  We propose a new forward electricity market framework that admits
heterogeneous market participants with second-order cone strategy sets, who
accurately express the nonlinearities in their costs and constraints through
conic bids, and a network operator facing conic operational constraints. In
contrast to the prevalent linear-programming-based electricity markets, we
highlight how the inclusion of second-order cone constraints enables
uncertainty-, asset- and network-awareness of the market, which is key to the
successful transition towards an electricity system based on weather-dependent
renewable energy sources. We analyze our general market-clearing proposal using
conic duality theory to derive efficient spatially-differentiated prices for
the multiple commodities, comprising of energy and flexibility services. Under
the assumption of perfect competition, we prove the equivalence of the
centrally-solved market-clearing optimization problem to a competitive spatial
price equilibrium involving a set of rational and self-interested participants
and a price setter. Finally, under common assumptions, we prove that moving
towards conic markets does not incur the loss of desirable economic properties
of markets, namely market efficiency, cost recovery and revenue adequacy. Our
numerical studies focus on the specific use case of uncertainty-aware market
design and demonstrate that the proposed conic market brings advantages over
existing alternatives within the linear programming market framework.
