采用最钝角松弛算法求解无功优化问题的线性规划模型,为解决线性化步长调整问题在该模型中增加了信赖域约束。首先,根据最钝角原理定义主元标的概念及其计算公式,计算各个不等式约束的主元标。然后,根据不等式约束的主元标值对其进行筛选,形成一个松弛的线性规划问题,用原始单纯形法对其求解。如果松弛问题的最优解能满足原问题的不等式约束,则直接获得原问题的最优解。否则,将所有剩余的约束条件全部添加到松弛模型中,得到改变约束条件顺序后的原问题,再用对偶单纯形法进行新的求解。该算法本质上是一种2阶段单纯形法,并且第二阶段的求解可以充分利用第一阶段松弛问题的解信息,大大提高第二阶段的计算效率。以5个试验系统和1个省级538节点实际系统为测试系统,通过与单纯形法、信赖域内点法进行比较,验证其有效性。
Linear programming (LP) model of reactive-power optimization problem is solved by the most-obtuse-angle relaxation algorithm (MRA), in which trust region constraints on linear step sizes are added, Firstly, the concept of pivoting indices and its calculation formulae are defined according to most-obtuse-angle principle, and pivoting indices corresponding to inequality constraints are computed. Then inequality constraints in the original LP model are filtered based on these values of pivoting indices and a relaxed LP model is established. This relaxed model is solved by primal simplex method. If this solution from the relaxed model satisfies inequality constraints of the original LP model, the solution is final result expected. Otherwise, all the remaining inequality constraints in the relaxed LP model are added into the relaxed model to obtain the original model with changed order of inequality constraints. This original model is solved by dual simplex method. In essence, the MRA is a twophase simplex method. Also solution in phase II can utilize solution obtained in phase I fully and hence computation efficiency is enhanced obviously. Results on five test systems and a 538-bus real system demonstrate effectiveness of the proposed algorithm by comparisons with simplex method and trust-region interior-point method.