基于凝聚函数的电力系统无功互补优化模型与算法

Reactive Power Optimization Model and Algorithm With Complementarity Constraints Based on Aggregate Function

基于非线性互补函数和凝聚函数提出了一种处理电力系统无功优化问题中离散变量的光滑化模型,并结合现代内点法对模型进行求解。所提方法首先在不考虑离散变量的情况下进行无功优化预计算,快速获取离散变量的两界,并以此构造互补约束条件;然后将互补约束转化为等价的非光滑方程组,并利用凝聚函数进行光滑逼近,从而将无功优化问题转化为一般的非线性规划问题进行求解,有效地解决了求解离散量时存在的时间与精度之间的矛盾。对30至1780节点系统的计算结果表明,该算法计算效率高、收敛性好,在求解含离散变量的大规模非线性规划问题中有很好的应用前景。

A smoothing complementarity function and solved by modem interior point discrete variables in reactive model based on nonlinear aggregate function, which is method, presented to cope with power optimization. At first, without considering discrete variables the pre-computation of reactive power optimization is performed to attain upper and lower bounds of discrete variables, and on this basis complementary constraints are constructed; then complementary constraints are turned into equivalent non-smooth equation set and smooth approximation is performed by aggregate function to turn the reactive power optimization into general nonlinear programming to solve it, thus the conflict between the time and the accuracy during the solution of discrete variables is resolved effectively. Simulation results of IEEE 30-bus system, IEEE ll8-bus system, IEEE 300-bus system, S-1047 system and XB-1780 system, which is a domestic planning system for a certain region in China, show that＇ the proposed method possesses high computational efficiency and its convergence rate is fast, so it is available to apply the proposed method in the solution of large-scale nonlinear programming containing discrete variables.