Home energy management under correlated uncertainties: A statistical analysis through Copula

Home energy management is a decision-making problem under uncertainty in internal parameters (e.g., loads), as well as in external parameters (e.g., outdoor temperatures, and energy prices). More specifically, the correlation among the uncertain parameters may affect the home energy management decisions and the resulting costs. To this end, this paper provides a statistical simulation framework, which allows to examine the potential impact of all significant correlations among the uncertain parameters involved in the home energy management problem, for the first time. A Copula-based scenario generation technique is used to generate the correlated scenarios of uncertain parameters. To generate more accurate scenarios, the probability of presence or absence of each uncertain load in each day is also considered. The correlation among the uncertain parameters is captured through the empirical statistical analysis of real-world data of a home located in Austin, Texas. Results through different cases show that ignoring the correlation among the uncertain parameters has significant effects on the outcomes of home energy management. More importantly, ignoring the correlation results in the estimation error of 21.7, 46.9 and 92% in the daily power consumption of interruptible, uninterruptible and thermostatically controlled loads, respectively.