This paper focuses the analysis around a grid-connected converter that operates under unbalanced voltage and current conditions. Two different scenarios have been selected to validate the proposed algorithms. In the first scenario, the converter operates as a reactive power compensator, exchanging reactive power with the grid, and minimizing the dc bus voltage oscillations. The second scenario is more challenging, since it operates as a load balancer. In this application, the unbalanced current consumption of the load is compensated by the converter, exchanging positive and negative sequence currents with the grid. Another objective in this second scenario is to compensate the reactive power of the unbalanced load. It is important to highlight that in both scenarios, any maximum limit of the converter can be exceeded due to the specific unbalanced voltage and current conditions. Three variables are considered critical for the converter: 1) output ac current limit; 2) output ac voltage limit; and 3) dc bus voltage oscillation limit. Thus, this paper proposes a control method, which limits online the reactive power reference in the first scenario and the exchanged current references in the second scenario in order not to exceed any of the mentioned critical variables. The corresponding experimental results are shown in Part II of this paper so as to validate the limitation algorithm obtained by means of the mathematical analysis carried out in Part I.