Distributed placement of power generation resources in uncertain environments.

To tackle the problem of long-term disasters of river basin by big dams and at the same time to meet the energy demands we propose a novel distributed allocation of power generation units along the river. The presented approach is applicable where a distribution of resources is required subject to challenges posed by uncertainty in the behavior of the environment. The problem of uncertainty is split into two parts. The short-term variations are taken care of using a distance based partitioning approach to determine the power unit co-ordinates and corresponding partitions of the geographic area based on the power demand. The key idea is to minimize the distance between probability distribution of the generated power and the total demand supposed to be catered in a local geographic partition. The long-term uncertainty is handled by assigning sleep/wake periods to the placed run-of-the-river (ROR)s. Numerical simulations on the water flow data of the Mississippi river is performed and it is shown that the proposed formulation is applicable for determining the initial unit placements and also in deciding the sleep/wake periods of the placed units. A comprehensive study of ROR placements upon varying the demand density, locality preference and time is performed. The solution based on the idea of disturb and settle can be computed in an efficient polynomial order complexity and offers exponential savings from the brute-force.