This study evaluates available analytical wake models for flow prediction inside and downstream of wind farms of different sizes and layouts using large-eddy simulation (LES), and introduces an enhanced analytical framework. All the tested analytical wake models, based on the superposition of individual turbine wakes, systematically overestimate the wake recovery both inside and downstream of the wind farms. The results indicate that the overestimation is linked to the assumption of linear or quasilinear wake expansion, which does not hold at large downstream distances. To address this issue, an enhanced analytical framework is proposed based on the extension of a recently developed streamwise scaling model for single wakes that eliminates the need for the linear wake expansion assumption. Since the new framework computes the wake expansion based on the near-wake length and the local turbulence intensity, different methods for their calculation and the superposition of turbulence intensity within wind farms are evaluated against the LES data. The identified best methods are incorporated into the new analytical framework. The proposed framework consistently yields more accurate power estimates and flow predictions inside and downstream of finite-size wind farms with different sizes and configurations.