Power system harmonics have received a great deal of attention in the past few decades due to the fact that harmonics can cause communication errors, overheating and hardware damage. Harmonic analysis is significant to effectively identify and help eliminate the harmonic sources in the system and thereby guarantees high levels of power quality. The research in this thesis focuses on the improvement of the accuracy and reliability of harmonic analysis in the power distribution network. First, an iterative observer-based algorithm is applied to harmonic estimation in the real-time environment. Comparing with the traditional harmonic estimation methods, the proposed algorithm goes beyond the framework of fixed frequencies, which can estimate harmonics with iteratively frequencies. Further, the analysis shows that the proposed method solves the time-delay problem during observer design for harmonic estimation. Second, the problem of harmonic sources identification is investigated. All the possible combinations of harmonic sources are carried out simultaneously in the power distribution network and consideration of time delays for the observer gain design. Finally, a passive filter method is presented for harmonic mitigation in power distribution networks with consideration of harmonic compensation. The parameters are mostly obtained by the first two algorithms, which make the three proposed methods to be a complete progress of harmonic analysis based on the iterative observer.