  The knowledge of accurate stellar parameters is a keystone in several fields
of stellar astrophysics, such as asteroseismology and stellar evolution.
Although the fundamental parameters can be derived both from spectroscopy and
multicolour photometry, the results obtained are sometimes affected by
systematic uncertainties. In this paper, we present a self-consistent spectral
analysis of the pulsating star RR Lyr, which is the primary target for our
study of the Blazhko effect. We used high-resolution and high signal-to-noise
ratio spectra to carry out a consistent parameter determination and abundance
analysis for RR Lyr. We provide a detailed description of the methodology
adopted to derive the fundamental parameters and the abundances. Stellar
pulsation attains high amplitudes in RR Lyrae stars, and as a consequence the
stellar parameters vary significantly over the pulsation cycle. The abundances
of the star, however, are not expected to change. From a set of available
high-resolution spectra of RR Lyr we selected the phase of maximum radius, at
which the spectra are least disturbed by the pulsation. Using the abundances
determined at this phase as a starting point, we expect to obtain a higher
accuracy in the fundamental parameters determined at other phases. The set of
fundamental parameters obtained in this work fits the observed spectrum
accurately. Through the abundance analysis, we find clear indications for a
depth-dependent microturbulent velocity, that we quantified. We confirm the
importance of a consistent analysis of relevant spectroscopic features,
application of advanced model atmospheres, and the use of up-to-date atomic
line data for the determination of stellar parameters. These results are
crucial for further studies, e.g., detailed theoretical modelling of the
observed pulsations.
