In the coming years, the satellite broadband market will experience significant increases in the service demand, especially for the mobility sector, where demand is burstier. Many of the next generation of satellites will be equipped with numerous degrees of freedom in power and bandwidth allocation capabilities, making manual resource allocation impractical and inefficient. Therefore, it is desirable to automate the operation of these highly flexible satellites. This paper presents a novel power allocation approach based on Deep Reinforcement Learning (DRL) that represents the problem as continuous state and action spaces. We make use of the Proximal Policy Optimization (PPO) algorithm to optimize the allocation policy for minimum Unmet System Demand (USD) and power consumption. The performance of the algorithm is analyzed through simulations of a multibeam satellite system, which show promising results for DRL to be used as a dynamic resource allocation algorithm.