  We present modeling and analysis of day-ahead spatio-temporal energy markets
in which each competitive aggregator aims at making the highest profit by
managing a complex mixture of different energy resources, such as conventional
generators, storage batteries, and uncertain renewable resources. First, we
develop an energy market model in terms of an adjustable robust convex program.
This market modeling is novel in the sense that the prosumption cost function
of each aggregator, which evaluates the cost to realize an amount of
spatio-temporal energy prosumption, is a multi-variable function resulting from
a "parameterized" max-min program, in which the variable of the prosumption
cost function is involved as a continuous parameter and the variable of
dispatchable resources is involved as an adjustable variable for energy
balance. This formulation enables to reasonably evaluate a reward for
intertemporal dispatchability enhancement and a penalty for renewable energy
uncertainty in a unified way. In addition, it enables to enforce a market
regulation in which every aggregator is responsible for absorbing his renewable
energy uncertainty by managing his own dispatchable energy resources. Second,
in view of social economy as well as personal economy, we conduct a numerical
analysis on the premise of several photovoltaic penetration levels. In this
numerical analysis, we demonstrate that renewable generators do not always have
priority of energy supply higher than conventional generators due to their
uncertainty and limited dispatchability, meaning that the merit order of
conventional and renewable generators can reverse. Furthermore, we analyze
long-term evolution of competitive energy markets demonstrating that there can
be found a social equilibrium of battery penetration levels, at which maximum
personal profit with respect to battery system enhancement is attained.
