We study how to embed systems that transform gas to power, or power to gas in the different energy grids, such as the gas, power, industry and heat grid in a distributed and optimal manner. The optimal control problem can be studied via dual decomposition, and made distributed for the exchange of energy between the agents. At the level of the grids, capacity issues play a role. Consequently, another level of optimization which is not fully distributed is added to the problem setting, intuitively playing the role of grid operator. In other words, agents make decisions based on local information, yet still coordinate their supply bids to the grid operators in order to avoid overloading the grids with the help of shadow prices. In addition, we study the optimality of the problem when the information exchange is done asynchronously.