  Solving power flow (PF) equations is the basis of power flow analysis, which
is important in determining the best operation of existing systems, performing
security analysis, etc. However, PF equations can be out-of-date or even
unavailable due to system dynamics and uncertainties, making traditional
numerical approaches infeasible. To address these concerns, researchers have
proposed data-driven approaches to solve the PF problem by learning the mapping
rules from historical system operation data. Nevertheless, prior data-driven
approaches suffer from poor performance and generalizability, due to overly
simplified assumptions of the PF problem or ignorance of physical laws
governing power systems. In this paper, we propose a physics-guided neural
network to solve the PF problem, with an auxiliary task to rebuild the PF
model. By encoding different granularity of Kirchhoff's laws and system
topology into the rebuilt PF model, our neural-network based PF solver is
regularized by the auxiliary task and constrained by the physical laws. The
simulation results show that our physics-guided neural network methods achieve
better performance and generalizability compared to existing unconstrained
data-driven approaches. Furthermore, we demonstrate that the weight matrices of
our physics-guided neural networks embody power system physics by showing their
similarities with the bus admittance matrices.
