Identification of harmonic sources contributing to harmonic distortion, and characterization of harmonic current injected by them, are crucial tasks in harmonic analysis of modern power systems. In this paper, these tasks are addressed based on the permissible current limits recommended by IEEE 519 Standard, with a determination of whether or not injected harmonics are within these limits. If limits are violated, the extent of the violations are characterized to provide information about harmonic current levels in the power system and facilitate remedial actions if necessary. A novel feature extraction method is proposed, whereby each set of harmonic measurements in a power system are transformed into a unique RGB image. Harmonic State Estimation (HSE) is discretized as a classification problem. Classifiers based on deep learning have been developed to subsequently locate and characterize harmonic sources. The approach has been demonstrated effectively both on the IEEE 14-bus system, and on a real transmission network where harmonics have been measured. A comparative study indicates that the proposed technique outperforms state-of-the-art techniques for HSE, including Bayesian Learning (BL), Singular Value Decomposition (SVD) and hybrid Genetic Algorithm Least Square (GALS) method in terms of accuracy and limited number of monitors.