随着高比例新能源的接入和电网规模不断扩大，传统优化模型无法应对电力系统中日益复杂的运行结构和不断增加的灵活资源。为了提高电网的经济性与安全性，有必要研究更为有效的优化模型及其求解算法，充分发挥可控资源的调节作用并求解得到最优的调度计划。本文针对电力系统优化模型及其求解算法中的关键问题展开了研究，构建了最优潮流的的凸松弛理论和方法，并对最优潮流在输配电网综合无功优化和分布式优化等方面的应用进行了研究，具体包括以下工作：（1）最优潮流模型是电力系统调度问题的最基础模型，是一个非凸优化问题，求解困难。本文提出了一种最优潮流凸松弛的可行解恢复算法，解决环网中凸松弛结果不可行的问题。算法保证收敛，且求出的可行解满足最优潮流原问题的KKT条件。该算法将非凸的最优潮流问题转化为凸优化问题的迭代求解，普遍适用于电力系统的规划和运行优化问题。（2）大规模新能源接入配电网后，独立的无功优化或网络重构无法单独解决由此引发的电压安全问题。本文提出了综合考虑无功优化和网络重构的配电网综合优化模型，是一个混合整数非线性规划问题。基于辐射网的精确凸松弛理论和本文提出的变压器分接头档位精确线性化方法，构建了该非凸模型的混合整数二阶锥规划求解算法，可以高效求出原问题的全局最优解。（3）输电网的结构优化是提高输电网经济性和安全性的有效手段，传统基于直流潮流的模型不能考虑无功和电压，无法准确求解该问题。本文提出了综合考虑最优潮流和结构优化的输电网优化凸松弛模型以及环网中凸松弛不精确情形下的可行解恢复方法。通过数值仿真，验证了当传统方法失效时，本文所提算法的可行性和最优性。（4）分布式最优潮流是多主体电网优化运行的必要手段，传统基于非凸最优潮流模型的分布式算法无法保证收敛性，而基于凸松弛模型的算法在环网中无法保证结果的可行性。本文基于凸松弛与可行解恢复算法的理论框架，提出了与集中式方法收敛性一致的分布式最优潮流算法。通过数值仿真，验证了所提算法在输电网和配电网分布式最优潮流计算中的良好收敛性。本文的研究旨在提高凸松弛理论在电力系统中的应用价值，为解决电力系统中大规模新能源接入的消纳问题，提供理论支持和方法指导。
With the integration of high-level new energy sources and the expansion of power grid, traditional optimization models can not cope with the increasingly complex operational structure and the growing flexible resources in power systems. In order to improve the economy and security of modern power systems, it is necessary to research on more effective optimization models and algorithms, make full use of the controllable resources and develope the optimal dispatch strategy. This dissertation aims at the optimization models and algorithms of the key operation and schedule problems in power systems, builds the convex relaxation theory and method of power system optimal power flow (OPF) problems, then studies on comprehensive optimization and distributed optimization of transmission and distribution networks based on OPF. This dissertation mainly includes the following work:(1) Optimal power flow is the basic model of power system scheduling problem, it is a non-convex optimization problem which is hard to solve. In this dissertation, a feasible solution recovery algorithm for convex relaxed OPF model is proposed to solve the problem that the convex relaxation is infeasible for mesh networks. The algorithm not only guarantees convergence, but can also obtain a feasible solution that satisfies the KKT conditions of the original OPF problem. The algorithm transforms the non-convex OPF problem into an iterative solution of convex optimization problems, which is generally applicable to the planning and optimization problems of modern power systems. (2) The traditional reactive power optimization or network reconfiguration cannot solve the voltage safety problem caused by the integration of large-scale new energy sources into distribution networks. This dissertation proposes a distribution network comprehensive optimization model that considers both reactive power optimization and network reconfiguration, which is a mixed-integer non-linear programming problem. Based on the accurate convex relaxation theory of radial network and precise linearization method of transformer OLTC, a mixed integer second-order cone programming algorithm for non-convex optimization model is proposed, which can efficiently find the global optimal solution of the original problem.(3) The optimal switching of transmission lines is an effective method to improve the economy and security of transmission networks. The traditional model based on DC power flow cannot precisely consider the reactive power and voltage, thus cannot solve the problem accurately. In this dissertation, a convex relaxation model of transmission network considering optimal power flow and optimal transmission switching is proposed, as well as a feasible solution recovery method because convex relaxation is not accurate in mesh networks. In numerical tests, the feasibility and optimality of the proposed algorithm are verified when traditional method fails.(4) Distributed optimal power flow is a necessary tool for multi-agent power systems’ operation and optimization. The traditional distributed algorithms based on non-convex OPF model cannot guarantee convergence, while the algorithms based on convex relaxation cannot guarantee feasibility. Based on the theoretical framework of convex relaxation and feasible solution recovery algorithm, this dissertation proposes a distributed OPF algorithm which has consistent convergence behavior with centralized methods. Numerical results prove the good convergence behavior of the proposed algorithm for the distributed OPF of transmission and distribution networks.The research in this dissertation aims to improve the application value of convex relaxation theory in power systems, and provide theoretical support and method guidance for solving the problem of large-scale new energy integration in modern power systems.
