带界约束的仿射尺度信赖域法的无功优化

Affine-scaling Trust-region Method with Simple Bounds for Reactive Power Optimization

为有效处理无功优化模型中不等式约束且不扩大问题的规模,建立了与无功优化问题的库恩-塔克(KKT)条件等价的新模型。通过引入对角矩阵,消去KKT系统中关于界约束的互补关系,减少了变量维数,并采用一类求解带界约束非线性方程组的仿射尺度信赖域算法。该算法具有信赖域的全局搜索性和牛顿法的超线性收敛性,并可保持无功界约束的可行性。对IEEE-30、57、118节点系统进行仿真计算,并与常规非线性优化方法比较,结果表明该方法具有较好的收敛特性和计算效果。

In order to effectively deal with inequality constraints of reactive power optimization model and not to expand the scale of the problem, the paper develops a new model equivalent to the KKT system of reactive power optimization. Through the introduction of a diagonal matrix,the complementary relationship on the constraints of the KKT system is eliminated and the variable dimension is reduced. For the new model, an affinescaling trust-region algorithm for nonlinear equations with bounds is used. The algorithm has global search characteristic of trust region and the super-linear convergence characteristic of Newton method, and retains the feasibility of boundary constraints for reactive power. Case studies on the IEEE 30,57,118 bus system show that comparing with the LP method, the new algorithm has better convergency and computation results.