Transient frequency deviation resulting from load pick-up operations is a barrier to DG-based service restoration. The prime mover dynamics and control-parameter configuration have a significant effect on the frequency response rate (FRR) in the restoration process, but have not been sufficiently considered in previous works. To address this issue, this letter analyzes the FRR based on the transfer function of the speed-regulator of a single master diesel generation unit, and simplifies the model through variable substitution and order reduction. A succinct FRR constraint is derived according to the characteristics of the standard Type 2 system. The simulation of the restoration process verifies the accuracy of the derivation.