Forecasting the Intra-Day Spread Densities of Electricity Prices

Abstract

Intra-day price spreads are of interest to electricity traders, storage and electric vehicle operators. This paper formulates dynamic density functions, based upon skewed-t and similar representations, to model and forecast the German electricity price spreads between different hours of the day, as revealed in the day-ahead auctions. The four specifications of the density functions are dynamic and conditional upon exogenous drivers, thereby permitting the location, scale and shape parameters of the densities to respond hourly to such factors as weather and demand forecasts. The best fitting and forecasting specifications for each spread are selected based on the Pinball Loss function, following the closed-form analytical solutions of the cumulative distribution functions.Energies 2020, 13, 687 2 of 31 opportunities for storage or load shifting, will depend upon the wind and solar forecasts, as well as demand and supply considerations. Furthermore, the price density functions are non-normal with skewness switching between positive and negative depending upon the dynamics of production of renewable energy [9]. Because of this non-Normality and the non-independence of each hourly price, spread densities cannot be easily derived as the difference of the price densities, and so we estimate and forecast the daily matrix of intraday spreads directly.We apply our spread densities formulation to the German market. This is the largest and the main daily reference market for wholesale power in Europe. It is also strongly influenced by wind and solar production, as well as providing a context where batteries and demand-side management are active innovations. The day ahead auction has been actively researched and closes at noon each day, with the vector of 24 hourly prices for the next day being released an hour later. For modeling the spread densities, we adapt the Generalised Additive Model for Location, Scale and Shape (GAMLSS) semi-parametric regression model [10], which has already been used effectively to form day-ahead densities of price levels in the German context [9]. Within this framework, the hourly electricity price spreads form a response variable, whose distribution function varies according to multiple exogenous factors. The GAMLSS framework allows choice from a wide range of distributions, whose distribution parameters change according to the exogenous variables specified using (non)linear relationships. The dynamic location, scale and shape parameters (related to the mean, volatility, skewness and kurtosis of price spreads) are therefore explicitly incorporated into the forecasting model. The paper proceeds by first describing the data and the density estimation process. In Section 2, we use the Pinball Loss function to select the best fitting density model with four distribution parameters. Then in Section 3, we undertake a rolling window forecasting evaluation and demonstrate the value of the dynamic, conditional latent parameter. Section 4 concludes.

Optimal Daily Trading of Battery Operations Using Arbitrage Spreads

“…Hence they are estimated directly. The same dataset (German day-ahead prices from 2012-2017) and modeling (multifactor skew-t) are used as in Abramova et al [22]. Since that work developed and validated the econometrics in detail, those estimated densities can be used as state-of-the-art.…”

“…The above model for forecasting all the day-ahead spreads was specified and estimated on four years of data. From a range of functional forms that fit the data well, six fourparameter density functions were found to be appropriate (see Abramova et al [22] for more details). In general, the skew-t was preferred, but not always.…”

“…This resulted in an upper triangular matrix of density estimates for each spread, where each matrix element contained information on the six distributions used and the four estimated parameters describing each distribution for the data relating to that spread only. The distribution which was found to fit each spread data best, was chosen as the 'best distribution' (see Abramova et al [22] for further details). The density functions have analytical solutions that allowed the q 05 and q 95 to be determined from their functional forms and the four forecast parameters.…”

“…To achieve this, the generalized additive model for location, scale and shape (GAMLSS) parametric regression model is used [21], which has previously been successfully applied to obtain day-ahead densities of price levels [20] and price spreads [22]. This paper extends that latter work on the econometrics of spreads to provide the basis for optimal battery operations.…”

“…The next sections review some of the background research on optimal battery operations followed by the formulation of an optimization model. The data are then described, and the features of the forecast spread densities, which are taken from Abramova et al [22] are summarized. In the subsequent section the results of using these density functions to create the optimal daily scheduling of battery storage are reported and the superior profitability compared to using normal densities is demonstrated through backtesting.…”