A framework for joint management of regional water-energy ... - Orbit

The constraints are mathematical expressions of the limitations that restrict
the alternatives of the decision makers, such as minimum irrigation allocations,
maximum power generation (installed capacity), minimum ecological
flows or maximum hydropower releases. The power and the water balance
are also described as constraints, using the estimated power demands and water
inflows.
When solved, the optimization problem provides optimal values for each decision
variable over the planning horizon. These values are optimal with respect
to the chosen performance criterion, which in this case is net costs
minimization.
Hydropower reservoirs make the problem more computationally demanding
because their storage couples successive time steps. It may be necessary to
reduce the number of reservoirs sent to the optimization algorithm by using
aggregation techniques. However, this is optional and depends on the number
of reservoirs in the system and the ability of the algorithm to handle multiple
reservoirs.
The reservoir aggregation technique and the optimization algorithms used in
this study are described in the following sections.
4.1 Reservoir aggregation
Because of curse of dimensionality mentioned above, it is not possible to use
discrete DP methods to optimize more than three or four reservoirs simultaneously.
Therefore, the volumes and flows representing the hydrological system
were converted to power and energy units, respectively, and aggregated
into equivalent energy reservoirs.
Two aggregation levels were applied depending on the optimization method.
When using SDP, the seven major river basins of the IP were aggregated into
one equivalent reservoir; when using SDDP, each river basin was aggregated
into one equivalent reservoir, resulting in a system of seven reservoirs in parallel.
Three conversion factors are used in the aggregation methodology (Table 7).
The energy equivalent of catchment runoff is a conversion factor based on the
hydropower equation that expresses the full hydropower potential of the runoff
generated in the catchment. The other two factors deal with irrigation: the
energy equivalent of catchment outflow indicates the amount of energy that is
lost when water is allocated to upstream irrigation, and the average energy
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