This paper studies the congestion control and energy flow allocation of renewable energy producers equipped with local energy storage devices and energy converters. The producers are embedded in the existing energy grids. Based on the producers' own measurements and some coordination with the grid operators, the energy producers adjust locally their supply levels injected to the energy grids so as to maximize their profit without exceeding the grid capacities. We incorporate an asynchronous implementation in the distributed supply coordination and prove its convergence. We implement the proposed algorithm for Power-to-Gas facilities embedded in the energy grids, which consist of a gas grid, mobility sector, and power grid, to demonstrate that the distributed asynchronous supply coordination achieves the same optimal performances as those of the synchronized distributed supply coordination.