Hedging Strategy and Electricity Contract Engineering - IFOR

S7 D7
min 8
0 if S
i
or D
p otherwise
l 6
173
The exercise functions, are in this case study only functions of spot price and
demand, not inflow. The reason for this is simply to be able to visualize the
exercise conditions in a 3D plot 3 and to simplify the interpretation of the results.
These exercise functions are as before given by step functions
g4i5 l
p max if S S4i
and D 6
D4l
0
6 (7.1)
otherwise
i5 l
g7
(7.2)
Due to the short horizon of two weeks no time component was taken into
account in the thresholds. These thresholds are presented in Table 7.3 and the
five spot thresholds and six demand thresholds build up 30 different exercise
functions for production and pumping respectively as in (7.1) and (7.2). One
could introduce even more exercise functions, which of course would result
in an equal or better expected profit. It would however not change the typical
results that we want to analyze.
The end water level constraint V end is obtained by running a one-year optimization
starting in the beginning of October, corresponding to a hydrological
year. The one-year optimization was a static one where the schedule was determined
at the beginning of the period for the whole year as in (6.35)-(6.44).
The reason for using a static dispatch is to keep the problem on a computationally
manageable size. As argued already in Chapter 6.6.3.1 the low inflow in
combination with the high prices in the winter implies that a basically full dam
at the beginning and hence end of the hydrological year, which in Switzerland
starts in October, is a fair assumption. The margin in this one-year optimization
was chosen to be 50 GWh. This together with a maximum water level of 1500
GWh gives us a starting and end level of 1450 GWh in the one year optimization.
The only output that interests us from this optimization is the optimal
water level over time. The result is presented in Figure 7.2, where one can see
the typical shape of the optimal water level with a low level in the summer and
a high level in the winter. One can see that major production is conducted in
3 By introducing inflow in the exercise functions the expected profit increased only
slightly with up to 1%, depending on the risk constraint C.