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A distributed convex optimization framework for energy trading of interconnected microgrids is investigated to improve the economy and reliability of system operation. In this work, a distributed energy trading approach for interconnected operation of islanded microgrids is studied. Specifically, the system includes several islanded microgrids that can trade energy in a given topology. A distributed iterative deep cut ellipsoid (DCE) algorithm is implemented with limited information exchange. This approach will address the scalability issue and also secure local information on cost functions. During the iterative process, the information exchange among interconnected microgrids is restricted to electricity prices and expected trading energy. Numerical results are presented in terms of the convergent rate of the algorithm for different topologies, and the performance of the DCE algorithm is compared with sub-gradient algorithm.