Optimizing the input vectors of applied artificial neural network models for wind power production forecasting

Abstract

The significant increase of wind energy production worldwide revealed the necessity of its accurate forecasting. However, this is a very complex and, despite the progress made, more accurate forecasting methods are still needed. Accurate forecasts will contribute to a better power plant and grid management by solving problems related to the distribution and storage of the produced electricity, maximizing thus the profits of wind energy investments, contributing ultimately to their further enhancement. Here we present the development and validation of selected artificial neural network (ANN) wind energy forecasting models that produce hourly forecasts for 24 hours forecast horizon. The models are developed and validated using wind speed, direction, and energy produced by a wind power plant located at a semi-mountainous area in Western Greece. The ANN forecasts are compared against those of the persistence method using the Root Means Square Error (RMSE) and the Mean Absolute Percentage Error (MAPE) statistics.

Keywords

Wind speed wind energy forecasting neural networks

Introduction

Wind is the most appealing form of renewable energy, as demonstrated by the constantly increasing number of wind-power generators installed globally (Chen et al., 2009; Ioakimidis et al., 2015). According to the World Wind Energy Association (WWEA) the worldwide wind capacity reached 744 GW in 2020 (World Wind Energy Association, 2021). In 2019, renewable energy sources made up 34% of gross electricity consumption in the EU-27. Wind and hydro power accounted for two-thirds of the total electricity generated from renewable sources (35% each) (Eurostat, 2020). Greece has set an ambitious target regarding the share of renewable energies and especially wind energy, in the energy budget of the country and achieved the 20% electricity production from renewable energies in 2019 (Figure 1) (Eurostat, 2020). However, there is still room for improvement; the new 35% coverage target for 2030 will lead to a more balanced energy mixture and reduce further the energy dependence of the country.

Figure 1.

Share of renewable energy in the EU member states 2019 (Eurostat, 2020).

In order to achieve such a target more wind power plants need to be built. However optimal operation of wind turbines faces a series of challenges among which is the important variability of wind speed (Du et al., 2018, 2019; Wang et al., 2020), that causes problems to their connection to the grid. Plant operators need to face these challenges and provide solutions leading to reliable coupling between the production and distribution of electricity. A major research priority toward such solutions is to improve the forecast of the operation and of the efficiency of wind power plants (Pinson et al., 2009; Thor and Weis-Taylor, 2002). Such solutions should aim to the optimization of wind farm operation processes like production programing or maintenance works, but also to electricity transportation and safety (Du et al., 2019; Wang et al., 2017).

Since the wind turbine power production depends on wind speed, a common forecasting approach is to “match” the forecasted wind speed values with the power curve of the turbine (Xu et al., 2012). There are many publications proving the research interest on the wind speed and on the produced wind power forecast (Colak et al., 2012; Lei et al., 2009; Zhu and Genton, 2012). This is a complex issue mainly because of the high uncertainty and important temporal and spatial variability of these two parameters (Yao et al., 2012). The forecast methods found in literature can be classified in four groups: numerical forecasts, statistical methods, artificial neural networks (ANN), and hybrid models. Interesting reviews on the development of short-term wind forecast tools are presented in (Costa et al., 2008; Jung and Broadwater, 2014; Kalogirou, 2001; Lei et al., 2009; Manero et al., 2018).

In this paper we propose a reliable forecast procedure to be part of the energy management tool of a wind power plant. The proposed method provides hourly electric energy forecasts produced by a wind turbine, for a 24 hours ahead forecast horizon, based on past in situ measurements of selected parameters. The method is based on ANN modeling that uses as inputs the energy produced by the wind turbine at previous time steps, the wind speed and direction measurements at the nacelle height, and the corresponding (ideal) power curve of the turbine. The proposed models are optimized using cross-validation via a trial-and-error approach.

The performance of the model is assessed by comparing the model forecast results with those obtained by the persistence method applied on the same input dataset. The persistence method is the benchmark of all wind energy forecast methods; it calculates a future value (independently of the time step value) by setting it equal to the mean of its last n values. However, in most cases only the last value (n = 1) is used (Alexiadis et al., 1998); in this paper we adopted this last approach.

Data description

Our data comes from a wind power plant located in a semi-mountainous area of western Greece, with an average altitude of 1 200 m (Figure 2). The nominal output power of the plant is 24 MW produced by 12 wind turbines of 2 MW each. We used 10-minute wind speed, direction and produced energy time series. The wind data are measured at the nacelle of one of the turbines and cover the period from January 1st to December 31st, 2013. The produced energy is recorded by the Supervisory Control and Data Acquisition (SCADA) system of the plant. Hourly electricity production data are calculated as sums of the 10-minute values over an hour. Data, prior to their use, have been subjected to the appropriate quality control and outliers have been removed. The descriptive statistics of the data after quality control, is shown in Table 1.

Figure 2.

Study area—the circles point to the power plant location.

Table 1.

Descriptive statistics of the data.

Data	Min	Mean	Max	SD
Mean wind speed (m s⁻¹)	0	7.4	26	4.4
Max wind speed (m s⁻¹)	0.3	11.0	42.1	5.5
Aggregated electricity production (kWh)	0	565.6	2006.0	622.7

Model selection

We propose a short-term forecast model using as input the closest to the forecast time step wind speed and direction, the produced energy, and the power curve of the wind turbine.

The relation between the input data and the energy produced by the turbine is modeled using an Artificial Neural Network model. The training algorithm, the activation function, the output function, and the network topology are determined via a trial and error approach. In this work we test the model performance for different input arrays, which are lagged input data time series.

The lags are selected by calculating the Auto-correlation Function (ACF) and Partial Auto-correlation Function of the input parameters (Flores et al., 2012). These two functions provide information about the degree of dependence between the current and past value of a parameter. The ACF and PACF results are illustrated in Figure 3. It can be seen that while for the maximum wind speed and for the produced electric energy, only the first lag provides the necessary information, the mean wind speed and direction are highly correlated with the past six values (t − 1, …, t − 6).

Figure 3.

The ACF and PACF of the 10-minutes input time series.

The ANN used is a feed-forward Multiple Layer Perceptron (MLP) (equation (1)):

y = f (\sum_{i = 1}^{n} w_{i} x_{i} + b)

(1)

with y the model output, x_i the input data, w_i the weights, b the bias, and f the activation function. A typical example of such a model is shown Figure 4. The model uses one hidden layer. Two training algorithms, namely the backpropagation (BPA) and the Levenberg–Marquardt (LM) algorithms have been tested. The activation function is the sigmoid-logistic function and the output function is the linear function. The optimum topology of the ANN is recalculated every time the input array changes.

Figure 4.

A typical diagram of an MLP feed-forward ööö.

Except of the above model, we developed an additional feed-forward neural network that uses as input wind speed and direction data with a 10-minute time step, in order to forecast the produced electric energy, based on 24-hours ahead wind speed forecasts. This model has a single hidden layer and it is trained using the BFGS algorithm, according to the procedure detailed in Kolokythas and Argiriou (2021).

ANN training of and topology optimization

The first 6 months (January 1st to June 30th, 2013) of the available data were used for the development of the forecast models. These were split into two sets, the first 60% for training and the remaining 40% for validation. The model parameters were determined by a trial-and-error approach. Over-fitting was avoided by applying a cross-validation approach. Two randomly 24-hour periods (i.e. 24 hourly values), those of June 30th and December 10th, 2013 have been used for the performance assessment of the forecast results.

Forecasting procedure

In order to derive the optimal model topology, we developed and assessed eight model variants. All models forecast the hourly produced electric energy for the next hour. The variants differ in the input parameters used, as described below:

Model 1—The electric energy (P) produced over the last hour.

Model 2—The electric energy produced over the last hour and the vector average of the last six 10-minute wind speed and direction values.

Model 3—The mean hourly wind speed for the next hour calculated from the 10-minute wind speed and direction data (the last six 10-minute values of each variable are used to forecast their next six values from which the 1-hour ahead hourly mean wind speed is calculated).

Model 4—The electric energy produced over the last hour and the mean hourly wind speed for the next hour as in Model 3.

Model 5—The electric energy produced over the last hour, the mean hourly wind speed for the next hour as in Model 3 and the mean maximum wind speed calculated as in Model 3.

Model 6—The electric energy produced over the last hour, the mean hourly wind speed for the next hour as in Model 3 and the ideal electric energy production for the next hour calculated from the power curve of the turbine using as input the forecasted wind speed values.

Model 7—The electric energy produced over the last hour, the mean hourly wind speed for the next hour as in Model 3, the ideal electric energy production for the next hour as in Model 6, and the difference between the ideal and the actual electric energy produced during the last hour.

Model 8—The electric energy produced over the last hour, the mean hourly wind speed for the next hour as in Model 3, the ideal electric energy produced during the last hour—calculated from the power curve of the turbine using the last six 10-minute wind speed values—as well as the difference between the ideal and the actual energy produced during the last hour.

The features of the above models are summarized in Table 2.

Table 2.

Model inputs and optimum topology. Models provide a forecast at time t.

	Input data	Model	Topology (input—hidden—output layers)	Learning algorithm	Iterations
Persistence	P(t − 1)	—	—	—	—
Model 1	P(t − 1)	MLP	1_2_1	BP	500
Model 2	P(t − 1), $\bar{U}$ (t − 1)	MLP	2_4_1	BP	1000
Model 3	$\hat{U}$ (t)	FFNN	1_3_1	BFGS	1000
Model 4	P(t − 1), $\hat{U}$ (t)	FFNN, MLP	2_5_1	BFGS-BP	1200
Model 5	P(t − 1), $\hat{U}$ (t), ${\hat{U}}_{\max}$ (t)	FFNN, MLP	3_6_1	BFGS-BP	1500
Model 6	P(t − 1), $\hat{U}$ (t), ${\hat{P}}_{optim}$ (t)	FFNN, MLP	3_6_1	BFGS-BP	1500
Model 7	P(t − 1), $\hat{U}$ (t), ${\hat{P}}_{optim}$ (t), $P_{optim}^{diff}$ (t − 1)	FFNN, MLP	4_7_1	BFGS-BP	1800
Model 8	P(t − 1), $\hat{U}$ (t), P_optim(t − 1), $P_{optim}^{diff}$ (t − 1)	FFNN, MLP	4_7_1	BFGS-BP	1800

$\bar{U}$ : Mean hourly wind speed; P_optim: hourly optimum electric energy production; $\hat{U}$ : mean hourly forecasted wind speed; ${\hat{P}}_{optim}$ : hourly forecasted optimum electric energy production; ${\hat{U}}_{\max}$ : mean maximum hourly forecasted wind speed; $P_{optim}^{diff}$ : hourly difference optimum-observed electric energy production.

It should be noted that the produced electric energy time series include negative values because the wind turbines sometimes consume more energy than they produce, mainly when the wind speed is lower than 3.1 m s⁻¹, or when the wind speed exceeds the cut-out limit, or in case of ice formation on the wind turbine wings. In this work we considered only the net energy production, by setting the negative values to zero. The input time series values are normalized within the range [0.001, 0.999], using equation (2):

y_{n o r m, i} = \frac{y_{o b s, i} - y_{m i n}}{y_{m a x} - y_{m i n}}

(2)

with y_norm,I the normalized value, y_obs,i the time series value at time step I, y_min and y_max the minimum and maximum value of the input array.

Model assessment

We tested the performance of the proposed models by comparing their forecast results to those obtained by the persistence model, also known as the “naïve predictor,” that assumes that the value of a variable at time t+k in the future remains the same as at time t:

\hat{P} (t + k | t) = P (t)

(3)

Despite its “naiveness,” the persistence model is highly accurate for very short-term forecasts, when compared to the majority of the existing physical and statistical models. It has been therefore decided that the ability of any new model to improve forecasts, should be first evaluated against the persistence model (Madsen et al., 2004, 2005; Soman et al., 2010).

Except from the comparison against the persistence model, the following three well-known statistical metrics have been used (Alexiadis et al., 1998; Flores et al., 2012):

root mean square error: $RMSE = \sqrt{\frac{1}{N} \sum_{t = 1}^{N} e_{t}^{2}}$

the mean absolute percentage error: $MAPE = \frac{1}{N} \sum_{i = 1}^{N} abs (e_{t}) \times 100$

with N the number of observations, e_t = y_t − F_t the forecast error, y_t the observation at time t, and F_t the forecast value at time t.

Results

Table 3 presents the model performance during their training. Figure 5 shows the respective normalized training error frequency. It can be seen that Models 7 and 8 exhibit the best performance during the training phase presenting the lower errors and variations compared to the other six models.

Table 3.

Training error statistics.

Training error statistics (kWh)
Model	RMSE	MAPE
1	255.37	54.35
2	251.79	56.65
3	77.52	44.99
4	74.57	38.46
5	70.99	25.88
6	71.73	45.16
7	57.66	30.04
8	58.78	30.92

Figure 5.

Training error of the developed model. Mean and standard deviation of each error series are also shown.

Figure 6 presents the forecast error boxplots for both forecasting periods. It can be seen that the model variants that use as input the 10-minute wind speed and direction time series, with the exception of Model 5 that uses the maximum (10-minute) wind speed instead, perform better than those that use hourly wind speed input data. Also, as before, it is Model 7, followed by Model 8, that shows the closest agreement to measurements. Additionally, there is also a clear difference in the forecasting results concerning the magnitude of the produced error, especially for those models using as inputs the 10-minute wind speed and direction time series.

Figure 6.

Forecast error boxplots. Upper graph: first forecasting period; lower graph: second forecasting period.

Table 4 provides the various metrics used for the evaluation of the models. The persistence model gives the worst scores in all cases. As already mentioned, scores are improved when 10-minute time step wind speed and direction time series are used as inputs. Forecasts are further improved when the ideal power production curve of the wind turbine is used as an additional input, namely in model 6, 7, and 8 that produce the lowest error scores.

Table 4.

Statistics for the aggregated electric energy production forecasts by the various model typologies for both forecasting periods.

Forecast statistic (kWh)
Model	June 30th, 2013		December 10th, 2013
	RMSE	MAPE	RMSE	MAPE
Persistence	337.9	40.4	373.8	241.8
1	323.5	33.9	362.1	228.8
2	319.1	34.4	356.4	235.9
3	73.7	9.4	171.9	53.6
4	72.47	9.3	169.1	58.4
5	280.5	29.8	173.7	183.9
6	69.27	9.3	169.3	56.6
7	63.8	8.7	159.3	51.7
8	68.6	10.2	164.2	54.3

An important performance index is also the percent improvement of the forecast results, against the persistence method results, as defined by equation (4):

Imp = \frac{S_{ref} - S}{S_{ref}} \times 100 %

(4)

with S_ref the forecast error of the persistence method and the forecast error of another forecast model topology. The results are provided in Table 5. It can be seen that almost all model typologies lead to better forecasts than those of the persistence method. The average percent improvement for both examined periods is 53% and 42% for the RMSE, and 55% and 52% for the MAPE respectively. The best results are those of Model 7 with an improvement of 81% for the RMSE and 75% for MAPE for the first period and 57% and 79% for the second period.

Table 5.

Forecast improvement the various model typologies against the persistence method.

Models improvement
	30th June 2013		10th December 2013
Model	RMSE	MAPE	RMSE	MAPE
Persistence	—	—	—	—
1	0.04	0.16	0.03	0.05
2	0.06	0.15	0.05	0.02
3	0.78	0.77	0.54	0.78
4	0.79	0.77	0.55	0.76
5	0.17	0.26	0.54	0.24
6	0.79	0.77	0.55	0.77
7	0.81	0.78	0.57	0.79
8	0.80	0.75	0.56	0.78

Figure 7 illustrates the electric energy production estimated by the persistence method and the proposed eight model typologies for both forecasting periods. With the exception of the persistence model and Models 1, 2, and 5, mainly for the first forecasting period, all other models provide satisfactory results and their forecasts are close to the measured values.

Figure 7.

Forecasted and real electric energy production time series. First forecasting period upper graph; second forecasting period lower graph.

Figure 8 illustrates the electric energy production estimates of the best performing Model 7 for both forecasting periods. The same figure also presents the differences between forecasts and the measurements.

Figure 8.

Upper row: real (black solid line) electric energy production and best forecasts (red dashed line—model 7); lower row: forecasting error for both periods.

Conclusions

This work focuses on the forecasting of electric energy production of a wind power plant. We developed eight Artificial Neural Network models having different topologies. Models were developed and tested against measured time series and compared with the persistence method forecasts, using as criteria for the model performance the RMSE and MAPE. Almost all the proposed models perform better than the persistence method. The best performing models are those that combine not only the energy output data but also the wind data at the location of the turbine, especially when using the FF-NN and BFGS algorithm. The model performance is further improved when the ideal power production curve of the wind turbine is used as additional input (Models 6, 7, and 8).

The best forecasts—with respect to the persistence method—were found to be those of Model 7. This model describes best the dynamics of the produced electric energy and shows the smallest errors.

We found that the energy production forecasts are significantly improved when we use as inputs (a) the forecasted wind speed values based on 10-minute wind speed and direction measurements and (b) the power curve of the wind turbine, both at the time of the forecast (not during the previous time step). This is because the wind speed forecasted using the proposed algorithm, is much closer to the measured wind speed values (Kolokythas and Argiriou, 2021). The use of past values of the difference between the actual and the ideal energy production, further enhance the forecast skill of the model.

Another important finding is that the use of the maximum wind speed time series does not improve the electric energy production forecast. On the contrary it was found that this model variant leads to higher errors, as shown in Figure 7 (Model 5, upper graph), because it overestimates the energy produced. This can be attributed to the fact that the maximum wind speed value is observed instantly within the hour—which is the time step of the proposed models; therefore, this is not reflected in the hourly average energy production. Furthermore, the wind turbines either cannot respond to significant wind speed fluctuations, or they may be stalled for safety reasons when the wind speed peaks exceed their cut-out value. These disruptions introduce discontinuities in the electricity production that cannot be modeled using the maximum wind speed as input.

Wind energy contributes significantly toward the sustainable development and should therefore attract significant investments (World Wind Energy Association, 2020). Further penetration of wind power plants in the energy market contributes also to the reduction of greenhouse gas emissions and the subsequent climate change. This can be achieved, among others with the better short-term wind energy production forecast.

This paper is a contribution toward this direction. It proposes an artificial neural network electric energy production forecasting model based on input data measured in situ at the production site, contributing thus to the optimal management of the wind power plant.

Footnotes

Acknowledgements

The authors would like to thank the company TERNA ENERGY S.A. for providing the data used in this work.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Athanassios A Argiriou

References

Alexiadis

Dokopoulos

Sahsamanoglou

, et al. (1998) Short-term forecasting of wind speed and related electrical power. Solar Energy 63: 61–68.

Chen

Guerrero

Blaabjerg

(2009) A review of the state of the art of power electronics for wind turbines. IEEE Transactions on Power Electronics 24: 1859–1875.

Colak

Sagiroglu

Yesilbudak

(2012) Data mining and wind power prediction: A literature review. Renewable Energy 46: 241–247.

Costa

Crespo

Navarro

, et al. (2008) A review on the young history of the wind power short-term prediction. Renewable and Sustainable Energy Reviews 12: 1725–1744.

Wang

Yang

, et al. (2018) Multi-step ahead forecasting in electrical power system using a hybrid forecasting system. Renewable Energy 122: 533–550.

Wang

Yang

, et al. (2019) A novel hybrid model for short-term wind power forecasting. Applied Soft Computing 80: 93–106.

Eurostat (2020) Renewable energy statistics. Available at: https://ec.europa.eu/eurostat/statistics-explained/index.php?title=Renewable_energy_statistics (accessed 4 May 2021).

Flores

Engel

Pinto

(2012) Autocorrelation, and partial autocorrelation functions to improve neural networks models on univariate time series forecasting. In: WCCI 2012 IEEE world congress on computational intelligence, Brisbane, Australia, 10–15 June 2012, pp.1–8. New York, NY: IEEE.

Ioakimidis

Genikomsakis

Dallas

, et al. (2015) Short-term wind speed forecasting model based on ANN with statistical feature parameters. In: IECON 2015 – 41st annual conference of the IEEE industrial electronics society, Yokohama, Japan, 9–12 November 2015, pp. 000971–000976. New York, NY: IEEE.

10.

Jung

Broadwater

(2014) Current status and future advances for wind speed and power forecasting. Renewable and Sustainable Energy Reviews 31: 762–777.

11.

Kalogirou

(2001) Artificial neural networks in renewable energy systems applications: A review. Renewable and Sustainable Energy Reviews 5: 373–401.

12.

Kolokythas

Argiriou

(2021) An application of a feed-forward neural network model for wind speed predictions. International Journal of Sustainable Energy. Epub ahead of print 20 April 2021. DOI: 10.1080/14786451.2021.1915315.

13.

Lei

Shiyan

Chuanwen

, et al. (2009) A review on the forecasting of wind speed and generated power. Renewable and Sustainable Energy Reviews 13: 915–920.

14.

Madsen

Kariniotakis

Nielsen

, et al. (2004) A protocol for standardizing the performance evaluation of short-term wind power prediction models. In: Global wind power conference 2004 conference proceedings, Chicago, IL.

15.

Madsen

Pinson

Kariniotakis

, et al. (2005) Standardizing the performance evaluation of short-term wind power prediction models. Wind Engineering 29: 475–489.

16.

Manero

Béjar

Cortés

(2018) Wind energy forecasting with neural networks: A literature review. Computación y Sistemas 22: 1085–1098.

17.

Pinson

Madsen

Nielsen

, et al. (2009) From probabilistic forecasts to statistical scenarios of short-term wind power production. Wind Energy 12(1): 51–62.

18.

Soman

Zareipour

Malik

, et al. (2010) A review of wind power and wind speed forecasting methods with different time horizons. In: North American power symposium (NAPS) 2010, Arlington, TX, 26–28 September 2010, pp.1–8. New York, NY: IEEE.

19.

Thor

S-E

Weis-Taylor

(2002) Long-term research and development needs for wind energy for the time frame 2000-2020. Wind Energy 5(1): 73–75.

20.

Wang

Niu

, et al. (2017) A novel hybrid system based on a new proposed algorithm—multi-objective whale optimization algorithm for wind speed forecasting. Applied Energy 208: 344–360.

21.

Wang

Niu

, et al. (2020) A novel framework of reservoir computing for deterministic and probabilistic wind power forecasting. IEEE Transactions on Sustainable Energy 11: 337–349.

22.

World Wind Energy Association (2020) World wind capacity at 6508 GW, Corona crisis will slow down markets in 2020 renewables to be core of economic stimulus programmes. Available at: https://wwindea.org/world-wind-capacity-at-650-gw/ (accessed 4 May 2021).

23.

World Wind Energy Association (2021) Worldwide wind capacity reaches 744 Gigawatts – An unprecedented 93 Gigawatts added in 2020. Available at: https://wwindea.org/worldwide-wind-capacity-reaches-744-gigawatts/ (accessed 4 May 2021).

24.

Dong

, et al. (2012) An intelligent dynamic security assessment framework for power systems with wind power. IEEE Transactions on Industrial Informatics 8: 995–1003.

25.

Yao

Dong

Meng

, et al. (2012) Quantum-inspired particle swarm optimization for power system operations considering wind power uncertainty and carbon tax in Australia. IEEE Transactions on Industrial Informatics 8: 880–888.

26.

Zhu

Genton

(2012) Short-term wind speed forecasting for power system operations. International Statistical Review 80: 2–23.