基于Sinkhorn分布鲁棒优化的综合能源系统最优能流方法

针对风电接入综合能源系统所带来的不确定性问题，提出一种基于Sinkhorn分布鲁棒优化的动态最优能流模型及求解方法。将风电的不确定性描述为包含概率分布信息的模糊不确定集，并将其构造为以风电出力经验分布为中心，以Sinkhorn距离为半径的Sinkhorn球。采用二分搜索的批量梯度下降法求解，以降低风电不确定性所带来的影响，并减少计算复杂度。算例结果表明，所提方法与随机优化和传统鲁棒优化方法相比，能更有效地平衡系统的鲁棒性与经济性。此外，所提方法在不同样本规模下的计算时间及目标函数均优于Wasserstein方法。

Optimal energy flow method of integrated energy system based on Sinkhorn distribution robust optimization

Aiming at the uncertainty problem brought by wind power access to the integrated energy system, a dynamic optimal energy flow model and solution method based on Sinkhorn distribution robust optimization are proposed. The uncertainty of wind power is described as a fuzzy uncertainty set containing probability distribution information, and it is constructed as a Sinkhorn sphere with the empirical distribution of wind power output as the center and the Sinkhorn distance as the radius. Then, a batch gradient descent method of binary search is used to solve the problem in order to reduce the impact of wind power uncertainty and the computational complexity. The results of case study show that the proposed method can effectively balance the robustness and economy of system compared with the stochastic optimization and traditional robust optimization. Moreover, the computational time and objective function of the proposed method are better than those of the Wasserstein method under different sample scales.