Stochastic Modeling of Wind Derivatives in Energy Markets

Benth, Fred Espen; Persio, Luca Di; Lavagnini, Silvia

doi:10.3390/risks6020056

Cited by 38 publications

(55 citation statements)

References 14 publications

(26 reference statements)

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“…This empirical evidence shows that the three variables are modelled together by introducing some dependence. Previous studies [2,18] only partially considered this dependence structure. In general, the introduction of multivariate model, from a theoretical point of view, allows a better description of the whole process, but it has an evident application problem: the number of parameters to be estimated increases a great deal, introducing estimation errors.…”

Section: Discussionmentioning

confidence: 99%

“…The income will, therefore, be subject not only to the random wind trend, and therefore to the energy produced, but also to the uncertainty of the spot price of electricity [17]. The income of a wind farm has been investigated by [18]. The authors applied an Ornstein-Uhlenbeck process to model wind speed and energy production and an inverse Gaussian process to represent the logarithm of electricity spot prices.…”

Section: Introductionmentioning

confidence: 99%

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A Multivariate High-Order Markov Model for the Income Estimation of a Wind Farm

2021

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The energy produced by a wind farm in a given location and its associated income depends both on the wind characteristics in that location—i.e., speed and direction—and the dynamics of the electricity spot price. Because of the evidence of cross-correlations between wind speed, direction and price series and their lagged series, we aim to assess the income of a hypothetical wind farm located in central Italy when all interactions are considered. To model these cross and auto-correlations efficiently, we apply a high-order multivariate Markov model which includes dependencies from each time series and from a certain level of past values. Besides this, we used the Raftery Mixture Transition Distribution model (MTD) to reduce the number of parameters to get a more parsimonious model. Using data from the MERRA-2 project and from the electricity market in Italy, we estimate the model parameters and validate them through a Monte Carlo simulation. The results show that the simulated income faithfully reproduces the empirical income and that the multivariate model also closely reproduces the cross-correlations between the variables. Therefore, the model can be used to predict the income generated by a wind farm.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Multivariate High-Order Markov Model for the Income Estimation of a Wind Farm

2021

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“…2 CIICESI, ESTG, Politécnico do Porto, Porto, Portugal. 3 ESTGA, CIDMA, University of Aveiro, Aveiro, Portugal. 4 DEGEIT, CIDMA, University of Aveiro, Aveiro, Portugal.…”

Section: Discussionmentioning

confidence: 99%

“…Di Persion et al [8] applies an exponential smoothing model, ARMA-ARIMA and ARIMA-GARCH models for forecast of energy load in the Italian energy market. In [3] the authors model the logarithm of the spot price of electricity with a normal inverse Gaussian process. Costa e Silva et al [7] presents time series data mining for forecasting energy prices of the Iberian market.…”

Section: Introductionmentioning

confidence: 99%

Inventory models with reverse logistics for assets acquisition in a liquefied petroleum gas company

et al. 2020

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This paper addresses a case study regarding inventory models for acquiring liquefied petroleum gas (LPG) cylinders. This is an industrial challenge that was proposed at an European Study Group with Industry, by a Portuguese energy company, for which the LPG cylinder is the main asset of its LPG business. Due to the importance of this asset, an acquisition plan must be defined in order to determine the amount of LPG cylinders to acquire, and when to acquire them, in order to optimize the investment. As cylinders are returned and refilled, the reverse logistic flows of these assets must be considered. As the classical inventory models are not suitable for this case study, three new inventory models, which account for the return of LPG cylinders, are proposed in this work. The first proposed model considers deterministic constant demand and continuous returns of LPG cylinders, with discrete replenishment from the supplier. The second model is similar, but for the case when the returned cylinders cover for the demand. A third model is also proposed considering that both the demand and the returns are stochastic in nature and the replenishment from the supplier is discrete. The three models address different scenarios that the company is either currently facing or is expecting to occur in the near future.

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“…The characterisation of the income of a wind farm is rarely investigated, and an exception is the contribution by Benth, Di Persio, and Lavagnini (2018). In their analysis, the authors applied an Ornstein–Uhlenbeck model for wind intensity and electric energy production as well as a normal inverse Gaussian (NIG) distribution for the modelling of the logarithm of electricity spot prices.…”

Section: Introductionmentioning

confidence: 99%

Performance estimation of a wind farm with a dependence structure between electricity price and wind speed

et al. 2020

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Box-Cox transformation, expected income, Monte Carlo simulation, probability integral transformation, vector autoregressive model, wind energy | CASULA et AL. Ornstein-Uhlenbeck model for wind intensity and electric energy production as well as a normal inverse Gaussian (NIG) distribution for the modelling of the logarithm of electricity spot prices. The authors also highlighted the importance of correctly modelling the structure of dependence between wind intensity and the price of electricity. To this end, they replaced the small jumps of the NIG process by a Brownian term. The main purpose of this contribution was to use climate derivatives to cope with losses due to the decrease in wind intensity or price of electricity. Benth et al. also aimed to provide closed formulas for pricing wind derivatives. Our work focuses on the generalisation of the aforementioned work in several directions. We first estimated numerically the income of a wind farm through the model described below and compared it with the empirical income (this type of analysis is not present in the mentioned work). Furthermore, we considered a dataset on an hourly basis. This aspect enables the collation of hourly estimates of the expected income over a given horizon. We have also verified that the income estimate is significantly different if we disregarded the dependence between the two main variables, namely, the price of electricity and wind intensity. In fact, if these two variables are modelled independently, the estimate of the expected income is also altered. Given that determining the income of a wind farm is essential to correctly model the wind intensity and the price of electricity, we briefly listed the main models traceable in the recent literature in comparison with the models applied in this contribution. For these variables, the bibliographic references are notably complete. Concerning the wind speed model, we used the Box-Cox transformation of the wind speed data, where the optimal exponent is determined such that the transformed values are close to a Gaussian distribution (Nowotarski & Weron, 2018; Uniejewski, Weron, & Ziel, 2019). A power transformation was applied by Sim, Maass, and Lind (2019) with the same purpose. The problem is that the wind speed lacks a Gaussian distribution but is typically presented as a Weibull distribution, as widely described in the literature (Chang, 2011). Furthermore, the distribution of wind speed has high tails, indicating that rare events are more frequent than those contemplated by a Gaussian distribution (D'Amico, Petroni, & Prattico, 2015; Van Kuik & Peinke, 2016). Then, we applied a combination of trigonometric functions after the Box-Cox transformation to consider the seasonality of the data. Finally, we deseasonalised the data and applied an autoregressive AR (n) process to cope with residual autocorrelation. Next, energy production can be deduced from wind speed by considering the power curve that characterises the wind turbine. This model permits the replication of the statistical be...

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Stochastic Modeling of Wind Derivatives in Energy Markets

Cited by 38 publications

References 14 publications

A Multivariate High-Order Markov Model for the Income Estimation of a Wind Farm

A Multivariate High-Order Markov Model for the Income Estimation of a Wind Farm

Inventory models with reverse logistics for assets acquisition in a liquefied petroleum gas company

Performance estimation of a wind farm with a dependence structure between electricity price and wind speed

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