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Shunt capacitors can be of great help in enhancing the performance of distribution systems. However, the addition of shunt capacitors may lead to high distortion levels causing damage to electric equipment of both the electric utility and customers. As a result, shunt capacitors should be optimally located and rated taking the presence of harmonics into account. The essential first step in solving the optimal placement and sizing problem is modeling system components in detail. In addition to system modeling, an efficient harmonic power flow program plays a vital role in studying system response characteristics when harmonics are being propagated in distribution systems. In this paper, part I in a series of three papers, three-phase representations of system components and a harmonic power flow algorithm (HPF) that exploits the unique characteristics of distribution systems are presented.