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Wind power prediction system for wind farm based on auto regressive statistical model and physical model Bingheng Wu, Mengxuan Song, Kai Chen, Zhongyang He, and Xing Zhang Citation: Journal of Renewable and Sustainable Energy 6, 013101 (2014); doi: 10.1063/1.4861063 View online: http://dx.doi.org/10.1063/1.4861063 View Table of Contents: http://scitation.aip.org/content/aip/journal/jrse/6/1?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Coupled wake boundary layer model of wind-farms J. Renewable Sustainable Energy 7, 023115 (2015); 10.1063/1.4915287 Unsteady vortex lattice method coupled with a linear aeroelastic model for horizontal axis wind turbine J. Renewable Sustainable Energy 6, 042006 (2014); 10.1063/1.4890830 An active power control strategy for wind farm based on predictions of wind turbine's maximum generation capacity J. Renewable Sustainable Energy 5, 013121 (2013); 10.1063/1.4792847 A full three dimensional Navier-Stokes numerical simulation of flow field inside a power plant Kaplan turbine using some model test turbine hill chart points AIP Conf. Proc. 1440, 285 (2012); 10.1063/1.4704228 Stanford Center for Integrated Turbulence Simulations Comput. Sci. Eng. 2, 54 (2000); 10.1109/5992.825749

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JOURNAL OF RENEWABLE AND SUSTAINABLE ENERGY 6, 013101 (2014)

Wind power prediction system for wind farm based on auto regressive statistical model and physical model Bingheng Wu, Mengxuan Song, Kai Chen, Zhongyang He, and Xing Zhanga) Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, People’s Republic of China (Received 21 July 2013; accepted 17 December 2013; published online 2 January 2014)

Extracting energy from renewable sources such as wind energy is widely investigated in the past decades to mitigate the global energy crisis and environmental pollution. For a wind farm that converts wind energy into electricity power, a real-time prediction system of the output power is significant. In this paper, a prediction system is developed with a method of combining statistical model and physical model. In this system, the inlet condition of the wind farm is forecasted by the auto regressive model. The flow field is computed by the Reynolds average Navier-stokes simulation in the computational fluid dynamics model. The wake flow is calculated by the particle model, which can be used over complex terrain. Taking also the terrain condition, the property of turbines and wake flow model into account, the output power of the wind farm can be further predicted. The proposed prediction system is tested by the data from Wattle Point Wind Farm in Australia. Through the data post-processing, the error of the mean daily output power is less than 5%. The proposed system is effective C 2014 AIP Publishing LLC. for power output prediction of wind farm. V [http://dx.doi.org/10.1063/1.4861063]

I. INTRODUCTION

With the growth in economic and the increasing in population, human demand for energy is rising rapidly. Fossil energy such as coal and oil are non-renewable as they have to go through hundreds of millions of years of geological processes to be generated. The burning of fossil energy with the generation of sulfur dioxide and dust has caused many environmental problems such as acid rain and photochemical smog problem. It also turns underground solid carbon into gaseous carbon dioxide released into the atmosphere, which intensifies the greenhouse effect, accelerates north and south polar ice to melt, and leads to a deadly threat to human civilization. Wind energy is one of the important renewable energies, which is widely investigated in the past decades. Global annual generating wind capacity has reached 430 TWh by the end of 2010, accounting for 2.5% of the world’s total electricity generation. The wind energy market in China develops quickly and its new wind capacity increased by 18.9 GW, accounting for 50.3% of the global growth in wind capacity in China in 2010.1 By the end of 2011, the total wind capacity has increased to 239 GW, accounting for 3% of the world’s total electricity generation.2 Compared with fossil energy, wind energy has its unique characteristics, such as low energy density, randomness, instability, and volatility, rapid changes in wind direction and magnitude, and is easily influenced by the geographical conditions and the surrounding environment. These characteristics make wind energy difficult to take up a large proportion in the grid. Once the penetrating power of wind power is greater than the limit proportion, the stability of

a)

Electronic mail: [email protected]

1941-7012/2014/6(1)/013101/14/$30.00

6, 013101-1

C 2014 AIP Publishing LLC V

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the grid and the power quality will be affected. Therefore, it is significantly important to develop a real-time prediction model for the wind farm to estimate the output of electricity power and support the safe operation of the wind power generation system. Up to present multiple wind speed prediction models have been proposed, which can be generally divided into two categories. The first are the physical models, which contain physical considerations to achieve high prediction precision, such as Numerical Weather Prediction (NWP) models. Based on the domain coverage, NWP models are divided into global models and Limited Area Models (LAM). Global models solve the primitive equations for the whole globe while LAM cover only limited domain.3 Global models include GME (German),4 NCEP/NCAR (USA),5 and ECMWF (EU).6 Several limited area models are developed and used to forecast mesoscale weather phenomena, such as High Resolution Model (HRM),7 Eta,8 fifth-generation Penn State/NCAR Mesoscale Model (MM5),9 etc. As NWP models solve the equations describing the atmospheric processes and the atmosphere changing with time, powerful computers are needed to do the huge calculation and the cost in the time and money are large. The others are the statistical models which are more suitable for short-term prediction, such as Auto Regressive Moving Average (ARMA) model, Kalman filters model, Artificial Neural Network (ANN), fuzzy logic models,10 etc. Torres et al. used the ARMA model and persistence models to predict the hourly average wind speed up to 10 h in advance. They proved that the transformation and standardization of the original series allow the use of ARMA models and these behave significantly better in the forecast than the persistence model, especially in the longer-term forecasts.11 Erdem developed four approaches based on ARMA model to perform the short-term forecasting and found they have the strengths and weaknesses for forecasting wind speed and direction.12 Bossanyi used Kalman Filters to do short-term wind prediciton.13 Louka et al. applied Kalman filtering as a post-processing method in numerical predictions of wind speed. The application leads to the elimination of any possible systematic errors, even in the lower resolution cases, contributing further to the significant reduction of the required computation time.14 Gong and Shi compared three different ANNs to compare the wind speed and found that the selection of neural network type and parameters greatly affects the performance of wind speed forecasting.15 Flores et al. presented a complete design and training of ARMA and ANN models through the use of Evolutionary Computation. The results show that ANN yield better forecasts than ARMA models in all the cases presented in the paper.16 Zhang et al. designed a probabilistic fuzzy system based prediction model for the short-term wind speed prediction. The effectiveness of the model is demonstrated by the simulations on a group of wind speed data.17 Vladislavleva et al. took a computer science perspective on energy prediction based on weather data and analyzed the important parameters as well as their correlation on the energy output. They use symbolic regression based on the genetic programming tool DataModeler. The method is simple and has important technological value and good prospect for conducting research.18 The prediction models have their own characteristics and they are applicable to different situations, so it is difficult to compare the accuracy of all the models. Statistical models need older data to learn the proper parameterizations. They have a quite good accuracy for rather short horizons while the prediction results are useless for longer prediction horizons, especially when the wind is influenced greatly by the terrain and obstacles. The actual terrain of the wind farm, obstacles and the properties of wind turbines are under consideration in the physical models. In the physical models, meteorology and atmospheric physics are usually used to simulate the flow field in macroscopic scale. They need much calculation time, so they are always applied in more than an hour interval prediction. In practice, both physical models and statistical models are utilized simultaneously to reduce prediction error. Kariniotakis et al. have developed the ANEMOS wind power prediction system combining multiple weather models as well as different physical and statistical wind power prediction models.19,20 Costa et al. proposed a mechanism to integrate statistical and physical models and developed an operational (on-line) tool oriented to the spot market and power system management.21,22 Besides the above, there is some software based on the combination between statistical models and physical models developed and applied to predict wind power in the world, such as Prediktor (Denmark), WPPT (Denmark), Zephyr (Denmark),

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EWind (USA), SOWIE (Germany), WPMS (Germany), Alea Wind (Spain), WPFS Ver (China), etc.23,24 For the efficiency of the calculation, in most commercial software the wake flow behind the wind turbine is simulated with the linear models or is even ignored which will lead prediction accuracy decreases. In this paper, a system is developed to do real-time prediction of wind farm output power with a combination of statistical model and physical model. In this system, the inlet condition of the wind farm is forecasted by the Auto Regressive (AR) model. The flow field is computed by the Reynolds Average Navier-Stokes Simulation (RANS) in the Computational Fluid Dynamics (CFD) model. The wake flow is calculated by the particle model, which can be used over complex terrain. Taking also the terrain condition, the property of turbines and wake flow model into account, the output power of the wind farm can be further predicted. The calculation time depends on the simulate domain and mesh size. For a wind farm, the calculation time is acceptable and the system can be applied to do less than an hour interval prediction. The configuration of prediction system as shown in Figure 1 can be divided into three main modules. 1. Statistical prediction. The measured weather data from weather station are given as the input of time series model, with which the future weather can be predicted and then it will be treated as the future inlet of the wind farm. 2. Physical prediction. The flow field of the wind farm can be simulated with the future inlet and the geographic information, the CFD model, the turbine properties, and the wake model. According to the power curve of the turbine, the output power can be further calculated. 3. Data post-processing. The data post-processing module is to improve the prediction results based on the error of the measured data and the simulation results of the wind farm.

II. COMPUTATIONAL MODELS A. Statistical model

With the time series model, the meaningful statistics and the other characteristics of the data are extracted to predict future values based on previously observed values. ARMA model

FIG. 1. Prediction system configuration.

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includes an AR part and a moving average (MA) part. ARMA (p,q) model refers to the model with p auto regressive terms and q moving average terms.25 The general formulation of the ARMA (p,q) model is given by yt ¼ /1 yt1 þ /2 yt2 þ    þ /p ytp þ et  h1 et1  h2 et2      hq etq ;

(1)

where /1 ;    ; /p are the auto regressive parameters, h1 ;    ; hq are the moving average parameters, yti ði ¼ 1; 2;    ; pÞ denote previously observed values, and etj ðj ¼ 0; 1;    ; qÞ denote a white noise series. The ARMA model degenerates to AR model as p ¼ 0 and MA model as q ¼ 0. In this paper, AR model is used to predict the inlet velocity of wind farm and MA model is ignored, that is, q ¼ 0. The model operates on-line and the updated cycle of input data is the same as the observation cycle. The order of AR model is chosen as p ¼ 120. The parameters in the AR model can be solved from Yule-Walker equation which is shown in the following equation:26 0

q0 B B q1 B B B⯗ @ qp

q1 q0 ⯗ qp1

10 1 0 1    qp q1 /0 C C B C    qp1 CB / C B q C CB B 1 C ¼ B 2 C; C .. B ⯗ C B ⯗ C A . ⯗ C A@ A @ / q p pþ1  q

(2)

0

where qk ðk ¼ 0; 1;    ; qÞ are the autocorrelation coefficients which are shown in Eq. (3) and y are the average values of the observed time series yn which are shown in Eq. (4). When the observed time series yn are updated, the parameters in the AR model are updated, nk X ½ðyt1  yÞðyt1k  yÞ i¼1 qk ¼ vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi : u nk uX t ½ðyt1  yÞ2 ðyt1k  yÞ2 

(3)

i¼1

y ¼

n 1X yi : n t¼1

(4)

B. Physical model 1. CFD model

With the development of calculating ability of computer, CFD has been increasingly used to simulate the flow fields and to research the characteristics of various kinds of fluids. There are three methods for numerical simulation of turbulent flow: Direct Numerical Simulation (DNS), RANS, and Large Eddy Simulation (LES). DNS resolves all the spatial scales of the motion, so it can only be used to simulate turbulent flow with low Reynolds number in simple geometric shapes due to the limitations of current computer capability. LES solves explicitly the large, non-universal scales of the flow while the small scales are modeled. RANS does not simulate the turbulence directly, but it is a simulation of its time-averaged statistics.27 RANS is used widely because of its efficiency and robust performance. Considering the accuracy and efficiency, the flow field on the complex terrain is simulated with RANS. As the Mach number of the airflow is smaller than 0.06, air is regarded as incompressible. Within the scope of the wind farm, the temperature and the density of air are considered as constants. The standard k  e model proposed by Jones and Launder28 is used as the twoequation turbulence closure for the incompressible RANS equations. The governing equations are shown below. The continuity equation, @ui ¼ 0: @xi

(5)

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The momentum equations, q

@ui uj @P @ 2 ui ¼ þ lt ; @xj @xj @xj @xi

(6)

k equations,

quj

  @k l @2k l @ui @uj 2 ¼ t þ t þ þ qe; @xj Prk @xj @xj 2 @xj @xi

(7)

e equations,   @e lt @ 2 e lt @ui @uj 2 e e2  C2 q ; ¼ þ C1 þ quj 2 @xj @xi k k @xj Pre @xj @xj

(8)

where ui(i ¼ 1,2,3) is the velocity components. P is the dynamic pressure. k is the turbulent kinetic energy, and e is the turbulent dissipation. lt is the turbulent viscosity coefficient and is 2 given by lt ¼ Cl q ke . The constants in the k  e equations are chosen as C1 ¼ 1:44; C2 ¼ 1:92; Prk ¼ 1:0; Cl ¼ 0:033.29 Zero gradient boundary conditions are applied to the walls, the outlet, side and top boundaries of the computational domain. At the inlet of the computational domain the wind velocity distribution has exponent relation to the height which is shown as U ¼ U1

 0:14 z ; h

(9)

where h is the reference height and U1 is the velocity at the reference height.30 In this paper, h equals to the height of the weather station and U1 is the wind speed measured by the weather station. 2. Wind turbine properties

The kinetic energy of the wind can be transformed into electrical energy through the wind turbines. When the wind speed increases to the cut-in wind speed from calm wind, the wind turbine begins to produce electricity. The rated power will be reached when the wind speed increases to the rated speed and it maintains the rated power until the wind speed increases to the cut-out wind speed. Once the wind speed reaches the cut-out wind speed, the wind turbines must be stopped to prevent damage. The power curve of wind turbine presents the relationship between the wind speed and the output power. The thrust coefficient curve of wind turbine presents the relationship between the wind speed and the thrust coefficient. With the local wind speed of wind turbine, the output power and the thrust coefficient can be calculated through the power curve and the thrust coefficient curve. 3. Wake model

As the wind downstream of the wind turbine has reduced speed and increased turbulence, the wake effect should been taken into account carefully. In most software for flow field simulation of wind farm, linear models are widely used to simulate the wake behind the wind turbine, which can calculate wake flow uncoupled with the flow field. In 1983, N. O. Jensen presented a simple linear model and tested its effectiveness by experimental data.31 In this model, the near field behind a wind turbine is neglected and the inlet is considered to be uniform. The linear dimension(radius r) of the spread area on flat terrain is proportional to downwind distance x. In 1994, Mosetti presented a wake model similar to the Jensen model for simplification of the wind field calculations.32 The wake model is shown in Figure 2. The

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FIG. 2. Schematic of wake model.

velocity outside the wake spread area is not influenced by the wake flow. Within the wake spread area, the velocity is expressed as  u ¼ u0 1 

 2a ; 1 þ að x=r1 Þ rffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1a ; r1 ¼ rr 1  2a

(10)

(11)

CT ¼ 4að1  aÞ;

(12)

1 ; 2lnðzt =z0 Þ

(13)



where u0 denotes the wind speed without turbines, a denotes the axial induction factor, x denotes the distance downstream of the turbine, and a denotes the entrainment constant. rr denotes the rotor radius; CT denotes the turbine thrust coefficient and it depends on wind speed and turbine type. zt denotes the hub height of the wind turbine. z0 denotes the surface roughness and z0 ¼ 0.3 is suitable for the surface of the suburban district.30 Linear models are simple and calculate the wake flow very efficiently. In the linear models, the wake flow characteristics are determined by the airflow characteristics of the impeller, but it is unreasonable to neglect the impact of the downstream flow to the wake flow. Speed in the cross-section perpendicular to the flow direction is identical and speed leaps on the edge of the wake region in the linear models. These characteristics do not match the actual wake flow. In fact, wind speed and direction are not uniform and the wake flow region is distorted by nonuniform airflow on complex terrain, so the wake flow is not similar to conical shape and it makes large error to apply the linear models on complex terrain. In 2012, Song et al. developed a particle model for calculating turbine wake flow during the optimization of wind farm micro-siting.33 The wake flow is treated as virtual particles generated by the turbine rotor and the concentration of the virtual particles represents the intensity of wake flow after they fully develop. Virtual particles do the production, convection, diffusion, and disappearance based on the flow field of the empty wind farm without wind turbines. During the simulation of particles, in each time step Dt, the convective displacement Dxc is expressed as Eq. (14) and the diffusive displacement Dxd of each particle is expressed as Eq. (15), Dxc ¼ uDt;

(14)

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Dxd ¼ rd

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2urDt log R cos 2pR1 ;

(15)

where u is the local velocity at the position of the particle in the empty wind farm, r is the rotor radius of the turbine, rd is the ratio of intensity of diffusion, and rd ¼ 0:23 is used.33 R and R1 are the uniformly distributed random numbers in the range of 0–1. Each particle disappears at a certain probability c, which is called the attenuation factor, and a value of 0.005 is suitable for c.33 After virtual particles develop fully, the relationship between the velocity of the flow field without and with wind turbines is shown in the following equation: u0 ¼ uð1  bcÞ;

(16)

where u denotes the velocity of the flow field of the wind farm without wind turbines, while u0 denotes the velocity of the flow field affected by wind turbines; c is the local relative density of the virtual particles, b is a coefficient which can be determined according to the linear model. In the cross-section of turbine rotor where the wake flow generates, the wake flow is not yet influenced by downstream flow, u0 should be the same in the linear model and the particle model. From Eqs. (10) and (16), b can be decided as b ¼ 2a:

(17)

The previous research considers the coefficient b is a constant which equals to 0.65.33 Actually, the thrust coefficient changes with the wind speed, so b is no longer a constant and it is decided by Eqs. (12) and (17). C. Data post-processing

With the combination of statistical model and physical model, the output power of wind farm can be further predicted. The actual output power can be measured and the error between the measured data and simulation results can be calculated. At the time of t ¼ nDt, where Dt is the time interval of the data series, the data are solved by the post-processing, expressed as Qn ¼ qn þ

k 1X ðMnj  qnj Þ; k j¼1

(18)

where Qn denotes the prediction result after processing at the time of nDt, qn denotes the prediction result before processing at the time of nDt, and Mk denotes the measured result at the time of kDt. In this paper, a value of 1 is used for k. III. NUMERICAL STUDY A. Case studied

In this section, a case is used to test the feasibility and accuracy of the wind power prediction system. In the case, the energy production of Wattle Point Wind Farm (WPWF) in Australia is investigated and predicted based on publicly available data of wind conditions. The energy production data are made publicly available by the Australian Energy Market Operator (AEMO) in real time to assist in maintaining the security of the power system.34 The output of the wind farms is available with a rate of one measurement every 5 min. WPWF is a wind farm located at 35.13 S, 137.71 E, onshore near Edithburgh of South Australia. This infrastructure includes 55 wind turbines with a design capacity of 90.75 MW.35 The Australian weather station ID022046 is 6 m high and located at 35.11 S, 137.74 E, the northeast of WPWF. The data of the weather station are available for free for a running observation time window of 72 h and is updated every 30 min.36 As the station is close to the wind farm, the data are treated as the boundary condition of WPWF.

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FIG. 3. The layout of wind turbines in Wattle Point Wind Farm.

Terrain elevation data is provided by ASTER (Advanced Spaceborne Thermal Emission and Reflection Radiometer) GDEM (Global Digital Elevation Model), a product of the Ministry of Economy, Trade, and Industry (METI) of Japan and the National Aeronautics and Space Administration (NASA) of USA. The layout of the wind farm is shown in Figure 3. The properties of the wind turbines are shown in Table I. The power curve of the turbine is plotted in Figure 4 and the thrust coefficient curve of the turbine is plotted in Figure 5. B. Wake model estimation

The actual measured data from WPWT is used to verify the effectiveness of the particle model. The wind direction and speed with a rate of one measurement every 30 min are obtained from the weather station from 00:00 March 19th to 00:00 April 15th in 2013. After data pre-processing,37 unreasonable data which are invalid or replicated are excluded and the rest 1076 records are statistically analyzed in accordance with 16 wind directions. Records of the same direction and speed are averaged to compare with the steady simulation results using RANS with linear and particle wake flow model, respectively. The records of West-SouthWest (WSW) wind direction are selected for the estimation, since they account for a relatively large share of 11.2% of the 16 wind directions. In Figure 6, the horizontal axis represents the wind speed while the vertical axis represents the output power of WPWF. The red solid curve is the actual measured output power, the green TABLE I. Properties of wind turbines. Properties

Value

Turbine type

Vestas V82

Rated power

1.65 MW

Rated wind speed Hub height Rotor diameter

12 m/s 68.5 m 82 m

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FIG. 4. The power curve of the wind turbine.

FIG. 5. The thrust coefficient curve of the wind turbine.

FIG. 6. The comparison between measured data and simulation results with different wake models in the WSW direction.

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dotted-dashed curve is the simulation output power with the linear wake flow model and the blue dashed curve is the simulation output power with the particle wake flow model. As the wind turbines take time to respond to the change of the incoming wind, it is an equitable appearance that the measured results are bigger in low wind speed and smaller in high wind speed. The results are summed in a different speed. The actual output power is 1 215 776 kW while the simulation results are 983 977 kW with the linear model and

FIG. 7. The wind rose of measured weather data and prediction results with statistical model on 26th, 27th, and 28th March. The subgraphs (a), (c), and (e) are measured data and the subgraphs (b), (d), and (f) are prediction results.

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TABLE II. Error analysis of wind speed and direction. Speed (m/s) Max absolute error of speed (m/s)

½0; 3Þ

½3; 6Þ

½6; 9Þ

½9; 12Þ

0.97

4.36

3.67

6.81

Max relative error of speed

49.65%

120.76%

58.67%

56.99%

Max absolute error of direction (deg) Mean absolute error of speed (m/s)

50.92 0.37

57.09 1.28

40.36 1.99

Root mean square error of speed (m/s) Mean absolute error of direction (deg) Root mean square error of direction (deg)

63.53 1.04

0.27

1.42

1.56

2.70

17.34 22.15

11.84 16.91

11.64 16.74

16.04 20.19

1 142 591 kW with the particle model. The results for the particle model are closer to the measured data than the ones for the linear model. The particle model is applied as the wake flow model in the output power estimation. C. Prediction results and error analysis

To test the prediction system, the measured weather data and the output power of WPWF are used. The wind direction and speed from the weather station from 00:00 March 19th to 23:30 March 25th in 2013 are treated as the history weather data for the first prediction. Once the measured data are updated, it will be added into the history data to do next prediction. Also, the statistical model is applied to predict the future weather data of next 3 days. The input data interval is 30 min and the prediction resolution is 30 min. The measured weather data and the prediction future weather from 00:00 March 26th to 23:30 March 28th in 2013 is counted to draw wind roses according to the wind direction and speed. Some statistical details are shown in Figure 7. In this case, the measured weather data are shown in the subgraphs (a), (c), and (e) of Figure 7 while the prediction future weather are shown in the subgraphs (b), (d), and (f) of Figure 7. The comparison between the measured weather data and the prediction future weather is made and the errors in several speed ranges are shown in Table II. The speed and direction have the maximum errors in the speed range of 3 m/s–6 m/s. The maximum relative error of the wind speed is 120.76% and the maximum error of the wind direction is 63.53 . According to the mean absolute error (MAE) and the root mean square error (RMSE), the accuracy in the speed and direction is acceptable. In the statistical model, it is necessary to know the history data and insure its accuracy because the prediction is only based on history data and the statistical model cannot promptly

FIG. 8. The comparison between the measured output power data and the prediction results before post-processing on 26th, 27th, and 28th March.

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TABLE III. Mean daily power output and errors before post-processing. Date

26th March

27th March

28th March

Measured data (MW)

51.21

63.13

42.88

Prediction result (MW) Absolute error (MW)

26.73 24.48

44.94 18.19

23.49 19.39

Relative error

47.80%

28.81%

45.22%

Mean absolute error (MW) Root mean square error (MW)

32.09 37.42

31.69 39.71

21.60 25.19

respond on the fluctuation of the data. Moreover, the periodicity and the trend of the history data will have an impact on the prediction. To reduce the errors of the statistical model, the accuracy, the periodicity and the trend of the history data should be considered seriously. The prediction future weather data by the statistical model are regarded as the inlet of WPWF. With terrain map, CFD model, layout of the wind turbines, properties of the wind turbine and the particle wake flow model which has been evaluated above, the flow filed of the wind farm can be simulated and the output power of the whole wind farm from 00:00 March 26th to 23:30 March 28th in 2013 can be calculated. The comparison between the measured output power data and the output power prediction results is shown in Figure 8. The blue solid curve is the measured output power data while the red dashed curve is the output power prediction results. Mean daily power output and errors of each day are shown in Table III and the maximum relative error is 47.80%. In the physical model, many influencing factors cause error, such as the inlet, terrain, CFD model, turbine properties, and wake flow. As the inlet of wind farm is predicted by the statistical model, the error in the statistical prediction module will be accumulated in the physical prediction module. The comparison between the measured data and the output power prediction results after data-processing are shown in Figure 9. The blue solid curve is the measured output power data while the red dashed curve is the output power prediction results after the postprocessing. It can be seen that the results after data-processing are in much better agreement with the measured data than the ones before data-processing. Mean daily power output and error of each day are shown in Table IV. It is noticed that the relative error of the mean daily power output is below 5% for the 3 days. The MAE and RMSE decrease comparing with the results before data-processing. The MAE range is below 20% of the name plate capacity of the wind farm.

FIG. 9. The comparison between the measured output power data and the prediction results after post-processing on 26th, 27th, and 28th March.

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TABLE IV. Mean daily power output and errors after post-processing. Date

26th March

27th March

28th March

Measured data (MW)

51.21

63.13

42.88

Prediction result (MW) Absolute error (MW)

48.76 2.45

63.42 0.29

43.20 0.32

Relative error Mean absolute error (MW) Root mean square error (MW)

4.78% 6.82 10.36

0.46% 12.56 18.95

0.75% 14.60 18.36

IV. CONCLUSIONS

In this paper, a wind power prediction system for wind farm based on statistical model and physical model is presented. AR model is used as the statistical model to predict the future inlet of the wind farm. In the physical model, the CFD is used to simulate the flow field of the wind farm. The particle model based on the turbine properties is applied to calculate the wake flow of the wind turbine. The output power of the turbine is calculated by the power curve. A data post-processing method is developed to reduce the system error. Measured data from Wattle Point Wind Farm are used to test the accuracy and effectiveness of the prediction system. In the wake flow model, some parameters are decided by turbine thrust coefficient and local wind velocity rather than constants in the previous study. The evaluation results show that the improvement of the wake model makes the simulation results match the actual flow field better. Meanwhile, the relative error of the daily output power is less than 5%. The MAE range is below 20% of the name plate capacity of the wind farm. The proposed prediction system is effective for power output prediction of wind farm. ACKNOWLEDGMENTS

This research was supported by the National High-Tech R&D Program (863 Program) of China (No. 2007AA05Z426), the International Scientific and Technological Cooperation Program (No. 2011DFG13020) and China Postdoctoral Science Foundation (No. 2013M530043). 1

World Wind Energy Association (WWEA), World wind energy report 2010 launched, see http://www.wwindea.org/ home/index.php?option=com_content&task=view&id=302&Itemid=43, 2011. 2 World Wind Energy Association (WWEA), World market recovers and sets a new record: 42 GW of new capacity in 2011, total at 239 GW, see http://www.wwindea.org/home/index.php?option=com_content&task=view&id =345&Itemid=43, 2012. 3 S. Al-Yahyai, Y. Charabi, and A. Gastli, “Review of the use of numerical weather prediction (NWP) models for wind energy assessment,” Renewable Sustainable Energy Rev. 14, 3192–3198 (2010). 4 See http://www.dwd.de/ for Deutscher wetterdienst (DWD), 2013. 5 See http://ncar.ucar.edu/learn-more-about/weather for National center for atmospheric research (NCAR), 2012. 6 ECMWF, ECMWF Annual Report 2012, see http://www.ecmwf.int/publications/annual_report/2012/pdf/Annual-report2012.pdf, 2012. 7 S. Al-Yahyai, Y. Charabi, and A. Gastli, “Estimating wind resource over Oman using meso-scale modeling,” in IEEE International Energy Conference and Exhibition (EnergyCon), Manama, Bahrain, 2010, pp. 536–541. 8 L. Lazic, G. Pejanovic, and M. Zivkovic, “Wind forecasts for wind power generation using the Eta model,” Renewable Energy 35, 1236–1243 (2010). 9 Z. C. Guo, D. H. Bromwich, and J. Cassano, “Evaluation of polar MM5 simulations of Antarctic atmospheric circulation,” Monthly Weather Rev. 131, 384–411 (2003). 10 A. Costa, A. Crespo, J. Navarro, G. Lizcano, H. Madsen, and E. Feitosa, “A review on the young history of the wind power short-term prediction,” Renewable Sustainable Energy Rev. 12, 1725–1744 (2008). 11 J. L. Torres, A. Garcia, M. De Blas, and A. De Francisco, “Forecast of hourly average wind speed with ARMA models in Navarre (Spain),” Sol. Energy 79, 65–77 (2005). 12 E. Erdem and J. Shi, “ARMA based approaches for forecasting the tuple of wind speed and direction,” Appl. Energy 88, 1405–1414 (2011). 13 E. A. Bossanyi, “Short-term wind prediction using Kalman filters,” Wind Eng. 9, 1–8 (1985). 14 P. Louka, G. Galanis, N. Siebert, G. Kariniotaki, P. Katsafados, and I. Pytharoulis, “Improvements in wind speed forecasts for wind power prediction purposes using Kalman filtering,” J. Wind Eng. Ind. Aerodyn. 96, 2348–2362 (2008). 15 G. Li and J. Shi, “On comparing three artificial neural networks for wind speed forecasting,” Appl. Energy 87, 2313C2320 (2010).

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Wu et al.

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16

J. J. Flores, M. Graff, and H. Rodriguez, “Evolutive design of ARMA and ANN models for time series forecasting,” Renewable Energy 44, 225–230 (2012). G. Zhang, H. X. Li, and M. Gan, “Design a wind speed prediction model using probabilistic fuzzy system,” IEEE Trans. Ind. Informatics 8, 819–827 (2012). 18 E. Vladislavleva, T. Friedrich, F. Neumann, and M. Wagner, “Predicting the energy output of wind farms based on weather data: Important variables and their correlation,” Renewable Energy 50, 236–243 (2013). 19 G. Kariniotakis, D. Mayer, J. Moussafir, R. Chevallaz-Perrier, J. Usaola, I. Sanchez et al., “ANEMOS: Development of a next generation wind power forecasting system for the large-scale integration of onshore and offshore wind farms,” in Proceedings of the CD-ROM, CD 2. (Brussels: European Wind Energy Association (EWEA), Madrid, 2003). 20 G. Kariniotakis, ANEMOS: Development of a Next Generation Wind Power Forecasting System for the Large-Scale Integration of Onshore and Offshore Wind Farms 2002–2006 (International Energy Agency (IEA), 2004). 21 A. Costa, A. Crespo, and E. Migoya, “First results from a prediction project,” in Proceedings of the European Wind Energy Conference, EWEC’03, Madrid, 2003. 22 A. Costa, A. Crespo, E. Feitosa, J. Navarro, P. Jimenez, E. Garcia et al., Mathematical and Physical Wind Power Forecasting Models: A Proposal for the UPMPREDICTION Project (International Energy Agency (IEA), 2004). 23 A. M. Foley, P. G. Leahy, A. Marvuglia, and E. J. McKeogh, “Current methods and advances in forecasting of wind power generation,” Renewable Energy 37, 1–8 (2012). 24 G. Gieble, “State-of-the-art in wind power forecasting,” see http://www.safewind.eu/index.php?option=com_content& view=category&layout=blog&id=86&Itemid=136, 2013. 25 Y. Wang, Time Series Analysis (China Renmin University Press, Beijing, 2005). 26 D. Mera and G. Tavares, “Optimization of ARMA (p,q) models for SISO multipath fading channel simulation with arbitrary correlation,” in 71st IEEE Vehicular Technology Conference (VTC 2010-Spring), Taipei, 2010, pp. 1–5. 27 P. Moin and K. Mahesh, “Direct numerical simulation: A tool in turbulence research,” Annu. Rev. Fluid Mech. 30, 539–578 (1998). 28 W. Jones and B. Launder, “The prediction of laminarization with a two-equation model of turbulence,” Int. J. Heat Mass Transfer 15, 301–314 (1972). 29 J. M. L. M. Palma, F. A. Castro, L. F. Ribeiro et al., “Linear and nonlinear models in wind resource assessment and wind turbine micro-siting in complex terrain,” J. Wind Eng. Ind. Aerodyn. 96, 2308–2326 (2008). 30 T. Burton, N. Jenkins, D. Sharps, and E. Bossanyi, Wind Energy Handbook (Wiley, 2011). 31 N. O. Jensen, “A note on wind generator interaction,” Risø National Laboratory, DK-4000 Roskilde, Denmark, 1983. 32 G. Mosetti, C. Polonic, and B. Diviacco, “Optimization of wind turbine positioning in large wind farms by means of a genetic algorithm,” J. Wind Eng. Ind. Aerodyn. 51, 105–116 (1994). 33 M. X. Song, K. Chen, Z. Y. He, and X. Zhang, “Wake flow model of wind turbine using particle simulation,” Renewable Energy 41, 185–190 (2012). 34 See http://www.nemweb.com.au/Reports/CURRENT/Next_Day_Actual_Gen/ for Australian Energy Market Operator, 2013. 35 See http://en.wikipedia.org/wiki/Wattle_Point_Wind_Farm for Wikipedia, Wattle Point wind farm, 2012. 36 Australian Government, “Latest weather observations for Edithburgh,” see http://www.bom.gov.au/products/IDS60801/ IDS60801.94809.shtml, 2013. 37 Methodology of Wind Energy Resource Assessment for Wind Farm Gb/T 18710-2002 (Chinese Edition), edited by P. Shi, R. Zhu, H. Lou et al. (China Standard Press, Beijing, 2002). 17

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