电工杯数学建模比赛部分赛题

PAGE请仔细阅读竞赛须知甲题：电站建设为满足甲地区对电能的需求，需建若干个电站，组成一个供电系统。为使问题简化，只考虑一个目标年，所有电站都新建，且只考虑一个目标年的供电。依据乙地区某年的负荷曲线（负荷与时间的关系），确定甲地区一个目标年内的电能需求量。乙地区某年内在时刻t的负荷（电站总输出功率）F(t)（单位：kw）为:数据在文件GDJM0399.dat中(可用各种编辑软件打开)，共3000个记录，每个记录有3个数，分别是(1)式中的t、x、f(x)。负荷持续时间曲线（需求量，即负荷的时间分布）是抛物线。需建n（n给定）个电站组成供电系统为甲地区供电。每个电站的费用由固定费用和运行费用构成。固定费用与装机容量（总供电能力（功率））成正比；单位时间的运行费用与输出功率的平方成正比。第i个电站的固定费用和运行费用的（比例）系数分别为。例如：i12i121.30.050.00310.012单位：元／kw单位：元／kw.小时请给出总费用最少的供电方案，给出各电站的装机容量（总功率）及其累计运行时间。按照上例中的数据进行计算，并给出结果；对任意正整数n，推广你的算法；试讨论若给定的数据有误差，如何处理。

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