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Power Plant Performance
are clear benefits to this approach. The spread can fluctuate parameters can be accurately estimated on the basis of a
between certain ‘logical’ boundaries, with the result that the limited set of historical data. The major parameters capture
(undesired) extreme outcomes are avoided. However, general level shifts, shifts from contango into backwardation
information is lost about the movement of underlying power and shifts in the size of the winter-summer spread (for power
and fuels prices, e.g. relevant for hedging decisions. This will and gas). The volatilities and correlations of the different
lead to various practical problems, for instance when maturitiesalongthecurvecanbecalibratedtoproperlymatch
combining a dedicated gas contract to the power plant. thehistoricalpricedata,bothbetweendifferentmaturitiesand
In short, we feel that the most common approaches are between different commodities. This is especially important
inadequate solutions when they are applied to power plant when hedging strategies are evaluated. The model also
evaluation projects. The alternative is the explicit contains spiky (‘regime-switching’) power and gas spot prices,
incorporation of fundamental price relationships. This mean-reverting to forward price levels, with appropriate
approach has the benefit that spark spreads remain at logical random hourly profiles.
levels,butthatinformationaboutunderlyingpricesisnotlost. The model as described produces realistic price simulations
Power prices are the result of the movement in underlying for individual commodities. At first sight, it also nicely ties
fuelandcarbonprices.Thisrelationshipcanbecapturedwith commodities together through correlations. Still, we
cointegration: power prices are cointegrated with price experienced that it does not produce realistic spreads between
movement of fuels (mainly coal and gas) and carbon. With commodities, whether it be oil-gas spreads, regional gas
cointegration, power prices are fundamentally driven by spreads or power-fuel spreads. Yet spreads are actually the
dynamicmarketmarginalcostsinpeakandoff-peakandwill most important input to most valuations, including power
react properly when commodities are substituted (for plant valuations.
instance, change from coal to natural gas in summer We solved the issue through cointegration, a Nobel Prize
periods). Actual commodity prices may temporarily deviate winning econometric innovation (Engle and Granger, 1987).
from the fundamental relationships, but not for too long and For spark and dark spreads it is complemented with the
not by too much. explicit incorporation of the merit order. Essentially, the
cointegrationapproachcapturesthecorrelationbetweenprice
Cointegrated Forward & Spot Price Simulations levels rather than (only) price returns. Intuitively, it uses a
KYOS started the development of a proprietary price regressiontofindthe‘stable’relationshipbetweencommodity
simulation model for energy commodities several years ago, prices and then assumes that ‘actual’ commodity prices move
part of which has been published in the literature (see e.g. De around this stable level. The concept is very similar to a spot
Jong, 2007). It is now in use by several leading commodity price mean-reverting around a forward price level. The
trading companies. Fuel and CO
2
prices are simulated first, primary challenge is to align the approach with the return-
with power prices following. The model captures the many driven movements of the forward curve, something we
shapes that forward curves display over their lifetime. They managed to resolve over time.
may, for example, turn from contango (future price higher Case Study: In order to bring this theoretical explanation to
thantoday)inbackwardation(futurepriceslowerthantoday). a practical level, we next consider a case study involving a
To capture these dynamics we use a multi-factor model whose power plant over a three year period.
50 worldPower2009
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