D题 风电场运行状况分析及优化

2016年高教社杯全国大学生数学建模竞赛题目（请先阅读“全国大学生数学建模竞赛论文格式规范”）D题风电场运行状况分析及优化风能是一种最具活力的可再生能源，风力发电是风能最主要的应用形式。我国某风电场已先后进行了一、二期建设，现有风机124台，总装机容量约20万千瓦。请建立数学模型，解决以下问题：附件1给出了该风电场一年内每隔15分钟的各风机安装处的平均风速和风电场日实际输出功率。试利用这些数据对该风电场的风能资源及其利用情况进行评估。附件2给出了该风电场几个典型风机所在处的风速信息，其中4#、16#、24#风机属于一期工程，33#、49#、57#风机属于二期工程，它们的主要参数见附件3。风机生产企业还提供了部分新型号风机，它们的主要参数见附件4。试从风能资源与风机匹配角度判断新型号风机是否比现有风机更为适合。为安全生产需要，风机每年需进行两次停机维护，两次维护之间的连续工作时间不超过270天，每次维护需一组维修人员连续工作2天。同时风电场每天需有一组维修人员值班以应对突发情况。风电场现有4组维修人员可从事值班或维护工作，每组维修人员连续工作时间（值班或维护）不超过6天。请制定维修人员的排班方案与风机维护计划，使各组维修人员的工作任务相对均衡，且风电场具有较好的经济效益，试给出你的方法和结果。附件1平均风速和风电场日实际输出功率表。附件2风电场典型风机报表。附件3风电场风机型号及其参数。附件4风机生产企业提供的新型号风机主要参数。附件1平均风速和风电场日实际输出功率表风电场日实际发电曲线统计表2015年1月1日功率单位：MW。风速单位：m/s

时间功率风速时间功率风速时间功率风速时间功率风速0:15344.16:15254.712:1502.318:15133.90:30244.96:30255.712:3002.318:30183.50:45364.76:45244.712:4512.518:45244.11:00295.67:00235.413:0012.519:00224.61:15215.17:15275.613:1522.519:15204.51:30193.97:30295.413:3022.419:30124.01:45254.27:45304.913:4502.219:4594.22:00244.38:0073.914:0002.120:00103.92:15365.98:1584.014:1502.120:15124.12:30304.78:3084.014:3002.020:30194.52:45254.28:4573.814:4502.020:45234.63:00244.09:0053.415:0001.921:00294.93:15244.09:1553.415:1501.921:15315.03:30254.39:30104.215:3001.921:30274.73:45254.39:4533.115:4502.021:45254.64:00213.910:0033.016:0002.022:00254.54:15193.710:1522.516:1502.022:15254.84:30254.010:3022.416:3002.122:30265.04:45254.110:4512.316:4502.122:45274.75:00254.311:0012.217:0002.123:00254.95:15294.411:1522.517:1523.223:15264.85:30364.511:3032.717:3063.823:30274.65:45305.711:4522.517:4563.923:45274.56:00315.612:0002.318:0094.10:00284.5风电场日实际发电曲线统计表2015年2月28日功率单位：MW。风速单位：m/s时间功率风速时间功率风速时间功率风速时间功率风速0:15556.06:151449.712:1514711.618:1513710.20:30746.46:301369.012:3014611.918:3013510.10:45786.56:451278.912:4514512.318:451299.91:001008.47:001439.513:0014611.719:001019.91:15987.27:151459.913:1514510.519:15759.01:301098.57:301419.413:3014511.419:30608.41:451108.77:451149.013:4514511.119:45568.52:001078.48:001088.214:0014510.720:00558.42:151018.28:151088.214:1514511.220:15566.52:301279.48:301168.514:3014511.420:30596.42:451499.58:451027.914:4514512.120:45606.43:001489.59:00987.415:0014511.121:00666.63:151459.49:15957.215:1514510.421:15566.53:301459.79:30987.415:3014510.721:30546.5

3:451459.89:451318.715:4514511.321:45547.14:001459.510:001288.516:0014611.022:00567.04:1514510.210:151439.616:1514510.922:15547.04:3014510.710:301459.616:3014510.722:30557.04:4514610.210:451459.916:4514511.422:45556.95:0014710.411:0014611.617:0014511.223:00566.45:1514710.311:1514511.717:1514511.223:15666.25:3014510.511:3014512.217:3014511.023:30506.45:4514510.611:4514612.117:4514510.623:45546.56:0014510.512:0014512.118:0014510.90:00656.7风电场日实际发电曲线统计表2015年3月22日功率单位：MW。风速单位：m/s时间功率风速时间功率风速时间功率风速时间功率风速0:15466.16:1502.912:1501.718:15386.00:30556.76:3001.312:3002.318:30365.90:45627.06:4501.912:4502.018:45355.81:00546.57:0002.313:0003.119:00355.71:15576.77:1501.113:1563.419:15355.61:30486.27:3002.113:30194.019:30325.31:45597.07:4502.013:45284.619:45305.02:00586.98:0001.914:00375.320:00274.72:15576.78:1501.414:15415.620:15255.02:30596.38:3001.614:30446.020:30234.42:45575.98:4501.214:45385.420:45184.23:00525.89:0001.015:00415.621:00234.43:15375.49:1501.315:15536.621:15294.83:30335.39:3001.715:30606.821:30315.03:45365.39:4502.015:45657.221:45335.24:00234.910:0002.216:00707.522:00325.14:15124.210:1502.516:15788.222:15325.14:30114.110:3002.316:30788.222:30335.54:45104.010:4501.816:45748.022:45345.45:00114.011:0002.017:00737.923:00345.55:1583.711:1501.917:15707.523:15355.65:3053.511:3001.717:30657.323:30355.55:4513.011:4501.617:45557.123:45355.46:0013.012:0002.118:00416.50:00355.5风电场日实际发电曲线统计表2015年4月12日功率单位：MW。风速单位：m/s时间功率风速时间功率风速时间功率风速时间功率风速

0:151078.96:15183.312:151088.118:1514211.10:301088.76:30143.412:30847.618:3013610.60:45928.46:45123.212:451028.318:451118.41:00857.87:0093.113:00867.419:001078.21:15817.77:1563.213:151058.019:15887.61:30737.37:3083.313:301168.519:30746.31:45557.07:45113.413:451158.419:45636.02:00656.98:00143.514:001138.320:00666.12:15666.88:15123.214:151138.420:15736.22:30706.98:3093.114:301239.020:30705.92:45646.78:45113.414:451168.720:45716.03:00586.99:00123.415:001208.921:00716.03:15606.59:15163.315:151349.321:15746.23:30576.49:30233.415:301118.421:30776.43:45526.39:45263.315:451349.321:45786.54:00556.010:00233.516:001128.322:00776.44:15576.010:15353.916:151429.522:15766.34:30475.810:30454.016:3016010.022:30786.64:45375.710:45807.316:451339.722:45605.75:00324.611:00847.517:001449.823:00675.95:15274.411:151058.017:159510.423:15635.85:30274.011:301268.217:3013610.623:30605.75:45263.711:451358.517:4513910.923:45615.76:00213.912:001288.318:0013810.80:00595.6风电场日实际发电曲线统计表2015年5月31日功率单位：MW。风速单位：m/s时间功率风速时间功率风速时间功率风速时间功率风速015395.0615375.31215294.81815164.5030405.2630325.11230354.9183094.5045425.4645345.21245325.3184583.8100455.7700355.31300135.5190093.9115475.8715405.6131585.2191543.6130506.0730445.8133035.0193053.6145516.1745415.5134513.3194533.4200606.0800405.4140064.2200093.8215556.6815285.51415224.82015134.2230556.6830245.31430486.32030154.2245556.6845205.41445486.52045184.9300556.6900185.01500527.02100345.9315556.6915185.11515567.32115546.5330516.1930125.31530517.62130757.5345445.7945125.21545357.92145847.7

4:00465.810:00135.216:00186.222:00887.94:15556.610:1584.816:1584.322:15707.04:30556.610:3044.716:3064.022:30576.54:45525.910:4584.316:45124.322:45305.55:00495.811:00114.117:00235.523:00265.05:15576.811:15124.317:15285.723:15255.25:30627.211:30214.417:30275.623:30255.35:45546.511:45254.617:45245.423:45265.26:00415.512:00344.718:00184.80:00245.0风电场日实际发电曲线统计表2015年6月6

日功率单位：2015年6月6

日功率单位：MW。风速单位：m/s时间功率风速时间功率风速时间功率风速时间功率风速0:15395.56:15696.812:15717.118:15204.80:30395.56:30998.012:30737.118:30154.60:45335.36:451078.412:45857.218:45134.51:00335.37:00767.513:00727.519:00114.31:15335.37:151179.413:15577.419:15104.21:30335.37:30948.013:30456.119:3094.01:45335.37:45586.513:45455.819:4573.82:00335.08:00465.914:00336.020:0023.32:15365.48:15545.814:15295.720:1533.42:30485.98:30606.214:30254.320:30103.92:45435.78:45586.914:45174.220:45124.23:00315.09:00717.415:00194.021:00204.33:15365.29:15707.515:15184.421:15204.33:30476.39:30446.515:3074.321:30215.03:45425.79:45306.215:45123.421:45225.04:00335.010:00206.216:00104.222:00235.14:15335.010:15456.216:1593.822:15245.24:30375.210:30426.316:3083.522:30245.34:45415.310:45536.716:45103.422:45255.45:00475.611:00486.017:00153.423:00255.45:15565.811:15335.417:15203.923:15255.55:30646.511:30284.717:30234.523:30255.55:45737.211:45516.017:45234.923:45255.56:00666.712:00556.218:00214.80:00255.5风电场日实际发电曲线统计表2015年7月31

日功率单位：MW。风速单位：m/s时间功率风速时间2015年7月31

日功率单位：MW。风速单位：m/s时间功率风速时间时间风速时间0:15386.26:15114.112:1583.818:1583.70:30366.66:30134.312:3054.118:30355.20:45376.66:45154.612:4544.218:45776.91:00386.47:00164.713:0043.419:00616.01:15336.37:15134.313:1502.919:15726.81:30345.27:30114.113:3002.719:30827.11:45275.37:4583.813:4502.719:45787.02:00205.08:0063.614:0002.120:00837.22:15205.08:1563.714:1502.220:15827.12:30215.18:3083.614:3002.620:30696.62:45225.28:4574.114:4502.620:45545.83:00205.19:0053.215:0002.621:00617.23:15104.09:1543.915:1574.721:15405.53:30114.19:3053.815:3074.021:30305.03:45134.39:4593.915:45124.221:45305.04:00154.510:00104.116:00144.522:00315.04:15134.410:15124.516:15134.322:15305.04:30134.310:30154.416:3063.622:30305.04:45104.010:45124.516:4593.922:45305.05:00104.011:00104.317:00144.423:00305.05:1573.711:15144.417:15144.423:15305.05:3043.411:30115.117:30225.023:30305.05:4553.511:45115.217:45154.523:45305.06:0083.712:0065.418:00124.30:00315.0风电场日实际发电曲线统计表2015年8月19日功率单位：MW。风速单位：m/s时间功率风速时间功率风速时间功率风速时间功率风速015657.861583.41215475.7181573.6030647.663053.01230435.4183083.6045576.464533.01245505.2184583.7100586.670013.01300546.5190083.5115496.071502.71315606.9191552.6130536.273002.31330606.9193002.5145566.474502.11345606.9194502.4200466.080002.31400586.9200002.1215415.981502.61415556.1201502.1230415.983002.51430586.1203002.5245496.084502.51445374.9204502.1300546.390002.51500344.8210002.2315486.091502.61515405.4211502.1330465.993063.71530304.4213002.3345436.1945103.81545273.9214502.2

4:00446.110:00153.916:00293.922:0002.54:15406.010:15404.116:15213.722:1502.24:30345.510:30424.216:30183.822:3002.24:45365.410:45394.016:45163.522:4502.35:00284.811:00383.917:00174.223:0002.35:15264.911:15183.817:15164.223:1502.35:30244.511:30596.817:30174.223:3002.55:45194.111:45566.517:45144.123:4502.16:00174.212:00475.818:00124.10:0002.1风电场日实际发电曲线统计表2015年9月21日功率单位：MW。风速单位：m/s时间功率风速时间功率风速时间功率风速时间功率风速015428.36151079.3121598.81815657.9030788.46301039.2123088.41830647.8045818.56451149.31245108.41845636.4100828.4700829.11300108.41900546.6115828.7715829.41315118.21915546.5130838.6730829.51330127.91930556.2145828.5745829.81345138.21945536.4200838.4800158.91400148.22000556.4215828.8815218.71415147.22015546.5230838.7830228.91430127.92030324.5245829.0845188.91445127.92045254.0300858.9900238.81500147.82100454.5315878.8915248.11515138.22115644.2330868.793069.11530128.12130888.2345838.894598.71545118.02145888.4400878.910:0078.81600138.42200848.6415869.010:1598.51615148.42215828.54301069.110:30118.91630148.42230828.24451029.010:45109.31645136.92245818.25001139.211:00109.41700126.42300828.45151069.311:1588.71715116.82315848.5530968.911:3078.91730137.42330828.35451029.011:4598.11745247.42345828.36001079.112:0088.11800607.60:00848.2风电场日实际发电曲线统计表2015年10月10日功率单位：MW。风速单位：m/s时间功率风速时间功率风速时间功率风速时间功率风速

0:15678.16:15294.512:15596.418:15264.20:30748.76:30304.712:30606.118:30214.10:45729.06:45274.812:45556.318:45224.21:00307.17:00254.713:00516.019:00244.21:15497.87:15224.513:15395.019:15214.11:30487.57:30224.713:30405.619:30204.01:45378.27:45275.013:45395.819:45194.42:00358.48:00325.214:00365.520:0063.62:15368.58:15394.914:15355.020:1563.62:30328.18:30415.114:30245.120:3043.32:45348.28:45435.314:45354.720:4533.23:00338.09:00215.015:00405.421:0013.03:15327.49:15184.415:15355.221:1513.03:30327.59:30195.015:30345.121:3002.73:45307.99:45245.715:45275.021:4502.24:00247.410:00406.216:00314.722:0002.14:15216.110:15375.716:15245.222:1502.24:30205.210:30496.516:30324.022:3002.14:45214.710:45506.116:45205.122:4502.55:00234.211:00586.617:00335.223:0002.65:15284.511:15666.817:15314.923:1502.75:30294.411:30656.017:30214.123:3002.75:45294.111:45656.117:45214.123:4502.86:00274.212:00666.218:00244.40:0002.8风电场日实际发电曲线统计表2015年11月1日功率单位：MW。风速单位：m/s时间功率风速时间功率风速时间功率风速时间功率风速0:15154.46:1501.612:15133.218:15927.90:30144.46:3001.512:30123.518:30947.90:45154.46:4501.512:45133.618:45997.91:00104.07:0001.613:00173.719:001017.91:1582.87:1502.013:15193.719:151027.91:3073.77:3002.413:30233.819:30987.81:4543.47:4502.513:45223.819:45987.82:0033.38:0002.714:00243.920:00987.82:1513.18:1593.414:15294.220:15877.82:3013.18:3093.214:30294.420:30867.22:4523.28:4583.514:45345.120:45897.93:0033.29:0083.615:00365.421:00897.83:1523.29:1593.215:15395.721:15877.93:3023.29:3093.115:30465.721:30897.83:4543.29:4583.515:45496.121:45877.8

4:0043.310:0083.516:00516.522:00847.84:1533.410:1583.516:15526.722:15877.84:3043.310:3083.116:30516.722:30847.44:4563.410:4593.216:45516.622:45897.85:0043.511:0093.217:00596.723:00897.45:1513.411:15163.917:15646.823:15847.85:3002.611:30203.917:30787.223:30827.95:4502.811:45153.917:45897.523:45847.96:0002.612:00153.818:00877.60:00827.2风电场日实际发电曲线统计表2015年12月28日功率单位：MW。风速单位：m/s时间功率风速时间功率风速时间功率风速时间功率风速0:15837.46:15365.212:1513.318:15124.00:30787.16:30264.612:3002.718:3083.90:45767.16:45284.712:4502.618:45104.01:00757.07:00314.913:0001.919:00134.11:15757.17:15385.213:1543.419:1583.81:30867.97:30425.413:3053.619:3043.51:45777.67:45334.913:4583.819:4513.22:00777.58:00284.714:0073.820:0002.02:15928.38:15254.214:15124.320:1501.82:30918.48:30305.014:30124.320:3001.52:45918.58:45365.314:45124.020:4501.73:00878.29:00415.515:0093.721:0002.03:15677.19:15285.415:1553.621:1501.53:30596.59:30345.215:3043.621:3001.43:45566.39:45325.015:4553.221:4501.54:00505.910:00284.716:0023.422:0001.64:15475.810:15153.916:1583.622:1502.04:30355.410:30164.116:3043.622:3002.14:45274.910:4573.616:4543.622:4502.05:00274.811:0053.517:0044.023:0001.85:15344.911:1563.617:15134.323:1501.95:30354.911:3033.417:30264.423:3002.05:45375.011:4523.317:45204.423:4502.16:00395.212:0033.318:00234.50:0002.2附件2风电场典型风机报表风电场典型风机报表日期：2015年01月15日时间2:004:006:008:0010:0012:0014:0016:0018:0020:0022:0024:004#风速(m/s)5.47.47.13.34.30.33.21.25.05.34.55.116#风速(m/s)7.04.77.43.44.20.42.24.05.15.35.45.224#风速(m/s)5.85.35.93.52.91.10.52.83.66.85.75.033#风速(m/s)6.55.75.41.83.00.81.63.04.46.57.74.649#风速(m/s)6.57.36.24.51.60.70.93.13.54.55.77.557#风速(m/s)8.26.77.34.50.31.31.13.05.15.04.45.2风电场典型风机报表风电场典型风机报表风电场典型风机报表风电场典型风机报表风电场典型风机报表风电场典型风机报表时间2:004:006:008:0010:0012:0014:0016:0018:0020:00224#风速（m/s）6.08.613.08.78.214.111.310.710.78.6716#风速（m/s）6.910.911.39.611.414.610.411.810.79.9424#风速（m/s）7.48.610.29.110.714.911.914.114.112.7733#风速（m/s）8.79.28.75.37.413.912.87.07.06.0649#风速（m/s）9.410.29.16.98.413.211.18.48.27.7657#风速（m/s）14.412.110.38.411.611.112.111.68.49.48日期：2015年02月28日时间2:004:006:008:0010:0012:0014:0016:0018:0020:0022:0024:4#风速（m/s）4.13.23.93.23.12.03.48.612.89.28.79.16#风速（m/s）3.02.62.71.81.71.93.48.711.710.17.47.24#风速（m/s）1.22.82.32.42.12.43.16.89.28.37.86.33#风速（m/s）3.51.71.51.02.11.71.28.110.210.49.98.49#风速（m/s）3.71.41.91.62.12.43.46.49.99.39.79.57#风速（m/s）1.82.93.51.21.71.94.08.210.210.211.49.日期：2015年03月31日时间2:004:006:008:0010:0012:0014:0016:0018:0020:0022:0024:004#风速（m/s）8.48.19.68.36.33.12.32.82.50.91.62.016#风速（m/s）9.47.76.37.26.95.12.94.13.62.12.22.124#风速（m/s）7.35.64.45.85.73.02.01.52.12.51.92.533#风速（m/s）8.23.96.96.22.53.62.52.42.42.11.82.249#风速（m/s）9.47.57.77.15.15.82.84.71.12.22.42.2日期：2015年04月22日

时间2:004:006:008:0010:0012:0014:0016:0018:0020:0022:0024:004#风速（m/s）7.46.45.98.17.16.37.96.13.03.43.63.716#风速（m/s）6.27.06.06.67.77.39.35.64.74.53.73.824#风速（m/s）4.55.76.36.25.64.25.64.03.03.53.53.233#风速（m/s）5.84.26.53.65.04.34.35.24.94.53.64.749#风速（m/s）6.87.15.95.08.27.65.54.85.24.94.14.657#风速（m/s）8.07.06.08.18.86.28.55.76.45.44.95.1日期：2015年05月29日57#风速(m/s)9.67.46.75.4 4.44.9 4.2 3.2 2.1 1.2 2.2 1.957#风速(m/s)9.67.46.75.4 4.44.9 4.2 3.2 2.1 1.2 2.2 1.9风电场典型风机报表风电场典型风机报表风电场典型风机报表风电场典型风机报表时间2:004:006:008:0010:0012:0014:0016:0018:0020:004#风速（m/s）7.25.84.26.66.94.33.44.95.29.416#风速（m/s）3.95.94.74.510.05.32.56.64.910.124#风速（m/s）4.13.23.33.77.37.43.26.03.58.133#风速（m/s）6.64.23.75.57.93.95.05.35.010.349#风速（m/s）7.62.93.26.58.84.25.96.18.612.157#风速（m/s）5.83.93.08.09.66.47.07.96.012.6日期：2015年06月01日时间2:004:006:008:0010:0012:0014:0016:0018:0020:0022:0024:004#风速(m/s)6.65.75.05.15.75.73.03.13.97.17.87.616#风速(m/s)4.73.43.95.02.93.94.54.43.76.06.66.724#风速(m/s)5.228.03.73.82.25.95.55.73.26.27.57.633#风速(m/s)6.84.54.54.72.33.54.94.74.18.45.56.249#风速(m/s)5.74.74.84.35.24.34.75.13.39.49.59.057#风速(m/s)6.24.95.13.96.55.43.24.23.96.76.26.0日期：2015年7月31日时间2:004:006:008:0010:0012:0014:0016:0018:0020:0022:0024:004#风速（m/s）4.53.62.81.81.55.71.23.25.75.69.28.516#风速（m/s）4.43.22.52.42.05.22.82.45.86.58.57.224#风速（m/s）4.23.82.91.21.90.81.12.35.05.79.88.233#风速（m/s）3.13.92.70.92.12.31.02.64.34.43.94.949#风速（m/s）2.94.13.11.71.72.22.32.54.24.05.06.057#风速（m/s）4.13.62.91.42.30.20.72.04.34.45.35.5日期：2015年8月7日

时间2:004:006:008:0010:0012:0014:0016:0018:0020:004#风速（m/s）1.22.24.34.910.29.210.612.64.58.916#风速（m/s）2.12.34.16.79.99.011.09.97.78.224#风速（m/s）1.92.14.26.87.66.07.48.29.48.933#风速（m/s）1.32.14.36.28.49.28.58.711.69.549#风速（m/s）1.41.84.18.08.512.211.712.57.57.257#风速（m/s）1.71.94.77.210.416.711.412.67.76.3日期：2015年9月10日时间2:004:006:008:0010:0012:0014:0016:0018:0020:004#风速（m