Abstract— Extracting maximum power and maintaining constant frequency at variable wind speed is the most demanding objective of wind energy system. Various classical control methodologies have been applied to achieve this objective. Due to the unpredictable nature of the wind speed, power varies during controller transition from one region to another. Adaptive neuro-fuzzy controllers are able to control complex non-linear process where the disturbances have a major impact on the control performance. In this paper a self-learning neuro-fuzzy control strategy based on feedback error learning is proposed. The objective is to control the pitch angle in various operating conditions by tuning the controller parameters online. Results are included which demonstrates the efficiency of the self-learning neuro-fuzzy controller in maintaining constant power in variable wind speed. Keywords— neuro-fuzzy control, pitch angle, doubly fed induction generator
I. INTRODUCTION Wind Speed is variable in nature and to control turbine
speed three methods have been widely used i.e. (a) passive stall (b) changing pitch angle of the turbine rotor blades [1] and (c) active stall [2].
In passive stall method the rotor blades are fixed at certain angle as compared to variable pitch angle method because passive stall has no control over speed of wind turbine and power when wind speed rises to certain level above rated. In the second case the pitch angle of the rotor blades continuously varies to maintain constant power at the output. In high rated wind turbines i.e. greater than 1 MW [2] active stall is used in which characteristics of both (a) and (b) method is utilized. In active stall when speed rises to the cut off speed the direction of the blades turns opposite to the direction of wind speed in order to reduce overloading on generator and wind turbine [3,4].
In Fig.1 wind speed profile curve is shown with different regions of operation. Wind speed below 5 m/sec is the cut off region, wind speed from 5 m/sec up to 15 m/sec is the rated speed region, wind speed above 15 m/sec is the above rated speed region and wind speed beyond 25 m/sec is the shutdown region. The wind turbine model used in this paper has rated speed region up to 12 m/sec instead of 15 m/sec.
All three regions of wind profile have different objectives which require effective online tuning of the controller
parameter to get satisfactory performance over the complete operating range of the wind turbine.
In modern wind turbine system despite of blade angle control; electromagnetic torque control is also used to maintain constant power. Torque control is mainly achieved at the rotor side of the generator by controlling voltage of the converter/inverter.
II. SYSTEM OVERVIEW Doubly Fed Induction Generator (DFIG) has been used with the wind turbine. In DFIG both stator and rotor are connected to the grid. There are two main reasons for incorporating DFIG in the system. The primary reason for selecting DFIG instead of SFIG (singly fed induction generator in which only stator is connected to the grid or network) in the model is to maintain constant frequency at variable speed with respect to the grid or the network in order to remain synchronized. The second reason is the size and cost of the power electronics devices used in AC/DC/AC inverter. It has to handle 30% of the generator rated output power whereas the power electronics devices used in SFIG type wind turbine model has to bare 100% of the generator rated power [3]. In this work DFIG from Sim-Power-System Matlab/SIMULINK blockset has been used. The block diagram of the complete system is shown in Fig. 2. It consists of a wind turbine, gear train, and DFIG. The stator of DFIG is directly connected to the grid, the rotor is connected to the grid via AC/DC/AC inverter and inductor.
The frequency at the stator of DFIG [3] is given by,
*
120rotor pole
stator rotor
n Nf f= + (1)
Where,
frotor is the frequency of the ac current that need to be fed into the doubly fed induction generator rotor winding for fstator to be equal to the frequency of the grid or network, expressed in Hz.
nrotor is the frequency of the rotational speed of the generator rotor expressed in rotation per minutes (r/min).
Npole is the number of magnetic pole per phase in the doubly wound induction generator.
International Conference on Renewable Energy Research and Applications Madrid, Spain, 20-23 October 2013
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Figure 1 Wind Speed Curve showing three different region of operation of wind turbine
The mechanical power [4] extracted from the wind speed can be computed as below from Equation (2).
31 [ ( , ) ]2mP ACp vλ β= (2)
‘ ’ is the air density,
‘A’ is the turbine swept area,
‘V’ is the wind speed,
Cp ( , ) is the power co-efficient,
‘ ’ is the pitch angle in degrees,
‘ ’ is the tip speed ratio and is given by
* /R vλ ω= (3) where
‘ ’ is the rotational speed, ‘R’ is the rotor radius and ‘v’ is the wind speed. It can be observed from Equation (2), in order to get maximum power at low, rated and high wind speed, power co-efficient variable should be varied. The plot of Cp and tip speed ratio ( ) at different values of pitch angle is shown in Fig.3. The maximum value of Cp is obtained at pitch angle zero, from low to rated wind speed the pitch angle should be kept zero in order to get maximum value of Cp. The pitch angle above rated wind speed should be varied in order to get low power co-efficient. At high wind speed i.e. above rated speed, pitch angle control as well as electromagnetic torque control is required to maintain constant frequency at constant power. This is achieved by controlling the frequency of the rotor side injected current by varying the modulation index of the PWM (pulse width modulation) voltage at the rotor side inverter as shown in Fig 2. In MATLAB model the power tracking curve is shown in Fig. 4. The power tracking curve has been used to obtain reference power at different rotor speeds.
Figure 2 Wind turbine with DFIG Generator (taken from Matlab)
Figure 3 Power Co-efficient Curve (taken from Matlab)
Figure 4 Mechanical power and turbine speed on different wind speed (all quantities are in per unit, taken from Matlab)
III. SELF TUNING NEURO FUZZY CONTROLLER The neuro-fuzzy control strategy [5,6] is shown in Fig.5.
This scheme consists of feed forward controller, reference model, an online identification algorithm along with a proportional controller. The reference model is used to generate reference signal suitable for tracking by the controller. The feed forward controller is a 0th Order TS model [7,8]. In this paper triangular membership functions with 50% overlap has been used for each input. Each input universe of
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discourse consists of ‘Pj’ fuzzy membership functions and the controller has ‘p’ number of rules: Rule 1: if x1 is A11, x2 is A21,,,,,,,,,,,,,,,,,,,,,,,,,, and xn is An1, then uf is w1 Rule 2: if x1 is A12, x2 is A22,,,,,,,,,,,,,,,,,,,,,,,,,, and xn is An2, then uf is w2. . . Rule i: if x1 is A1i, x2 is A2i,,,,,,,,,,,,,,,,,,,,,,,,,, and xn is Ani, then uf is wi. . . Rule p: if x1 is A1p1, x2 is A2p2,,,,,,,,,,,,,,,,,,,,,,, and xn is Anpn, then uf is wp. The output of feed forward controller will be (if weighted average defuzzification method is used for the case of partition of unity between triangular membership function) is given by
1( ) ( ( )) ( )
p
f i ii
u t a x t w t=
= (4)
( ) ( ) ( )T
fu t a t w t= (5) Where uf(t) is the feed forward control action at time ‘t’, x(t) = [ x1, x2, , , , , , xn] is the input vector at time ‘t’,
1 21 2( ( )) ( ). ( )......... ( )i i nii A A A na x t x x xμ μ μ=
is the product of the membership grades of the input antecedent in the ith rule, aT(t) = [ a1, a2, ..... , ap] is the transformed input vector, w(t) = [ w1(t), w2(t), ......, wp(t)] is the parameter vector at time ‘t’. The goal of the control strategy is to find the values in the parameters vector, so that neuro-fuzzy controller is trained to act as the inverse plant model. The exact inverse plant model is difficult to obtain practically (if not impossible) to compensate model mismatches and unmeasured disturbances, proportional controller has been added in the feedback path to compensate finite modelling errors and unmeasured disturbances. The correct control action is unknown a priori, therefore feedback error learning estimate the desired control action. A new signal is required to track the desired output, which is given by
( ) ( - ) ( )df fu t u t t e tγ= + (6) where the online learning rate, e(t) is the error signal and
( )fu t is the estimated desired control action. This error signal is used for model mismatches, and this approach is called Feedback error learning scheme. {x(t-td),uf(t)} pair will be used in the FLMS recursive learning mechanism to update the parameter vector, which take in account the strength and frequency of a particular rule that was fired in order to modify
only those parameters which was not previously updated correctly.
Figure 5 Self tuning Neuro Fuzzy Control Scheme
The updated controller parameter can be found using FLMS [10] algorithm given in Equation (7).
( -1) ( - ) ( )( ) ( -1)( - ) ( -1) ( - )
d
Td d
S t a t t tw t w ta t t S t a t t
δ εδ= + (7)
Where,
1 2( -1) { , ,.., ,.., }i pS t diag s s s s= (8)
1
, ( ), ( ) ( -1) ( )j i
p
i i i
j
s j i F t F t F t a t=
= ≠ = +∏ (9)
S(t) measure the strength and frequency of the particular rule that was fired. is the user selected parameter,
ˆ( ) ( ) - ( )f ft u t u tε = (10)
ˆ ( ) ( - ) ( -1)d
Tfu t a t t w t= (11)
The user selected parameter as in (5) and (7) can be obtained from equivalent model of the PI controller as described in [5].
IV. PITCH ANGLE CONTROL The block diagram of the neuro-fuzzy controller used to control the pitch angle of the wind turbine is shown in Figure 6.
Figure 6 Pitch angle control block diagram
In the proposed approach three triangular memberships
function are used for ‘ r’ and ‘Pitch Angle’. The membership functions are evenly distributed over the universe of discourse
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and have 50% overlap. The apex of the membership functions are at 0.0,0.5 and 1.0 respectively. There are nine rules in the neuro- fuzzy controller.
An artificial wind profile was generated in which the wind
velocity was gradually increased from (5 m/sec to 20m/sec). In order to verify the control performance of the neuro-fuzzy controller the artificial wind profile consisted of four regions. The wind profile is shown in Figure 7. When wind speed rises from 10 m/sec to 15 m/sec, the pitch angle, power and r remains constant at the desired value as shown in Fig 7 and 8 respectively. When wind speed varies from 15m/sec to 20 m/sec above rated speed, dip in power and r is observed (Fig 8). There is lot of oscillations in the pitch angle which is undesirable. The oscillations in the pitch angle reduces with time. As time increases the controller parameters are tuned and the performance improves. As demonstrated in Figure 8, power remains constant in the learning phase, the fluctuation in r also decreases. It can be easily observed from Fig 9 that the weights (controller parameters) are converging. One of the reasons for oscillations in the pitch angle and r is fewer number of membership functions in the above rated region(i.e. from 15 to 25 m/sec wind speed). One of the directions for future work is to redefine the membership functions in the above rated speed region. The increased resolution might reduce the rapid fluctuation in pitch angle and r.
0 100 200 300 400 500 600 700 8005
10
15
20Wind Speed (m/sec)
0 100 200 300 400 500 600 700 8000
5
10
15
20
25
30Pitch Angle(degrees)
Figure 7 Wind Speed varies (5-20m/sec), pitch angle (when input signal repeated one time)
0 100 200 300 400 500 600 700 800-1
-0.5
0
0.5
1Power (pu)
0 100 200 300 400 500 600 700 800
0.8
1
1.2
1.4
1.6wr(pu0
Figure 8 Power and r (when input signal repeated one time)
0 200 400 600 800-15
-10
-5
0
5w2
0 200 400 600 8000.1
0.1
0.1
0.1
0.1w2
0 200 400 600 8000.1
0.1
0.1
0.1
0.1w3
0 200 400 600 800-2000
-1000
0
1000w4
0 200 400 600 800-3000
-2000
-1000
0
1000w5
0 200 400 600 8000
500
1000
1500
2000w6
0 200 400 600 800-1000
-500
0
500w7
0 200 400 600 800-1500
-1000
-500
0
500w8
0 200 400 600 8000
200
400
600w9
Figure 9 Weights vector, wind speed (5-20m/sec) repeated one time.
In order to investigate the learning capability of the neuro-fuzzy controller the same wind profile (as shown in Figure 7) was repeated five times. The power & r remained constant throughout the interval of wind speed>12m/sec to 15 m/sec (as discussed earlier). When wind speed increases above rated the oscillations were observed.
The most important result was the ability of the controller to learn and to converge towards the true weight values. The weight parameter of the controller is shown in Fig 10. All the weights are converging and consequently the controller performance is improving with increased learning.
0 500 1000 1500-4
-2
0
2x 10
4 w1
0 500 1000 1500-15
-10
-5
0
5w2
0 500 1000 1500-15
-10
-5
0
5w3
0 500 1000 1500-3000
-2000
-1000
0
1000w4
0 500 1000 1500-600
-400
-200
0
200w5
0 500 1000 15000
2000
4000
6000w6
0 500 1000 1500-1000
-500
0
500w7
0 500 1000 1500-600
-400
-200
0
200w8
0 500 1000 15000
500
1000
1500w9
Figure 10 Weight vector, wind speed (5-20m/sec) repeated five times.
V. ELECTROMAGNETIC TORQUE CONTROL In above rated region of wind speed there is another
parameter (electromagnetic torque) which is to be controlled along with pitch angle in order to get constant power and frequency. One of the alternate procedures, to reduce fluctuation in pitch angle and r is to introduce an electromagnetic torque controller. The second controller can be a neuro-fuzzy controller. To control electromagnetic torque, the injected current in the rotor of the DFIG is varied by PWM (pulse width modulation voltage) of the rotor side inverter as shown in Fig 1. The proposed block diagram for the electromagnetic torque angle control is shown in Fig. 11. Our future work is directed to implement the torque controller as a neuro-fuzzy controller to compare the results with standard PID.
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Losses
r
Ir & Is
I_gc
Power Measurement
Power Referencer
V
IPower Regulator Current regulator
Rotor Current Measureemnt
Lqr_refSubtract Subtract
Ir
Vr
Figure 11 Block diagram of the electromagnetic torque control
VI. CONCLUSION Self tuning neuro-fuzzy controller was proposed as a pitch angle controller for maintaining constant power and r. DFIG was used in cascade with the wind turbine. In the case of variable wind speed self tuning neuro-fuzzy controller was able to maintain a constant output by effectively varying the pitch angle. The controller is able to learn the behaviour of the system and to maintain correct pitch angle as demonstrated by the simulation results. Future work includes comparison of the control performance with a gain scheduled PID controller and the inclusion of another controller for electromagnetic torque control.
REFRENCES
[1] E. B. Muhando, T. Senjyu, A. Yona, H. Kinjo, and T. Funabashi, “Disturbance rejection by dual pitch control and self-tuning regulator for wind turbine generator parametric uncertainty compensation,” IET Control Theory Applicat., vol. 1, pp. 1431–1440, 2007. [2] F. D. Bianchi, H. Battista, and R. J. Mantz, Wind Turbine Control Systems: Principles, Modelling and Gain Scheduling Design. London: Springer-Verlag, 2007. [3] Soliman, M., Malik, O.P., Westwick,D.T., "Multiple Model Predictive Control for Wind Turbines With Doubly Fed Induction Generators", IEEE Transactions on Sustainable Energy, Vol 2, Issue 3, 2011. [4] E. Muljadi and C.P. Butterfield,” Pitch-Controlled Variable-Speed Wind Turbine Generation” Presented at the 1999 IEEE Industry Applications, Society Annual Meeting, Phoenix, Arizona, October 3-7, 1999 [5] W. W. Tan and A. L. Dexter, "Self-learning neurofuzzy control of a liquid helium cryostat," Control Engineering Practice, vol. 7, pp. 1209-1220, 1999. [6] Kadri, M.B., Dexter, A.L., “Disturbance rejection in information-poor systems using an adaptive model-free fuzzy controller”, The 28th North American Fuzzy Information Processing Society Annual Conference, 14-17 June,2009, Page(s) 1-6, Ohio, USA. [7] Kadri, M.B., “Disturbance Rejection in model free adaptive control using feedback”, The 29th IASTED International Conference on Modeling Identification and Control (MIC 2010), 15-17 February, 2010, Innsbruck, Austria
[8] Kadri, M.B., Hussain, S., “Model Free Adaptive Control based on FRM with an approach to reduce the control activity”, 2010 IEEE International Conference on Systems, Man and Cybernetics (SMC 2010), 10-13 October, 2010, Istanbul, Turkey. [9] A. D. Hansen, P. Sorensen, F. Lov, and F. Blaabjerg, “Control of variable speed wind turbines with doubly-fed induction generators,” Wind Eng., vol. 28, pp. 411–443, 2004. [10] W. W. Tan and C. H. Lo, "Development of Feedback Error Learning Strategies for Training Neurofuzzy Controllers On-Line," IEEE International Fuzzy Systems Conference, pp. 1016-1021, 2001.
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