Hedging Strategy and Electricity Contract Engineering - IFOR

x k xëk
x ìk Ü xë k
0Ü x ìk
0Ü k 1Ü
è
S k î 0 S k î 0 á
è
6.4 Modeling of plants and their operational flexibility 125
Recall from Chapter 4.3 that because of the non-perfect pump efficiency èêé 1
we have to divide the dispatch in each period into one production part and one
pumping part
Ü K á á?á@á
Typically, it is not possible to simultaneously produce and pump, since the
same pipelines are used for production and pumping. Hence we would need to
impose that either production or pumping equals zero in each period
xëk x k
Ü k K (6.8)
0Ü 1Ü
ì á?á@á á
However, when the objective is to maximize the expected profit, this constraint
will for a non-perfect pump be redundant and hence not needed. A violation of
(6.8) would imply that pumping was conducted simultaneously with production.
Let k denote xëk x k , where k
minÛ and x ìk
is a feasible dispatch in
í
period k. One could change the dispatch in that period to xëk
and x ìk respectively
given xë Ý by
ì Ü
xëk
xëk
í k
x ìk
x ìk
í k Ü
where feasibility is assured by definition of í k. This change in dispatch would
not affect the stored water level V k . The effect on the electricity balance, on the
other hand, would change as
xëk
í k
x ìk
í k
xëk
x ìk
í k
k í
è
(6.9)
By assumption that (6.8) is í violated î k 0 and the efficiency of the nonperfect
pump is éïèðé 0 1, why (6.9) is strictly positive. The profit in period
k would therefore increase by
í k
k í
è