Modelling the variability of wind energy resource 

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Implication for energy management

Assessing wind energy production from surface wind speed is not straightforward and demands a lot of considerations. First, measurements are usually available at 10m which is a level of reference in meteorology. Wind turbines harvest wind at heights ranging from 50m to 140m (Hernandez et al., 2017), so that vertical extrapolation of the surface wind speed at the hub height is often necessary to evaluate the power production. The vertical extrapolation of wind speed is based on surface boundary layer theory and depends on many parameters so that it always induces uncertainties (Kubik et al., 2011). Second, assessing the resource for prospection purposes also should be based on a long time series of observations typically of the range of 30 years, which corresponds to the climatological scale. Indeed, climatology consists in a long time series that gathers the interannual variability modes of the variable of interest. Unfortunately, continuous and homogeneous observations are usually not available on such long time periods, so that numerical modelling and downscaling is needed to obtain a modelled long time series representative of a site or a region. The wind speed obtained is very often tted with the theoretical Weibull distribution which has over the years become a standard in the wind energy industry. This distribution is based on two parameters only and is thus easy to t, which is one of the main reasons of its widespread use. It shows good results in many regions, but its use has been challenged as it is not always the best theoretical distribution to represent observations, especially in mountainous regions (Drobinski et al., 2015; Jourdier and Drobinski, 2017; Earl et al., 2013). Finally, to obtain wind energy production, the power curve of a given turbine is applied to the wind speed distribution, which results in uncertainties. Indeed, in practice, the real power obtained from a turbine di ers from the one expected from the manufacturer’s power curve, for instance due to the variations of the air density or the varying intensity of turbulence.
If the assessment of the resource in advance for prospection purposes constitutes a domain in itself, the management of installed wind energy is also a large domain of interest. Indeed, energy transition from conventional production means as coal, gas, oil, and nuclear to mainly wind and solar energy constitutes a real change of paradigm. Wind and solar power production is naturally variable and hard to predict whereas conventional plants are much easier to control. The variability of the resource at di erent timescales raises many issues related to the economic viability of producers, the management of the supply and demand balance, but also to turbines maintenance planning, turbines safety, network safety etc. (Table 1.1).

Strategies for forecasting wind energy

State of the art

Several forecasting problems in the wind energy sector can be related to di erent scales of the atmospheric variability (Table 1.1). Di erent strategies for accurately forecasting wind speed and power have been developed depending on these di erent spatio-temporal scales. These strategies can usually be classi ed into 2 categories :
Statistical methods based on time series analysis. These methods are often based on tting relations or learning algorithms that are able to reproduce from past observations and/or explanatory variables, the variable of interest at a given horizon. Many models exist from the simplest linear regression, or autoregressive model, to much more complex models such as arti cial neural networks (ANN).
Physical methods based on numerical models that solve the physical equations driving the atmospheric motions. Wind speed and components from numerical models allows to compute wind energy production from the power curve given by wind turbine suppliers.
At very short timescales (below 30 minutes), for the safety of the electricity network, energy is exchanged on the balancing market so that ’real time’ forecasts are needed (Table 1.1 & 1.2). Turbulence in the near surface boundary layer is then of great importance when trying to forecast very short-term wind power. Persistence is a classical benchmark method for very short-term forecasts as the autocorrelation of the wind can be strong at very short-term horizons. Several statistical methods have been studied and can, in some cases, over-perform the persistence (See for instance (Dowell and Pinson, 2016; Potter and Negnevitsky, 2006; Carpinone et al., 2015)). Nowcasting is a method based on high resolution Numerical Weather Prediction (NWP) models with real-time assimilation and time extrapolation of observations. It was historically used to follow heavy precipitation events in real-time. Some tools have been developed to apply this method to wind energy forecasts. It is however expensive in terms of computing resources so that statistical methods are usually preferred in the wind energy sector due to operational constraints.
At short timescales, wind energy producers must sell energy on the day-ahead and intra-day energy market, on which energy is sold at maximum a day ahead but can also be sold from 30 minutes to several hours ahead (Table 1.1 & 1.2). Short-term forecasts of wind speed and power are thus vital for wind energy producers to operate their wind farms and sell their production in an optimal way.
Many studies focus on the short-term prediction of wind speed. Most of them use purely statistical methods fed with past observations as in Sfetsos (2002) who compare Arti cial Neural Networks (ANN) methods with Autoregressive Integrated Moving Average (ARIMA) models from 1 hour to 1 day or Gomes and Castro (2012) who also develop ANN and Autoregressive Moving Average (ARMA) models but only at 1 hour horizon or Barbounis et al. (2006) who uses ANN to forecast wind speed at 3 days horizons with hourly resolution. NWP forecasts are also found useful at this timescale. NWP predictions can be used as such (Wagenbrenner et al., 2016; Sperandio et al., 2013) or can be post-processed using statistical models (Horvath et al., 2011; Giorgi et al., 2011).
At the turbine and farm level, forecasts of sudden changes (also called ramps) of the wind speed have long been a point of concern, not only for marketing purpose, but also for turbine safety. Ramp detection is also a large eld of research and can be addressed by purely statistical methods (Wytock and Kolter, 2013; Cui et al., 2015) or NWP forecasts (Bossavy et al., 2013).
At medium-term timescales (several days to maximum 10 days), forecasting methods have also been investigated in depth. Benchmarks have been provided within the ANEMOS project (Kariniotakis and Mayer, 2004; Marti et al., 2006) as well as within the International Energy Agency (IEA) task 36 (Mohrlen et al., 2018). Several methods, mainly based on NWP ensemble forecast outputs, have been proposed and analysed (Taylor and Buizza, 2002; Roulston et al., 2003; Taylor et al., 2009; Wan et al., 2014; Alessandrini et al., 2015; Taillardat et al., 2016). At these timescales, NWP prediction model outputs are much more widely used because of their ability to accurately forecast relatively large-scale systems for time horizons of half a day to weeks. Moreover, studies have dealt with the assessment of proba-bilistic forecasts (Pinson et al., 2007; Mohrlen and Bessa, 2018) and the way to use them in risk assessment and decision making frameworks (Pinson et al., 2009b).
On much longer timescales and with very di erent motivations, the impact of climate change on wind speeds has also been addressed (Sailor et al., 2008; Najac et al., 2009; Pryor and Barthelmie, 2010) in order to assess trends of wind energy production for prospection purposes (Table 1.1).

Toward seasonal prediction

Whereas both relatively short and very long timescales have been thoroughly stud-ied, the intermediate timescale going from a fortnight to the seasonal horizon is a research topic for which not so many studies exist. This timescale is of inter-est for anticipating maintenance operations, and to a lesser extent for market risk management. In particular, seasonal forecasting is becoming very important for Transmission System Operators (TSOs) as the proportion of intermittent resources in the energy mix increases.
Figure 1.6 shows for a scenario of wind energy penetration (Burtin and Silva, 2015) (60% of renewables, and 280GW of onshore wind power installed in Europe) the daily wind power production computed from 30 climatic years (i.e reanalyzed years from ERA-Interim reanalysis ((Dee et al., 2011), for which the atmosphere state is estimated numerically from observations). It displays a strong seasonal vari-ability as the average capacity factor is 30% in winter and 15% in summer. However, the spread of the production amongst these 30 years is the most problematic for net-work management. Indeed, from year to year, the average daily onshore wind power in winter can vary from less than 50GW to more than 150GW.
TSOs are responsible for balancing supply and demand of energy and they are required to make seasonal projections, e.g., to guarantee the security of energy supply during the coming winter, which becomes more di cult with the increased variability of energy production. The risk of not being able to satisfy the energy demand may be quanti ed in terms of the notion of Loss of load expectation (LOLE). Quoting from (NationalGrid, 2016), the LOLE is a \measure of the risk across the whole winter of demand exceeding supply under normal operation. It gives an indication of the amount of time across the whole winter that the System Operator may need to call on a range of emergency balancing tools to increase supply or reduce demand. » For instance, a cold winter characterised by weaker winds than normal may in some cases lead to a lack of energy if not enough other production means have been made available upstream to meet the energy demands.
Figure 1.7 displays a sensitivity analysis performed before the winter of 2016/2017
Figure 1.6: Variability and dispersion of the capacity factor at the seasonal and interannual scale – EDF scenario of 60% REN in the European energy mix (Burtin and Silva, 2015)
by the European Network of Transmission System Operators for Electricity (ENTSOE), here for France and for the second week of January 2017 speci cally. It uses 14 cli-matic years to compute likely consumption and wind energy production. Informa-tion about the availability of other means of production for this winter, like nuclear plants in France, also plays a signi cant role in this sensitivity analysis. It shows that for low temperature and low wind energy capacity factor risks of de cit exist with the current European energy mix even after importing electricity from other countries (ENTSOE, 2016). It is thus essential to produce informative forecasts of surface wind speed at this timescale. Here, meteorological information comes only from a limited climatology (14 years). Note that we present here the risk of lower than expected production which is of high concern for TSOs, but the inverse risk of higher production than consumption is also hazardous as it may result in sharp drops of electricity prices.
In France, RTE (Reseau de Transport d’electricite) uses essentially the climato-logical surface wind speed to estimate the production at the seasonal scale. Indeed, at such long-term timescales, predictability of the weather is an open question, and it is particularly the case for surface variables which are in uenced by many small scale phenomena.
Nevertheless, some studies show good results in forecasting the monthly mean wind speed at several observation sites by using Arti cial Neural Network models (ANN) (Bilgili et al., 2007; More and Deo, 2003; Azad et al., 2014), giving an accu-rate trend of the wind speed a season ahead, but a limited information on the wind variability at higher frequency. Other authors forecasted daily mean wind speed at the seasonal scale using ANN (Azad et al., 2014; Wang et al., 2015; Guo et al., 2012) allowing to gather more information on the wind variability inside a given season , and also allowing to evaluate the energy production. Azad et al. (2014) interestingly decompose the wind speed signal at di erent scales (namely the yearly, monthly, and daily trends). Wang et al. (2015) uses the same idea of scale decomposition by com-bining a trend component with a seasonal component together modulated by higher frequency variations of the wind speed signal. As ANN behaves like a black box fed with data, the results are di cult to explain physically. Moreover, each method focuses on di erent observation sites, thus making comparisons di cult. In addi-tion, these studies provide ’point forecasts’, which give one value for the wind energy production at the seasonal horizon, but do not consider the uncertainty on the fore-cast (as a rule, forecast uncertainty is di cult to quantify with neural networks since the underlying probabilistic model is not easy to de ne). At such timescales, the idea of point forecast is very questionable due to the dominant chaotic nature of the atmospheric system at the timescale exceeding typically 10 days (Kalnay, 2003).
At this long-term horizon, the concept of probabilistic forecast therefore gains sense, not only because of the uncertain nature of the forecast, but also because the decision making process is based on probabilities. Decision processes may be of several nature. At the seasonal scale, on the producers’ side, turbines maintenance scheduling on days when production is expected to be lower than normal is a good example of a decision making process. On the side of TSOs, the amount of emergency production means needed to overpass a given risk of imbalance between supply and demand can be cited.
Even though there are few works on seasonal forecasts for surface wind speeds, seasonal forecasting of other meteorological quantities is a popular research topic with continuous improvement. For example, there have been many works on seasonal forecasts of recurrent oscillating patterns in the atmosphere, such as the El Nino which has strong impacts on the weather variability mainly in the paci c region, but also at the global scale (Owen and Palmer, 1987; Cassou, 2008). Its impacts on weather predictability have been highlighted especially in the tropics (Luo et al., 2005). Other recurrent oscillating patterns in the Northern hemisphere are related to European atmospheric circulation variability (Casanueva et al., 2014; Folland et al., 2008). Predictability of such oscillations has shown good skill (Dunstone et al., 2016; Smith et al., 2016) so that they may inform on the atmospheric circulation variability at the scale of the month and eventually the season (Davies et al., 1997; Rodwell et al., 1999; Johansson, 2006; Weisheimer et al., 2017). Particularly, the North Atlantic Oscillation (NAO) has strong impact on temperature, precipitation, wind speed in Europe as it is related to the storm track which is very active in winter (Lau, 1988; Rogers, 1997; Trigo et al., 2002; Scaife et al., 2014). Skill of ensemble forecasts systems in predicting NAO has been demonstrated by Scaife et al. (2014), as shown in Figure 1.8 which highlights that depending on the forecast ensemble size the correlation between observed and forecasted NAO seasonal index can be as much as 0.6 and theoretically may reach almost 0.8.
More recently, NWP seasonal ensemble forecasting systems have been shown to carry valuable information even at seasonal timescales and for surface variables linked to wind, solar, hydro power, and electricity demand (Dubus, 2012; Krakauer and Cohan, 2017; Torralba et al., 2017; Clark et al., 2017; Vitart and Robertson, 2018). Dubus (2012) shows that using European Center of Medium-range Forecast (ECMWF) monthly forecasts of surface temperature in France allow to be more accurate than forecast references (comparable to climatology) very often up to week 2, and sometimes to week 3 or 4. It is also shown that river discharge essential for the operation and planning of hydroelecricity can be linked to large-scale atmospheric circulation via an analog method which results on average in better skill scores than climatology. Krakauer and Cohan (2017) investigate the monthly based correlation between wind, solar energy and typical large scale atmospheric patterns, at the global scale. They show that the interannual variability of wind and solar energy resource can be related to these large-scale atmospheric patterns. Clark et al. (2017) show that, at the scale of Europe, the correlation between monthly mean 10m wind speed and temperature with the forecasted monthly index of NAO is signi cant. This suggests that useful forecasts could be obtained through this relationship. The NWP model forecasts assessed are shown to give more valuable signal in the West of France and over the North Sea compared to other regions. Torralba et al. (2017) assess the ECMWF seasonal ensemble forecasts skill for forecasting the seasonal mean of the surface wind speed in winter, at a global scale. The study shows that, after bias-correction and calibration of the ensemble, reliable forecasts of the seasonal mean of the surface wind speed are available in di erent regions of the world. Forecast skill is demonstrated especially in the tropics, but also at mid-latitude, in the North Atlantic region where the installed capacity is important.

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Objectives of the work

The general problem raised in this work is to know whether seasonal ensemble fore-casts from NWP models allow to go further than the current climatological approach to forecast the wind energy resource, production, and potential risk of imbalance be-tween production and consumption at the seasonal scale.
As explained, at the seasonal scale, the main accurate information we can expect from NWP forecasts is the representation of the large-scale ow. Especially, they should have skill in forecasting large-scale atmospheric recurrent patterns such as the NAO which strongly in uence the European climate, and in particular the surface wind speed.
In this context, we de ne three main objectives for the thesis :
The rst aim is to relate the surface wind speed in France to the large scale circulation of the atmosphere. This relation will serve to estimate part of the variability of the surface wind speed from information on the large scale atmospheric state. More particularly, we want to show that a major part of the interannual variability of the surface wind speed in France is explained by the large scale ow.
Second, the thesis aimed at showing that the information on the large scale at-mospheric circulation contained in seasonal ensemble forecasts provides useful information on the surface wind speed, on monthly to seasonal timescales.
The third objective is to show that the approach described above can be used directly for assessing the risk of imbalance between consumption and produc-tion at the seasonal horizon. This implies to de ne risk indicators that quantify the potential imbalance between production and consumption, and to develop a methodology to estimate the risk from seasonal forecasts.
Finally, while the central aim of the thesis has focused on seasonal forecasting, a complementary objective has been to intiate a comparison between modeled winds and observed winds. A rst aim has been to test, for one location, how accurate the modeled winds are, and a second aim has been to explore how much information could be gained by post-processing the model output (downscaling).

Outline

Chapters 2 and 3 adress the rst and second objectives. They describe two method-ologies to model the relationship between large scale circulation patterns and local surface winds and to obtain, from seasonal forecasts information, the likely surface winds at locations in France.
In the second chapter we model the local surface wind speed distribution in the parametric setting, by assuming that it follows the two-parameter Weibull law. We show that the models are more accurate than the climatology in some regions and seasons. The study also highlights that the hypothesis of theoretical Weibull distri-bution leads to errors in the representation of the wind speed distribution. Comput-ing the capacity factor from the obtained distributions shows that the wind power output is overestimated by all methods including parametric and non-parametric climatology. However, it is also shown that no valuable signal of the large-scale circulation variability remains in the forecasted ensemble mean after at most one month.
In the third chapter, we use a non-parametric method to reconstruct and forecast the daily wind speed distribution from a fortnight to 3-month horizon in France using again the information coming from the large-scale circulation of the atmosphere. The conditional probability density function of the wind speed knowing a single index which summarises the information on the large scale circulation of the atmosphere is estimated by kernel density estimation. The model is shown to be well calibrated as well as more accurate than the seasonal climatology in reconstructing wind speed distribution. While applying the method to seasonal forecast ensemble, we show that post-processing allows to recalibrate and sharpen the ensemble so that even at the seasonal scale, the method can be more accurate than climatology for speci c regions and seasons.
In the fourth chapter, we adress the third objective and turn to modelling the risk of imbalance between consumption and wind energy production at the seasonal scale, in winter and fall. Two types of risk measures are de ned : one measures the probability of deviation of consumption and production from their climatolog-ical means, and the other measures the risk of encountering extreme situations of imbalance. Using again the valuable information on the large-scale circulation, we build the seasonal joint distribution of the national consumption and the national wind energy production to compute the rst risk measure. It is shown that we ac-curately reconstruct the variability of the risks of imbalance. Signi cant deviation from the climatological state are well highlighted by the model, especially in winter, when the model retrieves 75% to 80% of the deviations. In fall, signi cant devia-tions from climatology are less frequent, and the model performs worse. The second risk measure is estimated by quantile regression. Reconstructed quantiles are shown to be reliable, and the model highlights risky extreme events that could be very persistent.

Table of contents :

1 Introduction 
1.1 Renewable energy growth
1.2 Variability and its implications
1.2.1 Atmospheric variability
1.2.2 Implication for energy management
1.3 Strategies for forecasting wind energy
1.3.1 State of the art
1.3.2 Toward seasonal prediction
1.4 Objectives of the work
1.5 Outline
1.6 Description of the Data
1.6.1 ERA-Interim Reanalysis
1.6.2 ECMWF seasonal ensemble forecasts
1.6.3 Principal component analysis
2 Modelling the variability of wind energy resource 
2.1 Introduction
2.2 Data & Methods
2.2.1 Data
2.2.2 Methods
2.3 Evaluating the reconstruction methods
2.3.1 Performance of methods for wind speed distribution reconstruction
2.3.2 Performance of the methods for estimating the capacity factor
2.4 Towards monthly and seasonal forecast of the wind speed distribution
2.5 Conclusion
3 Probabilistic forecasts of the wind at the seasonal scale 
3.1 Introduction
3.2 Data & Methods
3.2.1 Data : ECMWF reanalysis and seasonal ensemble forecasts
3.2.2 Methods
3.3 Evaluation and optimization of the model
3.3.1 Diagnostic tools
3.3.2 Optimization of the model
3.4 Probabilistic wind speed forecasting at the monthly and seasonal horizon
3.4.1 Methodology
3.4.2 Results
3.5 Conclusion
4 Measuring the Risk of supply and demand imbalance at the Sea- sonal scale 
4.1 Introduction
4.2 Data & Methodology
4.2.1 Data
4.2.2 Modelling the joint PDF of Consumption and Production
4.2.3 Risk measures
4.3 Estimation of the risk measures
4.3.1 Modelling the risk of deviation from climatological means
4.3.2 Modelling the risk of extreme situations
4.4 Explanatory value of the rst PCs
4.5 Discussion and concluding remarks
5 From Numerical Weather Prediction outputs to accurate local sur- face wind speed 
5.1 Introduction
5.2 Data and Methodology
5.2.1 Data
5.2.2 Methodology
5.3 The relationship between analysed and observed winds
5.3.1 10m/100m wind speed variability comparison
5.3.2 Reconstruction of the 10m/100m observed wind speed using NWP outputs
5.4 Summary and concluding remarks
Conclusion

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