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This paper presents an analytical model, oriented to study harmonic mitigation aspects in AC grids. As it is well known, the presence of non-desired harmonics in AC grids can be palliated in several manners. However, in this paper, a power electronic-based active impedance at selective frequencies (ACISEF) is used, due to its already proven flexibility and adaptability to the changing characteristics of AC grids. Hence, the proposed analytical model approach is specially conceived to globally consider both the model of the AC grid itself with its electric equivalent impedances, together with the power electronic-based ACISEF, including its control loops. In addition, the proposed analytical model presents practical and useful properties, as it is simple to understand and simple to use, it has low computational cost and simple adaptability to different scenarios of AC grids, and it provides an accurate enough representation of the reality. The benefits of using the proposed analytical model are shown in this paper through some examples of its usefulness, including an analysis of stability and the identification of sources of instability for a robust design, an analysis of effectiveness in harmonic mitigation, an analysis to assist in the choice of the most suitable active impedance under a given state of the AC grid, an analysis of the interaction between different compensators, and so on. To conclude, experimental validation of a 2.15 kA ACISEF in a real 33 kV AC grid is provided, in which real users (household and industry loads) and crucial elements such as wind parks and HVDC systems are near inter-connected.