含抽水蓄能电网安全约束机组组合问题的混合整数线性规划算法

抽水蓄能机组的投运对电网发电调度计划的制定具有很大影响,建立了含抽水蓄能机组电网的安全约束机组组合模型。以考虑了抽水蓄能机组启停费用的所有机组总运行费用为目标函数,根据抽水蓄能机组的不同运行工况给出旋转备用容量的解析表达式,同时在系统功率平衡约束中考虑了网络损耗的影响,并考虑了抽水蓄能机组的运行调度约束及网络安全约束。为了保证模型求解的可靠性和提高模型求解的计算效率,将目标函数进行分段线性化,并根据抽水蓄能机组的运行特点将其旋转备用容量约束等价转化为线性表达式。同时采用一种动态分段线性化方法近似逼近网络损耗,从而将机组组合模型转化为混合整数线性规划模型,并采用成熟的数学优化求解器CPLEX进行求解。对某实际23机306节点电网算例的计算结果表明,所提出的混合整数线性规划调度模型的网损逼近效果合理正确,算法求解速度快,具有较好的工程实用价值。

Mixed integer linear programming algorithm for solving security constrained unit commitment problem of power grid with pumped storage hydro

The operation of Pumped Storage Hydro (PSH) units has great influence on the compilation of generation scheduling of power grid, a security constrained unit commitment model of power grid with PSH units is established. In the model, total operation cost of all units which includes the start up / stop down cost of PSH units is considered as the objective function, an analytical expression of the spinning reserve capacity of PSH units is given according to different operation conditions, and the network loss is considered in the power balance constraint of the system, the operation scheduling constraints of PSH units and the network security constraints are also considered. In order to ensure the reliability and improve the calculation efficiency of model solution, the objective function is piecewise linearized and the spinning reserve capacity constraint of PSH units is equivalently transformed into a linear expression according to their operation characteristics. Meanwhile, a dynamic piecewise linearization method is adopted to approximate the network loss, so that the unit commitment model is transformed into a Mixed Integer Linear Programming (MILP) model, which can be solved by using the mature mathematical optimization solver CPLEX. Test results on an actual power grid of 23 units and 306 buses demonstrate that the approximation effect of network loss in the proposed MILP model is reasonable and correct, and the proposed algorithm is fast and has good practical value in engineering. This work is supported by National Basic Research Program of China (973 Program) (No. 2013CB228205), Natural Science Foundation of Guangdong Province (No. 2015A030313233), and Science and Technology Project of Shenzhen Power Supply Bureau Co., Ltd (SZKJXM20160174).