A Gaussian RBF Network Based Wind Speed Estimation Algorithm for Maximum Power Point Tracking

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Energy Procedia

Energy Procedia (2011)12 000–000 Energy 00 Procedia (2011) 828 – 836

www.elsevier.com/locate/procedia

ICSGCE 2011: 27–30 September 2011, Chengdu, China

A Gaussian RBF Network Based Wind Speed Estimation Algorithm for Maximum Power Point Tracking Lei Tian*, Qiang Lu, Wen-zhuo Wang State Grid Electric Power Research Institute, Nanjing, 210003 China

Abstract This paper proposes a Gaussian radial basis function network (GRBFN) based wind speed estimation algorithm for maximum power point tracking (MPPT) of wind power generation system (WPGS). A specific design of the proposed control algorithm for the WPGS with a doubly-fed induction generator (DFIG) is presented. The aerodynamic characteristics of the turbine are approximated by a GRBFN based nonlinear input-output mapping. Based on this nonlinear mapping, the wind speed is estimated from the measured generator electrical output power while taking into account the power losses in system and the dynamic process of shaft system. The estimated wind speed is then used to determine the optimum DFIG rotor speed for maximum wind power extraction. Then the DFIG rotor speed is controlled with the wind speed change, the maximum power extraction can be achieved. Simulation model of 1MW WPGS is built in MATLB/SIMULINK software. The validity and feasibility of the proposed control algorithm is verified by simulation experiment. The simulation results show that the wind speed can be estimated accurately and WPGS can operate in the optimum operating point without mechanical anemometer.

© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of University of Electronic © 2011and Published by Elsevier Selection and/or peer-review under responsibility of ICSGCE 2011 Science Technology of ChinaLtd. (UESTC). Keywords: GRBFN; Wind speed estimation; Sensorless control; DFIG;MPPT; Vector control

1. Introduction Variable speed WPGS is more attractive than fixed speed systems because of the more efficient energy production, improved power quality. Under the condition of a various wind speed, the generator speed can be regulated to the optimum speed with the changes of wind speed. Then the maximum power point tracking can be realized [1-2].In most controller designs of variable speed WPGS, the anemometers which are placed surrounding the wind turbine at some distance are used to measure wind speed information. These mechanical sensors not only increase the cost, but reduce the control effect and affect

* Corresponding author. Tel.: +86-18761868769. E-mail address: [email protected].

1876-6102 © 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of University of Electronic Science and Technology of China (UESTC). doi:10.1016/j.egypro.2011.10.109

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the reliability of the overall system. Currently, for the above-mentioned disadvantages of wind speed sensor, many sensorless MPPT control methods have been proposed. The autoregressive statistical model is used to predict wind speed in [3]. This method may result in a complex computation and the predict accuracy can not enough for MPPT control. A polynomial is used to approximate the wind turbine aerodynamic characteristics in [4], the wind speed is then estimated by calculating the roots of the polynomial. This also causes complex timeconsuming computation. In [5], the maximum power point is commonly determined from the WPGS power-speed curves using a lookup table program. If the mechanical power of turbine is known, the wind speed can be estimated from the lookup table program. But this method will need significant memory space to obtain an accurate wind speed estimation. A GRBFN is used for wind speed estimation in this paper. The GRBFN is trained offline using a training data set and its parameters are calculated. The GRBFN are then used for online estimation of the wind speed. The accuracy of wind estimation also depends on the wind turbine mechanical power estimation. So the mechanical power of turbine is estimated from the measured generator electrical output power while taking into account the power losses in system and the dynamic process of shaft system. According to the information of rotor speed, pitch angle and mechanical power, approximation aerodynamic characteristics model of turbine can be obtained to predict wind speed. The DFIG optimum speed is calculated from the estimated wind speed. Then the DFIG rotor speed is controlled by vector control to track the optimum speed and the MPPT can be realized. 2. Dynamic Modeling of Wind Power Generation System The structure diagram is shown in Fig. 1. The turbine is connected with DFIG by a gearbox. The stator is directly connected to the grid while the rotor is fed through a converter.

isabc

Lf

Ps , Q s

Pg , Q g

irabc

Vdc C

vrabc

i gabc

v gabc

Fig. 1. Structure of doubly fed wind power generation system.

2.1. Aerodynamic model of turbine The aerodynamic model of turbine can be characterized by the C p − λ − β curves. C p is the power coefficient, which is a function of tip speed ratio λ and pitch angle β . The tip speed ratio λ is given by ωR λ= (1) v where ω is the rotational speed of turbine, v is wind speed, R is the blade length. The relationship of

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C p with λ and β can be described as [6] 12.5 ⎧ 116 − 0.4 β − 5)e λi ⎪C p (λ , β ) = 0.22( ⎪ λi (2) ⎨ 1 1 0.035 ⎪ = − 3 ⎩⎪ λi λ − 0.08β β + 1 When the wind speed is below rated wind speed, pitch angle is fixed to zero. In a certain wind speed, the relationship of C p with λ is shown in Fig. 2. According to aerodynamic characteristics of turbine, the aerodynamic power captured from wind are given by [7] 1 Pr = ρ SCP (λ , β )v3 (3) 2 where Pr is the aerodynamic power, ρ is air density, S is the swept area of turbine.

0.6

power coefficient

0.5

Cpm=0.48

0.4 0.3 0.2 0.1 0 -0.1 0

2

4

λopt=8.05 6 8 10 tip speed ratio

12

14

Fig. 2 Aerodynamic characteristic of turbine.

2.2. Doubly-fed induction generator modle The dynamic model of a three-phase DFIG in dq synchronous rotating coordinate is described as [8]

Vds = rs ids − ω sψ qs + Vqs = rs iqs + ω sψ ds + Vdr = rr idr − sω sψ qr Vqr = rr iqr + sω sψ dr ψ ds ψ qs ψ dr ψ qr

dψ ds dt dψ qs

dt dψ dr + dt dψ qr + dt

= Lls ids + Lm (ids + idr ) = Ls ids + Lm idr = Lls iqs + Lm (iqs + iqr ) = Ls iqs + Lm iqr = Llr idr + Lm (ids + idr ) = Lm ids + Lr idr = Llr iqr + Lm (iqs + iqr ) = Lm iqs + Lr iqr

Ls = Lls + Lm Lr = Llr + Lm Te =

3 pLm (iqs idr − ids iqr ) 2

(4)

(5) (6) (7)

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3 (vds ids + vqs iqs ) 2 (8) 3 Qs = (vqs ids − vds iqs ) 2 where ωs is the synchronous rotational speed, sωs is the slip speed, Lls , Llr and Lm are the stator leakage, rotor leakage and mutual inductances, respectively, V denotes voltage, ψ denotes flux linkage, p is the pairs of pole, subscript of s, r denotes the stator and rotor and subscript d, q denotes d-axis and qaxis. Ps =

2.3. Mechanical drive system model The shaft system of the WPGS is represented by a two-mass system, in which separate masses are used to represent the low-speed turbine and the high-speed generator, and the connecting flexible shaft is modeled as a spring and a damper. The motion equations are then given by d ωr Pm 2Jt = − Dt ωt − Dtg (ωt − ωr ) − Ttg dt ωt (9) Pe d ωr 2J g = Ttg + Dtg (ωt − ωr ) − Dg ωr − dt ωr (10) dTtg = K tg (ωt − ωr ) dt (11) where ωt and ωr are the turbine and generator rotor speed, respectively; Pm and Pe are the mechanical power of the turbine and the electrical power of the generator, respectively; Ttg is an internal torque of the model; Ht and Hg are the inertia constants of the turbine and the generator, respectively; Dt and Dg are the mechanical damping coefficients of the turbine and the generator, respectively; Dtg is the damping coefficient of the flexible coupling (shaft) between the two masses; Ktg is the shaft stiffness. 3. Wind Speed Estimation

3.1. Design of RBFNN

vˆw

Fig. 3. Gaussian RBFNN apprpximation model of turbine.

If the information of mechanical power is known, the wind turbine rotational speed and pitch angle, the wind speed can be calculated from the inverse function of (3). But this inverse function is nonlinear and is difficult to solution. In order to solve this problem, the GRBFN, well known for nonlinear approximation, is used in this paper. The approximation model of turbine in GRBFN is shown in Fig.3.

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The input-output relationship of GRBFN is given by ⎛ x−C 2 ⎞ h j ⎟ (12) vˆw = b + ∑ v j exp ⎜ − 2 ⎜ ⎟ βj 1 ⎝ ⎠ where x = [ Pm , ωt , β ] is the input vector, C j is the center of the jth unit in the hidden layer, h is the number of RBF units, b and v j are the bias width and weight between hidden and output layers, vˆw is the output that denotes the estimation wind speed. The GRBFN is trained offline using a training data set which contains the whole operating range. The sample of turbine speed and wind speed are obtained with the increments of 0.01 rad/s and 0.03 m/s, respectively. The pitch angle is fixed to zero. At each sample data of turbine speed, wind speed and pitch angle, the mechanical power of turbine can be calculated from (3). Then the training data set is created by combining all the sample data of turbine speed, mechanical power, pitch angle and wind speed, given by A = X ; Vw (13) X = { Pm (i, j , k ), ωt (i ), β (k ) |

i = 1,..., I ; j = 1,..., J ; k = 1,..., K }

V w = {vw ( j ) | j = 1,..., J }

(14) (15)

where X is the input of the training data set and Vw is the output of training data set. After the training data speed has been determined, the parameters of the GRBFN can be obtained by offline training and the optimization procedure in [9].

3.2. Estimation of turbine mechanical power The mechanical power of turbine is estimated from the measured electrical power of DFIG. Because of the use of gearbox, there are great dynamic processes in mechanical drive system. So considering the dynamic processes is very important to estimation the mechanical power. Adding (9) and (10) we can get d ωt d ωr Pm Pe + Ploss 2Ht (16) + 2H g = − ωt ωr dt dt where Ploss is the total power losses in the WPGS. Rewriting (15) in the discrete format ⎡ ω (t ) − ωt (t − 1) Pm(t ) = ⎢ 2 H t t + Δt ⎣ 2H g

ωr (t ) − ωr (t − 1) Δt

+

Pe (t ) + Ploss (t ) ⎤ ⎥ ωt (t ) ωr (t ) ⎦

(17)

Equation (17) can be used to estimate mechanical power. 4. Wind Speed Estimation Based Maximum Power extraction Control

4.1. The Principle of Maximum Power Extraction Control In the variable speed stage, in order to realize MPPT the rotational speed of WPGS must be regulated with wind speed, making WPGS operating in the optimum tip speed ratio λopt . The optimum rotor speed ωr* of DFIG can be calculated from the estimation wind speed vˆw , given by λ vˆ ωr* = opt w (18) R

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The principle of wind speed estimation based MPPT is shown in Fig. 4. Since the wind speed is normally varying fast and randomly, but the responses of WPGS are relatively slow because of its inertia. So a low-pass filter must be provided to smooth the rotor speed command.

vˆw

ωr*

Fig. 4. Wind speed estimation based maximum wind power trackining.

4.2. Stator Flux Oriented Vector Control In the stator flux oriented reference frame, the d-axis is aligned with the stator flux linkage ψs, namely, ψds=ψs and ψqs=0. From the above condition and DFIG mathematical model, we can obtain the following relationships − Lm ims iqr (19) Te = Ls 3 ωs L2m ims (ims − idr ) 2 Ls di vdr = rr idr + σ Lr dr − sωsσ Lr iqr dt diqr ⎛ σ L i + L2m ims ⎞ + sωs ⎜ r dr vqr = rr iqr + σ Lr ⎟ dt Ls ⎝ ⎠ vqs − rs iqs ims = ωs Lm

Qs =

(20) (21) (22) (23)

L2m (24) Ls Lr According to the mechanical drive system model in (9)-(11) and assuming Dt = Dg =0, the transfer function between generator rotor speed and electromagnetic torque can be described as 2 J t s 2 + Dtg s + K tg ωr 1 (25) = Te 2( J t + J g ) s 2 J t J g 2 s + Dtg s + K tg Jt + J g From equation (19) and (25), we can see that the DFIG rotor speed can be controlled by q-axis rotor current component iqr . From (20) we know, the reactive power of DFIG can be controlled by q-axis rotor current component idr. The principle of stator flux linkage oriented vector control is shown in Fig. 5.

σ = 1−

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sωs σLr iqr

Qs*

L2 i + σLr idr sωs m ms Ls i

udr′

•dr qr

uqr′

i

ω r*

ωr

udr∗

u

• qr

C

* u rabc

idr

Qs

iabcr

iqr

θr

sωs

ωs

θs d/dt

ωr

∫ dt uαβs iαβs

usabc

isabc

udqs idqs

Fig. 5. Principle of stator-flux oriented vector control for DFIG.

5. Simulation Analysis of Control System The simulation parameters used in this paper is shown in Table. 1. In the real system, the wind speed is always changes. A four-component wind model is used to verify the proposed estimation algorithm in the simulation [10]. The estimation of mechanical power is shown in Fig. 6. Based on the estimated mechanical power, the wind speed is then estimated by proposed algorithm. Fig. 7 shows the wind speed estimation results. The estimation error is only almost in ± 0.2m/s. That illustrates the proposed algorithm is enough to predict wind speed. The rotor speed tracking result is shown in Fig. 8. The change of tip speed ratio is shown in Fig. 9. The tip speed ratio waves around 8 and its average value is 8.01, which is very close to the theoretical value 8.05. Table 1: The Simulation Parameters

Rated power Rated wind speed Blade radius Rotational speed range Inertia Pairs of pole Stator voltage Rotational speed range Inertia Stator resistance Stator leakage reactance Rotor resistance Rotor leakage reactance Excitation reactance

Parameters of turbine 1000kW 13.5m/s 30.3m 12~21.5r/min 830000kg·m2 Parameters of generator 2 690V 1000~1800r/min 59 kg·m2 0.0018Ω 0.0227Ω 0.002Ω 0.0363Ω 1.37Ω

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8

5

mechanical power(W)

14

x 10

theoretical value estimation value

12 10 8 6 4 0

10

times(s)

20

30

Fig. 6. Estimation result of mechanical power.

15

actual value estimation value

wind speed (m/s)

14 13 12 11 10 0

5

10

15

times(s)

20

25

30

Fig. 7. Estimation result of wind speed 170

actual vaule optimum vaule

rotor speed (rad/s)

165 160 155 150 145 140 0

Fig. 8. The tracking result of rotor speed.

10

times(s)

20

30

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actual value average value

8.2

tip speed ratio

8.15 8.1 8.05 8 7.95 7.9 7.85 7.8 0

5

10

15 times (s)

20

25

30

Fig. 9. Change of tip speed ratio

6. Conclusion GRBFN is accurate enough to approximate the nonlinear relationship of turbine aerodynamic characteristics. The proposed wind speed estimation algorithm can estimate wind speed under the affect of drive system dynamic process. The problem that mechanical anemometer is inaccurate in measuring wind speed can be solved and the system cost is reduced. The optimum rotor speed of DFIG can be calculated from the estimated wind speed. Using the stator flux oriented vector control, the DFIG rotor speed can be controlled to track the optimum speed fast and accrately. In the process of wind speed change, the WPGs can operate around the optimum tip speed ratio and the MPPT can be realized. References [1] Hu Dong-liang, Zhao Cheng-yong, “The out characteristic analysis of variable speed constant frequency wind generating set,” Journal of North China Power Electric University, vol. 35, Jul. 2008, pp.1-6. [2] Li Hui, He Bei, “Control strategy of maximizing the wind energy for wind turbines with a DFIG,” Acta Energiae Solaris Sinica, vol. 29, Jul. 2008, pp. 797-803. [3] K. Tan and S. Islam, “Optimum control strategies in energy conversion of PMSG wind turbine system without mechanical sensors,” IEEE Trans. Energy Conversion, vol.19, Jun. 2004 , pp. 392-399. [4] S.Bhowmik, R.Spee and J.H.R, “Performance optimization for doubly fed wind power generation systems,” IEEE Trans. Ind. Appl., vol. 35, Aug. 1999, pp.949-958. [5] H. Li, K. L, “Shi. Neural network based sensorless maximum wind energy capture with compensated power coefficient,” IEEE Trans. Ind. Appl., vol. 41, Dec. 2005, pp.1548-1556. [6] Slootweg J G , Kling W L, Polinder H, “Dynamic modeling of a wind turbine with doubly fed induction generator,” Power Engineering Society Summer Meeting. Vancouver, Canada, Jan. 2001, pp.644-649. [7] Ye Hang-ye,Wind turbines control technology.Beijing:China Machine Press, 2002. [8] Zhao Dong-li, Guo Jin-dong, Xu Hong-hua, “The study and realization on the decouping control of active and reactive power of a variable speed constant frequency doubly fed induction generator,” Acta Energiae Solaris Sinica, vol. 27, Feb. 2006, pp.55-56. [9] W. Qiao, R.G. Harley, “Optimization of radial basis function widths usingparticle swarm optimization,”IEEE Swarm Intell.Symp.Dec. 2006, pp.55-60. [10] Ekanayake, J.B, Holdsworth, L, Wu, X., Jenkins, N. Dynamic modeling of Doubly Fed Induction generator wind turbines. IEEE Transaction on Power Systems, 2003, 2:803-809.

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