  Traditionally, most consumers of electricity pay for their consumptions
according to a fixed rate. With the advancement of Smart Grid technologies,
large-scale implementation of variable-rate metering becomes more practical. As
a result, consumers will be able to control their electricity consumption in an
automated fashion, where one possible scheme is to have each individual
maximize its own utility as a noncooperative game. In this paper,
noncooperative games are formulated among the electricity consumers in Smart
Grid with two real-time pricing schemes, where the Nash equilibrium operation
points are investigated for their uniqueness and load balancing properties. The
first pricing scheme charges a price according to the average cost of
electricity borne by the retailer and the second one charges according to a
time-variant increasing-block price, where for each scheme, a zero-revenue
model and a constant-rate revenue model are considered. In addition, the
relationship between the studied games and certain competitive routing games
from the computer networking community, known as atomic flow games, is
established, for which it is shown that the proposed noncooperative game
formulation falls under the class of atomic splittable flow games. The Nash
equilibrium is shown to exist for four different combined cases corresponding
to the two pricing schemes and the two revenue models, and is unique for three
of the cases under certain conditions. It is further shown that both pricing
schemes lead to similar electricity loading patterns when consumers are only
interested in minimizing the electricity costs without any other profit
considerations. Finally, the conditions under which the increasing-block
pricing scheme is preferred over the average-cost based pricing scheme are
discussed.
