Optimal Dynamic Management of a Renewable Energy Source under Uncertainty

Catherine Bobtcheff


We consider a risk averse social planner who has access to different energy sources to produce electricity; hydroelectricity is produced with a dam and thermal electricity is obtained from an unlimited supply at some exogenous cost. The dam is supplied with a random water flow. The presence of constraints on a minimal and maximal storage capacity makes electricity consumption smoothing possible only when the quantity of water available to the agent lies in a certain range that is determined. Consumption smoothing is possible even when the dam is almost empty thanks to the alternative costly energy source. Moreover, a comparative statics analysis reveals that the marginal propensity to produce hydroelectricity is an increasing function of the cost of the second technology. Therefore, the availability of the fossil source at a low cost improves time diversification. Finally, the optimal electric park is composed of a number of dams that increases with the cost of the alternative technology.


Intertemporal Expected Utility Maximization; Hydroelectricity; Thermal Power; Investment Under Uncertainty; Prudence;

JEL codes

  • C61: Optimization Techniques • Programming Models • Dynamic Analysis
  • Q25: Water
  • Q42: Alternative Energy Sources

See also

Published in

Annales d'Économie et de Statistique, Paris: Institut national de la statistique et des études économiques, vol. 103-104, December 2011, pp. 143–174