Large Artificial Intelligence (AI) training workloads spanning several tens of thousands of GPUs present unique power management challenges. These arise due to the high variability in power consumption during the training. Given the synchronous nature of these jobs, during every iteration there is a computation-heavy phase, where each GPU works on the local data, and a communication-heavy phase where all the GPUs synchronize on the data. Because compute-heavy phases require much more power than communication phases, large power swings occur. The amplitude of these power swings is ever increasing with the increase in the size of training jobs. An even bigger challenge arises from the frequency spectrum of these power swings which, if harmonized with critical frequencies of utilities, can cause physical damage to the power grid infrastructure. Therefore, to continue scaling AI training workloads safely, we need to stabilize the power of such workloads. This paper introduces the challenge with production data and explores innovative solutions across the stack: software, GPU hardware, and datacenter infrastructure. We present the pros and cons of each of these approaches and finally present a multi-pronged approach to solving the challenge. The proposed solutions are rigorously tested using a combination of real hardware and Microsoft's in-house cloud power simulator, providing critical insights into the efficacy of these interventions under real-world conditions.