论文标题
连续开关模型和启发式功能系统中的混合问题问题
Continuous Switch Model and Heuristics for Mixed-Integer Problems in Power Systems
论文作者
论文摘要
许多电源系统操作和计划计算（例如，传输和生成开关和放置）解决了混合企业非线性问题（MINLP）的二进制变量，代表决定将设备连接到网格的决定。具有非线性交流网络约束的二进制变量使此问题NP障碍。对于大型现实世界网络，为这些问题获得AC可行的最佳解决方案是计算挑战性的，并且在当今最先进的工具中通常无法实现。在这项工作中，我们通过用基于电路的连续开关模型来表示二进制变量，将MINLP决策问题映射到一组等效电路中。我们通过受控的非线性阻抗来表征连续开关模型，该模型更亲密地模拟了现实世界开关的身体行为。该映射有效地将MINLP问题转化为NLP问题。我们在数学上表明这种转变是MINLP问题的紧张放松。为了快速且稳健的收敛，我们开发了物理驱动的同型和牛顿 - 拉夫森阻尼方法。为了验证这种方法，我们在实用的墙壁上售出的大型系统（$> $ 70,000的公共汽车）的凭经验表明了强大的融合，达到了AC可行的最佳选择。我们比较我们的结果，并显示出对行业标准工具和其他二元放松方法的改进。
Many power systems operation and planning computations (e.g., transmission and generation switching and placement) solve a mixed-integer nonlinear problem (MINLP) with binary variables representing the decision to connect devices to the grid. Binary variables with nonlinear AC network constraints make this problem NP-hard. For large real-world networks, obtaining an AC feasible optimum solution for these problems is computationally challenging and often unattainable with state-of-the-art tools today. In this work, we map the MINLP decision problem into a set of equivalent circuits by representing binary variables with a circuit-based continuous switch model. We characterize the continuous switch model by a controlled nonlinear impedance that more closely mimics the physical behavior of a real-world switch. This mapping effectively transforms the MINLP problem into an NLP problem. We mathematically show that this transformation is a tight relaxation of the MINLP problem. For fast and robust convergence, we develop physics-driven homotopy and Newton-Raphson damping methods. To validate this approach, we empirically show robust convergences for large, realistic systems ($>$ 70,000 buses) in a practical wall-clock time to an AC-feasible optimum. We compare our results and show improvement over industry-standard tools and other binary relaxation methods.
