As independent service providers increasingly inject power (from renewable sources like wind) into the power distribution system, the power distribution system will likely experience increasingly significant fluctuations in power supply. Fluctuations in power generation, coupled with time-varying consumption of electricity on the demand side and the massive scale of power distribution networks present the need to not only design decentralized power allocation policies, but also understand how robust they are to dynamic demand and supply. In this paper, via an Online Decentralized Dual Descent (OD3) Algorithm, with communication for decentralized coordination, we design power allocation policies in a power distribution system. Based on the OD3 algorithm, we determine and characterize (in the worst case) how much of observed social welfare andprice volatility can be explained by fluctuations in consumption utilities of users and capacities of suppliers. In coordinating the power allocation, the OD3 algoritihm uses a protocol in which the users’ consumption at each time-step depends on the coordinating (price) signal, which is iteratively updated based on aggregate power consumption. Convergence properties and performance guarantees of the OD3 algorithm is analyzed by characterizing the difference between the online decision and the optimal decision. As more renewable energy sources are integrated into the power grid, the results in this paper providea framework to understand how volatility in the power systems propagate to markets. The theoretical results in the paper are validated and illustrated by numerical experiments.