  A classical problem in power systems is to allocate in-coming (elastic or
inelastic) demands without violating the operating constraints of electric
networks in an online fashion. Although online decision problems have been
well-studied in the literature, a unique challenge arising in power systems is
the presence of non-linear constraints, a departure from the traditional
settings. A particular example is the capacity constraint of apparent power,
which gives rise to a quadratic constraint, rather than typical linear
constraints. In this paper, we present a competitive randomized online
algorithm for deciding whether a sequence of inelastic demands can be allocated
for the requested intervals, subject to the total satisfiable apparent power
within a time-varying capacity constraint. We also consider an alternative
setting with nodal voltage constraint, using a variant of the online algorithm.
Finally, simulation studies are provided to evaluate the algorithms
empirically.
