近年来，大量的可再生能源通过集中式与分布式的方式接入到各级电网，这使得不同等级的电网之间紧密耦合在一起，传统的各级电网之间割裂的运行方式不再适用，电网的优化运行需要各级之间的有效协同。另一方面，伴随着我国配电侧的市场化改革，微电网、虚拟电厂等自治实体接入到了电网中。考虑到各级自治电网数据信息隐私与调度运行独立性，电网优化运行的全局协同需要按照分解协调的方式来展开。然而，配电网与微电网中的高比例分布式电源使得电网特性日益复杂，各级电网控制对等，不再具备典型的主从特性，已有的分解协调算法受制于协调效率、优化问题性质等原因并不能够适应各种各样可能的场景。本文在这一背景下对复杂电网的多级嵌套分解协调优化运行理论开展研究，提出了适用于连续非线性规划问题的多参数空间投影分解理论，实现了多级嵌套的分解协调算法，并应用于多级电网协同的状态估计、经济调度、最优潮流等功能中。本文的主要工作总结如下。（1）提出了面向多级协同优化问题的嵌套分解协调算法。算法面向一般的非线性规划问题，构建了下级优化问题关于边界参数空间的近似投影函数，从而形成稳定且高效收敛的两级分解协调算法。进一步将该两级优化问题的分解协调算法严格扩展到了多级优化问题中，并给出了算法的收敛性与最优性理论证明。（2）建立了多级电网协同抗差状态估计模型并提出其分解协调算法。该算法的每次迭代与下级电网的坏数据分布估计相关联，利用坏数据的稀疏性保证了算法的高效收敛性。通过算例仿真验证了协同抗差状态估计的必要性与分解协调算法的精度和收敛性。（3）建立了多级电网协同经济调度模型并提出其分解协调算法。算法将下级电网调度的最优目标投影到了边界注入功率空间，得到精确的投影函数与相应的作用域，在不考虑下级电网时间耦合约束场景下所提分解协调算法无需迭代。通过算例仿真验证了协同经济调度的经济效益与分解协调算法的计算性能优势。（4）建立了多级电网协同最优潮流模型并提出其分解协调算法。算法能够有效应对最优潮流问题中的非线性约束，通过构建下级电网对边界参数空间的近似目标投影函数大幅加速计算收敛。通过算例仿真验证了协同最优潮流在保证安全前提下所实现的最优经济效益，以及算法的高效收敛性和数值稳定性。
In recent years, massive renewable energy sources have been integrated into different levels of the electric power grid through both centralized and distributed manners. Electric power grids of different levels are becoming increasingly strongly coupled. Therefore, the optimal operation of multilevel electric power grids can no longer be carried out separately, and the coordination among each other is of great necessity. Meanwhile, the market-oriented reform of distribution grids enables the participation of autonomous entities in electric power grids, which includes microgrids, virtual power plants, etc. Considering the information privacy and independence of different autonomous grids, the coordination of multilevel electric power grids should be carried out in a decentralized manner. However, the growing penetration of renewable energy sources complicates the operation of electric power grids. Electric power grids of different levels are becoming equivalent and no longer have the typical master-slave characteristics. Consequently, existing decentralized methods cannot satisfy all scenarios due to restrictions from low computation efficiencies and complex optimization problem characteristics.This thesis investigates the multilevel nested decentralized optimal operation theory for complex electric power grids, proposes a multi-parametric projection decomposition algorithm to solve general continuous nonlinear programs, develops a multilevel nested decentralized method, and applies the proposed decentralized method into the coordinated state estimation, economic dispatch, and optimal power flow of multilevel electric power grids. A brief summary of this thesis is as follows.First, this thesis proposes a nested decentralized method to solve multilevel coordinated optimization problems. The proposed method adapts to general nonlinear programs, and approximate projection functions on boundary parameter spaces of lower optimization problems are constructed, thereby forming a bilevel decentralized algorithm with stable and efficient convergence. Furthermore, the proposed decentralized method is extended from bilevel to multilevel through a rigorous nested decentralized framework. The convergence and optimality of the proposed method have been proved theoretically.Second, this thesis constructs a coordinated robust state estimation model of multilevel electric power grids and proposes a decentralized method to solve the model. Each iteration of the proposed method correlates a specific bad data distribution estimation of lower-level electric power grids. The sparsity of bad data guarantees the fast convergence of the proposed method. Case studies demonstrate the necessity of coordinated robust state estimation and the exactness and convergence of the proposed method.Third, this thesis constructs a coordinated economic dispatch model of multilevel electric power grids and proposes a decentralized method to solve the model. The proposed method projects the optimal objective of lower-level electric power grids into the space of boundary injection power. Accurate projection functions of lower-level electric power grids along with corresponding active regions are achieved. Moreover, when coupling constraints among dispatch periods of lower-level grids are not considered, the proposed method can be furthered developed into a non-iterative manner. Case studies demonstrate the economic benefits of coordinated economic dispatch and the advantages of the proposed method on computation performances.Last, this thesis constructs a coordinated optimal power flow model of multilevel electric power grids and proposes a decentralized method to solve the model. The proposed method can effectively handle nonlinear constraints in optimal power flow problems. The convergence of the proposed method is significantly accelerated by computing the approximate objective projection of lower-level electric power grids on boundary parameter space. Case studies demonstrate that the coordinated optimal power flow can achieve optimal economic benefits with guaranteed safety of multilevel electric power grids. The efficient convergence and numerical stability of the proposed method have also been validated.
