The energy transition challenges operational tasks based on simulations and optimisation. These computations need to be fast and flexible as the grid is ever-expanding, and renewables' uncertainty requires a flexible operational environment. Learned approximations, proxies or surrogates -- we refer to them as Neural Solvers -- excel in terms of evaluation speed, but are inflexible with respect to adjusting to changing tasks. Hence, neural solvers are usually applicable to highly specific tasks, which limits their usefulness in practice; a widely reusable, foundational neural solver is required. Therefore, this work proposes the Residual Power Flow (RPF) formulation. RPF formulates residual functions based on Kirchhoff's laws to quantify the infeasibility of an operating condition. The minimisation of the residuals determines the voltage solution; an additional slack variable is needed to achieve AC-feasibility. RPF forms a natural, foundational subtask of tasks subject to power flow constraints. We propose to learn RPF with neural solvers to exploit their speed. Furthermore, RPF improves learning performance compared to common power flow formulations. To solve operational tasks, we integrate the neural solver in a Predict-then-Optimise (PO) approach to combine speed and flexibility. The case study investigates the IEEE 9-bus system and three tasks (AC Optimal Power Flow (OPF), power-flow and quasi-steady state power flow) solved by PO. The results demonstrate the accuracy and flexibility of learning with RPF.

翻译：能源转型对基于仿真与优化的运行任务提出了挑战。随着电网不断扩展以及可再生能源的不确定性要求灵活的运行环境，这些计算需要具备快速性和适应性。学习型近似方法、代理模型或替代模型——我们将其统称为神经求解器——在评估速度方面表现优异，但在适应任务变化方面缺乏灵活性。因此，神经求解器通常仅适用于高度特定的任务，这限制了其实际应用价值；我们需要一种可广泛复用、基础性的神经求解器。为此，本研究提出了基于残差的潮流计算（RPF）模型。RPF基于基尔霍夫定律构建残差函数，以量化运行条件的不可行性。通过最小化残差可确定电压解；为实现交流可行性，需要引入额外的松弛变量。RPF天然构成了受潮流约束任务的基础性子任务。我们建议采用神经求解器学习RPF以发挥其速度优势。此外，与常规潮流模型相比，RPF能提升学习性能。为解决运行任务，我们将神经求解器集成至"预测-优化"（PO）框架中，以兼顾速度与灵活性。案例研究基于IEEE 9节点系统，通过PO方法求解三个任务（交流最优潮流、潮流计算及准稳态潮流）。结果验证了基于RPF学习方法的准确性与灵活性。