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Wind Power Forecasting
10th IFAC Symposium on Control of Power and Energy Systems 10th IFAC Symposium on 4-6, Control Tokyo, Japan, September 2018of Power and Energy Systems 10th IFAC Symposium on 4-6, Control Tokyo, Japan, September 2018of Power and Energy Systems Available www.sciencedirect.com 10th IFAC Symposium on Control of Power andonline EnergyatSystems Tokyo, Japan, September 2018of Power and Energy Systems 10th IFAC Symposium on 4-6, Control Tokyo, Japan, September 4-6, 2018 Tokyo, Japan, September 4-6, 2018
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IFAC PapersOnLine 51-28 (2018) 414–419
Wind Power Forecasting Wind Power Forecasting Wind Forecasting WindQ.Power Power Chen*, Forecasting K. A. Folly** WindQ.Power Chen*, Forecasting K. A. Folly**
Q. Q. Chen*, Chen*, K. K. A. A. Folly** Folly** Q. Chen*, K. A. * Electrical Engineering Department,Folly** University of Cape Town, * Cape Electrical Engineering Department, University of Cape Town, Town, South Africa, (e-mail: [email protected]) ** Cape Electrical Engineering Department, University of Cape Town, Town, South Africa, (e-mail: [email protected]) Electrical Engineering Department, University **Cape Electrical Engineering Department, Universityof ofCape CapeTown, Town, Town, South Africa, (e-mail: [email protected]) * Electrical Engineering Department, University of Cape ** Electrical Engineering Department, University of CapeTown, Town, Cape Town,Africa, South(Tel: Africa, (e-mail: [email protected]) Cape ** Town, South 0216504490; e-mail: [email protected]) Electrical Engineering Department, University of Cape Town,Africa, South(Tel: Africa, (e-mail: [email protected]) Cape ** Town, South 0216504490; e-mail: [email protected]) Electrical Engineering Department, University of Cape Cape Town, Town, Cape Town, South (Tel: e-mail: Electrical Engineering Department, University of Cape Town, Cape ** Town, South Africa, Africa, (Tel: 0216504490; 0216504490; e-mail: [email protected]) [email protected]) Cape Town, Southwind Africa, (Tel: 0216504490; [email protected]) Abstract: Accurate short-term power forecast is very e-mail: important for reliable and efficient operation Abstract: Accurate short-term wind power forecast is veryThere important for reliable and efficient operation of power Accurate systems with high wind wind power powerforecast penetration. are many conventional and operation artificial Abstract: short-term is very important for reliable and efficient of power systems with high wind power penetration. There are many conventional and artificial Abstract: Accurate short-term wind power forecast is veryaccurate important for power reliableforecasting. and efficient operation intelligence methods that have been developed to achieve wind Time-series of power systems with high wind power penetration. There are many conventional and artificial Abstract: Accurate short-term wind power forecast is very important for reliable and efficient operation intelligence methods that have been developed to achieve accurate wind power forecasting. Time-series of power systemsarewith highto wind powerrobust, penetration. There many conventional and artificial based algorithms known be simple, and have beenare used inpower the past for forecasting with intelligence methods that have developed to accurate wind forecasting. Time-series of power systems hightobeen wind powerrobust, penetration. There many conventional and artificial based algorithms arewith known be simple, andhave have beenare used inpower the past for forecasting with intelligence methods that have been developed to achieve achieve accurate wind forecasting. Time-series some level of success. Recently some researchers advocated for artificial-intelligence based based algorithms are known be simple, robust, and have been used in the past for forecasting with intelligence methods that haveto been developed to achieve accurate windfor power forecasting. Time-series some level of success. Recently some researchers have advocated artificial-intelligence based based algorithms are known to be simple, robust, and have been used in the past for forecasting with methods suchofassuccess. ArtificialRecently Neural Networks (ANNs), Fuzzy Logic, etc., for for forecasting because ofbased their some level some have artificial-intelligence based algorithms are known to beNetworks simple, robust, andFuzzy have advocated been used in past for forecasting with methods such Artificial Neural (ANNs), Logic, etc., forthe forecasting because ofbased their some level ofassuccess. Recently some researchers researchers have advocated for artificial-intelligence flexibility. This paper presents a comparison of conventional and two artificial intelligence methods for methods such as Artificial Neural Networks (ANNs), Fuzzy Logic, etc., for forecasting because of their some level of success. Recently some researchers have advocated for artificial-intelligence based flexibility. This presents a comparison of conventional and two artificial intelligence methods for methods such aspaper Artificial Neural Networksmethod (ANNs), Fuzzy Logic, etc., for forecasting because of their wind power forecasting. The conventional discussed in this paper is the Autoregressive Moving flexibility. This presents aa comparison of conventional and two artificial intelligence methods for methods such aspaper Artificial Neural Networksmethod (ANNs), Fuzzy Logic, etc., for forecasting because of their wind power forecasting. The conventional discussed in this paper is the Autoregressive Moving flexibility. This paper presents comparison of conventional and two artificial intelligence methods for Average (ARMA) whichThe is conventional one of the most robust and simple time-series methods. The artificial wind power forecasting. method discussed in this paper is Autoregressive Moving flexibility. This paper presents a comparison of conventional and two artificial methods for Average (ARMA) which is conventional one of Neural the most robust and simple time-series methods. The artificial wind power forecasting. The method discussed in this paper is the theintelligence Autoregressive Moving intelligence methods are Artificial Networks (ANNs) and Adaptive Neuro-fuzzy Inference Average (ARMA) which is one of the most robust and simple time-series methods. The artificial wind power forecasting. The conventional method discussed in this paper is the Autoregressive Moving intelligence methods are Artificial Neural Networks (ANNs) and Adaptive Neuro-fuzzy Inference Average (ARMA) Simulation which is one of for thevery-short-term most robust and time-series methods. TheANNs artificial Systems (ANFIS). results and simple short-term forecasting show that and intelligence methods are Artificial Neural Networks (ANNs) and Adaptive Neuro-fuzzy Inference Average (ARMA) which is one of for thevery-short-term most robust and simple methods. TheANNs artificial Systemsare (ANFIS). Simulation results and short-term forecasting showforecasting, that and intelligence methods are Artificial Neural Networks (ANNs) andtime-series Adaptive Neuro-fuzzy Inference ANFIS suitable for the very-short-term (10 minutes ahead) wind speed and power and Systems (ANFIS). Simulation results for very-short-term and short-term forecasting show that ANNs and intelligence methods are Artificial Neural Networks (ANNs) and Adaptive Neuro-fuzzy Inference ANFIS are suitable for the very-short-term (10 minutes ahead) wind speed and power forecasting, and Systems (ANFIS). Simulation results for(1 very-short-term and speed short-term forecasting show that ANNs and the ARMA is suitable for thevery-short-term short-term hour ahead) wind andspeed power forecasting. ANFIS are suitable for (10 minutes ahead) wind and power Systems (ANFIS). Simulation results for(1 very-short-term and short-term forecasting showforecasting, that ANNs and the ARMA is suitable thevery-short-term short-term hour speed andspeed power forecasting. ANFIS are suitable forforthe the (10 ahead) minuteswind ahead) wind and power forecasting, and the ARMA is suitable for the short-term (1 hour ahead) wind speed and power forecasting. ANFIS are suitable for the very-short-term (10 minutes ahead) wind speed and power forecasting, © 2018, IFAC (International of(1 Automatic Control) by Elsevier Ltd. All rights reserved.and Keywords: Wind power artificial neural networks, ARMA, ANFIS. the ARMA is suitable forforecasting, theFederation short-term hour ahead) windHosting speed and power forecasting. Keywords: power artificial neural networks, ARMA, the ARMA Wind is suitable forforecasting, the short-term (1 hour ahead) wind speed and ANFIS. power forecasting. Keywords: Wind power forecasting, artificial neural networks, ARMA, ANFIS. networks, Keywords: Wind power forecasting, artificial neural ARMA, ANFIS. networks, Keywords: Wind power forecasting, artificial neural ARMA, that ARMA andANFIS. the two artificial methods (ANNs and 1. INTRODUCTION that ARMA and the for twotheartificial methods (10 (ANNs and ANFIS) are suitable very-short-term minutes 1. INTRODUCTION that ARMA and the two artificial methods (ANNs and ANFIS) are suitable for the very-short-term (10 minutes ARMA and the(1two artificial methods (ANNs and 1. INTRODUCTION ahead) and short-term hour ahead) wind power(10 forecasting. With the depletion of energy resources and the that 1. conventional INTRODUCTION ANFIS) are suitable for the very-short-term minutes that ARMA and the two artificial methods (ANNs and ahead) and short-term (1 hour ahead) wind power(10 forecasting. With the depletion of conventional energy resources and the ANFIS) are suitable for the very-short-term minutes 1. INTRODUCTION deterioration of the environment, renewable energy will ahead) and short-term (1 hour ahead) wind power forecasting. ANFIS) are suitable for the very-short-term (10 minutes With the of conventional energy resources andwill the The paper organized(1ashour follows: The nextpower section discusses deterioration of the environment, renewable energy andisshort-term ahead) wind forecasting. With the depletion depletion conventional energy resources the ahead) gradually become aofcrucial energy source (Ma, et al.,and 2009). The paper organized follows: The next section discusses ahead) andisshort-term (1ashour ahead) wind power forecasting. deterioration of the environment, renewable energy will With the depletion of conventional energy resources and the the time-scale classification and wind power forecasting. gradually become a crucial energy source (Ma, et al., 2009). deterioration of the of environment, renewable energy will The paper is organized as follows: The next section discusses Wind energy is one the most available, affordable, and the time-scale classification and wind power forecasting. The paper is organized as follows: The next section discusses gradually become aa crucial source (Ma, et al., deterioration of the environment, renewable energy will 3 and classification 4 reviewed and the wind Autoregressive Moving Wind energy is sources. one of theenergy mostthis, available, affordable, and Section gradually become crucial energy source (Ma, et al., 2009). 2009). the time-scale power forecasting. The paper is organized as follows: The next section discusses efficient energy Despite wind speed varies from Section 3 and 4 reviewed the Autoregressive Moving the time-scale classification and wind power forecasting. Wind energy is one of the most available, affordable, and gradually become a crucial energy source (Ma, et al., 2009). Average (ARMA) method and the artificial intelligence efficient energy sources. Despite this, wind speed varies from Windtoenergy is oneit of the mosttoavailable, affordable, and Section 3 and 4 reviewed the Autoregressive Moving the time-scale classification and wind power forecasting. time time and; is difficult accurately predict wind Average (ARMA) method and the artificial intelligence Section 3 and 4 reviewed the Autoregressive Moving efficient energy sources. Despite this, wind speed varies from Wind energy is one of the most available, affordable, and methods, (ARMA) respectively. Section 5 the is concerned with data time to(Wu time and; it 2007). is difficult to accurately efficient energy sources. Despite this, wind speedpredict varies wind from Average method and artificial intelligence Section 3 and 4 reviewed the Autoregressive Moving power & Hong, methods, respectively. Section 5 is concerned with data Average (ARMA) method and the artificial intelligence time to time and; it is difficult to accurately predict wind efficient energy sources. Despite this, wind speed varies from collection and analysis. Section 6 presents the simulation power Hong,it 2007). time to(Wu time& and; is difficult to accurately predict wind Average methods, respectively. Section 5 is concerned with data (ARMA) method and the artificial intelligence collection and analysis. Section 6 presents the simulation Section 5 Conclusion is concernedis with power (Wu & Hong, time toare time it 2007). is difficult accurately predict wind methods, results andrespectively. detailed discussions. givendata in There many methods that havetobeen developed to handle power (Wu & and; Hong, 2007). collection and analysis. Section 6 presents the simulation methods, respectively. Section 5 is concerned with data results and detailed discussions. Conclusion is given in There are many methods that have been developed to handle collection and analysis. Section 6 presents the simulation power (Wu & Hong, 2007). Section 7. wind speed prediction. The conventional method presented in results and detailed discussions. Conclusion is given collection and analysis. Section 6 presents the simulation Section 7. There are many methods that have been developed to handle wind speed prediction. The conventional method presented in and detailed discussions. Conclusion is given in in There are many methods that autoregressive have been developed toaverage handle results this paper is the time series moving Section 7. results and detailed discussions. Conclusion is given in wind speed The conventional method presented in There are many methods that have been developed toaverage handle this isprediction. theARMA time series autoregressive moving 7. windpaper speed prediction. The conventional method presented in Section (ARMA). In an model, the future value of a variable this is the time series autoregressive moving average windpaper speedIn The conventional method presented in Section 7. (ARMA). an ARMA model, the future value of a variable this paper isprediction. thebe time series autoregressive moving average is assumed to equal to a linear function of some past 2. TIME-SCALE CLASSIFICATION AND WIND POWER (ARMA). ARMA model, the value aa variable this paper In istoan thebe time series moving average is assumed equal to aautoregressive linear function ofof past 2. TIME-SCALE CLASSIFICATION WIND POWER (ARMA). In an ARMA model, the future future value of some variable observations and random errors (Zhang, 2003). FORECASTINGAND is assumed to be equal to a linear function of some past (ARMA). an be ARMA the future valueofof some a variable 2. TIME-SCALE CLASSIFICATION WIND observations and random errors (Zhang, 2003). FORECASTINGAND is assumedInto equalmodel, to a linear function past 2. TIME-SCALE CLASSIFICATION AND WIND POWER POWER observations and random errors (Zhang, 2003). is assumed to be equal to a linear function of some past FORECASTING 2. TIME-SCALE CLASSIFICATION AND WIND POWER The artificial intelligent methods that are discussed are observations and random errors (Zhang, 2003). FORECASTING The artificial methods that2003). are the discussed are 2.1 Time-scale Classification observations andintelligent random errors (Zhang, FORECASTING Artificial Neural Networks (ANNs) and AdaptiveThe artificial intelligent methods that are discussed are 2.1 Time-scale Classification Artificial Neural Networks (ANNs) and the AdaptiveThe artificial intelligent methods that are discussed are network-based Fuzzy Inference System (ANFIS). An ANN is Artificial Neural Networks (ANNs) and AdaptiveThe artificial intelligent methods that(ANFIS). are the discussed are network-based Fuzzy Inference System An ANN is 2.1 2.1 Time-scale Time-scale Classification Classification Artificial Neural Networks (ANNs) and the Adaptiveable to perform a nonlinear mapping between a set of input 2.1 Time-scale Classification network-based Fuzzy Inference System (ANFIS). An ANN is Artificial Neural Networks (ANNs) and the Adaptiveable to perform a nonlinear mapping between a set of input Different authors have different opinions about the time-scale network-based Fuzzy Inference System (ANFIS). An ANN is and output variables. An ANFIS is abetween fuzzy system whose Different authors have differentofopinions about the time-scale able to perform a nonlinear mapping a set of input network-based Fuzzy Inference System (ANFIS). An ANN is classification of the operation electricity systems. (Soman, and output variables. An ANFIS is a fuzzy system whose able to perform a nonlinear mapping between a set adjusted of input Different parameters of the membership function have been authors have different opinions about the time-scale classification of the operation of electricity systems. (Soman, and output variables. An ANFIS is a fuzzy system whose able to perform a nonlinear mapping between a set of input Different authors have different opinions about the time-scale et al., 2010; Wu & Hong, 2007; Zhang, 2003; Zhao, et al., parameters of the membership function have been adjusted and output variables. Anlearning ANFISmethods is a fuzzy system whose classification by using neuro-adaptive like the techniques of the operation of electricity systems. (Soman, Different authors have different opinions about the time-scale et al., 2010; Wu & Hong, 2007; Zhang, 2003; Zhao, et al., parameters of the membership function have been adjusted classification of the operation of electricity systems. (Soman, and output variables. An ANFIS is a fuzzy system whose 2011) separate the time-scale for the operation of electricity by using neuro-adaptive learning methods like the techniques parameters of the membership function have been adjusted et used for neuro-adaptive training neurallearning networks (Adaptive neural-fuzzy al., 2010; Wu & Hong, 2007; Zhang, 2003; Zhao, et al., classification of the operation of electricity systems. (Soman, 2011) separate the time-scale for the operation of electricity by using methods like the techniques al., 2010; Wu categories. & Hong, 2007; Zhang, 2003; Zhao, of et the al., parameters of the membership function have been adjusted et systems into four Table 1 shows a summary used for neuro-adaptive training neurallearning networks (Adaptive neural-fuzzy by using methods like the techniques modeling, 2017). 2011) separate the time-scale for the operation of electricity et al., 2010; Wu & Hong, 2007; Zhang, 2003; Zhao, et al., systems intoclassification four categories. Table 1 shows a summary of the used for training neural networks (Adaptive neural-fuzzy 2011) separate the time-scale for the operation of electricity by using neuro-adaptive learning methods like the techniques modeling, 2017). time-scale for different forecasting techniques used for training neural networks (Adaptive neural-fuzzy systems into four categories. Table 1 shows a summary of the 2011) separate the time-scale for the operation of electricity time-scale different forecasting techniques modeling, 2017). systems into four categories. Table 1 shows a summary of the used training neural networks (Adaptive neural-fuzzy et classification al., 2010; Wu for & Hong, 2007; Zhang, 2003; Zhao, In thisfor paper, the Autoregressive Moving Average (ARMA) (Soman, modeling, 2017). time-scale classification for different forecasting techniques systems into four categories. Table 1 shows a summary of the (Soman, et al., 2010; Wu & Hong, 2007; Zhang, 2003; Zhao, In this paper, the Autoregressive Moving Average (ARMA) modeling, 2017). time-scale classification for different forecasting techniques al., 2011). is compared with artificial intelligence methods (ARMA) such as et (Soman, et al., 2010; Wu & Hong, 2007; Zhang, 2003; Zhao, time-scale classification for different forecasting techniques In this paper, the Autoregressive Moving Average et al., 2011). is compared with artificial (ANNs) intelligence methods such as (Soman, et al., 2010; Wu & Hong, 2007; Zhang, 2003; Zhao, In this paper, the Autoregressive Moving Artificial Neural Networks and Average Adaptive(ARMA) Neuroet al., 2011). (Soman, et al., 2010; Wu & Hong, 2007; Zhang, 2003; Zhao, is compared with artificial intelligence methods such as In this paper, the Autoregressive Moving Average (ARMA) Artificial Neural Networks (ANNs) and Adaptive Neurois compared with artificial intelligence methods such as et al., 2011). fuzzy Inference Systems (ANFIS). Simulation resultsNeuroshow et al., 2011). Artificial Neural Networks (ANNs) and Adaptive is compared with artificial intelligence methods such as fuzzy Inference Systems (ANFIS). Simulation results show Artificial Neural Networks (ANNs) and Adaptive Neurofuzzy Inference (ANFIS). results show Artificial NeuralSystems Networks (ANNs)Simulation and Adaptive fuzzy Inference Systems (ANFIS). Simulation resultsNeuroshow fuzzy Inference Systems (ANFIS). Simulation results show
Copyright © 2018, 2018 IFAC 414Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © IFAC (International Federation of Automatic Control) Copyright © 2018 IFAC 414 Peer review under responsibility of International Federation of Automatic Control. Copyright © 2018 IFAC 414 10.1016/j.ifacol.2018.11.738 Copyright © 2018 IFAC 414 Copyright © 2018 IFAC 414
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air density, temperature and barometric pressure measured at the site is given by (3) (Olaofe, 2013).
Table 1. Time-horizon classification for wind power forecasting.
𝑔𝑔ℎ
𝑃𝑃
𝜌𝜌(𝑡𝑡) = ( ) 𝑒𝑒 −(𝑅𝑅𝑅𝑅) 𝑅𝑅𝑅𝑅
(3)
where 𝜌𝜌(𝑡𝑡) is the time varying air density in (kg/m3), 𝑃𝑃 is barometric pressure in (Pa), T is the air temperature in (K), R is the specific gas constant for dry air, 287.058 (J/(kg.K)), g is the gravity of Earth, 9.81(m/s2), h is the hub height above ground level in (m) (Olaofe, 2013). 2.3 Performance Measurements It is difficult to accurately measure the performance of different wind speed and power forecasting models by comparing the forecasted wind speed plots against the actual wind speed plots. In this paper, the predictive performance was quantified by using the mean absolute error (MAE) and the root mean square (RMSE). The RMSE and MAE are defined as in (4) and (5), respectively (Mbuvha, 2017):
The very-short-term and short-term time horizons are the main focus of this paper, as they are suitable for the real-time grid operations and load increment/decrement decisions. 2.2 Wind Speed Versus Wind Power
1
𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 2 ) 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 = √ ∑𝑁𝑁 ℎ=1(𝑣𝑣ℎ − 𝑣𝑣ℎ
The output power of a wind turbine depends on the wind speed, which varies over a wide range of time and depends on regional landscape type, weather patterns, and seasonal variations (Wu & Hong, 2007) (Soman, et al., 2010).
𝑁𝑁
1
𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 | MAE = ∑𝑁𝑁 ℎ=1 |𝑣𝑣ℎ − 𝑣𝑣ℎ 𝑁𝑁
1 2
𝑃𝑃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 (𝑣𝑣) =
𝜌𝜌(𝑡𝑡)𝐴𝐴𝜈𝜈 3
(1)
1
(2)
2
𝜌𝜌(𝑡𝑡)𝐴𝐴𝜈𝜈 3 𝐶𝐶𝑝𝑝 (𝑣𝑣)
(5)
𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓
The available and realistic wind power moving across the rotor blades per unit sweep area are defined as (1) and (2), respectively (Olaofe, 2013): 𝑃𝑃𝑎𝑎𝑎𝑎 (𝑣𝑣) =
(4)
and 𝑣𝑣ℎ are the forecast and actual wind where 𝑣𝑣ℎ speed at time h, respectively; N is the number of forecast samples. This model can also be used to measure the performance of the wind power forecasting models. In this case “v” will be replaced by “P” to denote power. Small RMSE and MAE errors means that the difference between forecast wind speed/power and the actual wind speed/power is small. If RMSE and MAE are small enough, then the forecasting models will be deemed adequate.
where 𝑃𝑃𝑎𝑎𝑎𝑎 (𝑣𝑣) is the ideal available wind power and 𝑃𝑃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 (𝑣𝑣) stands for the realistic power generated by the wind turbine in Watts(W), 𝜌𝜌(𝑡𝑡) is time varying air density, which depends on surrounding atmospheric pressure and temperature. A is the sweep area of the blades in (m2), and v is wind speed (m/s). The ideal available wind power (𝑃𝑃𝑎𝑎𝑎𝑎 (𝑣𝑣) ) is related to the power 𝑃𝑃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 (𝑣𝑣) that can be generated by a wind turbine by means of the power coefficient (𝐶𝐶𝑝𝑝 ). The 𝐶𝐶𝑝𝑝 for a particular turbine is determined by the tip angle, the blade design and the relationship between wind speed and rotor speed. The maximum power coefficient (Betz limit) is 0.593 (Carrillo, et al., 2013). However, this value is not achievable in practice. The power coefficient at various operating conditions were not available. For the purpose of comparison, 0.5 was used as the power coefficient for all three models.
2.4 Power Law Equation The wind speed data provided by the Wind Atlas of South Africa were measured at maximum 62 m above ground which is lower than the minimum hub height of 80m for Vestas V90/1800 wind turbine which was selected for this study. As a result, the power law equation was used to estimate the wind speed at the desired hub height by using the wind speed measured at the lower height as inputs. Power law equation is given as (Joustra, 2014): ℎ
(𝑣𝑣1 ) = (𝑣𝑣0 ) ( 1 ) ℎ0
𝛼𝛼
(6)
where 𝑣𝑣1 is the wind speed measured at ℎ1 meters above ground and 𝑣𝑣0 is the wind speed measured at ℎ0 meters above ground. In this paper, ℎ1 = 90 m and ℎ0 = 62 m. The representative surface roughness exponent (α) at a specific
As indicated in (1) and (2), the air density is one of the very important factors affecting the amount of wind power generated by the wind turbine. The relationship between the 415
IFAC CPES 2018 416 Tokyo, Japan, September 4-6, 2018
Q. Chen et al. / IFAC PapersOnLine 51-28 (2018) 414–419
where Cov stands for the covariance, and Var stands for the variance.
site is dependent on the terrain condition. The roughness exponent value of 0.089 was obtained by using (6) (Kwon, 2010).
The partial autocorrelation function (PACF) was used to measure the degree of association between 𝑦𝑦𝑡𝑡 and 𝑦𝑦𝑡𝑡−𝑘𝑘 when the effects of other time lags 𝑦𝑦𝑡𝑡−1 , … , 𝑦𝑦𝑡𝑡−𝑘𝑘−1 are removed.
3. AUTOREGRESSIVE MOVING AVERAGE (ARMA) Many existing time-series methods can be used to forecast wind speed and power. The ARMA is one of the most robust and simple time-series methods. As a result, the ARMA method was used in this paper. The ARMA model consists of two components, namely, autoregressive (AR) and moving average (MA). In an AR model, a variable value in one period is related to its values in the previous periods. In a MA model, the possibility of a relationship between a variable and the residuals from previous periods is accounted for. Integrated term (I) in an ARIMA model is used when a variable 𝑦𝑦𝑡𝑡 is not stationary. The wind data used in this paper is stationary. Therefore, integrated term was not required. ARIMA models without integrated term is ARMA.
Table 2. Properties of ACF and PACF. ACF PACF
∑𝑝𝑝𝑖𝑖=1 𝛷𝛷𝑖𝑖 𝑦𝑦𝑡𝑡−𝑖𝑖 + ∑𝑞𝑞𝑗𝑗=1 𝜃𝜃𝑗𝑗 𝑒𝑒𝑡𝑡−𝑗𝑗 + 𝜀𝜀𝑡𝑡
(7) 4. ARTIFICIAL INTELLIGENCE METHODS 4.1 Artificial Neural Network ANNs can model complex non-linear relationships and approximate measurable functions to forecast wind speed and power. They are some of the most widely used models in the last decade for forecasting future events (Ma, et al., 2009) (Hippert, et al., 2001).
The Box-Jenkins methodology was used by (Burnham & Anderson, 2002) to fit an ARMA model to a set of wind speed data. In the first step, all the unusual observations were identified by plotting the wind speed data against time. Variances were stabilized in the second step by using a BoxCox (The Box-Cox transformation, 2017). In the third step, the Dickey-Fuller test was carried out to test the stationarity of the wind speed data. Equation (8) was constructed to check the stationarity of the wind speed data.
The key element of an ANN is the interconnected neurons. Each neuron or node works as an independent computation unit which is defined as (More & Deo, 2003): 𝑌𝑌 = 𝑓𝑓[∑(𝑥𝑥1 𝑤𝑤1 + 𝑥𝑥2 𝑤𝑤2 +𝑥𝑥3 𝑤𝑤3 + ⋯ ) + 𝛽𝛽)
(8)
𝑝𝑝−1
There are many neural network architectures that have already been developed and implemented for forecasting applications. The ANN work-horse, the multilayer perceptron uses feed-forward architecture. The feed-forward multilayer network is a network in which no loop occurs in the network path (Aggarwal, et al., 2005). The structure of a feed-forward neural network with two input nodes, five hidden nodes, and on output node is shown in Fig. 1 (More & Deo, 2003).
(9)
The next step is to use the autocorrelation function (ACF) and the partial autocorrelation function (PACF) to find a suitable ARMA model. The ACF is the proportion of the autocovariance of 𝑦𝑦𝑡𝑡 and 𝑦𝑦𝑡𝑡−1 to the variance of a dependent variable 𝑦𝑦𝑡𝑡 as given in (10) (Katchova, 2017), 𝐴𝐴𝐴𝐴𝐴𝐴(𝑘𝑘) =
𝐶𝐶𝐶𝐶𝐶𝐶(𝑦𝑦𝑡𝑡 ,𝑦𝑦𝑡𝑡−𝑘𝑘 ) 𝑉𝑉𝑉𝑉𝑉𝑉 (𝑦𝑦𝑡𝑡 )
(11)
where 𝑥𝑥1 , 𝑥𝑥2 , 𝑥𝑥3 , … are the input variables, such as wind speed, wind direction, temperature, etc; 𝑤𝑤1 , 𝑤𝑤2 , 𝑤𝑤3 , … are the connection weights; 𝛽𝛽 is the bias value; f is the transfer function, which can be identity function or sigmoidal function.
Where 𝜌𝜌 is coefficient of 𝑦𝑦𝑡𝑡−1 , 𝑒𝑒𝑡𝑡 is error term. The model (8) is non-stationary, or a unit root is present if | 𝜌𝜌| =1. The stationarity of the model with a drift and additional lags of the dependent variable can be tested by using an augmented Dickey-Fuller test. It is defined as: 𝛥𝛥𝛥𝛥𝑡𝑡 = 𝜇𝜇 + (𝜌𝜌 − 1)𝑦𝑦𝑡𝑡−1 + ∑𝑗𝑗=1 𝜃𝜃𝑗𝑗 𝛥𝛥𝛥𝛥𝑡𝑡−1 + 𝜀𝜀𝑡𝑡
ARMA (p, q) Tails off Tails off
The next step is to find the preferred models based on the white noise test and goodness of fit. The final step was then to check if the residuals look like white noise by plotting the ACF of residuals. The ‘forecast’ package in R was used to model ARMA models. In this paper several models have been investigated and it was found that ARMA (2, 1) which consists of the 2nd order of the autoregressive and the 1st order of moving average has the best criteria test results. Therefore, it was used for the wind speed and power forecasting.
Where 𝑦𝑦𝑡𝑡 is a variable at time t, 𝛷𝛷𝑖𝑖 is the 𝑖𝑖th autoregressive parameter, 𝜃𝜃𝑗𝑗 the 𝑗𝑗th parameter of moving average, 𝑒𝑒𝑡𝑡−𝑗𝑗 is the lagged error term at time t-j, 𝜀𝜀𝑡𝑡 the error term at time t.
𝛥𝛥𝛥𝛥𝑡𝑡 = (𝜌𝜌 − 1)𝑦𝑦𝑡𝑡−1 + 𝑒𝑒𝑡𝑡
MA (q) Cuts off after lag q Tails off
The properties of the ACF and PACF were used to determine the number of order of AR and MA (Katchova, 2017).
ARMA (p, q) denotes an ARMA model with p autoregressive lags, q moving average lags. It can be defined as: 𝑦𝑦𝑡𝑡 =
AR (p) Tails off Cuts off after lag p
(10)
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Step 2. Create the network. The sigmoid function in the hidden layer was used to reduce the effect of extreme input values. Step 3. Configure the network by dividing input vectors and target vectors into three sets, namely, training set, validation set, and testing set. 70% of data were used for training. Both validation and testing set used 15% of data. The best number of hidden neurons were selected by checking the performance of the model with different hidden neurons. 10 hidden neurons were used in this paper. Step 4. Initialize the weights and biases for the network. The initial weight and biases were selected based on the relationship between the input and target data. Step 5. Select Bayesian Regularization as the training algorithm, as it can result in good generalization for difficult, or small wind dataset. Step 6. Validate the network. Step 7. Use the network to forecast wind speed and power by importing the historical data into the input nodes.
Fig. 1: Structure of a feed-forward neural network with two input nodes, five hidden nodes and one output node. As can be seen in Fig. 1, there are two layers in the feedforward neural network, namely, the hidden layer and output layer. The number of input nodes in the input layer is based on a prior knowledge of the behaviour of the system. Each input node represents an input variable which can be wind speed, wind direction or temperature and etc. It is harder to decide on the number of neurons in the hidden layer as compared to those of the input or output layers. (Hippert, et al., 2001) suggest using trial and error method to find a suitable number of neurons in the hidden layer. The number of output neurons required is dependent on the forecasting profiles.
4.2 Adaptive-network-based Fuzzy Inference System (ANFIS) The adaptive neuro-fuzzy inference system (ANFIS) is a system with the combination of fuzzy logic technique and neuro network technique which bring the learning capabilities of the neural networks to fuzzy inference systems (MathWorks, 2017). In an ANFIS, the neuro-adaptive learning methods are used to adjust the parameters of the membership function. The shape of the membership functions is changing accordingly with the parameters. The structure of the neuro-fuzzy model for wind power forecasting can be presented as a special multilayer feedforward neural network.
There are three commonly used forecasting profiles, namely, iterative, multi-model and single-model. Iterative forecasting is done by forecasting a unit of wind data at a time. Multimodel forecasting is a common method for forecasting with regression; the number of models used depends on the gap between forecasting. The advantage of using multi-model forecasting is that each ANN is relatively small. Therefore, the overfitted is unlikely to happen. Single-model multivariable forecasting is done by using multiple variables as inputs to forecast multiple wind speeds as outputs at once (Hippert, et al., 2001). Single-model multivariable forecasting profile was used in this paper.
Two commonly used fuzzy inference methods are Mamdani and Sugeno-type. In this paper, the Sugeno-type method is used in the ANFIS because it works well with adaptive techniques and optimization (Sugeno-type fuzzy inference, 2017). Therefore, the output membership functions are limited to constant and linear. The input to the model were maximum, minimum, and average wind speed measured at 62 m above ground.
A training method was chosen for the neural network to fit the inputs and targets. Three commonly used training algorithms are Levenberg-Marquardt, Bayesian Regularization, and Scaled Conjugate Gradient. LevenbergMarquardt requires more memory for computation but takes less time (Hagan & Menhaj, 1994). Bayesian Regularization usually requires more computation time, but it can result in good generalization for difficult, noisy or small datasets (Ticknor, 2013). Scaled Conjugate Gradient is suitable for large problems as it uses gradient calculations which require less memory (Saini & Soni, 2002) (Lazarevska, 2016).
The hybrid optimization method consisting of the backpropagation gradient descent and least-squares were used in this paper. The membership function used in this paper is Gaussian as it has similar shape as wind speed data. Training epochs and the training error tolerance needed to be specified once the optimization method is selected. The training process stopped when either training error tolerance or training epochs reached the predefined goals. The last step is to verify the performance of the model by using validation dataset and evaluation metrics (Adaptive neural-fuzzy modeling, 2017).
In this paper, seven steps have been followed in the design process of the ANNs as discussed below. Step 1: Collect, pre-process, and analyse wind data. The input to the model are the maximum, minimum and average wind speed measured at 62 m above ground.
5. DATA COLLECTION AND ANALYSIS The data used in this paper are collected from the Wind Atlas of South Africa. The data sets contain wind speed (m/s) 417
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measured at different heights, wind direction (°TN), temperature (°C), atmospheric pressure (hPa), and relative humidity (%) with 10 minutes resolution for the period from Midnight 31 December 2010 to Midnight 1 January 2017. The data were analysed before applying them to the forecasting models as inputs. Descriptive statistics were used to summarize data from a sample using indices such as the mean, maximum, minimum and standard deviation. Inferential statistics were used to describe associations within the data by figuring out the correlation and regression (Descriptive and inferential statistics, 2017). 6. SIMULATION RESULTS AND DISCUSSION 6.1 Wind Power Forecasting The forecast wind speeds were converted to the estimated wind speed at the hub height by using the power law equation (6). The estimated wind speeds at the hub height were then used to calculate the estimated wind power by using (2). Since there is no actual wind power data collected in this paper, the actual wind speed data were used to calculate the “calculated actual wind power”. The plots of the calculated wind power and the very-short-term forecast wind power are shown in Fig. 2.
Fig. 3: Plots of the calculated actual wind power and the forecast wind power of the ARMA (2, 1), ANN and ANFIS over short-term (1 hour ahead) time horizon. As can be seen in Fig. 3, the plot of forecast wind power (red dot-dash line) of the ARMA (2, 1) tracks the calculated actual wind power closely for the most of samples. The plots of ANN (orange solid line) and ANFIS (purple dot line) have similar shape. This is expected as both methods have good training ability. The margin between the forecast wind power of ANN and the calculated actual wind power (blue solid line) is small for the most of samples. However, the margin between samples 120 to samples 130 is big. This is due to the sharp increase of the calculated actual wind power. The ANN wasn’t able to accurately forecast wind power when the difference between adjacent samples is big. The evaluation results will be much better if the margin between samples 120 to samples 130 is reduced. Table 2 quantifies the performance of each model. Table 2: Summary of the normalized RMSE and MAE for wind power forecast. Time Horizon
Fig. 2: Plots of the calculated actual wind power and the forecast wind power of the ARMA (2, 1), ANN and ANFIS over very-short-term (10 minutes ahead) time horizon.
Very-shortterm (10 minutes ahead) Short-term (1 hour ahead)
As can be seen in Fig. 2, the plots of all three models track the plot of the calculated actual wind power closely. This agree with the result as suggested by (Chang, 2014) (Ma, et al., 2009).
ARMA
Artificial Neural Network RMSE MAE [%] [%]
RMSE [%]
MAE [%]
5.8
4.2
5.6
11.3
8.8
18.1
ANFIS
RMSE [%]
MAE [%]
3.8
5.7
3.9
12.3
18.4
12.2
As can be seen in Table 2, all three models perform well for the very-short-term time horizon wind power forecasting. For the short-term forecasting, the ARMA has the lowest forecasting errors among the three models. The evaluation results for very-short-term forecast are expected, as all three methods are very good at very-short-term wind power forecasting. However, the short-term forecast results of the ANN and ANFIS are not as good as one would have expected. It can be seen from table 2 that RMSE and MAE values increase with the forecasting time horizon. Therefore,
Fig. 3 shows the plots of the calculated wind power, the forecasted wind power using ARMA, ANNs, and ANFIS for short-term time horizon.
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we can conclude that the performances of all the models degrade with the increases of the prediction lead time.
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turbines. Renewable and Sustainable Energy Reviews, Vol. 21, pp. 572-581. Chang, W.-Y., (2014). A Literature Review of Wind Forecasting Methods. Journal of Power and Energy Engineering , Vol. 2, pp. 161-168. Hagan, M. T. & Menhaj, M. B., (1994). Training feedforward networks with the Marquardt Algorithm. IEEE Transactions on Neural Networks, 5(6), pp. 989-993. Hippert, H. S., Pedreira, C. E. & Souza, R. C., (2001). Neural networks for short-term load forecasting: a review and evaluation. IEEE Transactions on Power Systems, 16(1), pp. 44-54. Joustra, Y., (2014). Forecasting of wind power production in the Netherlands, Enschede, Netherlands: University of Twente. Katchova, A., (2017). Econometrics Academy. [Online] Available at: https://sites.google.com/site/econometricsacademy/econo metrics-models/time-series-arima-models [Accessed 31 October 2017]. Kwon, S.-D., (2010). Uncertainty analysis of wind energy potential assessment. Applied Energy, Vol. 87, pp. 856865. Lazarevska, E., (2016). Comparison of different models for wind speed prediction. Florence, Italy, s.n. Ma, L. Luan, S. Jiang, C. Liu, H. Zhang, Y. (2009). A review on the forecasting of wind speed and generated power. Renewable and Sustainable Energy Reviews, Vol. 13, pp. 915-920. MathWorks, T., (2017). Fuzzy Logic Toolbox™ User's Guide. Natick, MA: The MathWorks, Inc.. Mbuvha, R., (2017). Bayesian neural networks for short term wind power forecasting. Stockholm, Sweden: KTH Institute of Technology School of Computer Science and Communication. More, A. & Deo, M., (2003). Forecasting wind with neural networks. Marine Structures, Vol. 16, pp. 35-49. Olaofe, Z. O., (2013). Wind energy generation and forecasts: a case study of Darling and Vredenburg sites. Msc Thesis Cape Town: University of Cape Town. Saini, L. M. & Soni, M. K., (2002). Artificial neural networkbased peak load forecasting using conjugate gradient methods. IEEE Transactions on Power Systems, 17(3), pp. 907-912. Soman, S. S., Zareipour, H., Malik, O. & Mandal, P., (2010). A review of wind power and wind speed forecasting methods with different time horizons. In: EEE, ed. North American Power Symposium (NAPS). s.l.:s.n., pp. 1-8. Ticknor, J. L., (2013). A Bayesian regularized artificial neural network for stock market forecasting. Expert Systems with Applications, Vol. 40, pp. 5501-5506. Wu, Y.-K. & Hong, J.-S., (2007). A literature review of wind forecasting technology in the world. IEEE, Lausanne, Switzerland. Zhang, G. P., (2003). Time series forecasting using a hybrid ARIMA and neural network model. Neurocomputing, Vol. 50, pp. 159-175.
7. CONCLUSIONS Based on the evaluation results, the ARMA (2, 1) has the lowest wind power forecasting error over the short-term time horizon. It has 3.5% and 3.4% less MAE errors than the ANNs and ANFIS respectively. The difference among shortterm wind power forecasting errors of three models is well within the errors commonly found in the collected data. Therefore, more data and simulations are required to make valid comparison. The performance of artificial intelligence methods, (ANNs and ANFIS) perform and the conventional method over the very-short-term time horizons is very similar. All three models have less than 6% very-short-term wind power forecasting errors. The ANNs and ANFIS have similar performance results. According to the evaluation results, both artificial intelligence and conventional methods are suitable for the very-short-term and short-term wind power forecasting.
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Wind Power Forecasting Wind Power Forecasting Wind Forecasting WindQ.Power Power Chen*, Forecasting K. A. Folly** WindQ.Power Chen*, Forecasting K. A. Folly**
Q. Q. Chen*, Chen*, K. K. A. A. Folly** Folly** Q. Chen*, K. A. * Electrical Engineering Department,Folly** University of Cape Town, * Cape Electrical Engineering Department, University of Cape Town, Town, South Africa, (e-mail: [email protected]) ** Cape Electrical Engineering Department, University of Cape Town, Town, South Africa, (e-mail: [email protected]) Electrical Engineering Department, University **Cape Electrical Engineering Department, Universityof ofCape CapeTown, Town, Town, South Africa, (e-mail: [email protected]) * Electrical Engineering Department, University of Cape ** Electrical Engineering Department, University of CapeTown, Town, Cape Town,Africa, South(Tel: Africa, (e-mail: [email protected]) Cape ** Town, South 0216504490; e-mail: [email protected]) Electrical Engineering Department, University of Cape Town,Africa, South(Tel: Africa, (e-mail: [email protected]) Cape ** Town, South 0216504490; e-mail: [email protected]) Electrical Engineering Department, University of Cape Cape Town, Town, Cape Town, South (Tel: e-mail: Electrical Engineering Department, University of Cape Town, Cape ** Town, South Africa, Africa, (Tel: 0216504490; 0216504490; e-mail: [email protected]) [email protected]) Cape Town, Southwind Africa, (Tel: 0216504490; [email protected]) Abstract: Accurate short-term power forecast is very e-mail: important for reliable and efficient operation Abstract: Accurate short-term wind power forecast is veryThere important for reliable and efficient operation of power Accurate systems with high wind wind power powerforecast penetration. are many conventional and operation artificial Abstract: short-term is very important for reliable and efficient of power systems with high wind power penetration. There are many conventional and artificial Abstract: Accurate short-term wind power forecast is veryaccurate important for power reliableforecasting. and efficient operation intelligence methods that have been developed to achieve wind Time-series of power systems with high wind power penetration. There are many conventional and artificial Abstract: Accurate short-term wind power forecast is very important for reliable and efficient operation intelligence methods that have been developed to achieve accurate wind power forecasting. Time-series of power systemsarewith highto wind powerrobust, penetration. There many conventional and artificial based algorithms known be simple, and have beenare used inpower the past for forecasting with intelligence methods that have developed to accurate wind forecasting. Time-series of power systems hightobeen wind powerrobust, penetration. There many conventional and artificial based algorithms arewith known be simple, andhave have beenare used inpower the past for forecasting with intelligence methods that have been developed to achieve achieve accurate wind forecasting. Time-series some level of success. Recently some researchers advocated for artificial-intelligence based based algorithms are known be simple, robust, and have been used in the past for forecasting with intelligence methods that haveto been developed to achieve accurate windfor power forecasting. Time-series some level of success. Recently some researchers have advocated artificial-intelligence based based algorithms are known to be simple, robust, and have been used in the past for forecasting with methods suchofassuccess. ArtificialRecently Neural Networks (ANNs), Fuzzy Logic, etc., for for forecasting because ofbased their some level some have artificial-intelligence based algorithms are known to beNetworks simple, robust, andFuzzy have advocated been used in past for forecasting with methods such Artificial Neural (ANNs), Logic, etc., forthe forecasting because ofbased their some level ofassuccess. Recently some researchers researchers have advocated for artificial-intelligence flexibility. This paper presents a comparison of conventional and two artificial intelligence methods for methods such as Artificial Neural Networks (ANNs), Fuzzy Logic, etc., for forecasting because of their some level of success. Recently some researchers have advocated for artificial-intelligence based flexibility. This presents a comparison of conventional and two artificial intelligence methods for methods such aspaper Artificial Neural Networksmethod (ANNs), Fuzzy Logic, etc., for forecasting because of their wind power forecasting. The conventional discussed in this paper is the Autoregressive Moving flexibility. This presents aa comparison of conventional and two artificial intelligence methods for methods such aspaper Artificial Neural Networksmethod (ANNs), Fuzzy Logic, etc., for forecasting because of their wind power forecasting. The conventional discussed in this paper is the Autoregressive Moving flexibility. This paper presents comparison of conventional and two artificial intelligence methods for Average (ARMA) whichThe is conventional one of the most robust and simple time-series methods. The artificial wind power forecasting. method discussed in this paper is Autoregressive Moving flexibility. This paper presents a comparison of conventional and two artificial methods for Average (ARMA) which is conventional one of Neural the most robust and simple time-series methods. The artificial wind power forecasting. The method discussed in this paper is the theintelligence Autoregressive Moving intelligence methods are Artificial Networks (ANNs) and Adaptive Neuro-fuzzy Inference Average (ARMA) which is one of the most robust and simple time-series methods. The artificial wind power forecasting. The conventional method discussed in this paper is the Autoregressive Moving intelligence methods are Artificial Neural Networks (ANNs) and Adaptive Neuro-fuzzy Inference Average (ARMA) Simulation which is one of for thevery-short-term most robust and time-series methods. TheANNs artificial Systems (ANFIS). results and simple short-term forecasting show that and intelligence methods are Artificial Neural Networks (ANNs) and Adaptive Neuro-fuzzy Inference Average (ARMA) which is one of for thevery-short-term most robust and simple methods. TheANNs artificial Systemsare (ANFIS). Simulation results and short-term forecasting showforecasting, that and intelligence methods are Artificial Neural Networks (ANNs) andtime-series Adaptive Neuro-fuzzy Inference ANFIS suitable for the very-short-term (10 minutes ahead) wind speed and power and Systems (ANFIS). Simulation results for very-short-term and short-term forecasting show that ANNs and intelligence methods are Artificial Neural Networks (ANNs) and Adaptive Neuro-fuzzy Inference ANFIS are suitable for the very-short-term (10 minutes ahead) wind speed and power forecasting, and Systems (ANFIS). Simulation results for(1 very-short-term and speed short-term forecasting show that ANNs and the ARMA is suitable for thevery-short-term short-term hour ahead) wind andspeed power forecasting. ANFIS are suitable for (10 minutes ahead) wind and power Systems (ANFIS). Simulation results for(1 very-short-term and short-term forecasting showforecasting, that ANNs and the ARMA is suitable thevery-short-term short-term hour speed andspeed power forecasting. ANFIS are suitable forforthe the (10 ahead) minuteswind ahead) wind and power forecasting, and the ARMA is suitable for the short-term (1 hour ahead) wind speed and power forecasting. ANFIS are suitable for the very-short-term (10 minutes ahead) wind speed and power forecasting, © 2018, IFAC (International of(1 Automatic Control) by Elsevier Ltd. All rights reserved.and Keywords: Wind power artificial neural networks, ARMA, ANFIS. the ARMA is suitable forforecasting, theFederation short-term hour ahead) windHosting speed and power forecasting. Keywords: power artificial neural networks, ARMA, the ARMA Wind is suitable forforecasting, the short-term (1 hour ahead) wind speed and ANFIS. power forecasting. Keywords: Wind power forecasting, artificial neural networks, ARMA, ANFIS. networks, Keywords: Wind power forecasting, artificial neural ARMA, ANFIS. networks, Keywords: Wind power forecasting, artificial neural ARMA, that ARMA andANFIS. the two artificial methods (ANNs and 1. INTRODUCTION that ARMA and the for twotheartificial methods (10 (ANNs and ANFIS) are suitable very-short-term minutes 1. INTRODUCTION that ARMA and the two artificial methods (ANNs and ANFIS) are suitable for the very-short-term (10 minutes ARMA and the(1two artificial methods (ANNs and 1. INTRODUCTION ahead) and short-term hour ahead) wind power(10 forecasting. With the depletion of energy resources and the that 1. conventional INTRODUCTION ANFIS) are suitable for the very-short-term minutes that ARMA and the two artificial methods (ANNs and ahead) and short-term (1 hour ahead) wind power(10 forecasting. With the depletion of conventional energy resources and the ANFIS) are suitable for the very-short-term minutes 1. INTRODUCTION deterioration of the environment, renewable energy will ahead) and short-term (1 hour ahead) wind power forecasting. ANFIS) are suitable for the very-short-term (10 minutes With the of conventional energy resources andwill the The paper organized(1ashour follows: The nextpower section discusses deterioration of the environment, renewable energy andisshort-term ahead) wind forecasting. With the depletion depletion conventional energy resources the ahead) gradually become aofcrucial energy source (Ma, et al.,and 2009). The paper organized follows: The next section discusses ahead) andisshort-term (1ashour ahead) wind power forecasting. deterioration of the environment, renewable energy will With the depletion of conventional energy resources and the the time-scale classification and wind power forecasting. gradually become a crucial energy source (Ma, et al., 2009). deterioration of the of environment, renewable energy will The paper is organized as follows: The next section discusses Wind energy is one the most available, affordable, and the time-scale classification and wind power forecasting. The paper is organized as follows: The next section discusses gradually become aa crucial source (Ma, et al., deterioration of the environment, renewable energy will 3 and classification 4 reviewed and the wind Autoregressive Moving Wind energy is sources. one of theenergy mostthis, available, affordable, and Section gradually become crucial energy source (Ma, et al., 2009). 2009). the time-scale power forecasting. The paper is organized as follows: The next section discusses efficient energy Despite wind speed varies from Section 3 and 4 reviewed the Autoregressive Moving the time-scale classification and wind power forecasting. Wind energy is one of the most available, affordable, and gradually become a crucial energy source (Ma, et al., 2009). Average (ARMA) method and the artificial intelligence efficient energy sources. Despite this, wind speed varies from Windtoenergy is oneit of the mosttoavailable, affordable, and Section 3 and 4 reviewed the Autoregressive Moving the time-scale classification and wind power forecasting. time time and; is difficult accurately predict wind Average (ARMA) method and the artificial intelligence Section 3 and 4 reviewed the Autoregressive Moving efficient energy sources. Despite this, wind speed varies from Wind energy is one of the most available, affordable, and methods, (ARMA) respectively. Section 5 the is concerned with data time to(Wu time and; it 2007). is difficult to accurately efficient energy sources. Despite this, wind speedpredict varies wind from Average method and artificial intelligence Section 3 and 4 reviewed the Autoregressive Moving power & Hong, methods, respectively. Section 5 is concerned with data Average (ARMA) method and the artificial intelligence time to time and; it is difficult to accurately predict wind efficient energy sources. Despite this, wind speed varies from collection and analysis. Section 6 presents the simulation power Hong,it 2007). time to(Wu time& and; is difficult to accurately predict wind Average methods, respectively. Section 5 is concerned with data (ARMA) method and the artificial intelligence collection and analysis. Section 6 presents the simulation Section 5 Conclusion is concernedis with power (Wu & Hong, time toare time it 2007). is difficult accurately predict wind methods, results andrespectively. detailed discussions. givendata in There many methods that havetobeen developed to handle power (Wu & and; Hong, 2007). collection and analysis. Section 6 presents the simulation methods, respectively. Section 5 is concerned with data results and detailed discussions. Conclusion is given in There are many methods that have been developed to handle collection and analysis. Section 6 presents the simulation power (Wu & Hong, 2007). Section 7. wind speed prediction. The conventional method presented in results and detailed discussions. Conclusion is given collection and analysis. Section 6 presents the simulation Section 7. There are many methods that have been developed to handle wind speed prediction. The conventional method presented in and detailed discussions. Conclusion is given in in There are many methods that autoregressive have been developed toaverage handle results this paper is the time series moving Section 7. results and detailed discussions. Conclusion is given in wind speed The conventional method presented in There are many methods that have been developed toaverage handle this isprediction. theARMA time series autoregressive moving 7. windpaper speed prediction. The conventional method presented in Section (ARMA). In an model, the future value of a variable this is the time series autoregressive moving average windpaper speedIn The conventional method presented in Section 7. (ARMA). an ARMA model, the future value of a variable this paper isprediction. thebe time series autoregressive moving average is assumed to equal to a linear function of some past 2. TIME-SCALE CLASSIFICATION AND WIND POWER (ARMA). ARMA model, the value aa variable this paper In istoan thebe time series moving average is assumed equal to aautoregressive linear function ofof past 2. TIME-SCALE CLASSIFICATION WIND POWER (ARMA). In an ARMA model, the future future value of some variable observations and random errors (Zhang, 2003). FORECASTINGAND is assumed to be equal to a linear function of some past (ARMA). an be ARMA the future valueofof some a variable 2. TIME-SCALE CLASSIFICATION WIND observations and random errors (Zhang, 2003). FORECASTINGAND is assumedInto equalmodel, to a linear function past 2. TIME-SCALE CLASSIFICATION AND WIND POWER POWER observations and random errors (Zhang, 2003). is assumed to be equal to a linear function of some past FORECASTING 2. TIME-SCALE CLASSIFICATION AND WIND POWER The artificial intelligent methods that are discussed are observations and random errors (Zhang, 2003). FORECASTING The artificial methods that2003). are the discussed are 2.1 Time-scale Classification observations andintelligent random errors (Zhang, FORECASTING Artificial Neural Networks (ANNs) and AdaptiveThe artificial intelligent methods that are discussed are 2.1 Time-scale Classification Artificial Neural Networks (ANNs) and the AdaptiveThe artificial intelligent methods that are discussed are network-based Fuzzy Inference System (ANFIS). An ANN is Artificial Neural Networks (ANNs) and AdaptiveThe artificial intelligent methods that(ANFIS). are the discussed are network-based Fuzzy Inference System An ANN is 2.1 2.1 Time-scale Time-scale Classification Classification Artificial Neural Networks (ANNs) and the Adaptiveable to perform a nonlinear mapping between a set of input 2.1 Time-scale Classification network-based Fuzzy Inference System (ANFIS). An ANN is Artificial Neural Networks (ANNs) and the Adaptiveable to perform a nonlinear mapping between a set of input Different authors have different opinions about the time-scale network-based Fuzzy Inference System (ANFIS). An ANN is and output variables. An ANFIS is abetween fuzzy system whose Different authors have differentofopinions about the time-scale able to perform a nonlinear mapping a set of input network-based Fuzzy Inference System (ANFIS). An ANN is classification of the operation electricity systems. (Soman, and output variables. An ANFIS is a fuzzy system whose able to perform a nonlinear mapping between a set adjusted of input Different parameters of the membership function have been authors have different opinions about the time-scale classification of the operation of electricity systems. (Soman, and output variables. An ANFIS is a fuzzy system whose able to perform a nonlinear mapping between a set of input Different authors have different opinions about the time-scale et al., 2010; Wu & Hong, 2007; Zhang, 2003; Zhao, et al., parameters of the membership function have been adjusted and output variables. Anlearning ANFISmethods is a fuzzy system whose classification by using neuro-adaptive like the techniques of the operation of electricity systems. (Soman, Different authors have different opinions about the time-scale et al., 2010; Wu & Hong, 2007; Zhang, 2003; Zhao, et al., parameters of the membership function have been adjusted classification of the operation of electricity systems. (Soman, and output variables. An ANFIS is a fuzzy system whose 2011) separate the time-scale for the operation of electricity by using neuro-adaptive learning methods like the techniques parameters of the membership function have been adjusted et used for neuro-adaptive training neurallearning networks (Adaptive neural-fuzzy al., 2010; Wu & Hong, 2007; Zhang, 2003; Zhao, et al., classification of the operation of electricity systems. (Soman, 2011) separate the time-scale for the operation of electricity by using methods like the techniques al., 2010; Wu categories. & Hong, 2007; Zhang, 2003; Zhao, of et the al., parameters of the membership function have been adjusted et systems into four Table 1 shows a summary used for neuro-adaptive training neurallearning networks (Adaptive neural-fuzzy by using methods like the techniques modeling, 2017). 2011) separate the time-scale for the operation of electricity et al., 2010; Wu & Hong, 2007; Zhang, 2003; Zhao, et al., systems intoclassification four categories. Table 1 shows a summary of the used for training neural networks (Adaptive neural-fuzzy 2011) separate the time-scale for the operation of electricity by using neuro-adaptive learning methods like the techniques modeling, 2017). time-scale for different forecasting techniques used for training neural networks (Adaptive neural-fuzzy systems into four categories. Table 1 shows a summary of the 2011) separate the time-scale for the operation of electricity time-scale different forecasting techniques modeling, 2017). systems into four categories. Table 1 shows a summary of the used training neural networks (Adaptive neural-fuzzy et classification al., 2010; Wu for & Hong, 2007; Zhang, 2003; Zhao, In thisfor paper, the Autoregressive Moving Average (ARMA) (Soman, modeling, 2017). time-scale classification for different forecasting techniques systems into four categories. Table 1 shows a summary of the (Soman, et al., 2010; Wu & Hong, 2007; Zhang, 2003; Zhao, In this paper, the Autoregressive Moving Average (ARMA) modeling, 2017). time-scale classification for different forecasting techniques al., 2011). is compared with artificial intelligence methods (ARMA) such as et (Soman, et al., 2010; Wu & Hong, 2007; Zhang, 2003; Zhao, time-scale classification for different forecasting techniques In this paper, the Autoregressive Moving Average et al., 2011). is compared with artificial (ANNs) intelligence methods such as (Soman, et al., 2010; Wu & Hong, 2007; Zhang, 2003; Zhao, In this paper, the Autoregressive Moving Artificial Neural Networks and Average Adaptive(ARMA) Neuroet al., 2011). (Soman, et al., 2010; Wu & Hong, 2007; Zhang, 2003; Zhao, is compared with artificial intelligence methods such as In this paper, the Autoregressive Moving Average (ARMA) Artificial Neural Networks (ANNs) and Adaptive Neurois compared with artificial intelligence methods such as et al., 2011). fuzzy Inference Systems (ANFIS). Simulation resultsNeuroshow et al., 2011). Artificial Neural Networks (ANNs) and Adaptive is compared with artificial intelligence methods such as fuzzy Inference Systems (ANFIS). Simulation results show Artificial Neural Networks (ANNs) and Adaptive Neurofuzzy Inference (ANFIS). results show Artificial NeuralSystems Networks (ANNs)Simulation and Adaptive fuzzy Inference Systems (ANFIS). Simulation resultsNeuroshow fuzzy Inference Systems (ANFIS). Simulation results show
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air density, temperature and barometric pressure measured at the site is given by (3) (Olaofe, 2013).
Table 1. Time-horizon classification for wind power forecasting.
𝑔𝑔ℎ
𝑃𝑃
𝜌𝜌(𝑡𝑡) = ( ) 𝑒𝑒 −(𝑅𝑅𝑅𝑅) 𝑅𝑅𝑅𝑅
(3)
where 𝜌𝜌(𝑡𝑡) is the time varying air density in (kg/m3), 𝑃𝑃 is barometric pressure in (Pa), T is the air temperature in (K), R is the specific gas constant for dry air, 287.058 (J/(kg.K)), g is the gravity of Earth, 9.81(m/s2), h is the hub height above ground level in (m) (Olaofe, 2013). 2.3 Performance Measurements It is difficult to accurately measure the performance of different wind speed and power forecasting models by comparing the forecasted wind speed plots against the actual wind speed plots. In this paper, the predictive performance was quantified by using the mean absolute error (MAE) and the root mean square (RMSE). The RMSE and MAE are defined as in (4) and (5), respectively (Mbuvha, 2017):
The very-short-term and short-term time horizons are the main focus of this paper, as they are suitable for the real-time grid operations and load increment/decrement decisions. 2.2 Wind Speed Versus Wind Power
1
𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 2 ) 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 = √ ∑𝑁𝑁 ℎ=1(𝑣𝑣ℎ − 𝑣𝑣ℎ
The output power of a wind turbine depends on the wind speed, which varies over a wide range of time and depends on regional landscape type, weather patterns, and seasonal variations (Wu & Hong, 2007) (Soman, et al., 2010).
𝑁𝑁
1
𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 | MAE = ∑𝑁𝑁 ℎ=1 |𝑣𝑣ℎ − 𝑣𝑣ℎ 𝑁𝑁
1 2
𝑃𝑃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 (𝑣𝑣) =
𝜌𝜌(𝑡𝑡)𝐴𝐴𝜈𝜈 3
(1)
1
(2)
2
𝜌𝜌(𝑡𝑡)𝐴𝐴𝜈𝜈 3 𝐶𝐶𝑝𝑝 (𝑣𝑣)
(5)
𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓
The available and realistic wind power moving across the rotor blades per unit sweep area are defined as (1) and (2), respectively (Olaofe, 2013): 𝑃𝑃𝑎𝑎𝑎𝑎 (𝑣𝑣) =
(4)
and 𝑣𝑣ℎ are the forecast and actual wind where 𝑣𝑣ℎ speed at time h, respectively; N is the number of forecast samples. This model can also be used to measure the performance of the wind power forecasting models. In this case “v” will be replaced by “P” to denote power. Small RMSE and MAE errors means that the difference between forecast wind speed/power and the actual wind speed/power is small. If RMSE and MAE are small enough, then the forecasting models will be deemed adequate.
where 𝑃𝑃𝑎𝑎𝑎𝑎 (𝑣𝑣) is the ideal available wind power and 𝑃𝑃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 (𝑣𝑣) stands for the realistic power generated by the wind turbine in Watts(W), 𝜌𝜌(𝑡𝑡) is time varying air density, which depends on surrounding atmospheric pressure and temperature. A is the sweep area of the blades in (m2), and v is wind speed (m/s). The ideal available wind power (𝑃𝑃𝑎𝑎𝑎𝑎 (𝑣𝑣) ) is related to the power 𝑃𝑃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 (𝑣𝑣) that can be generated by a wind turbine by means of the power coefficient (𝐶𝐶𝑝𝑝 ). The 𝐶𝐶𝑝𝑝 for a particular turbine is determined by the tip angle, the blade design and the relationship between wind speed and rotor speed. The maximum power coefficient (Betz limit) is 0.593 (Carrillo, et al., 2013). However, this value is not achievable in practice. The power coefficient at various operating conditions were not available. For the purpose of comparison, 0.5 was used as the power coefficient for all three models.
2.4 Power Law Equation The wind speed data provided by the Wind Atlas of South Africa were measured at maximum 62 m above ground which is lower than the minimum hub height of 80m for Vestas V90/1800 wind turbine which was selected for this study. As a result, the power law equation was used to estimate the wind speed at the desired hub height by using the wind speed measured at the lower height as inputs. Power law equation is given as (Joustra, 2014): ℎ
(𝑣𝑣1 ) = (𝑣𝑣0 ) ( 1 ) ℎ0
𝛼𝛼
(6)
where 𝑣𝑣1 is the wind speed measured at ℎ1 meters above ground and 𝑣𝑣0 is the wind speed measured at ℎ0 meters above ground. In this paper, ℎ1 = 90 m and ℎ0 = 62 m. The representative surface roughness exponent (α) at a specific
As indicated in (1) and (2), the air density is one of the very important factors affecting the amount of wind power generated by the wind turbine. The relationship between the 415
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where Cov stands for the covariance, and Var stands for the variance.
site is dependent on the terrain condition. The roughness exponent value of 0.089 was obtained by using (6) (Kwon, 2010).
The partial autocorrelation function (PACF) was used to measure the degree of association between 𝑦𝑦𝑡𝑡 and 𝑦𝑦𝑡𝑡−𝑘𝑘 when the effects of other time lags 𝑦𝑦𝑡𝑡−1 , … , 𝑦𝑦𝑡𝑡−𝑘𝑘−1 are removed.
3. AUTOREGRESSIVE MOVING AVERAGE (ARMA) Many existing time-series methods can be used to forecast wind speed and power. The ARMA is one of the most robust and simple time-series methods. As a result, the ARMA method was used in this paper. The ARMA model consists of two components, namely, autoregressive (AR) and moving average (MA). In an AR model, a variable value in one period is related to its values in the previous periods. In a MA model, the possibility of a relationship between a variable and the residuals from previous periods is accounted for. Integrated term (I) in an ARIMA model is used when a variable 𝑦𝑦𝑡𝑡 is not stationary. The wind data used in this paper is stationary. Therefore, integrated term was not required. ARIMA models without integrated term is ARMA.
Table 2. Properties of ACF and PACF. ACF PACF
∑𝑝𝑝𝑖𝑖=1 𝛷𝛷𝑖𝑖 𝑦𝑦𝑡𝑡−𝑖𝑖 + ∑𝑞𝑞𝑗𝑗=1 𝜃𝜃𝑗𝑗 𝑒𝑒𝑡𝑡−𝑗𝑗 + 𝜀𝜀𝑡𝑡
(7) 4. ARTIFICIAL INTELLIGENCE METHODS 4.1 Artificial Neural Network ANNs can model complex non-linear relationships and approximate measurable functions to forecast wind speed and power. They are some of the most widely used models in the last decade for forecasting future events (Ma, et al., 2009) (Hippert, et al., 2001).
The Box-Jenkins methodology was used by (Burnham & Anderson, 2002) to fit an ARMA model to a set of wind speed data. In the first step, all the unusual observations were identified by plotting the wind speed data against time. Variances were stabilized in the second step by using a BoxCox (The Box-Cox transformation, 2017). In the third step, the Dickey-Fuller test was carried out to test the stationarity of the wind speed data. Equation (8) was constructed to check the stationarity of the wind speed data.
The key element of an ANN is the interconnected neurons. Each neuron or node works as an independent computation unit which is defined as (More & Deo, 2003): 𝑌𝑌 = 𝑓𝑓[∑(𝑥𝑥1 𝑤𝑤1 + 𝑥𝑥2 𝑤𝑤2 +𝑥𝑥3 𝑤𝑤3 + ⋯ ) + 𝛽𝛽)
(8)
𝑝𝑝−1
There are many neural network architectures that have already been developed and implemented for forecasting applications. The ANN work-horse, the multilayer perceptron uses feed-forward architecture. The feed-forward multilayer network is a network in which no loop occurs in the network path (Aggarwal, et al., 2005). The structure of a feed-forward neural network with two input nodes, five hidden nodes, and on output node is shown in Fig. 1 (More & Deo, 2003).
(9)
The next step is to use the autocorrelation function (ACF) and the partial autocorrelation function (PACF) to find a suitable ARMA model. The ACF is the proportion of the autocovariance of 𝑦𝑦𝑡𝑡 and 𝑦𝑦𝑡𝑡−1 to the variance of a dependent variable 𝑦𝑦𝑡𝑡 as given in (10) (Katchova, 2017), 𝐴𝐴𝐴𝐴𝐴𝐴(𝑘𝑘) =
𝐶𝐶𝐶𝐶𝐶𝐶(𝑦𝑦𝑡𝑡 ,𝑦𝑦𝑡𝑡−𝑘𝑘 ) 𝑉𝑉𝑉𝑉𝑉𝑉 (𝑦𝑦𝑡𝑡 )
(11)
where 𝑥𝑥1 , 𝑥𝑥2 , 𝑥𝑥3 , … are the input variables, such as wind speed, wind direction, temperature, etc; 𝑤𝑤1 , 𝑤𝑤2 , 𝑤𝑤3 , … are the connection weights; 𝛽𝛽 is the bias value; f is the transfer function, which can be identity function or sigmoidal function.
Where 𝜌𝜌 is coefficient of 𝑦𝑦𝑡𝑡−1 , 𝑒𝑒𝑡𝑡 is error term. The model (8) is non-stationary, or a unit root is present if | 𝜌𝜌| =1. The stationarity of the model with a drift and additional lags of the dependent variable can be tested by using an augmented Dickey-Fuller test. It is defined as: 𝛥𝛥𝛥𝛥𝑡𝑡 = 𝜇𝜇 + (𝜌𝜌 − 1)𝑦𝑦𝑡𝑡−1 + ∑𝑗𝑗=1 𝜃𝜃𝑗𝑗 𝛥𝛥𝛥𝛥𝑡𝑡−1 + 𝜀𝜀𝑡𝑡
ARMA (p, q) Tails off Tails off
The next step is to find the preferred models based on the white noise test and goodness of fit. The final step was then to check if the residuals look like white noise by plotting the ACF of residuals. The ‘forecast’ package in R was used to model ARMA models. In this paper several models have been investigated and it was found that ARMA (2, 1) which consists of the 2nd order of the autoregressive and the 1st order of moving average has the best criteria test results. Therefore, it was used for the wind speed and power forecasting.
Where 𝑦𝑦𝑡𝑡 is a variable at time t, 𝛷𝛷𝑖𝑖 is the 𝑖𝑖th autoregressive parameter, 𝜃𝜃𝑗𝑗 the 𝑗𝑗th parameter of moving average, 𝑒𝑒𝑡𝑡−𝑗𝑗 is the lagged error term at time t-j, 𝜀𝜀𝑡𝑡 the error term at time t.
𝛥𝛥𝛥𝛥𝑡𝑡 = (𝜌𝜌 − 1)𝑦𝑦𝑡𝑡−1 + 𝑒𝑒𝑡𝑡
MA (q) Cuts off after lag q Tails off
The properties of the ACF and PACF were used to determine the number of order of AR and MA (Katchova, 2017).
ARMA (p, q) denotes an ARMA model with p autoregressive lags, q moving average lags. It can be defined as: 𝑦𝑦𝑡𝑡 =
AR (p) Tails off Cuts off after lag p
(10)
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Step 2. Create the network. The sigmoid function in the hidden layer was used to reduce the effect of extreme input values. Step 3. Configure the network by dividing input vectors and target vectors into three sets, namely, training set, validation set, and testing set. 70% of data were used for training. Both validation and testing set used 15% of data. The best number of hidden neurons were selected by checking the performance of the model with different hidden neurons. 10 hidden neurons were used in this paper. Step 4. Initialize the weights and biases for the network. The initial weight and biases were selected based on the relationship between the input and target data. Step 5. Select Bayesian Regularization as the training algorithm, as it can result in good generalization for difficult, or small wind dataset. Step 6. Validate the network. Step 7. Use the network to forecast wind speed and power by importing the historical data into the input nodes.
Fig. 1: Structure of a feed-forward neural network with two input nodes, five hidden nodes and one output node. As can be seen in Fig. 1, there are two layers in the feedforward neural network, namely, the hidden layer and output layer. The number of input nodes in the input layer is based on a prior knowledge of the behaviour of the system. Each input node represents an input variable which can be wind speed, wind direction or temperature and etc. It is harder to decide on the number of neurons in the hidden layer as compared to those of the input or output layers. (Hippert, et al., 2001) suggest using trial and error method to find a suitable number of neurons in the hidden layer. The number of output neurons required is dependent on the forecasting profiles.
4.2 Adaptive-network-based Fuzzy Inference System (ANFIS) The adaptive neuro-fuzzy inference system (ANFIS) is a system with the combination of fuzzy logic technique and neuro network technique which bring the learning capabilities of the neural networks to fuzzy inference systems (MathWorks, 2017). In an ANFIS, the neuro-adaptive learning methods are used to adjust the parameters of the membership function. The shape of the membership functions is changing accordingly with the parameters. The structure of the neuro-fuzzy model for wind power forecasting can be presented as a special multilayer feedforward neural network.
There are three commonly used forecasting profiles, namely, iterative, multi-model and single-model. Iterative forecasting is done by forecasting a unit of wind data at a time. Multimodel forecasting is a common method for forecasting with regression; the number of models used depends on the gap between forecasting. The advantage of using multi-model forecasting is that each ANN is relatively small. Therefore, the overfitted is unlikely to happen. Single-model multivariable forecasting is done by using multiple variables as inputs to forecast multiple wind speeds as outputs at once (Hippert, et al., 2001). Single-model multivariable forecasting profile was used in this paper.
Two commonly used fuzzy inference methods are Mamdani and Sugeno-type. In this paper, the Sugeno-type method is used in the ANFIS because it works well with adaptive techniques and optimization (Sugeno-type fuzzy inference, 2017). Therefore, the output membership functions are limited to constant and linear. The input to the model were maximum, minimum, and average wind speed measured at 62 m above ground.
A training method was chosen for the neural network to fit the inputs and targets. Three commonly used training algorithms are Levenberg-Marquardt, Bayesian Regularization, and Scaled Conjugate Gradient. LevenbergMarquardt requires more memory for computation but takes less time (Hagan & Menhaj, 1994). Bayesian Regularization usually requires more computation time, but it can result in good generalization for difficult, noisy or small datasets (Ticknor, 2013). Scaled Conjugate Gradient is suitable for large problems as it uses gradient calculations which require less memory (Saini & Soni, 2002) (Lazarevska, 2016).
The hybrid optimization method consisting of the backpropagation gradient descent and least-squares were used in this paper. The membership function used in this paper is Gaussian as it has similar shape as wind speed data. Training epochs and the training error tolerance needed to be specified once the optimization method is selected. The training process stopped when either training error tolerance or training epochs reached the predefined goals. The last step is to verify the performance of the model by using validation dataset and evaluation metrics (Adaptive neural-fuzzy modeling, 2017).
In this paper, seven steps have been followed in the design process of the ANNs as discussed below. Step 1: Collect, pre-process, and analyse wind data. The input to the model are the maximum, minimum and average wind speed measured at 62 m above ground.
5. DATA COLLECTION AND ANALYSIS The data used in this paper are collected from the Wind Atlas of South Africa. The data sets contain wind speed (m/s) 417
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measured at different heights, wind direction (°TN), temperature (°C), atmospheric pressure (hPa), and relative humidity (%) with 10 minutes resolution for the period from Midnight 31 December 2010 to Midnight 1 January 2017. The data were analysed before applying them to the forecasting models as inputs. Descriptive statistics were used to summarize data from a sample using indices such as the mean, maximum, minimum and standard deviation. Inferential statistics were used to describe associations within the data by figuring out the correlation and regression (Descriptive and inferential statistics, 2017). 6. SIMULATION RESULTS AND DISCUSSION 6.1 Wind Power Forecasting The forecast wind speeds were converted to the estimated wind speed at the hub height by using the power law equation (6). The estimated wind speeds at the hub height were then used to calculate the estimated wind power by using (2). Since there is no actual wind power data collected in this paper, the actual wind speed data were used to calculate the “calculated actual wind power”. The plots of the calculated wind power and the very-short-term forecast wind power are shown in Fig. 2.
Fig. 3: Plots of the calculated actual wind power and the forecast wind power of the ARMA (2, 1), ANN and ANFIS over short-term (1 hour ahead) time horizon. As can be seen in Fig. 3, the plot of forecast wind power (red dot-dash line) of the ARMA (2, 1) tracks the calculated actual wind power closely for the most of samples. The plots of ANN (orange solid line) and ANFIS (purple dot line) have similar shape. This is expected as both methods have good training ability. The margin between the forecast wind power of ANN and the calculated actual wind power (blue solid line) is small for the most of samples. However, the margin between samples 120 to samples 130 is big. This is due to the sharp increase of the calculated actual wind power. The ANN wasn’t able to accurately forecast wind power when the difference between adjacent samples is big. The evaluation results will be much better if the margin between samples 120 to samples 130 is reduced. Table 2 quantifies the performance of each model. Table 2: Summary of the normalized RMSE and MAE for wind power forecast. Time Horizon
Fig. 2: Plots of the calculated actual wind power and the forecast wind power of the ARMA (2, 1), ANN and ANFIS over very-short-term (10 minutes ahead) time horizon.
Very-shortterm (10 minutes ahead) Short-term (1 hour ahead)
As can be seen in Fig. 2, the plots of all three models track the plot of the calculated actual wind power closely. This agree with the result as suggested by (Chang, 2014) (Ma, et al., 2009).
ARMA
Artificial Neural Network RMSE MAE [%] [%]
RMSE [%]
MAE [%]
5.8
4.2
5.6
11.3
8.8
18.1
ANFIS
RMSE [%]
MAE [%]
3.8
5.7
3.9
12.3
18.4
12.2
As can be seen in Table 2, all three models perform well for the very-short-term time horizon wind power forecasting. For the short-term forecasting, the ARMA has the lowest forecasting errors among the three models. The evaluation results for very-short-term forecast are expected, as all three methods are very good at very-short-term wind power forecasting. However, the short-term forecast results of the ANN and ANFIS are not as good as one would have expected. It can be seen from table 2 that RMSE and MAE values increase with the forecasting time horizon. Therefore,
Fig. 3 shows the plots of the calculated wind power, the forecasted wind power using ARMA, ANNs, and ANFIS for short-term time horizon.
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we can conclude that the performances of all the models degrade with the increases of the prediction lead time.
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7. CONCLUSIONS Based on the evaluation results, the ARMA (2, 1) has the lowest wind power forecasting error over the short-term time horizon. It has 3.5% and 3.4% less MAE errors than the ANNs and ANFIS respectively. The difference among shortterm wind power forecasting errors of three models is well within the errors commonly found in the collected data. Therefore, more data and simulations are required to make valid comparison. The performance of artificial intelligence methods, (ANNs and ANFIS) perform and the conventional method over the very-short-term time horizons is very similar. All three models have less than 6% very-short-term wind power forecasting errors. The ANNs and ANFIS have similar performance results. According to the evaluation results, both artificial intelligence and conventional methods are suitable for the very-short-term and short-term wind power forecasting.
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