论文标题
一种新型的Riemannian优化方法，用于径向分布网络负载流问题
A Novel Riemannian Optimization Approach to the Radial Distribution Network Load Flow Problem
论文作者
论文摘要
在本文中，我们将径向电分布网络中的负载流（LF）问题提出为无约束的Riemannian优化问题，由两个歧管组成，我们考虑了替代性撤回和初始化选项。我们的贡献是一种新颖的LF溶液方法，我们表明，它属于Riemannian近似牛顿方法的家族，保证了单调下降和局部超级线性收敛速率。据我们所知，这是采用Riemannian优化的第一种精确的LF解决方案方法。几个测试网络上的广泛数值比较表明，该方法的表现优于其他黎曼优化方法（梯度下降，牛顿），并且与传统的牛顿 - 拉夫森方法相当的性能，尽管可以通过保证来融合。我们还考虑了通过提出方法的第一次迭代获得的近似LF解决方案，我们表明它在LF文献中的表现明显优于其他近似值。最后，我们得出了与众所周知的向后扫描方法的有趣比较。
In this paper, we formulate the Load Flow (LF) problem in radial electricity distribution networks as an unconstrained Riemannian optimization problem, consisting of two manifolds, and we consider alternative retractions and initialization options. Our contribution is a novel LF solution method, which we show belongs to the family of Riemannian approximate Newton methods guaranteeing monotonic descent and local superlinear convergence rate. To the best of our knowledge, this is the first exact LF solution method employing Riemannian optimization. Extensive numerical comparisons on several test networks illustrate that the proposed method outperforms other Riemannian optimization methods (Gradient Descent, Newton's), and achieves comparable performance with the traditional Newton-Raphson method, albeit besting it by a guarantee to convergence. We also consider an approximate LF solution obtained by the first iteration of the proposed method, and we show that it significantly outperforms other approximants in the LF literature. Lastly, we derive an interesting comparison with the well-known Backward-Forward Sweep method.
