Widespread renewable energy resources cause shortterm supply-demand imbalance. It is desirable to use Demand Response (DR) for solving balancing problem. Controlling consumers' energy storages (ES) is promising in this regard. However, consumer's ES based DR for short-term supplydemand imbalance suffers from reliability problems caused by both, unexpected state of charge (SoC) saturation/depletion due to state variation of distributed ESs and the low quality of the Internet, i.e. communication delay and interruption. In this paper, we propose "Hierarchical Hybrid Control (HHC)" as a novel DR scheme, which guarantees accurate and fast response of consumer's ES based DR continuously for frequency regulation regardless of weak communication links and ESs' state variations. We demonstrate robustness against SoC saturation/depletion of ESs as well as tolerance for communication delay/interruption by simulation.Index Terms--batteries, battery management systems, demand response, energy management, supply and demand