Joint decisions of renewable energy investment and daily energy procurement in smart microgrids

This paper explores the joint decision-making problem of renewable energy investment and daily electricity procurement within smart microgrids. By considering time-of-use pricing, demand shifting, and the intermittent nature of renewable energy, we develop a two-stage optimization model: the first stage uses a quadratic investment cost function to determine renewable energy capacity, while the second stage adopts a stochastic decision-making approach based on two-point probability distributions to manage traditional energy procurement under uncertain renewable output. Our findings indicate that higher nighttime electricity prices encourage greater reliance on renewable energy, although this does not necessarily lead to increased investment in renewable capacity. Additionally, through comparative statics analysis, we reason that advancements in home automation will reduce the psychological cost of demand shifting, yet renewable energy investment does not straightforwardly increase due to associated uncertainties. To empirically support our analysis, we simulate one year of demand and wind generation data from PJM RTO, revealing that even a small-scale wind turbine requires more than five years to recover its investment costs. To further reason about policy implications, we extend our model by introducing two policy measures, renewable energy buyback and carbon emission penalties, and demonstrate analytically and numerically that a buyback policy boosts investment but may paradoxically increase reliance on traditional sources, while carbon emission penalties effectively reduce traditional energy use without necessarily increasing renewable energy investment.