European Wind Energy Conference, February-March 2006, Athens. Subject. Meteorology: forecasting, resource assessment methods & satellite observation

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1 European Wind Energy Conference, February-March 06, Athens Subject. Meteorology: forecasting, resource assessment methods & satellite observation Modelling the Integration of Mathematical and Physical Models for Short-term Wind Power Forecasting Alexandre Costa 1 Antonio Crespo 2 Jorge Navarro 3 alexandre.araujo@ciemat.es crespo@enerflu.etsii.upm.es jorge.navarro@ciemat.es araujo@enerflu.etsii.upm.es Ana Palomares 4 Henrik Madsen ana.palomares@ciemat.es hm@imm.dtu.dk 1,2 Laboratorio de Mecánica de Fluidos Departamento de Ingeniería Energética y Fluidomecánica, ETSII, Universidad Politécnica de Madrid - UPM C/José Gutiérrez Abascal, 2, 28006, Madrid, Spain Tel.: / Fax.: ,3,4 Wind Energy, Division of Renewable Energies, CIEMAT Av. Complutense, 22, Ed. 42, 280, Madrid, Spain Tel.: / Fax.: Informatics and Mathematical Modelling - IMM, Technical University of Denmark - DTU Richard Petersens Plads, Building 321, Office 019, 2800, Kgs. Lyngby, Denmark Tel.: / Fax.: Abstract Mathematical/statistical models based on purely autoregressive, fuzzy autoregressive and neural networks are being tested for wind power forecasting. Also, ical/meteorological models based on geostrophic wind estimates are being conjugated with a proposed sectorial discretization of the problem, in which the microscale orographic corrections and stability (non-neutral regime) corrections are applied only for those sectors where these corrections are capable of decreasing the prediction error. The time-scales (time-steps and horizons) have been defined and the parameter estimation and architecture optimisation methods have been developed. The Project focuses on short-range prediction oriented to the sales in the spot market, power system management and scheduling some maintenance tasks in the wind farms. The aim is to develop a real time computational tool in which the ematical and ical forecasts are related in order to track always the best estimate. In this way, advanced statistical tools are being employed to find the best functions relating both forecasts, thus minimising the error of the final model. Results on a wind farm (from the company Acciona Energía) at the Northeast region of Spain are presented (32 machines of 660 kw). Hourly data of one year was selected, considering wind speed and direction from a reference mast and power output from all wind turbines. Apart from these measured data, reanalysis data from the ERA Project (ECMWF) are employed to the validation of the ical models. The models are tuned to use the meteorological forecast data in an optimal way. 1. Introduction This work tries to give a contribution to the development of a research field poorly explored yet: the true integration between two distinct and complementary research lines, ematical/statistical and ical/meteorological models for short-term prediction of wind farms output. In this sense, one of the first attempts is being carried out in Denmark [Madsen et al., 00a,b; Giebel et al., 01; Landberg, 01].

2 The aim of the present work is the development of a final model (and corresponding computational tools) integrating both ematical and ical models for short-term prediction. For the purposes of this work, short-term must be understood as a forecast horizon of 2 or 3 days ahead typically, with a time-step of 1 or 3 hours. The developed models and tools are basically oriented to: management of systems with wind farms, optimising the planning for the other sources (e.g., thermal units schedule) in order to increase fuel saving, to decrease the spinning reserve etc.; requirements for the wind energy sales in the spot market; scheduling of some maintenance tasks in wind farms. The final model [Costa, 0] is composed of two models of different natures: ematical/statistical and ical/meteorological. Both models (ematical and ical), running simultaneously, produce forecasts of the total wind farm output (cf. Figure 1). The final output from the final model is then a function of these forecasts, a function modelled by a proposed model called here best intersection point tracking (b.i.tracking) [Costa et al., 04] for a real-time operation. Regarding the ematical model [Costa et al., 03], three structures varying from the most simple to the most complex were evaluated: autoregressive models [Box and Jenkins, 1976; Bossanyi, 198; Ljung, 1987; Torres et al., 0], fuzzy logic based models [Sugeno and Yasukawa, 1993; Kariniotakis et al., 1996] and neural networks [Haykin, 1994; Castillo et al., 1999]. The ematical/statistical models (here, purely time series based models, without meteorological data as inputs) are used because of their capacity of extracting information from the time series (on-line measurements) and (with this information) generating low error estimates in a shorter forecast horizon (up to 3 or 6 hours ahead). Regarding the ical model [Costa, 0], also three different structures (here, called as mod1, mod2 and mod3) were evaluated, based on the downscaling of geostrophic wind estimates [Landberg, 01]. All these structures make use of meteorological data as inputs and the main differences between them are related to the stability regime and the definition of the inputs to the power curve modelling. With respect to the stability, mod1 is based on neutral stability, whereas mod2 and mod3 are thought for non-neutral. Concerning the power curve modelling, mod1 and mod2 are based on the conversion of wind forecasts at the site of an anemometrical reference mast into forecasts of the wind farm total output power. In its turn, mod3 is based on the individual conversion of wind forecasts at the site of a wind turbine into forecasts of the turbine output power, being the wind farm total output power computed as the sum of that of all turbines. The ical/meteorological models are used because of the wider range of their forecast horizon, typically up to 48 or 72 hours ahead. In this work, as a first approach, only the outputs from the two structures presenting the best results (one from the three ematical/statistical models and the other from the three ical/meteorological models) are considered as inputs to the final model. In a future approach, all the six structures will be proven as an ensemble. 2. b.i.tracking ** The ematical/statistical models (here, purely time series based models, without meteorological data as inputs) generally present lower errors within a shorter forecast horizon (up to a quarter of a day typically). Beyond this shorter horizon, these models usually present considerably lower performance. In its turn, the ical/meteorological models are characterised by a wider range of the forecast horizon, i.e., a low slope error curve. For this reason, ical/meteorological models usually overcome ematical/statistical models beyond the shorter horizon. Thus, a natural choice for a combination of both forecasts starts from a tracking of the intersection point between both error curves. After this tracking, the idea is to minimise the error of the final model, giving more emphasis to ematical forecasts below the tracked intersection point and more emphasis to ical forecasts above the referred point (cf. Figure 2). 3. Mathematical Model Three structures were evaluated on the data of one year (hourly averaged recordings) from the Aritz wind farm. In a first approach, only the power time series (total output from the wind farm) was applied as input to the models (for future improvements, exogenous variables will be tried). With respect to the training, the parameters of the autoregressive models were estimated through the adaptive recursive least mean squares method (cf. [Ljung, 1987]). The fuzzy logic based models (with autoregressive models in the conclusions) were trained with a stochastic gradient descent method (cf. [Darken and Moody, 1992]). The feedforward fully connected neural networks were trained with ** Pat Pending.

3 the error back-propagation method (cf. [Haykin, 1994]). From these structures, the best results have been obtained by the fuzzy models with an hourly time-step and a forecast horizon of h (cf. Figure 3). 4. Physical Model The three ical/meteorological structures were evaluated on the same year of data as the ematical/statistical structures, considering that the ical model was firstly checked with reanalysis data and, after this, it was tuned for operation with meteorological forecast data. Concerning the structure mod1, the approach was to get data from meteorological centres (considering them as geostrophic wind estimates) and downscale them to the level of the anemometrical reference mast of the wind farm. At this level, data were corrected for effects of the surrounding terrain (e.g., an increasing of wind speed in the top of a hill). Both wind speed and direction were corrected for the effect of the local orography and, after this, converted into farm output power through a sector-wise power curve modelling. The structure mod2 was the same as mod1, except that a non-neutral model was employed to the downscaling to the level of the anemometrical reference mast. The structure mod3 was based on the employment of mod2 to the downscaling to the level of all individual wind turbines in the farm, being considered the wake effects between rotors [Crespo et al., 1999]. The individual wind turbine output power was computed through a sector-wise power curve modelling. The farm output power was the sum over all turbines. Here, the problem was divided into 12 sectors with a width of o, being the local orographic corrections and the stability corrections applied only for those sectors where these corrections were able to decrease the prediction error. From these ical/meteorological structures, the best results (regarding power prediction) have been obtained by mod1 with the following time-steps: 03/to/24/by/03 and 24/to/36/by/06 (cf. Figure 4).. Final Model Here, the b.i.tracking is proposed as the key for the integration of both ematical and ical models into a final model, being the major difficulty for the integration between the ematical and ical models the fact that the former performs 24 launches per day (at each hour), while the last performs only two launches per day (at 00 and 12 h). Thus, a model developed to integrate both types of forecast must be synchronized with the instants in which both models actualize their forecasts simultaneously. Starting at the time instant 00 h (hereafter, called launching 1), the ematical model launches forecasts for the instants h, while the ical model launches forecasts for the instants h. At the time instant 01 h (hereafter, called launching 2), the ematical model actualizes its forecasts, launching new forecasts for the instants h, while the ical model maintains its forecasts made in the launching 1. The ematical model follows actualizing its forecasts throughout launchings more (hereafter, called launching 3 to launching 12), while the ical model maintains its forecasts made in the launching 1. At the time instant 12 h, the ical model turns to actualize its forecasts together with the ematical model. In this way, a cycle for the occurrences of a simultaneous actualization from both models is established, with a period of 12 launchings (cf. Table 1). Therefore, the launching made at the instant 12 h is the same as launching 1, the launching made at the instant 13 h is the same as launching 2 and so on. For each one of the above referred 12 launchings in the period, the role of the b.i.tracking is to make a combination of the ematical and ical forecasts just at the moments in which both forecasts coincide. For example, considering launching 1 and remembering that this launching is composed by the predictions made at the instants 00 and 12 h, the combination is carried out only at the instants h (for predictions made at the instant 00 h) and h (for predictions made at the instant 12 h). This combination is taken into account by the final model, whenever it presents a smaller error than the purely ematical and purely ical forecasts. The final model was thought to produce the first 6 steps ahead (at least) with an hourly time-step (holding in mind, for instance, the requirements of the Spanish intra-day market [OMEL, 0]). The combination made by the b.i.tracking is employed by the final model in order to improve the forecasts in a medium horizon (generally, from 3 to 9 hours ahead). In a short horizon, the purely ematical forecasts are adopted by the final model (generally, from 1 to 3 hours ahead). In a long horizon, the purely ical forecasts are adopted by the final model (generally, from 9 up to 36 hours ahead). In order to realize the b.i.tracking, neural networks were proven, being considered one network for each one of the 12 launchings. 4 architectures were evaluated (from the simplest with only 1 neuron linearly activated to the most complex presenting the layer structure ---1 with sigmoidal functions in the hidden layers and a linear function in the output layer). The results for each one of the 12 launchings and from each one of the 4 architectures

4 proven are presented in Figure. These architectures were proven to combine the outputs from the ematical and ical structures which achieved the best overall performance concerning the prediction of the wind farm total output power: Fuzzy(3) and mod1 hereafter, these structures will be simply called as and Remembering that the combination is taken into account only when it presents a smaller error than the purely ematical and purely ical forecasts, it can be viewed that the architecture obtained the best results for all launchings. For instance, for launching 1 (Figure a), the final model predicts using the following forecasts, being the steps ahead defined with regard to the actualization of (cf. Table 1): from (Fuzzy(3)), for the steps ahead h; from b.i.tracking (), for the steps ahead h; from (mod1), for the steps ahead h. It must be observed that the subset of the first 6 steps ahead (formed by the forecasts taken from and the forecast for the step 06 h taken from the b.i.tracking) has an hourly time-step, in accordance with one of the requirements for the final model (exigency from the Spanish intra-day market). Now, considering the example of launching 2 (Figure b), the final model predicts using the following forecasts, being the steps ahead defined with regard to the actualization of (cf. Table 1): from (Fuzzy(3)), for the steps ahead h; from b.i.tracking (), for the steps ahead 0 08 h; from (mod1), for the steps ahead h. Again, it must be observed that the subset of the first 6 steps ahead (formed by the forecasts taken from and the forecast for the step 0 h taken from the b.i.tracking) has an hourly time-step. Comparing, for instance, the graphs of launching 1 (Figure a) and launching 2 (Figure b), it can be observed that the takes advantage from an improvement of in a medium horizon. In launching 1, and present the same Mean Squared Error (MSE) at the step ahead 06 h (around 27 MW 2 ) and produces an MSE about MW 2. In this case, both models ( and ) have launched their forecasts at 00 h and the steps outside and inside the square brackets in the figure are the same. In launching 2, maintains its MSE from the forecasts launched at 00 h (the steps outside the square brackets are related to this past launching of at 00 h). In its turn, actualizes its forecasts, launching new forecasts at 01 h (the steps inside the square brackets are related to this real-time launching of at 01 h). This actualization results in a reduction of the MSE of and takes benefit from this, decreasing its MSE from MW 2 to 18 MW 2 at the step ahead 0 h (related to the real-time launching of ). 6. Conclusions and Perspectives Here, the proposed final model achieved an important improvement over the persistence in the whole horizon from 1 to 36 hours ahead (being emphasized that the persistence follows as the most extended reference model to contrast new proposed models, despite the polemics about the adequacy of the employment of persistence as a reference model). In a short horizon (typically, from 1 to 3 hours ahead), the ematical/statistical models overcame all other proven models, being the fuzzy logic based models slightly superior to the feedforward neural networks and substantially superior to the autoregressive models in the Aritz wind farm (cf. [Costa, 0]). In a medium horizon (typically, from 3 to 9 hours ahead), the proposed b.i.tracking (combination of both ematical and ical forecasts) presented a significant reduction of the MSE with regard to the purely ematical and purely ical forecasts. In a long horizon (typically, from 9 up to 36 hours ahead), the ical/meteorological models overcame all other proven models. With respect to these latter models, the comparison between mod1 (purely neutral) and mod2 (non-neutral) indicated that the neutral model can be improved by a non-neutral approach to predict the wind, if a sector-wise division of the problem is carried out. Nevertheless, with respect to power prediction (i.e., after the power curve modelling see Figure 1), it was observed that mod1 achieved slightly better results than mod2 and both structures mod1 and mod2 presented sensibly better results than mod3 (cf. [Costa, 0]). Regarding the power predictions from mod1 and mod2, the power curve modelling (here, implemented through feedforward neural networks) demonstrated an incapability of taking advantage from the slight superiority of the wind predictions from mod2. This seems to be due to the fact that mod2 indeed presented an

5 improvement only for low wind speeds (a range of speeds around the cut-in of the wind turbines). For high wind speeds, mod2 (non-neutral approach) behaves as mod1 (neutral approach). Concerning mod3, the worst results presented by this model are due to the fact that, in the absence of wind observation at the location of the wind turbines, the sectorial assessment of the error for stability, orographic and wake corrections could not be carried out for each one of the turbines. Thus, considering the proximity between the reference mast and the wind turbines in the farm (the most distant turbine is at 2 km from the reference mast), mod3 was based (for all wind turbines in the farm) on the employment of the same set up as for mod2 (a part from the wake corrections for all sectors), remembering that the set up for mod2 was based on the sectorial assessment (of the error) with respect to the location of the reference mast. During the development of the methods and methodologies employed in this work, some lessons were learned. From these lessons, some topics are clearly identified as an object for immediate future researches, in order to improve the developed models and to start up an operational (on-line) tool, such as: methods which are able to provide reliable estimates of the uncertainty of the predictions; development of probabilistic models (e.g., Bayesian networks, ensemble forecasts based models); MOS techniques; further research on the adaptive parameter estimation, since the models have to automatically adopt to changes in the farm and in the surroundings; development of accurate upscaling methods; development of more accurate downscaling methods, for neutral as well as non-neutral ; employment of new orographic models, more accurate on complex terrain; employment of mesoscale models in order to increase the spatial and time resolution of the meteorological services, taking into account local thermal phenomena (neglected by microscale and macroscale models); tuning of the models for operational forecast data; research on meteorological data from distinct services (ECMWF, NCEP, INM etc.); development of accurate power curve models; accurate recordings of meteorological variables at the locations of the wind turbines in the farm; utilization of wind observations and meteorological data as exogenous variables for the ematical/statistical models; methods for the on-line standardization of the time series; methods for the definition of the order of ematical/statistical models (e.g., embedding theory). Acknowledgments The authors would like to express their gratitude to the authorities from the company Acciona Energía, European Centre for Medium-Range Weather Forecasts and the Spanish National Institute of Meteorology for providing the data here employed. References Bossanyi, E. (198): Stochastic wind prediction for turbine system control, In: Proceedings of 7th British Wind Energy Association Conference, Oxford. Box, G. and Jenkins, G (1976): Time series analysis: forecasting and control, Holden-Day, Oakland. Castillo, E.; Cobo, A.; Gutiérrez, J. and Pruneda, E. (1999): Functional networks with applications. A neural based paradigm, Ed. Kluwer Academic Publishers. Costa, A.; Crespo, A. and Migoya, E. (03): First results from a prediction project, In: Proceedings of European Wind Energy Conference, Madrid. Costa, A.; Crespo, A.; Feitosa, E.; Navarro, J.; Jiménez, P.; García, E.; Madsen, H.; Nielsen, H. and Nielsen, T. (04): Mathematical and ical wind power forecasting models: a proposal for the UPMPREDICTION project, In: Proceedings of Second Joint Action Symposium on Wind Forecasting Techniques, International Energy Agency (IEA), Lyngby.

6 Costa, A. (0): Mathematical/Statistical and Physical/Meteorological Models for Short-term Prediction of Wind Farms Output, PhD Thesis, Escuela Técnica Superior de Ingenieros Industriales, Universidad Politécnica de Madrid. Crespo, A.; Hernández, J. and Frandesen, S. (1999): Survey of modelling methods for wind turbine wakes and wind farms, In: Wind Energy, 2, pp.1-24, John Wiley & Sons. Darken, C. and Moody, J. (1992): Towards faster stochastic gradient search, In: Advances in Neural Information Processing Systems 4: 09-16, Morgan Kaufmann, San Mateo. Giebel, G.; Landberg, L.; Nielsen, T. and Madsen, H. (01): The Zephyr-Project The next generation prediction system, In: Proceedings of European Wind Energy Conference, Copenhagen. Haykin, S. (1994): Neural networks a comprehensive foundation, Ed. Prentice-Hall International. Kariniotakis, G.; Nogaret, E. and Stavrakakis, G. (1996): A fuzzy logic and a neural network based wind power forecasting model, In: Proceedings of European Union Wind Energy Conference, Göteborg. Landberg, L. (01): Short-term prediction of local wind, RIS -R-702(EN), RIS National Laboratory, Roskilde. Ljung, L. (1987): System identification theory for the user, Ed. Prentice-Hall International. Madsen, H.; Nielsen, T.; Nielsen, H. and Landberg, L. (00a): Short-term prediction of wind farm electricity production, In: Proceedings of European Congress on Computational Methods in Applied Sciences and Engineering, Barcelona. Madsen, H.; Landberg, L.; Giebel, G.; Nielsen, T. and Nielsen, H. (00b): Zephyr and short-term wind power prediction models, In: Proceedings of Wind power for the 21st century, Kassel. OMEL (0): Sugeno, M. and Yasukawa, T. (1993): A fuzzy-logic-based approach to qualitative modelling, In: IEEE Transactions on Fuzzy Systems 1(1). Torres, J.; García, A.; De Blas, M. and De Francisco, A. (0): Forecast of hourly average wind speed with ARMA models in Navarre (Spain), In: Solar Energy 79: 6-77, Ed. Elsevier.

7 meteorological services Figure 1. All the structures proven for the composition of the final model. geostrophic drag law under neutral surface wind under neutral geostrophic drag law under nonneutral surface wind under non-neutral geostrophic drag law under nonneutral surface wind under non-neutral autoregressive models fuzzy logic neural networks local orographic corrections at the site of the reference mast local orographic corrections at the site of the reference mast local orographic corrections at the sites of the wind turbines on-line measurements local wind at the site of the reference mast local wind at the site of the reference mast local wind at the sites of the wind turbines wake effects statistical model exogenous variables power curve modelling power curve modelling power curve modelling wind power forecasts Mathematical Model wind power forecasts wind power forecasts wind power forecasts mod1 mod2 mod3 Physical Model b.i.tracking final forecasts

8 MSE b.i.tracking 3 9 ematical/statistical step ahead (h) ical/meteorological Figure 2. The idea behind the b.i.tracking. MSE (MW 2 ) persist fuzzy(3) 0 0 (a) step ahead (h) improvement over persistence (%) 0 0 (b) step ahead (h) Figure 3. (a) MSE for persistence and Fuzzy(3); (b) improvement of Fuzzy(3) over persistence on the MSE basis persist mod MSE (MW 2 ) 0 improvement over persistence (%) (a) step ahead (h) (b) step ahead (h) Figure 4. (a) MSE for persistence and mod1; (b) improvement of mod1 over persistence on the MSE basis.

9 [3] 6 [6] 9 [9] [2] 6 [] 9 [8] [1] 6 [4] 9 [7] 12 [] 4 MSE (MW 2 ) 6 [3] 9 [6] 12 [9] 6 [2] 9 [] 12 [8] 0 6 [1] 9 [4] 12 [7] [] 9 [3] 12 [6] [9] 9 [2] 12 [] [8] 9 [1] 12 [4] [7] 18 [] 12 [3] [6] 18 [9] 12 [2] [] 18 [8] [] step-ahead (h) 12 [1] [4] 18 [7] 21 [] Figure. From the left to the right and up to down: (a) to (l): launching 1 to launching 12.

10 Table 1. Launchings of the model (hours in red) and model (hours in blue) (the hours in bold/underline are the instants in which the forecasts are launched) launching launching launching launching launching launching launching launching launching launching launching launching launching