  The proliferation of small-scale renewable generators and price-responsive
loads makes it a challenge for distribution network operators (DNOs) to
schedule the controllable loads of the load aggregators and the generation of
the generators in real-time. Additionally, the high computational burden and
violation of the entities' (i.e., load aggregators' and generators') privacy
make a centralized framework impractical. In this paper, we propose a
decentralized energy trading algorithm that can be executed by the entities in
a real-time fashion. To address the privacy issues, the DNO provides the
entities with proper control signals using the Lagrange relaxation technique to
motivate them towards an operating point with maximum profit for entities. To
deal with uncertainty issues, we propose a probabilistic load model and robust
framework for renewable generation. The performance of the proposed algorithm
is evaluated on an IEEE 123-node test feeder. When compared with a benchmark of
not performing load management for the aggregators, the proposed algorithm
benefits both the load aggregators and generators by increasing their profit by
17.8%and 10.3%, respectively. When compared with a centralized approach, our
algorithm converges to the solution of the DNO's centralized problem with a
significantly lower running time in 50 iterations per time slot.
