Optimal Energy Consumption Model for Smart Grid Households With Energy Storage

In this paper, we propose to model energy consumption of smart grid households with energy storage systems as an inter-temporal trading economy. Smart homes define optimal consumption as either balancing/leveling consumption using energy storage devices 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. In cost minimization scheme, household is the sole beneficiary and its consumption profile is highly nonuniform and there is no incentive for the utility company to support this scheme. On the other hand, in consumption leveling/balancing scheme there is an incentive for both the household and utility company to support this scheme due to reduction in consumption costs for the former and uniform demand for the latter. Due to varying nature of energy requirements of households and market energy prices over different time periods in a day, households face a tradeoff between consuming to meet their current energy requirements and/or storing energy for future consumption and/or spending energy stored in the past. These tradeoffs are modeled using inter-temporal trade and consumption preferences of households 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 certain 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 close to 1 with about 8% reduction in consumption costs in consumption balancing/leveling scheme and the least possible amount for the electricity bill with about 12% reduction in consumption costs in cost minimization scheme.