YBa2Cu3O7-δ coated conductors have very slow normal-zone propagation velocity, which renders quench detection and protection very difficult. To develop effective quench detection methods, it is paramount to study the underlying behavior that drives quench propagation at the micrometer-scale level. Toward this end, numerical mixed-dimensional models, composed of multiple high-aspect-ratio thin layers, are developed. The high-aspect-ratio modeling issues are tackled by approximating the thin layers either as a 2-D surface or as an analytical contact resistance interior boundary condition, which also acts as a coupling bridge between the 2-D and 3-D behaviors. The tape models take into account the thermal and electrical physics of each layer in actual conductor dimensions and are implemented using commercial finite-element analysis software. In the first part of this two-part paper, the mixed-dimensional models are introduced and then computationally and experimentally validated. Validations are gauged by comparisons in normal-zone propagation velocity and in the time-dependent voltage and temperature profiles. Results show that the mixed-dimensional models can not only effectively address the high-aspect-ratio modeling issues of thin films but also accurately and efficiently reproduce physical quench phenomena in a coated conductor.