Rooftop and Community Solar Adoption with Income Heterogeneity

Abstract

Each household in a population characterized by income heterogeneity faces random demand for electricity and decides if and when it should adopt a solar product, rooftop solar or community solar. A central planner, aiming to meet an adoption level target within a set time, offers net metering and subsidy on solar products and minimizes its total cost. Our focus is on analyzing the interactions of three new features we add to the literature: income diversity, availability of community solar, and consideration of adoption timing. {Methodology and results:} We develop a bilevel optimization formulation to derive the optimal subsidy policy. The upper level (planner's) problem is a constrained non-linear optimization model in which the planner aims to minimize the average subsidy cost. The lower level (household's) problem is an optimal stopping formulation, which captures the adoption decisions of the households. We derive a closed-form expression for the distribution of optimal adoption time of households for a given subsidy policy. We show that the planner's problem is convex in the case of homogeneous subsidy for the two products. {Managerial implications:} Our results underscore the importance for planners to consider three factors - adoption level target, time target, and subsidy budget - simultaneously as they work in tandem to influence the adoption outcome. The planners must also consider the inclusion of community solar in their plans because, as we show, community and rooftop solar attract households from different sides of the income spectrum. In the presence of income inequality, the availability of community makes it easier to meet solar adoption targets.