求解最优潮流问题的混合线性锥规划法

Solution of Optimal Power Flow Problems by Mixed Cone Linear Programming

单一线性锥规划方法求解最优潮流(optimal power flow,OPF)问题时,锥变量仅局限于某个单一锥集合,使得锥规划模型的构造缺乏灵活性,建模难度较大。为此,基于混合线性锥规划(mixed cone linear programming,MCLP)方法,提出了求解OPF问题的3种MCLP模型—MCLP-OPF。该模型采用不同的锥变量来构建原始OPF问题的锥松弛模型,锥变量可同时取自半正定锥、二阶锥和非负多面体锥。引入MCLP-OPF问题的可行域"厚度",并根据该"厚度"大小选择直接内点法或齐次自对偶(homogeneous self-dual,HSD)内点法求解。从C-703节点等6个测试系统的仿真结果可以看到,相较于半定规划法,MCLP-OPF提高了锥规划方法的建模效率、求解效率和存储效率,更适于求解大规模电力系统问题。

The way to solve the optimal power flow（OPF） problem by a single cone linear prog＋ramming,whose variables are limited to a single cone collection,make the structure of the conic programming model short of flexibility and difficult to model.Therefore,based on mixed cone linear programming（MCLP）,three MCLP models to solve the OPF problem（MCLP-OPF） were presented.The cone relaxation model of the original OPF problem is built through different cone variables,which can be taken from semi-definite cones,second-order cones and nonnegative polyhedral cone simultaneously.By introducing ＂thickness＂ of the feasible region,the MCLP-OPF models are solved via interior point method（IPM） or homogeneous self-dual（HSD） IPM according to the magnitude of the ＂thickness＂.Simulation results of 6 test systems such as C-703 bus power system show that,compared with the semi-definite programming,MCLP-OPF improves the modeling efficiency,solving efficiency and storage efficiency of conic programming,and is more suitable for solving large-scale power system problems.