基于凸松弛理论的有源配电网有功-无功分布式协调优化研究

随着随机间歇式分布式能源和增量配电网的快速发展，传统集中优化方法，面临无法保护信息隐私和单点失效问题，而研究不确定条件下分布式协调优化的理论和方法是可行之路。本项目拟首先基于高斯混合分布建立不同分布式能源节点的统一随机模型，然后从矩阵流形优化的角度，研究高斯混合模型参数优化问题的测地线凸松弛方法，得到高斯混合模型参数的全局最优解；接着利用高斯分布的可逆性，建立计及节点功率不确定性的等价确定性模型，针对交直流混合网络约束、离散变量造成确定性模型非凸的问题，研究轻载时基于分段线性化的凸松弛模型和重载时基于多阶矩量的凸松弛模型，确定精确凸松弛的充分条件，得到可鲁棒和高效求解的凸优化模型；最后在凸模型基础上，研究分布式协调优化的加速收敛机理，实现较少区域间数据交换量的全分布式优化，促进可再生能源消纳。本项目研究为实现含高比例分布式能源配电网的全局经济运行提供切实可行的理论依据和技术储备。

With the fast development of uncertain and intermittent distributed energy resources and incremental distribution network, traditional centralized optimization has encountered problems on protecting information privacy and single point failure of system. Therefore, study on distributed optimization method considering uncertainty is one feasible direction. In this project, an unified node power gauss mixture model is established and a geodesic convex relaxation method is proposed for model parameter calculation to obtain global optimal results. Then, according to invertible feature of gauss model, an equivalent deterministic model can be obtained from uncertainty-constrained programming model. Since nonconvex caused by network constraints of three-phase hybrid ac-dc distribution network and discrete variables, convex relaxation based on piece-wise linearization under light load and moment theory based convex relaxation under heavy load are studied, sufficient condition to obtain convex relaxation model with high precision is proposed and this convex model can be solved robustly and efficiently. Based on convex model, the mechanism to accelerate convergence of distributed optimization will be studied. It will be a fully distributed optimization manner with small amount of information exchanged between zones to improve renewable energy accommodation. Research of this project will provide practical theory basis and technical reservation for global economic operation of distribution network with high penetration of distributed energy resources.