This paper proposes a novel singularity-free prescribed-time distributed resource allocation algorithm. By scaling fixed-time systems using the time space deformation method, the proposed algorithm avoids the singularity problem caused by time-varying high-gain functions. To make the algorithm applicable to second-order multi-agent systems, a singularity-free prescribed-time signal tracking controller is also proposed. Finally, the performance of the proposed algorithm is verified through a power allocation task based on actual wind farm data.