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

The weekly transition probability matrices were calculated from the 30-year
series of aggregated equivalent energy inflows.
4.2.2 SDP representing irrigation as a constraint
The objective was to determine production levels of thermal and hydropower
units such as to minimize expected production cost, subject to meeting the
power demand d t and the irrigation demand w t for every time step t until the
end of the planning horizon T.
Let c be the 1 × I vector of constant marginal costs for every non-hydro producer
i, and p t a 1 × I vector of power production for every producer i during
time step t. The recursive SDP equation of the optimal value function
F * (E t ,Q t-1 ) can be written as:
é L
l
* k
T
*
æ öù
Ft ( Et, Qt- 1)
= min akl F t+ 1
Et+
1,
Q
c p + å ´ ç t
çè ÷ ø
(1)
p
êë
l=
1
úû
where a k,l is the transition probability from inflow Q k in stage t – 1, to inflow
Q l in stage t. Q t was defined as the mean weekly energy inflow within each of
the classes defined in Section 4.1, and was calculated by multiplying the runoff
to each catchment with its respective runoff energy equivalent.
The problem in (1) is subject to constraints on equivalent energy balance (2),
minimum and maximum hydropower generation (3), minimum and maximum
equivalent energy storage (4), power demand fulfilment (5), and minimum
and maximum thermal power generation (6):
T
t
=
t-1
+
t
-
t
-
t
E E Q u w H
(2)
0 Ht
£ £ H
(3)
E £ Et
£ E
(4)
I
å pit ,
= dt -Ht
(5)
i=
1
0 pit
,
pi
£ £ (6)
where H t is hydropower production. Upstream irrigation abstractions are considered
as sinks in the balance equation of the equivalent energy reservoir
T
( uw ) , and downstream irrigation allocations are represented as a timedependant
lower bound on hydropower releases:
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