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.
An important revenue stream for electric battery operators is often arbitraging the hourly price spreads in the day-ahead auction. The optimal approach to this is challenging if risk is a consideration as this requires the estimation of density functions. Since the hourly prices are not normal and not independent, creating spread densities from the difference of separately estimated price densities is generally intractable. Thus, forecasts of all intraday hourly spreads were directly specified as an upper triangular matrix containing densities. The model was a flexible four-parameter distribution used to produce dynamic parameter estimates conditional upon exogenous factors, most importantly wind, solar and the day-ahead demand forecasts. These forecasts supported the optimal daily scheduling of a storage facility, operating on single and multiple cycles per day. The optimization is innovative in its use of spread trades rather than hourly prices, which this paper argues, is more attractive in reducing risk. In contrast to the conventional approach of trading the daily peak and trough, multiple trades are found to be profitable and opportunistic depending upon the weather forecasts.
In article the role of logistic coordination in increase of stability of deliveries chains is considered. This problem is investigated by the author from positions of integrated management of the integrated chains of deliveries on the basis of a combination of system, process and situational approaches. On the basis of the review of scientific works of representatives of school of management of chains of deliveries the author makes the conclusion about the need of formation and development of the system of through management of chains of deliveries allowing to align in the best way interests of participants of logistic process — suppliers, the focal companies, logistic intermediaries, consumers. At the same time special relevance, according to the author, in modern conditions is represented by a social orientation of logistic business — orientation not only to profits, but, also on interests of consumers and the accounting of requirements of the environment. Article is intended for scientists, heads and specialists of the logistic companies, teachers, graduate students, undergraduates and students studying in the «Logistics and Management of Chains of Deliveries» direction.
This paper formulates dynamic density functions, based upon skewed-t and similar representations, to model and forecast electricity price spreads between different hours of the day. This supports an optimal day ahead storage and discharge schedule, and thereby facilitates a bidding strategy for a merchant arbitrage facility into the day-ahead auctions for wholesale electricity.The four latent moments of the density functions are dynamic and conditional upon exogenous drivers, thereby permitting the mean, variance, skewness and kurtosis of the densities to respond hourly to such factors as weather and demand forecasts. The best specification for each spread is selected based on the Pinball Loss function, following the closed form analytical solutions of the cumulative density functions. Those analytical properties also allow the calculation of risk associated with the spread arbitrages. From these spread densities, the optimal daily operation of a battery storage facility is determined.Whilst day ahead electricity price forecasting has been a topic of substantial and wide ranging research in terms of methods, the focus has mostly been upon price levels for the delivery periods (usually hourly) in the following day. More recently there has been an interest in density forecasts for the hourly prices, motivated by considerations of risk management, see (Weron, 2014;Nowotarski and Weron, 2017) for extensive reviews.In this paper we provide a new formulation with a focus upon price spreads, and specifically we forecast the density functions for the intraday spreads in the day-ahead prices. The optimal operation of storage facilities, e.g. batteries, or load shifting programmes, e.g. demand-side management, over daily cycles depends upon these spreads if they are operated as merchants, arbitraging buying and selling from the wholesale market. Furthermore if risk is a consideration, analysis of the mean-differences in price levels would be inadequate, and we therefore directly estimate the density functions of all hourly spreads in prices at the day-ahead stage. Our specification, estimation and forecasting of these arbitrage spreads is new and computationally-intensive. We then show how these spread densities can support the optimal daily operation of a risk-constrained merchant battery facility.In contrast to the body of work on gas and other storable commodities, e.g. (Boogert and De Jong, 2011;Secomandi, 2018), because of the daily periodicity in electricity prices and the predominance of the day-ahead auctions, which typically set all hourly prices for the following day simultaneously, the operational horizon for storage and load shifting is usually episodic on a daily basis. So the continuous time, dynamic optimisation formulations used for gas and other commodity storage operations are less appropriate for electricity, and furthermore the stochastic simplifications generally required in the analysis of these other models would not meet the requirements of adequate fit to the more complex power price dynamics. Thus...
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