Because of automotive electrification, fan system noises previously hidden by the internal combustion engine could become key contributors to the overall noise behavior. Metrics like overall sound pressure level or Loudness are first order metrics enabling noise ranking. Yet, second order factors, that are relevant to assess annoyance, are not correctly described using a single criterion. This paper studies the applicability of various psychoacoustic annoyance models in an attempt to address the subjective perception of sound quality. Based on pairwise comparisons through a jury test with a set of 8 noises at similar overall levels, the combined impact of several psychoacoustics metrics was previously determined. This computation includes a signal modulation metric, a frequency content balance and a tonal criterion. To complete this approach, the correlation for fan system noise annoyance ranking based on this jury test is compared with several psychoacoustic annoyance criteria. These models start from the initial Zwicker and Fastl model to later extensions including tonal contributions such as Schneider, More, Di or Cerkovnik. The low correlation between jury rankings and annoyance models highlights that general models are not applicable to low pressure axial fans and that the dominant contribution of Loudness in psychoacoustic annoyance calculation is biasing the comparison of similar overall sound pressure level sounds. Regarding Cerkovnik, which is dedicated to computer fans, similar poor applicability to automotive fans is highlighted. Through a new multi-linear regression with better correlation, when the metric focusing on High Frequencies is replaced by Loudness, the modified equation linking Loudness, Sharpness, Tonality and Roughness is then well correlated to jury tests.