Physics-Informed GNN for non-linear constrained optimization: PINCO a solver for the AC-optimal power flow

Abstract

The energy transition is driving the integration of large shares of intermittent power sources in the electric power grid. Therefore, addressing the AC optimal power flow (AC-OPF) effectively becomes increasingly essential. The AC-OPF, which is a fundamental optimization problem in power systems, must be solved more frequently to ensure the safe and cost-effective operation of power systems. Due to its non-linear nature, AC-OPF is often solved in its linearized form, despite inherent inaccuracies. Non-linear solvers, such as the interior point method, are typically employed to solve the full OPF problem. However, these iterative methods may not converge for large systems and do not guarantee global optimality. This work explores a physics-informed graph neural network, PINCO, to solve the AC-OPF. We demonstrate that this method provides accurate solutions in a fraction of the computational time when compared to the established non-linear programming solvers. Remarkably, PINCO generalizes effectively across a diverse set of loading conditions in the power system. We show that our method can solve the AC-OPF without violating inequality constraints. Furthermore, it can function both as a solver and as a hybrid universal function approximator. Moreover, the approach can be easily adapted to different power systems with minimal adjustments to the hyperparameters, including systems with multiple generators at each bus. Overall, this work demonstrates an advancement in the field of power system optimization to tackle the challenges of the energy transition. The code and data utilized in this paper are available at https://anonymous.4open.science/r/opf_pinn_iclr-B83E/.

Figures (4)

• Figure 1: Schematic of the PINCO method architecture. This diagram illustrates the input data (in red) and the output generated by the neural network (in green). The constant parameters specific to the power grid, as defined by the optimization problem in Section \ref{['sec:acopf']}, are fed directly into the physics-informed loss function.
• Figure 2: Power grid model as graph. The input features assigned to each node are red, and the predicted quantities at the node level are green. The zoom visualizes how multiple generators per node are modeled; the grey node is the artificial node created to account for additional generators at the node.
• Figure 3: Average differences between solutions from PINCO and the MIPS solver on a logarithmic scale. Phase angle ($\theta$) and voltage magnitude ($V$) differences are averaged across all nodes and normalized by their maximum values. Active ($P_g$) and reactive power ($Q_g$) differences are averaged at generator buses and normalized by total demand.
• Figure 4: MIPS and PINCO inference times in logarithmic scale, tested using the same conditions on the same device eulerwiki.