Forecasting models of wind power in Northeastern of Brazil

Abstract—Wind Power forecasting is extremely important to assist in planning and programming studies for the operation of wind power generation. Several studies have shown that the Brazilian wind potential can contribute significantly to the electricity supply, especially in the Northeast Brazil, where winds present an important feature of being complementary in relation to the flows of the San Francisco River. However, using wind power to generate electricity has some drawbacks, such as uncertainties in generation and some difficulty in planning and operation of the power system. This paper presents actual results of wind power forecasting for two parks in the region of northeastern Brazil with four different models. Models that perform power generation forecasting using the forecasted wind speeds and the wind power curve of the park are called Wind to Power (W2P) and models that perform power generation forecasting using the historical power generation of the park are called Power to Power (P2P). The models perform forecasting of wind power generation with 6 hours ahead, discretized by 10 minutes and with 5 days ahead, discretized by 30 minutes. Models that directly predict the wind power (P2P) got the best results. These models were more suitable for use in the power systems operation planning considering the wind parks analyzed in northeastern Brazil.I.I NTRODUCTIONmong all alternative energy sources currently explored, wind energy is one of the most successful. One reason for this is the incentive policy by various countries, which ensures the purchase of electricity produced from wind power, even if it does not offer competitive prices. Germany and Denmark were the first countries to adopt policies to encourage the development of wind generation, followed by several countries, including Brazil. With the creation of the Incentive Program for Alternative Sources of Electric Energy (PROINFA) [1] in Brazil, around 1000 MW have been installed in wind farms by 2011. Note that the Manuscript received February 28, 2013.Ronaldo R. B. de Aquino, is with the Federal University of Pernambuco- UFPE, Academico Helio Ramos s/n, Cidade Universitária, Cep: 50.740-530 – Recife – PE – Brazil (corresponding author to provide phone: 55-81-21268986;e-mail: rrba@ufpe.br).Teresa B. Ludermir, is with the Federal University of Pernambuco-UFPE (e-mail:tbl@cin.ufpe.br).Otoni Nobrega Neto, is with the Federal University of Pernambuco- UFPE (e-mail:otoni.nobrega@ufpe.br).Aida A. Ferreira, is with the Federal Institute of Education, Science and Technology of Pernambuco-IFPE, Av Professor Luis Freire, 500, Cidade Universitaria, Cep:50.740-530 – Recife – PE – Brazil (e-mail: aidaferreira@.br).Milde M. S. Lira, is with the Federal University of Pernambuco -UFPE (e-mail: milde@ufpe.br).Manoel A. Carvalho Jr, is with the Federal University of Pernambuco- UFPE (e-mail:macj@ufpe.br). wind energy is the one with the highest growth in northeastern Brazil from 796 MW in 2011 to 6,405 MW in 2016, which corresponds to a growth of 4.9% to 24.4% of the total installed power [2]. This demonstrates the importance of wind generation for the electric and energetic operation planning of the Brazilian interconnected electric system.Because of the importance of wind generation in Europe, the ANEMOS project was created. The reports [3] and [4] have presented the state of the art and a protocol for models evaluation for wind power forecasting (WPF), respectively. The use of wind energy for electric power generation presents some inconveniences related to the uncertainties in the generation. Such inconveniences are basically caused by the variability of the wind speed. Therefore, the application of tools or techniques that are able to forecast the energy to be generated by those sources is essential to an appropriate integration of the wind source with the electric power system [5] and [6].As shown in [7], the time frontiers that separate the different time horizons are not consensus defined for the WPF problem, but usually can be classified in three categories: the very short term limited to four hours; the short term limited to fourth-eight hours; and the medium term from very short term up to seven days ahead.Many researchers, motivated by the importance of wind power forecasting for the integration of this energy in the electrical system, developed models for the three forecasting horizons using many techniques of artificial intelligence.A very-short term WPF was presented in [8], using as solution technique, a data mining approach with a forecasting of four hours ahead. In [9], a very-short term WPF was presented for forecasting three hours ahead, using multilayer perceptron (MLP), wavelet transform (WT), adaptive-network-based fuzzy inference systems (ANFIS) and particle swarm optimization.A short term WPF was shown in [10], [11] and [12]. In the first article, the authors used MLP, wavelet transform and neuro-fuzzy system to perform a forecasting of 24 hours ahead. In the second, the authors used a numerical weather prediction (NWP) combined with a radial basis function (RBF) network and fuzzy logic to perform a forecasting of 48 hours ahead. In the third, the authors used a reservoir compute approach to perform a forecasting of 24 hours ahead.A medium term WPF, in accordance to [7], was developed in [13] and [14] using locally recurrent multilayer networks combined with NWP as forecasting model.This paper shows a very-short term WPF for forecasting 6 hours ahead and a medium term WPF for forecasting 5 daysForecasting Models of Wind Power in Northeastern of Brazil Ronaldo R. B. de Aquino, Teresa B. Ludermir, Otoni Nobrega Neto, Aida A. Ferreira,Milde M. S. Lira, Manoel A. Carvalho Jr.Aahead, both based on neural network approach.The structure of this paper is as follows: in section II, the composition and analysis of the wind speed time series are shown. Then, in section III, the data preprocessing is presented. The study and development of the models are accomplished and analyzed in section IV. Comparisons between forecasts obtained with the proposed and reference models are done in section V. Finally, in section VI, conclusions are drawn.II. A RRANGEMENT FOR THE TIME SERIESReal data from two wind farms (Park A and B) located in two states of northeastern coast line Brazil are used in this work. The time series available for model development were: number of active machinery, wind speed, temperature (in Celsius), pressure, direction, and average wind power. All variables were provided in intervals of 4 seconds and transformed in mean values at intervals of 10, 30 and 60 minutes. Besides these data, we used time series of forecasting hourly average wind speed for the 5-day horizon, provided daily by the numerical model ETA, resulting in 120 values.Due to the low quality of the series was not possible using some of the variables, although some are of utmost importance for accuracy of the models. Thus, the models developed were based only on series of power and speed (actual and forecasting). The historical data set corresponds to the period from April 2010 to July 2012.The period used for training models that perform forecasting of wind power generation with 6 hours ahead were from 04/01/2010 to 12/31/2011. The period used for simulations were from 01/01/2012 to 07/31/2012.The period used for training models that perform forecasting of wind power generation with 5 days ahead were from 04/01/2010 to 05/31/2011. The period used for simulations was from 01/01/2012 to 07/31/2012.Fig. 1 and Fig. 2 represent the dispersion of data pairs of average wind speed (x axis) and wind power (y axis) provided by the park. The red curve is the power curve, PC(v), obtained regarded as the feature of grouping wind. The green curves are PC(v) ± 3.σ(v), where σ(v) is the standard deviation for small region centered at v. The curves were normalized by the total number of machines in eachpark.Fig. 1. Historical data of the wind speed and power generation time seriesfor the Park A.Fig. 2. Historical data of the wind speed and power generation time series for the Park B.III. D ATA P REPROCESSINGIn this section, the basic procedures for processing the wind speed data are defined before creating the proposed forecasting models.A. NormalizationThe forecasting models based on Artificial Neural Networks (ANN) demand consistent treatment of the data in order to guarantee reasonably good performance and their effective application. In general, normalization is a straightforward and effective treatment for the data [15].Normalization is carried out to assure that all variables used in the model inputs have equal importance during training; therefore the activation functions of artificial neurons are limited. In this paper, the data were normalized according to (1), also shown in [15], whose values ranged from 0 to 1.minmax min)()(X X X t X t X −−=(1)where:X and X are the wind speed time series non-normalized and normalized, respectively; max X andmin X are the maximum and the minimum absolute value ofthe wind speed time series, respectively.B. Definition of Forecast ErrorsTwo types of errors are used in this paper to illustrate the performance of the wind power forecasting model: the mean squared error– MSE, according to (2), and the normalized mean absolute error – NMAE, according to (3).,)(1)(12∑=+=N t s s k t e N k MSE(2) Where N is the number of data used for the model evaluation; k is the forecasting horizon (number of time-steps); e s (t+k ) is the error corresponding to time t+k for the wind power forecasting made at origin time t ; and s (t+k ) is the measured wind power at time t+k .,)(100)(1∑=+⋅=Nt P instPk t e P N k NMAE(3)Where N is the number of data used for the model evaluation; k is the forecast horizon (number of time-steps); e P (t+k ) is the error corresponding to time t+k for the power generation forecast made at origin time t ; and P inst is the installed wind power capacity.C. Reference Models It is worthwhile developing and implementing a wind power forecasting tool if it is able to beat reference models, which are the result of simple considerations and not ofmodeling efforts. Probably the most common reference model used in the frame of wind power prediction or in themeteorological field is the persistence model [3]. This naive predictor tool assumes that the conditions at the time of theforecast will not change. For example, if it is sunny and 40o Celsius today, the persistence method predicts that it will be sunny and 40oCelsius tomorrow. The persistence method works well when weather patterns change very little and features on the weather maps move very slowly. It also works well in places like Northeast Brazil, where summer time weather conditions vary little from day to day. The persistence forecast method tends to be used as benchmark against which all other models are compared [5]. The persistence was measured as shown in (4):),()(t y k t y PERS =+(4) Where y PERS (t+k ) is the power generation forecasting for time t+k ; and y (t ) is the measured power generation at timet . In this work, we also used the daily persistence. This model performs the prediction considering that the variable’s future value will be the same as the last one measured 24 hours before.),24()(_−+=+k t y k t y D PERS(5) IV. D EVELOPMENT OF THE F ORECASTING M ODELS In this paper models that perform power generationforecasting using the forecasted wind speeds and the windpower curve of the park are called Wind to Power (W2P)and models that perform power generation forecasting usingthe historical power generation of the park are called Powerto Power (P2P).This paper presents two different models (W2P and P2P)for the forecast of wind power generation with 6 hoursahead, discretized by 10 minutes and two different models(W2P and P2P) for the forecast of wind power generationwith 5 days ahead, discretized by 30 minutes.All of them were developed using Multi-Layer Perceptron(MLP), in accordance with ours previous experience [15]. It is important to note that this form of prediction was used because it is robust and adequate to the problem, as well as due to data quality. A more sophisticated approach could have been used [10], but the database prevented their use at this time.To perform the data handling and the development of the proposed models, MATLAB® software and the Neural Network Toolbox™ Version 6.0.2 (R2009a) were used.A. Models for 6 hours aheadThe Wind to Power forecast model for 6 hours ahead (W2P 6h ) is composed of six ANN, one for each hour. The ANN for the first hour is illustratedFig. 3. The outputs are the six 10min intervals that compose the first hour.Fig. 3. Wind to Power model with forecasting of 6 hours ahead (W2P 6h ).Where: • h – Hour of forecasting, discretized by 10 minutes. • V h-i – Actual average wind speed in the h-i time. Thisbox represents a vector with six values of 10 minutes, where i is the before quantity hours.• P h-i – Actual average active power in the h-i time.This box represents a vector with six values of 10 minutes, where i is the before quantity hours. • V p (l) – Forecasting average wind speed for the l-th output (l = 1, 2,..., 36). • P p (l) -Forecasting average active power for the l-th output (l = 1, 2,..., 36). • CM 1 –Code of the month in which the forecast is being made, first value.• CM 2 –Code of the month in which the forecast is being made, second value.• CH -Code of the forecasting first hour.The Power to Power forecast model for 6 hours ahead(P2P 6h) is composed of six ANN one for each hour. TheANN for the first hour is illustrated in Fig. 4. The outputs are the six 10min intervals that compose the first hour. Observe that the models use two fields to represent the months (CM 1 and CM 2) because they were encoded by sine V h-2V h-3 V h-24V h-25 V h-23CM 1CH CM 1and cosines. The models use the time in decimal value in the range 0 to 1.Fig. 4. Power to Power forecasting model for 6 hours ahead (P2P 6h ).B. Models for 5 days aheadThe Wind to Power forecast model for 5 days ahead (W2P 5d ) and the Power to Power forecast model for 5 days ahead (P2P 5d ) are composed of five ANN, one for each day. Fig. 5Fig. 5 and Fig. 6 show these models. The outputs are the fourth-eight 30min intervals that compose the day. It is important to note that the first 6 hours (or 12 outputs) of these models come from the six hour ahead models (W2P 6h and P2P 6h ). Where:• V pm (h ) –Forecasting average wind speed by numerical model ETA for the hour h (h = 1, 2,..., 120).• V p (l ) -Forecasting average wind speed for the l-th output (l = 1, 2,..., 240).• V (h-i ) - actual average wind speed for the hour h (h = 1, 2,..., 120 ; i = 1, 2, ..., 24).• P p (l ) -Forecasting average active power for the l-th output (l = 1, 2,..., 240).• P (h-i ) -actual average active power for the hour h (h = 1, 2,..., 120 ; i = 1, 2, ..., 24).• CM 1: Code of the month in which the forecast is being made, first value.• CM 2: Code of the month in which the forecast is being made, second value.C. Training of the ANN Forecasting ModelsAll training databases were normalized to lie within the interval [0, 1] and divided in three sets: training set (60%), validation set (20%), and test set (20%).The method for improving generalization and avoid overfitting is called early stopping. This technique is automatically provided for all of the supervised network creation functions in Neural Network Toolbox™ of MATLAB®.Fig. 5. Wind to Power forecasting model for 5 days ahead (W2P 5d ). P h-2 P h-3 P h-24 P h-25 P h-23 CM 1 CHCM 1 V pm 7V pm 24 CM 1 CM 2VV pm 97V pm 120 CM 1CM 2Fig. 6. Power to Power forecasting model for 5 days ahead (P2P 5d ).The ANN models are formed by MLP fully connected neural networks whose training algorithms is Resilient Propagation (RPROP). The ANN architectures consist of an input layer, a hidden layer and an output layer. The number of neurons in the hidden layer was determined by varying the number of neurons in this layer. The amount that provided the best performance during training, in the validation dataset, was thus selected. The hidden layer neurons use the hyperbolic tangent activation function. The number of neurons in the output layer is the same of the number of exits in the model. The neuron activation function used was sigmoid logistics.D. Choosing the Best ANN for Each ModelThe best ANN for each neural model was chosen by 10-fold cross-validation method, where 10 partitions were randomly generated to train, validate and test the ANNs. In this method, the samples are divided into 10 mutually exclusive partitions. For each of 10 iterations, d different partitions are used to test the ANNs and all the others (10 – d) are used to train and validate [15].It is expected that by applying this technique, the mean absolute error value in each experiment on the test set represents the expected output of the ANN created by the 10 experiments, as shown in [16] and [17]. In this paper, the selection of the best ANN was done based in the fold with lower MAE, averaged in ten initializations.V. R ESULTS AND C OMPARISONSThis section presents results and comparisons between W2P 6h , P2P 6h and Pers (persistence) for the 6 hours ahead forecasting and the comparisons between W2P 5d , W2P 5d and Pers_D (diary persistence) for the 5 days ahead forecasting. It’s well known that forecasting accuracy depends on the specific challenges of wind park location, the surrounding terrain, local climatology and data collection. But even so, we will make some comparisons in order to contextualize our work within the state of the art.A. 6 Hours Ahead Wind Power ForecastingThe results (Fig. 7) presented in the simulation period for the park A shows that since the first 10 min interval the P2P 6h model is similar to reference model. The hourly average Fig.8 shows for the first hour identical results between Pers model and P2P 6h model.The W2P 6h model overcomes the Pers model after the third hour. However, never overcomes P2P 6h that is the bestmodel from the second hour, Fig. 8.Fig. 7. NMAE (% of wind farm capacity) of power generation forecasts for Park A . Average of simulation period in intervals of 10min.CM CM 1 CM CM 2As an example a simulation is presented in Fig.9 for the Park A, in which the wind power generation (actual) and models predictions (P2P 6h , W2P h6 and Pers) can becompared.Fig. 8. NMAE (% of wind farm capacity) of power generation forecasts forPark A . Average of simulation period for each hour.Fig. 9. Wind power generation forecasts for Park A. Simulation for February, 01, 2012 at 8h.The Fig. 10 shows the results of the NMAE to the Park B in the simulation period, in which the P2P 6h model has smaller errors from the first to twelfth interval of 10 min. From the second hour W2P 6h model outperforms the otherssee Fig. 11.Fig. 10. NMAE (% of wind farm capacity) of power generation forecasts forPark B . Average of simulation period in intervals of 10min.Fig. 11. NMAE (% of wind farm capacity) of power generation forecasts forPark B . Average of simulation period for each hour.Fig. 12. Wind of power generation forecasts for Park B . Simulation for May, 15, 2012 at 8h.As an example a simulation is presented in Fig. 12 for the Park B, in which the wind power generation (actual) andmodels predictions (P2P 6h , W2P 6h and PERS) can be compared. In Fig. 8 and Fig. 11 we can observed that the average errors for 06 hours ahead is about 15% and 12% for the Park A and Park B, respectively. Noting that the error in the firsthour of 7.83% and 6.39% for Parks A and B, respectively. These results are similar to others as we can be observed in reference [3], [7], [8] and [11].B. 5 Days Ahead Wind Power ForecastingForecasting from 1 to 72 hours ahead, on an hourly basis, were characterized as medium term WPF in [3] and [7]. However, it is not easy to find references to studies with more than 72 hours ahead and discretized in 10 or 30 minutes.As shown in [7], typical model results for the WPF problem up to 48 hours ahead is around 13-16%.WPF models with forecasting of 72 hours ahead, in a 1 hour step, [13] and [14]. Although they use the same database of a 10.2 MW wind farm, they are dealing with many different recurrent ANNs. For reference [13] the best predictor presents a NMAE of 13.0%, while [14] shows a NMAE of 11.0%.The results presented in the simulation period for the Park A (Fig. 13) shows clearly that W2P 5d and P2P 5d models are superior to the model PERS_D in the first 48 intervals of 30 min. After this interval there are intervals in which the PERS_D model presents small error. However, in Fig.14 can be observed that the daily errors for P2P 5d and W2P 5d models are small than the PERS_D model. And the smallest average error, 20.74%, was obtained by the model W2P 5d . In case it is considered only the first three days (72 hours ahead prediction) daily error average falls to 19.00%.Fig. 13. NMAE (% of wind farm capacity) of power generation forecastsfor Park A . Average of simulation period in intervals of 30 min.Fig. 14. NMAE (% of wind farm capacity) of power generation forecastsfor Park A . Average of simulation period for each day.Fig. 15. Wind power generation forecasts for Park A. Simulation on March, 29, 2012 at 9h.As an example a simulation is presented in Fig.15 and Fig.18 for the Park A and B, respectively, in which the wind power generation(actual) and models predictions(P2P 5d , W2P 5d and PERS_D) can be compared and verified the difficulty of carrying out this prediction.Results presented for the simulation period for the park B, Fig. 16, and show that the model W2P 5d has high errors between the intervals 24-50 and 190-205. Fig. 17 shows that the P2P 5d model has small average error. And the smallest average error, 14.48%, was obtained by the model P2P 5d . In case it is considered only the first three days (72 hours ahead prediction) daily error average falls to 13.68%.Fig. 16. NMAE (% of wind farm capacity) of power generation forecasts forPark B . Average of simulation period in intervals of 30 min.Fig. 17. NMAE (% of wind farm capacity) of power generation forecastsfor Park B . Average of simulation period for each day.Fig. 18. Wind power generation forecasts for Park B. Simulation on February, 01, 2012 at 9h.VI. C ONCLUSIONSThe models developed in this paper are based on time series analysis of wind speeds and wind power through computational intelligence. The forecast horizons presented fall within very short-term forecasts for up to six hours ahead and medium-term forecasts up to five days ahead, which is an appropriate horizon to subsidize the operation planning of power systems.All developed models provided good forecasts for all the look-ahead times considered, for the shorter ones (from 1 to 6 hours ahead) and for the medium ones (from 1 to 120 hours ahead)These good forecasts were comparable with the ones of the references presented here.In the case of Park A the model W2P 5d was the best in the average of the day and also for each day. In the case of the Park B the P2P 5d model was the best.R EFERENCES[1] Incentive Program for Alternative Sources of Electric Energy –PROINFA. Available: /elb/data/Pages/LUMISABB61D26PTBRI E.htm[2] The Energy Operation Plan- PEN, National Electric System Operator-ONS. Available:.br/download/avaliacao_condicao/operacao_energe tica/PEN%202012_VOL1_RELATORIO%20EXECUTIVO.pdf[3] H. 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