Cell-free Massive multiple-input multiple-output (CF-mMIMO) is one of the most promising technologies. It is crucial to examine the performance of CF-mMIMO systems in real-world scenarios, particularly the hardware impairments caused by nonlinear power amplifiers (PAs). This paper’s main objective is to thoroughly examine CF-mMIMO under PA non-linearity at user equipment (UE), focusing on power allocation performance. We provide closed-form expressions for uplink achievable data rates while accounting for the nonlinear behavior of the PA. We extensively examine power control strategies. Initially, we explore full power transmission and Channel Inversion. Then, we address the non-convex problem of maximizing both the sum rate (MSR) and the minimum rate (MMR) of users using the single condensation method (SCM) and successive convex approximation (SCA) algorithm. We propose iterative algorithms to optimize the ultimate geometric programming (GP) problem and find the optimal power control coefficients. Results confirm that the proposed nonlinearity-aware power control yields substantial enhancements in net throughput compared to conventional algorithms. This underscores the superiority of integrating the nonlinearity of PAs into the power allocation strategy. The proposed MSR algorithm not only enhances the sum throughput but also increases the minimum net throughput and Jain’s fairness index of net throughput.