Christian Kaps

Globally, 1.5 billion people live off the grid, their only access to electricity often limited to operationally-expensive fossil fuel generators. Solar power has risen as a sustainable and less expensive option, but its generation is variable during the day and non-existent at night. Thanks to recent technological advances, which have made large-scale electricity storage economically viable, a combination of solar generation and storage holds the promise of cheaper, greener, and more reliable off-grid power in the future. Still, it is not yet well-understood how to jointly determine optimal capacity levels for renewable generation and storage. Our work aims to shed light on this question by developing a model of strategic capacity investment in both renewable generation and storage to match demand with supply in off-grid use-cases, while relying on fossil fuel as backup. Since the exact model is intractable, we develop two newsvendor-like approximations that are analytically tractable, yield precise values for the optimal investment decisions and profit in some cases, and provide bounds to the optimal investment decisions and profits in all other cases. We use these approximations to obtain additional insights into the problem. First, we find that solar generation and storage capacity levels are strategic complements, except in cases with very high penetration of either technology, when they surprisingly turn into strategic substitutes, with implications for long-term investment decisions. Second, we develop a simple heuristic to determine which technology, within a given portfolio, can turn a profit in the broadest set of market conditions, and thus is likely to be adopted first. We find that currently, low-efficiency, cheap technologies such as thermal can more easily turn a profit in off-grid applications than high-efficiency, expensive ones such as lithium-ion batteries. To conclude, we calibrate our models to measure the accuracy of our solutions utilizing real-life data from three geographically-diverse islands, and then use our approximations to provide high-level insights on the role that large-scale storage will play in the years ahead as technology improves, carbon taxes are levied, and solar becomes cheaper.

In this paper method and practice of cross-efficiency calculation is discussed. The main methods proposed in the literature are tested not on a set of artificial data but on a realistic sample of input-output data of European warehouses. The empirical results show the limited role which increasing automation investment and larger warehouse size have in increasing productive performance. The reason is the existence of decreasing returns to scale in the industry, resulting in sub-optimal scales and inefficiencies, regardless of the operational performance of the facilities. From the methodological perspective, and based on a multidimensional metric which considers the capability of the various methods to rank warehouses, their ease of implementation, and their robustness to sensitivity analyses, we conclude to the superiority of the classic Sexton et al. (1986) method over recently proposed, more sophisticated methods.