Hedging Strategy and Electricity Contract Engineering - IFOR

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160 Power portfolio optimization
Eq. õ x c L z #
á (6.54) áá
á (6.55) á á á
áá
á (6.56) áá
á (6.57) áá
á (6.59) áá
á á á á á á
á á á á á á
á á á
(6.60) áá á
(6.61) á á á
á áá
ô # r n 2K K J J 1
1
J
K J
K J
1
1
1
á á
lar,
matrix.
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Tab. 6.2: Structure of the A á matrix. áá
denotes a diagonal á á
and á á á á
denotes a full, á áá
á
denotes a triangu-
á á
denotes a diagonal band sub-
As seen in Table 6.2 the constraint (6.56) and (6.57) and the spill over variables
regulating the water level build up the majority of the matrix. One could
however relax some of these constraints. For example, in a short horizon
optimization in the winter, when the dams are basically full, the constraint
that the water level must be non-negative could be excluded from the problem.
Further, in the summer when the water level is low, the upper constraint on
the water level can be relaxed and the spill over variables could be eliminated.
This would dramatically reduce the size of the problem. The feasibility of the
solution, although very probable, must then be checked ex-post. To keep the
size of the problem within reasonable boundaries, the proposed relaxation of
the water level constraints and the corresponding spill-over variables should
however be done whenever possible. Another possibility to decrease the size
of the problem is to aggregate a number of periods into one. This would
however only serve as an approximate solution. The hydro storage plant’s
options would then have an average spot price as underlying and not the
actual spot price. This should hence preferably be done during times when the
stochastic factors are fairly stable, for example, by dividing each day into only
one peak period and one off-peak period. The well known fact that the value
of a portfolio of options is greater than the value of an option on a portfolio,
however implies that an aggregation of periods would underestimate the value