Abstract
Predicting future solar conditions is important for electricity industries with solar power generators to quote a day-ahead sales contract in the electricity market. If a prediction error exists, the market-monitoring agent has to prepare another power generation resource to immediately compensate for the shortage, resulting in an additional cost. In this context, a penalty may be required depending on the size of the prediction error, which may lead to a significant loss for solar power producers. Because the main source of such losses is from prediction errors of solar conditions, they can instead effectively utilize a derivative contract based on solar prediction errors. The objective of this work is to provide such a derivative contract, namely, a prediction error weather derivative. First, defining a certain loss function, we measure the hedge effect of the derivative on solar radiation prediction error, thereby verifying that the existing hedging method for wind power can also be applied to solar power generation with periodic trends. By introducing the temperature derivative on the absolute prediction error, we also propose a cross-hedging method, where we demonstrate not only a further variance reduction effect when used with solar radiation derivatives, but also a certain hedge effect obtained even when only the temperature derivative is used. For temperature derivative pricing and optimal contract volume estimation, we propose a method using a tensor-product spline function that simultaneously incorporates the smoothing conditions of both the direction of intraday time trend and seasonal trend, and consequently verify its effectiveness.
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Notes
Note that under Japan's current institution, most of the renewable power producers are not subject to the application of imbalance price, since all the output is purchased at a fixed price determined in advance under the Feed-In Tariff Law (Instead, imbalance risk is borne by retailers or system operators). In the future, however, it is assumed that the scheme will be shifted to a system where renewable power producer themselves make predictions and bear the imbalance risk.
In Japan, this penalty term is supposed to be included in the imbalance price applied from April 2019.
The solar radiation derivative is assumed to be contracted without transaction costs, that is, it satisfies the equation \( {\text{Mean}}\left[ {\psi \left( {\varepsilon_{R,n} } \right)} \right] = 0 \). Note that we assume the same condition for the solar radiation derivative on absolute prediction errors \( \psi \left( {\left| {\varepsilon_{R,n} } \right|} \right) \), which will be introduced later.
In this study, we construct GAM using the function gam () in the R 3.5.1 package “mgcv” (https://cran.r-project.org), where gam () adopts general cross-validation criterion to calculate the smoothing parameter \( \lambda \) (Wood 2017).
For example, Wood (2013) modeled the density of mackerel eggs in the ocean using a thin plate spline with latitude and longitude as explanatory variables, which can be said to be an intuitive case using the isotropic nature of the function.
For allocating periodic dummy variables, we use the method proposed in Yamada et al. (2015) (the same applies hereafter).
With the permission of the owner, we use the data of the private roof-mounted power system in Hiroshima city.
Downloaded from https://www.data.jma.go.jp/gmd/risk/obsdl.
Downloaded from http://weather-transition.gger.jp.
We use the data from June 1, 2016 to May 31, 2017.
In the weather forecast publicly announced by the JMA, we cannot obtain the hourly predicted temperature values for the next day, so we newly introduce this pricing method.
We use the data from June 1, 2016 to May 31, 2017, during which it was possible to obtain past weather forecasts.
Since the coefficient of the loss on the absolute output prediction error is set to 1, the value obtained by multiplying the vertical axis by \( c \) is equivalent to the actual payoff (same applies to the subsequent sections).
Equation (13) has a term with crossing variables attached to the tensor product spline, but since the intersection term only replaces the new function multiplying the basis function of the tensor product spline by the crossing variable, it can be estimated by the same procedure using normal GAM, in the same idea as described in Yamada (2018).
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The second author is supported by Grant-in-Aid for Scientific Research (A) 16H01833 from Japan Society for the Promotion of Science (JSPS).
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Matsumoto, T., Yamada, Y. Cross Hedging Using Prediction Error Weather Derivatives for Loss of Solar Output Prediction Errors in Electricity Market. Asia-Pac Financ Markets 26, 211–227 (2019). https://doi.org/10.1007/s10690-018-9264-3
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DOI: https://doi.org/10.1007/s10690-018-9264-3
Keywords
- Cross hedge
- Non-parametric regression
- Minimum variance hedge
- Prediction errors
- Solar power energy
- Weather derivatives