基于拉格朗日函数鞍距分配的广义内点法

摘要

不等式约束的处理是电力系统优化分析中比较困难的问题.文中根据拉格朗日函数的鞍点理论,将优化问题的等式约束进行松弛,形成计及等式约束的原始问题以及相应的对偶问题.通过定义原始和对偶问题之间的鞍距,并将鞍距在不等式约束之间进行分配,从而形成不同的针对不等式约束拉格朗日乘子的修正方程,进一步形成不同的优化算法.推导表明,内点罚函数法只是拉格朗日鞍点理论应用的一个特例.所提出的基于拉格朗日函数鞍距分配的广义内点法可以在电力系统优化分析中进行应用,将其应用于大规模间歇式电源接入情况下的电力系统最大传输能力问题中时,IEEE 30节点系统的计算结果及IEEE 14节点系统中不同算法的比较结果表明,此算法能够有效处理潮流问题不等式约束.%The problem of handling inequality constraints is a difficult task in power system optimization analysis.The equality constraints of an optimization problem are slackened according to the theories of Lagrange function saddle point,so that the primal problem and the corresponding dual problem considering equality constraints are introduced.By defining the saddle space between the primal and dual problem and distributing the saddle space among inequality constraints,the modified equations in allusion to the Lagrange multipliers of inequality constraints are put forward.Furthermore,different optimization algorithms will come into being.The derivation shows that the interior point function method is just a particular case of Lagrange saddle point theory"s application.The proposed method can be applied in power system optimization analysis, especially for the task of maximum transmission ability of power system.The calculation result in IEEE 30-bus system and comparison of the result among different algorithms in IEEE 14-bus system demonstrate that the method is effective for handling the problems of load flow inequality constraints.