We develop a dynamic optimization model to study the link between photovoltaic (PV) investments, energy production, and environmental impact. The model is formulated as a continuous-time optimal control problem with one control variable (investment) and two state variables (energy output and emissions). Applying Pontryagin’s maximum principle, we derive a closed-form solution for the optimal investment path. Key inputs include PV productivity, costs, depreciation, and emission savings versus fossil fuels. The results show that the optimal investment increases with the efficiency of PV, the ecological benefits and the weight given to sustainability, identifying conditions in which PV increases both energy output and emission reduction. We also find that better storage technologies improve the long-term viability of renewables and may be more politically feasible than carbon taxation. Simulations test the sensitivity of the net zero year to cost changes, regional differences, and shocks from environmental policies in China and the US, offering policy-relevant insights to align renewable energy investments with environmental and economic goals.
The sustainable future is now: A dynamic model to advance investments in PV and energy storage
Nazaria Solferino
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2026-01-01
Abstract
We develop a dynamic optimization model to study the link between photovoltaic (PV) investments, energy production, and environmental impact. The model is formulated as a continuous-time optimal control problem with one control variable (investment) and two state variables (energy output and emissions). Applying Pontryagin’s maximum principle, we derive a closed-form solution for the optimal investment path. Key inputs include PV productivity, costs, depreciation, and emission savings versus fossil fuels. The results show that the optimal investment increases with the efficiency of PV, the ecological benefits and the weight given to sustainability, identifying conditions in which PV increases both energy output and emission reduction. We also find that better storage technologies improve the long-term viability of renewables and may be more politically feasible than carbon taxation. Simulations test the sensitivity of the net zero year to cost changes, regional differences, and shocks from environmental policies in China and the US, offering policy-relevant insights to align renewable energy investments with environmental and economic goals.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
