We propose a physics-inspired data-driven model that can estimate the power outputs of all wind turbines in any layout under any wind conditions. The proposed model comprises two parts: (1) representing a wind farm configuration with the current wind conditions as a graph, and (2) processing the graph input and estimating power outputs of all the wind turbines using a physics-induced graph neural network (PGNN). By utilizing the form of an engineering wake interaction model as a basis function, PGNN effectively imposes physics-induced bias for modelling the interaction among wind turbines into the network structure. simulation study shows that the combination of a graph representation of a wind farm and PGNN produce not only accurate and generalizable estimations but also physically explainable estimations. That is, the computing and reasoning procedures of PGNN can be understood by analyzing the intermediate features of the model. We also conduct a layout optimization experiment to show the effectiveness of PGNN as a differentiable surrogate model for wind farm power estimations. (C) 2019 Elsevier Ltd. All rights reserved.