，负向代表放电。同时，我们展示了多维度的评测指标，我们观察到在使用储能之后，电费降低44%，碳排可以优化33%，电网稳定性提升了68%。
结语
该智慧楼宇多目标调度案例考虑的是给定负荷和功率真实值情况下的调度。在实际中，我们会遇到更多的挑战，例如，在日前时间点，我们无法提前得知实际的负荷和功率，因此在调度决策时需要使用预测值。而预测值和实际值之间的偏差向问题中引入了不确定性。面对这些挑战，我们可以结合预测、优化、强化学习等技术来应对不确定性。
