Abstract

The sizing of rooftop solar energy systems is commonly based on the most visible load or on generic end-use allocations, leading to an inadequate distribution of the limited rooftop area between heat and electricity. This study formalizes the energy audit within a three-level deterministic framework that selects and sizes solar technologies by energy vector: demand is first decomposed by vector; the technology for the thermal vector is then selected through a levelized cost of heat selection ratio ψ, while the photovoltaic system of the electrical vector is sized for self-consumption; and the rooftop area is finally allocated among vectors according to marginal value per unit area. In a 75-bed university residence in Cienfuegos, Cuba, air conditioning is the dominant energy end-use in terms of installed power (accounting for 77% of the connected load), whereas the thermal vector dominates annual energy consumption (domestic hot water: 127,440 versus 76,818 kWh/year for electricity; thermal-to-electric ratio 1.66). Solar thermal technology has been selected for the thermal vector (0.018 versus 0.088 USD/kWhth; ψ=0.21, a robust value according to the sensitivity analysis), and the marginal value (≈111 versus ≈32 USD/(m2·year)) allocates 104 m2 to solar thermal collectors and 134 m2 to photovoltaic energy, thereby reversing the original design that prioritized photovoltaic energy. The resulting portfolio achieves an annual solar fraction close to 100% in both vectors on an energy balance basis, avoids 86.5 t of operational CO2 emissions per year, and combines a simple payback of 1.1 years (solar thermal) with a net present value of 55,327 USD and an internal rate of return of 28% (photovoltaics). The sizing decision is shown to be robust to the choice of statistical design criterion (median, mean, P90, maximum), and none of the three framework decisions is reversed under ±30% parameter variations. By replacing the subjective weightings of multi-criteria methods with observable economic criteria, the framework provides a replicable and auditable design protocol.

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