  In this paper, we propose a two-stage electricity market framework to explore
the participation of distributed energy resources (DERs) in a day-ahead (DA)
market and a real-time (RT) market. The objective is to determine the optimal
bidding strategies of the aggregated DERs in the DA market and generate online
incentive signals for DER-owners to optimize the social welfare taking into
account network operational constraints. Distributionally robust optimization
is used to explicitly incorporate data-based statistical information of
renewable forecasts into the supply/demand decisions in the DA market. We
evaluate the conservativeness of bidding strategies distinguished by different
risk aversion settings. In the RT market, a bi-level time-varying optimization
problem is proposed to design the online incentive signals to tradeoff the RT
imbalance penalty for distribution system operators (DSOs) and the costs of
individual DER-owners. This enables tracking their optimal dispatch to provide
fast balancing services, in the presence of time-varying network states while
satisfying the voltage regulation requirement. Simulation results on both DA
wholesale market and RT balancing market demonstrate the necessity of this
two-stage design, and its robustness to uncertainties, the performance of
convergence, the tracking ability, and the feasibility of the resulting network
operations.
