In this work, a dissipativity based distributed economic model predictive control (DEMPC) approach is developed for the operation of battery energy storage (BES) networks in residential microgrids. With the presence of a microgrid power market (MPM), control of the BES systems is formulated as a self-interested distributed control problem, as individual DEMPC controllers minimize their local economic cost functions based on the price prediction of MPM. Due to the intermittent nature of photovoltaic (PV) power generations and load demands, the DEMPC without proper coordination or constraints may lead to excessive energy trading and price oscillations in MPM. To solve this problem, dissipativity theory with dynamic supply rates is adopted in this paper to deal with the interactions between individual users and the MPM. The microgrid-wide performance requirement of attenuation of the net power fluctuations with respect to time-varying PV generation and demands, is converted into the dissipative trajectory constraints imposed on individual DEMPC controllers. The proposed approach is scalable as it does not require online iterative optimizations across the controller network. A case study is presented to illustrate the proposed method.