This paper presents a universal model formulation for solving Optimal Power Flows for hybrid AC/DC grids. The prowess of the new formulation is that it (i) provides a direct link between AC and DC parts of the grid allowing for solving the entire network within a unified frame of reference (not sequentially) and (ii) can realistically model any element within the AC/DC power grid, ranging from conventional AC transmission lines to multiple types of AC/DC interface devices such as Voltage Source Converters (VSC) by introducing additional control variables. The model is formulated in such a way that it does not make a distinction, from a mathematical perspective, between AC and DC elements and the ensuing optimal power flow (OPF) problem can be solved via model-based optimization solvers as a mathematical programming problem. Simulations carried out using a variety of non-linear gradient-based solvers in AIMMS© on a small contrived and a large realistic test system (modified PEGASE) clearly show that the universal model is on par with existing methodologies for solving OPFs both in accuracy of the solution and computational efficiency. Meanwhile, simulations carried out on a series of AC and AC/DC test systems show that the model is scalable and stays computationally tractable for larger system sizes without sacrificing convergence time.

中文翻译：

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用于解决混合 AC/DC 电网中最优潮流的通用分支模型

本文提出了用于求解混合 AC/DC 电网的最佳潮流的通用模型公式。新公式的强大之处在于它 (i) 在电网的交流和直流部分之间提供了直接链接，允许在统一的参考框架内（而不是按顺序）求解整个网络，并且 (ii) 可以对其中的任何元素进行实际建模通过引入额外的控制变量，AC/DC 电网，从传统的 AC 传输线到多种类型的 AC/DC 接口设备，例如电压源转换器 (VSC)。该模型的制定方式使其从数学角度不区分交流和直流元件，随后的最优潮流 (OPF) 问题可以通过基于模型的优化求解器作为数学规划问题解决. 在 AIMMS© 中使用各种基于非线性梯度的求解器在小型设计和大型现实测试系统（修改后的 PEGASE）上进行的模拟清楚地表明，通用模型与现有的求解 OPF 的方法在精度和解和计算效率。同时，在一系列 AC 和 AC/DC 测试系统上进行的仿真表明，该模型具有可扩展性，并且在不牺牲收敛时间的情况下，对于更大的系统规模在计算上保持易处理。