The
parametric rule for the management of multiple reservoir systems
The model that determines
the management of the hydrosystem follows an operation rule. An
operation rule is a law (equation or chart) that specifies the amount
to be released for various purposes as a function of system states and
parameters (ReVelle, 1999).
A feasible mathematical
expression for the operation rules of the reservoir system is (Nalbantis
and Koutsoyiannis, 1997):
Si*
= Ki - ai K
+ bi V
where Ki
the net storage capacity of the i reservoir, K is the total
capacity of the system, V is the total active storage of the system
(i.e., the total water availability), Si*
stands as the target storage for the i reservoir at the end of
each time step and ai, bi
are unknown parameters.
The total storage
of the system V can be calculated assuming that the sum of reservoir
releases satisfies exactly the downstream demand D and also that
there exists an estimation of hydrological inflows (i.e., via stochastic
forecast).
The initial
rules are corrected according to an adjusting procedure, in order to satisfy
reservoir capacity constraints, and thus they become nonlinear. Nevertheless,
the final operating rule is completely determined from the initial values
of parameters, irrespectively of all corrections.
A great
advantage of the above formulation is that the total number of control
variables of the system reduces to 2N and thus becomes independent
of the simulation length.
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