In this paper, we propose to model the energy consumption of smart grid households with energy storage systems as an intertemporal trading economy. Intertemporal trade refers to transaction of goods across time when an agent, at any time, is faced with the option of consuming or saving with the aim of using the savings in the future or spending the savings from the past. Smart homes define optimal consumption as either balancing/leveling consumption such that the utility company is presented with a uniform demand or as minimizing consumption costs by storing energy during off-peak time periods when prices are lower and use the stored energy during peak time periods when prices are higher. Due to the varying nature of energy requirements of household and market energy prices over different time periods in a day, households face a trade-off between consuming to meet their current energy requirements and/or storing energy for future consumption and/or spending energy stored in the past. These trade-offs or consumption preferences of the household are modeled as utility functions using consumer theory. We introduce two different utility functions, one for cost minimization and another for consumption balancing/leveling, that are maximized subject to respective budget, consumption, storage and savings constraints to solve for the optimum consumption profile. The optimization problem of a household with energy storage is formulated as a geometric program for consumption balancing/leveling, while cost minimization is formulated as a linear programming problem. Simulation results show that the proposed model achieves extremely low peak to average ratio in the consumption balancing/leveling scheme with about 8% reduction in consumption costs and the least possible amount for electricity bill with about 12% reduction in consumption costs in the cost minimization scheme.
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