一种用于分解协调无功优化的全分邻近中心算法

A Full Decomposition Proximal Center Algorithm for Decomposition and Coordination of Reactive Power Optimization

针对无功优化分解协调模型求解中增广拉格朗日函数不可分的问题,在邻近中心算法基础上提出一种适用于特殊等式约束优化问题、可实现所有步骤分解计算的全分邻近中心算法。该算法通过邻近函数构造平滑同时可分的拉格朗日函数,并通过最优梯度更新拉格朗日乘子,只需要在相邻分区之间交换边界节点信息即可实现全网无功优化的分解协调计算。与通过对偶梯度更新拉格朗日乘子的分解算法相比,它不但可以直接确定计算所用参数,而且可以大大提高收敛速度。算例结果表明,所提算法可以实现全网无功优化的分解协调计算,并且其计算效率远高于基于辅助问题原理的分解协调算法。

Aiming at the inseparable problem of the augmented Lagrangian fimction of decomposition-coordination model of reactive power optimization, on the basis of proximal center algorithm, a full decomposition proximal center algorithm which can make all steps separated for optimization problems which contain special equality constraints was proposed. The algorithm constructs smooth and decomposable Lagrangian function using proximal function and updates Lagrangian multipliers using optimal gradient. It can be used for decomposition and coordination of reactive power optimization of the whole network, which only needs to exchange the information of boundary nodes between adjacent sub-areas. Compared with the algorithms which update Lagrangian multipliers using dual gradient, it can choose the parameters used unambiguously and improve the computing speed significantly. The simulation shows the algorithm can realize decomposition and coordination of reactive power optimization of the whole network, and its computational efficiency is much higher than the decomposition and coordination algorithm based on auxiliary problem principle.