Intertemporal trading economy model for smart grid household energy consumption

In his paper, we propose to model the energy consumption of smart grid households with energy storage systems (ESS) as an intertemporal trading economy. Intertemporal trade refers to transaction of goods across time when an agent, a any time, is faced with the option of consuming and/or saving with the aim of using the savings in the future and/or spending the savings from the past. Smart homes define optimal consumption as balancing/leveling their consumption profile such that the utility company is presented with a more uniform demand. 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 sorting energy for future consumption and/or spending energy stored in the past. These trade-offs or consumption preferences of the household are modeled as a Cobb-Douglas utility function using consumer theory. This utility function is maximized subject to budge and storage constrains to solve for the optimal consumption profile. We graphically illustrate the process of computing the optimal consumption point when a day is divided into two or three time periods. For higher dimensional multi-period models, we formulae the optimization problem as a geometric program (GP). Simulation results show that the proposed approach is able to achieve a uniform consumption profile with extremely low peak to average ratio (PAR) close to 1 in addition to reducing consumption costs for the household by about 6%.