  With the sustained deployment of distributed generation capacities and the
more proactive role of consumers, power systems and their operation are
drifting away from a conventional top-down hierarchical structure. Electricity
market structures, however, have not yet embraced that evolution. Respecting
the high-dimensional, distributed and dynamic nature of modern power systems
would translate to designing peer-to-peer markets or, at least, to using such
an underlying decentralized structure to enable a bottom-up approach to future
electricity markets. A peer-to-peer market structure based on a Multi-Bilateral
Economic Dispatch (MBED) formulation is introduced, allowing for
multi-bilateral trading with product differentiation, for instance based on
consumer preferences. A Relaxed Consensus+Innovation (RCI) approach is
described to solve the MBED in fully decentralized manner. A set of realistic
case studies and their analysis allow us showing that such peer-to-peer market
structures can effectively yield market outcomes that are different from
centralized market structures and optimal in terms of respecting consumers
preferences while maximizing social welfare. Additionally, the RCI solving
approach allows for a fully decentralized market clearing which converges with
a negligible optimality gap, with a limited amount of information being shared.
