As the communication needs in the smart distribution grid continue to rise, using existing resources to meet this growing demand poses a significant challenge. This paper researches on spectrum allocation strategies utilizing cognitive radio (CR) technology. We consider a model containing strong time-sensitive and regular communication service requirements such as distribution terminal communication services, which can be seen as a user with primary data (PD) and weak time-sensitive services such as power quality monitoring, which can be seen as a user with secondary data (SD). To fit the diversity of services in smart distribution grids (SDGs), we formulate an optimization problem with two indicators, including the sum of SD transmission rates and the maximum latency of them. Then, we analyze the two convex sub-problems and utilize convex optimization methods to obtain the optimal power and frequency bandwidth allocation for the users with SD. The simulation results indicate that, when the available transmission power of SD is low, Maximization of Transmission Sum Rate (MTSR) achieves lower maximum transmit time. Conversely, when the available transmission power is high, the performance of Minimization of the Maximum Latency (MML) is better, compared with MTSR.