A Virtual Graph Constrained Learning Method for Power Flow Calculation

To enhance the practical consistency and interpretability of deep learning approaches in power flow (PF) calculation, this letter proposes a virtual graph constrained message passing neural network (VGC-MPNN) for PF analysis, which defines a virtual graph from the mathematical expression of variables to enhance the binding force of power flow equations. Different from the existing methods that simply adopt the form of penalty function to learn the physical constraints, the proposed method empowers the mathematical expression into the feedforward process of the neural network to ensure a consistent solution, which performs internal solution logic instead of fitting the labeled output of the Newton-Raphson solver. Numerical analysis shows that the proposed VGC-MPNN could guarantee the physical consistency of original PFEs and improve the sensitivity of physical non-convergence, while the topological adaptability is also proved by considering network variations.