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## Über dieses Buch

Gathering selected, revised and extended contributions from the conference ‘Forecasting and Risk Management for Renewable Energy FOREWER’, which took place in Paris in June 2017, this book focuses on the applications of statistics to the risk management and forecasting problems arising in the renewable energy industry. The different contributions explore all aspects of the energy production chain: forecasting and probabilistic modelling of renewable resources, including probabilistic forecasting approaches; modelling and forecasting of wind and solar power production; prediction of electricity demand; optimal operation of microgrids involving renewable production; and finally the effect of renewable production on electricity market prices. Written by experts in statistics, probability, risk management, economics and electrical engineering, this multidisciplinary volume will serve as a reference on renewable energy risk management and at the same time as a source of inspiration for statisticians and probabilists aiming to work on energy-related problems.

## Inhaltsverzeichnis

### Chapter 1. Marginal Weibull Diffusion Model for Wind Speed Modeling and Short-Term Forecasting

We propose a dynamical model for the wind speed which is a Markov diffusion process with Weibull marginal distribution. It presents several advantages, namely nice modeling features both in terms of marginal probability density function and temporal correlation. The characteristics can be interpreted in terms of shape and scale parameters of a Weibull law which is convenient for practitioners to analyze the results. We calibrate the parameters with the maximum quasi-likelihood method and use the model to generate and forecast the wind speed. We have tested the model on wind-speed datasets provided by the National Renewable Energy Laboratory. The model fits well the data and we obtain a very good performance in point and probabilistic forecasting in the short-term in comparison to the benchmark.
Alain Bensoussan, Alexandre Brouste

### Chapter 2. From Numerical Weather Prediction Outputs to Accurate Local Surface Wind Speed: Statistical Modeling and Forecasts

Downscaling a meteorological quantity at a specific location from outputs of Numerical Weather Prediction models is a vast field of research with continuous improvement. The need to provide accurate forecasts of the surface wind speed at specific locations of wind farms has become critical for wind energy application. While classical statistical methods like multiple linear regression have been often used in order to reconstruct wind speed from Numerical Weather Prediction model outputs, machine learning methods, like Random Forests, are not as widespread in this field of research. In this paper, we compare the performances of two downscaling statistical methods for reconstructing and forecasting wind speed at a specific location from the European Center of Medium-range Weather Forecasts (ECMWF) model outputs. The assessment of ECMWF shows for 10 m wind speed displays a systematic bias, while at 100 m, the wind speed is better represented. Our study shows that both classical and machine learning methods lead to comparable results. However, the time needed to pre-process and to calibrate the models is very different in both cases. The multiple linear model associated with a wise pre-processing and variable selection shows performances that are slightly better, compared to Random Forest models. Finally, we highlight the added value of using past observed local information for forecasting the wind speed on the short term.
Bastien Alonzo, Riwal Plougonven, Mathilde Mougeot, Aurélie Fischer, Aurore Dupré, Philippe Drobinski

### Chapter 3. Stochastic Lagrangian Approach for Wind Farm Simulation

We present a stochastic Lagrangian approach for atmospheric boundary layer simulation. Based on a turbulent-fluid-particle model, a stochastic Lagrangian particle approach could be an advantageous alternative for some applications, in particular in the context of down-scaling simulation and wind farm simulation. This paper presents two recent advances in this direction, first the analysis of an optimal rate of convergence result for the particle approximation method that grounds the space discretisation of the Lagrangian model, and second a preliminary illustration of our methodology based on the simulation of a Zephyr ENR wind farm of six turbines.
Mireille Bossy, Aurore Dupré, Philippe Drobinski, Laurent Violeau, Christian Briard

### Chapter 4. Day-Ahead Probabilistic Forecast of Solar Irradiance: A Stochastic Differential Equation Approach

In this work, we derive a probabilistic forecast of the solar irradiance during a day at a given location, using a stochastic differential equation (SDE for short) model. We propose a procedure that transforms a deterministic forecast into a probabilistic forecast: the input parameters of the SDE model are the AROME numerical weather predictions computed at day $$D-1$$ for the day D. The model also accounts for the maximal irradiance from the clear sky model. The SDE model is mean-reverting towards the deterministic forecast and the instantaneous amplitude of the noise depends on the clear sky index, so that the fluctuations vanish as the index is close to 0 (cloudy) or 1 (sunny), as observed in practice. Our tests show a good adequacy of the confidence intervals of the model with the measurement.
Jordi Badosa, Emmanuel Gobet, Maxime Grangereau, Daeyoung Kim

### Chapter 5. Homogeneous Climate Regions Using Learning Algorithms

Climate analysis is extremely useful to understand better the differences of electricity consumption within the French territory and to help electricity consumption forecasts. Using a large historical data base of 14 years of meteorological observations, this work aims to study a segmentation of the French territory based on functional time series of temperature and wind. In a first step, 14 clustering instances, one for each year, have been performed using, for each instance, one year of data. Each year, the clustering exhibits several homogeneous and spatially connected regions. Benefits of this approach let to study the stability of the previous regions over the years and to highlight the inter-annual variability of the French climate. A final aggregation of all clustering instances shows a segmentation map in easily interpretable, geographically connected climate zones over the last years. Especially, we observe that the number of clusters remains extremely stable through the years. Exhibiting stable homogeneous regions bring then some valuable knowledge for potentially installing new wind or solar farms on the French territory.
Mathilde Mougeot, Dominique Picard, Vincent Lefieux, Miranda Marchand

### Chapter 6. Electricity Demand Forecasting: The Uruguayan Case

The development of new electricity generation technologies has given new opportunities to developing economies. These economies are often highly dependent on fossil sources and so on the price of petrol. Uruguay has finished the transformation of its energetic mix, presenting today a very large participation of renewable sources among its production mix. This rapid change has demanded new mathematical and computing methods for the administration and monitoring of the system load. In this work we present enercast, a R package that contains prediction models that can be used by the network operator. The prediction models are divided in two groups, exogenous and endogenous models, that respectively uses external covariates or not. Each model is used to produce daily prediction which are then combined using a sequential aggregation algorithm. We show by numerical experiments the appropriateness of our end-to-end procedure applied to real data from the Uruguayan electrical system.
Andrés Castrillejo, Jairo Cugliari, Fernando Massa, Ignacio Ramirez

### Chapter 7. A Flexible Mixed Additive-Multiplicative Model for Load Forecasting in a Smart Grid Setting

This paper presents a mixed additive-multiplicative model for load forecasting that can be flexibly adapted to accommodate various forecasting needs in a Smart Grid setting. The flexibility of the model allows forecasting the load at different levels: system level, transform substation level, and feeder level. It also enables us to conduct short-term, medium and long-term load forecasting. The model decomposes load into two additive parts. One is independent of weather but dependent on the day of the week (d) and hour of the day (h), denoted as $$L_0(d,h)$$. The other is the product of a weather-independent normal load, $$L_1(d,h)$$, and weather-dependent factor, f(w). Weather information (w) includes the ambient temperature, relative humidity and their lagged versions. This method has been evaluated on real data for system level, transformer level and feeder level in the Northeastern part of the USA. Unlike many other forecasting methods, this method does not suffer from the accumulation and propagation of errors from prior hours.
Eugene A. Feinberg, Jun Fei

### Chapter 8. A Generic Method for Density Forecasts Recalibration

We address the calibration constraint of probability forecasting. We propose a generic method for recalibration, which allows us to enforce this constraint. It remains to be known the impact on forecast quality, measured by predictive distributions sharpness, or specific scores. We show that the impact on the Continuous Ranked Probability Score (CRPS) is weak under some hypotheses and that it is positive under more restrictive ones. We used this method on temperature ensemble forecasts and compared the quality of the recalibrated forecasts with that of the raw ensemble and of a more specific method, that is Ensemble Model Output Statistics (EMOS). Better results are shown with our recalibration rather than with EMOS in this case study.
Jérôme Collet, Michael Richard

Open Access

### Chapter 9. Anticipating Some of the Challenges and Solutions for 60% Renewable Energy Sources in the European Electricity System

In this study, EDF R&D used the EU “high RES” (RenewableEnergy Sources) scenario of the 2011 European Energy Roadmap, reaching 60% of renewables generation by 2030 including 40% from variable RES (such as wind and solar), and analysed its implications on system development and operation. The analysis was based on an in-house chain of power system planning, dispatch and simulation tools. The study indicates that a strong development of variable RES generation would imply significant changes to the thermal generation mix required to balance supply and demand, with the need for less base load power plants and for more flexible units. The study shows that conventional plants are still required to ensure security of supply and, in order to reach a high level of decarbonation, low carbon base plants are essential. Furthermore, the results also underline the strong interest of deploying a certain level of interconnections, especially around the North Sea and France: it is a very efficient way to optimize the systems costs since these ensure that electricity generated by RES can reach demand and curtailment can be avoided, while also enabling the sharing of backup plants and of RES and demand diversity. Storage and flexible demand play a complementary role as flexibility providers, as a complement to thermal plants and RES curtailment. The potential for cost effective additional storage will however depend on the zone and on the possibility to deploy the other existing levers. Storage is particularly interesting in island systems with limited flexibility such as the UK. Load generation balancing will be highly dependent on weather conditions and its associated uncertainty that will increase the need for operation margins at different lead times and reserves. In order to limit the impact of this uncertainty, forecasting tools and the operational practices will play an important role. An increase of variable RES in the mix leads to challenges in terms of dynamic stability, with frequency excursion potentially reaching security limit. These challenges are linked to the fact that variable RES are interfaced with the system by power electronics and do not naturally contribute to system inertia, which is a key factor in maintaining system security. In order to maintain system security, some curtailment or the deployment of innovative solutions such as fast frequency response from battery storage and RES are required. Lastly, the economics of such a system would be a significant challenge, as the cost of the infrastructure is high while the market profitability of RES decreases with RES penetration since it is exposed to a “cannibalisation effect”.
Vera Silva, Miguel López-Botet Zulueta, Ye Wang, Paul Fourment, Timothee Hinchliffe, Alain Burtin, Caroline Gatti-Bono

### Chapter 10. A Joint Model for Electricity Spot Prices and Wind Penetration with Dependence in the Extremes

This article analyses the dependence between electricity spot prices and the wind penetration index in the European energy market. The wind penetration index is given by the ratio of the wind energy production divided by the total electricity production. We find that the wind penetration has an impact on the intensity of the spike occurrences in the electricity prices, and we formulate a joint model for electricity prices and wind penetration and calibrate it to recent data. We then use the new joint model in an application where we assess the impact of the modelling assumptions on the potential income of an electricity distributor who buys electricity from a wind farm operator.
Thomas Deschatre, Almut E. D. Veraart

### Chapter 11. The Optimal Control of Storage for Arbitrage and Buffering, with Energy Applications

We study the optimal control of storage which is used for both arbitrage and buffering against unexpected events (shocks), with particular applications to the control of energy systems in a stochastic and typically time-heterogeneous environment. Our philosophy is that of viewing the problem as being formally one of stochastic dynamic programming (SDP), but of recasting the SDP recursion in terms of functions which, if known, would reduce the associated optimisation problem to one which is deterministic, except that it must be re-solved at times when shocks occur. In the case of a perfectly efficient store facing linear buying and selling costs the functions required for this approach may be determined exactly; otherwise they may typically be estimated to good approximation. We provide characterisations of optimal control policies. We consider also the associated deterministic optimisation problem, outlining an approach to its solution which is both computationally tractable and—through the identification of a running forecast horizon—suitable for the management of systems over indefinitely extended periods of time. We give examples based on Great Britain electricity price data.
James Cruise, Stan Zachary

### Chapter 12. Optimal Management of a Wind Power Plant with Storage Capacity

We consider the problem of a wind producer who has access to the spot and intraday electricity markets and has the possibility of partially storing the produced energy using a battery storage facility. The aim of the producer is to maximize the expected gain of selling in the market the energy produced during a 24-h period. We propose and calibrate statistical models for the power production and the intraday electricity price, and compute the optimal strategy of the producer via dynamic programming.
Jérôme Collet, Olivier Féron, Peter Tankov
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