Hedging Strategy and Electricity Contract Engineering - IFOR

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minÛ I k Ü p max ÝaÜ x ìk
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154 Power portfolio optimization
trage deals. Observe that the optimal portfolio, where no pumping is allowed,
will utilize as much risk as possible. Hence the risk constraint (6.36) will, if
the general constraint (6.44) allows it, be binding. Further, since we assume
that hourly futures are traded, we are not adding a new instrument to our optimization
by allowing pumping, except for the possibility to virtually store
electricity. Consequently the optimal production portfolio, where pumping is
allowed xú will equal the optimal production portfolio, without pumping xú
plus the optimal combination of these arbitrage deals. Secondly, if the market
would be dominated by hydro storage plants with a pump efficiency of è , then
the future prices in different periods would be related by a absence of arbitrage
argument as
F Û iÜ jÝ F Û iÜ kÝaÜ i and k î j á
One should however keep in mind that a hydro storage plant is associated with
substantial capital costs, why this arbitrage argument is only applicable for
existing plants. Further, the pump and turbine capacity is in most market small
compared to the total capacity and in reality the inflow is stochastic.
Even without the pumping capacity the dam however facilitates storage possibilities,
which certainly has some value. Let us in the same manner as in the
case of pumping define the value of a hydro plant with no dam. i.e with no storage
capacity with ! as the expected profit given by the optimization program
(6.35)-(6.44) with V 0 V max V end 0. What we actually model is now a
run river plant and the dispatch will consequently be given by
Ü K á á@á?á
Production has to equal inflow in each period and if the technical constraints on
the turbines prohibits this, then the production will be given by that maximum
possible capacity and the excess inflow will be lost through spill over. Similarly
to the characterization of the value of pumping we can write the value of storage
! ! as . The value of a hydro storage plant with pump capacity can hence in
the static case be decomposed as in Figure 6.6,
In Chapter 5 we mentioned that the hydro storage plant can be suitable for
hedging volume risk. This is however not possible with the static strategy, since