出版社：Institute for Operations Research and the Management Sciences (INFORMS), Applied Probability Society
摘要：We study the stability of a Markovian model of electricity pro-duction and consumption that incorporates production volatility dueto renewables and uncertainty about actual demand versus plannedproduction. We assume that the energy producer targets a fixed en-ergy reserve, subject to ramp-up and ramp-down constraints, andthat appliances are subject to demand-response signals and adjusttheir consumption to the available production by delaying their de-mand. When a constant fraction of the delayed demand vanishes overtime, we show that the general state Markov chain characterizing thesystem is positive Harris and ergodic (i.e., delayed demand is boundedwith high probability). However, when delayed demand increases bya constant fraction over time, we show that the Markov chain is non-positive (i.e., there exists a non-zero probability that delayed demandbecomes unbounded). We exhibit Lyapunov functions to prove ourclaims. In addition, we provide examples of heating appliances that,when delayed, have energy requirements corresponding to the twoconsidered cases
