When the power grid presents an unobservable state due to insufficient measurement configuration

traditional state estimation methods fail to accurately detect the power grid's harmonic distribution. Therefore

this paper proposes a harmonic state estimation method

which combines the mechanism of harmonic propagation and generative adversarial networks (GAN) to estimate the harmonic state of unobservable nodes. Firstly

the unobservable region is simplified using the network topology equivalent method

and the harmonic transfer equations between the state variables of unobservable nodes and the virtual state variables of boundary nodes are derived

which is used as the basis for the integration of the mechanism and GAN. Secondly

a GAN-based harmonic state estimation model is constructed

which formulates a loss function based on harmonic state equations and transfer equations. The loss function incorporates measurement residuals and the mean square error of virtual state quantities at boundary nodes as penalization terms

thereby refining the training process of the model via harmonic equations. Furthermore

a residual model incorporating attention mechanisms is used to improve the structure of generator

and the convolutional neural networks are employed to improve the the structure of discriminator. Besides

the patch GAN is utilized for local data discrimination

so the feature mining capabilities of the model can be enhanced. Finally

the effectiveness of the proposed method is validated through simulation tests on the IEEE 33-node system.