Installation of renewable capacities to meet energy demand and emission constraints under uncertainty

What the paper says

This paper focuses on minimizing the costs of installing renewable energy capacity while meeting emission constraints under uncertainty in both energy demand and renewable production. We consider a setting where decision-makers must determine when and how much renewable capacity to install, balancing investment costs with future emissions. Our optimization problem combines cost minimization with a probabilistic constraint on total accumulated emissions, reflecting regulatory limits that may be exceeded only with small probability. We examine different investment strategies, allowing for one or multiple installation times, and provide explicit solutions in simplified cases. Our main insight is that, under reasonable assumptions on costs and uncertainty, a single, well-timed investment is optimal and may be delayed to reduce costs when uncertainty and discounting are accounted for. These results challenge common stepwise installation strategies and suggest that committing to a single large investment, possibly postponed, may be more cost-effective and efficient in reaching emission targets. Our findings offer practical guidance for policymakers and energy planners on how to balance costs, timing and environmental goals when expanding renewable energy capacity under uncertainty.