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For the efficient operation of the smart grid, it is important that there is an instant by instant matching between the electricity supply and the power consumption. Electrical power storage provides a viable solution to managing power supply and electrical loads as well as unexpected imbalances. Electricity suppliers could deploy electricity storage facilities at various levels of the smart grid system: generation, transmission, substations and residential level. Storage would significantly address the power quality and reliability problems through peak shaving and frequency control. It also reduces the need for huge infrastructural expenditures by making them more efficient. At the residential level, smart storage together with dynamic pricing in the deregulated electricity markets presents the electricity suppliers with a strategy to achieve grid stability. In this paper, we consider a smart grid environment with a high penetration of households' storage batteries. By using an appropriate electricity price structure, the electricity supplier influences households' electricity consumption. On the other hand, the households aim to minimize their electricity bills by capitalizing on price fluctuation to schedule their electrical appliances and coordinate the charging and discharging of their batteries. The electricity supplier has a dynamic power limit for each hour that must not be exceeded by the hourly aggregate load of the households. Further, we assume that in supplying electrical power, the households' electrical devices are given priority over their storage devices. The policy is such that batteries will be charged by the residual power after the appliances loads have been satisfied. The households have to compete for the residual electricity so as to maximize the state of charge of their batteries. We have therefore modeled this system as a non-cooperative Nash equilibrium game where the households are considered as selfish but rational players whose obj- ctives are to optimize their individual utilities.