Satisfiability of Elastic Demand in the Smart Grid

We study a stochastic model of electricity production and consumption where appliances are adaptive and adjust their consumption to the available production, by delaying their demand and possibly using batteries. The model incorporates production volatility due to renewables, ramp-up and rampdown time, uncertainty about actual demand versus planned production, delayed and evaporated demand due to adaptation to insufficient supply. We study whether threshold policies stabilize the system. The proofs use Markov chain theory on general state space. Keywords-Dynamical Systems, Smart Grids, Elastic Demand, Macroscopic Model, Stability