Optimal exploitation of energy resources: Solar power and electricity generation in below sea level basins (Q1072446)

This paper analyzes the generation of hydroelectric power by the transfer of seawater to locations which are significantly below sea level (e.g., the Dead Sea in Israel and the Qatara depression in Egypt) combined with solar energy that via evaporation will perpetuate the hydroelectric power capacity. Two scenarios are depicted. The first focuses on optimal planning of the canal capacity and optimal use of its water to generate hydroelectric power while filling the basin to its steady-state level. The second includes the impact of solar pools as a new technology whose date of adoption is a random event. It is shown that the optimal flow of water through the canal depends on the relationship between optimal canal capacity and the rate of water evaporation in the basin. The optimal design of the canal project can be considered a hybrid between depletion of a natural resource (the height differences in filling up the basin) and use of a renewable resource (solar energy to evaporate the basin water). The optimal policy is shown to consist of sequential intervals, some of which may vanish under certain conditions: first, the operation of the canal at full capacity; then the gradual decrease of water flow at a rate equal to the elasticity of the marginal product of electricity generation times the sum of interest rate and the marginal evaporation rate; and, finally, the stabilization of the water flow at the rate of steady-state evaporation. The stochastic model with the introduction of solar pools technology treated as a random event is formulated as a two- stage maximization problem. It is shown that, in contrast to the scenario without solar pools, the canal may be operated underutilizing its capacity in the initial period. But even in this case, the quantity of water flowing through the canal is a nonincreasing monotonic function over time with a jump in the quantity of flow at the date the solar pools are introduced.