Smart home economic operation under uncertainty: comparing monte carlo and stochastic optimization using gaussian and KDE-based data

This paper investigates optimal day-ahead operation of a building-scale energy hub equipped with photovoltaics and a battery. Electricity demand and PV availability are uncertain and are represented in two ways: (i) thin-tailed normal distributions and (ii) kernel density estimation (KDE) fitted to empirical CityLearn data. For each representation we evaluate (a) deterministic Monte Carlo analysis, where the hub is optimised separately for 1 000 daily scenarios, and (b) a two-stage stochastic optimisation that fixes one set of decisions for hours 0–11 and adapts for hours 12–23 after conditions are observed. Gaussian inputs yield clustered costs (mean= $51.6, σ= $0.2) and a 99 % CVaR below $52, suggesting negligible risk. KDE inputs raise the Monte Carlo mean to $80.6 and lift the 99 % CVaR to $114, exposing heavy-tailed risk. Within the stochastic model the identical first-stage policy costs $79.0 with Gaussian data but only $71.3 with KDE, as recourse exploits sunny scenarios and trims the 95 % CVaR from $106.4 to $93.5. Consequently, Gaussian assumptions obscure true operating costs and financial exposure, whereas incorporating empirically derived KDE uncertainty within stochastic optimisation both lowers the average cost and provides stronger protection against extreme cost outcomes.