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.