  Power distribution systems are experiencing a large-scale integration of
Converter-Interfaced Distributed Energy Resources (CIDERs). This complicates
the analysis and mitigation of harmonics, whose creation and propagation are
facilitated by the interactions of converters and their controllers through the
grid. In this paper, a method for the calculation of the so-called Harmonic
Power-Flow (HPF) in three-phase grids with CIDERs is proposed. The
distinguishing feature of this HPF method is the generic and modular
representation of the system components. Notably, as opposed to most of the
existing approaches, the coupling between harmonics is explicitly considered.
The HPF problem is formulated by combining the hybrid nodal equations of the
grid with the closed-loop transfer functions of the CIDERs, and solved using
the Newton-Raphson method. The grid components are characterized by compound
electrical parameters, which allow to represent both transposed or
non-transposed lines. The CIDERs are represented by modular linear
time-periodic systems, which allows to treat both grid-forming and
grid-following control laws. The method's accuracy and computational efficiency
are confirmed via time-domain simulations of the CIGR\'E low-voltage benchmark
microgrid. This paper is divided in two parts, which focus on the development
(Part I) and the validation (Part II) of the proposed method.
