Research on Speed Control System for Fixed-Pitch Wind Turbine Based on Disturbance Observer

Zurong Hu, Junqi Wang, Yundong Ma, Xing Yan Automation Institute, NUAA

Nanjing, Jiangsu, China

Abstract—Considering the characteristics of fixed-pitch variable-speed wind turbine operating in all operating wind speed, the small signal model was established, which indicates that the system is unstable in high wind speed. In this paper, the use of disturbance observer for aerodynamic torque estimation and compensation was presented, which is to eliminate the unstable factors in the system itself and make the system into a stable linear system. And then the speed control system was designed based on the RT-LAB real time simulation system. The results show that the fixed-pitch variable speed wind turbines can be operated stably in all operating wind speed and the speed control system have good at tracking changing wind velocity, which indicated that fixed-pitch variable speed wind turbine can be operated not only for MPPT in low wind speed but also for constant power control in high wind speed. Keywords— Wind power generation; fix-pitch wind turbine; speed control; disturbance observer

I INTRODUCTION

Compared to the constant speed wind turbines, the variable speed wind turbines can be controlled for Maximum Power Point Tracking (MPPT) in wide wind speed, which makes the variable wind turbines have more annual energy output under the same wind condition than constant speed wind turbines [1]–[4]. But traditional pitch-controlled variable speed wind turbines need complex pitch control system, which increases the cost and reduces the reliability. Unlike the pitch-controlled variable speed wind turbines, fixed-pitch variable speed wind turbines operate by the way of variable speed control in all operating wind speed to achieve its output power control. The structure of this unit is relatively simple, and because the wind turbines operate in variable speed, the power coefficient is also relatively high. In high wind, owing to the operating point of wind turbines changing in large scale and the influences of the non-linear relation among the aerodynamic torque, rotational speed and wind speed, the speed control system of fixed-pitch variable speed wind turbines have already turned into an unstable non-linear system [5–8]. So the design of speed control system needs much higher requirements.

In this paper, the use of disturbance observer for aerodynamic torque estimation and compensation was presented, which is to eliminate the unstable factors in the

system itself and make the system into a stable linear system.And then the speed control system was designed based on the RT-LAB real time simulation system. The results show that the fixed-pitch variable speed wind turbines can be operated stably in all operating wind speed and the speed control system have good at tracking changing wind velocity, which indicated that fixed-pitch variable speed wind turbines can be operated not only for MPPT in low wind speed but also for constant power control in high wind speed.

II SMALL-SIGNAL MODEL

The RT-LAB model of fixed pitch variable speed wind turbines is depicted in Fig.1. Boost convertor is used to stabilize the dc bus voltage .And its output voltage is decided by the output power of wind turbines.

As a result of the permanent magnet synchronous motor direct driven by a variable speed wind turbine, its mathematical model is very simple .However; this model can reflect the basic dynamic characteristics of variable speed wind turbines.

BdtdJTT em (1)

Where J is the moment of inertia of the rotor system; is the rotor speed; B is the friction coefficient; Tm is the aerodynamic torque; Te is the electrical torque of the generator;

The aerodynamic torque produced by the wind on the blades is:

)(21

T32

m CVRT (2)

Where is the air density; R is the turbine radius; CT( ) is the torque coefficient; Assumption that the wind turbines operating point can be expressed with the Subscript op, thepartial derivative of Tm with respect to the turbine speed and wind speed can be obtained as follow:

978-1-4244-4702-2/09/$25.00 ©2009 IEEE

)(21

opT2

op3

opm

ddC

VRT (3)

)]()(2[21

opT

opopTop3

opm

ddC

CVRVT

(4)

The partial derivative of equation (1) with respect to the turbine speed and wind speed is derived in the same way.

VTBdt

dJ e (5)

So the transfer function from the rotor speed to the electrical torque is:

BJssT

s 1)()(

e

(6)

Figure 2 shows the torque-coefficient curve of the fixed-pitch wind turbines. In region BC, the gradient value of CT curve is negative, so <0. In this region, the wind turbines can operate stably without special control. In region AB, the gradient value of CT curve is positive, so >0.Because the friction coefficient B is very small, the system has the right half plane pole. So the system is unstable. In region OA, the gradient value of CT curve is close to zero, so 0. It is beyond the scope of the variable-speed operation, so it will not be discussed in this paper. When the wind turbine is operating in region AB, if the disturbance causes the increase of the rotor speed, then the tip speed, , will increase, and the torque coefficient CT will increase, also. Finally it will cause the increase of the aerodynamic torque Tm, which will cause the rotor speed becoming much larger. So the system can not operate stably.

Based on the above analysis, the speed control system of the wind turbine is shown in Fig.2. Where T(s) is the close loop transfer function of the electrical torque, which can be expressed as T(s)=1/(3Ts+1). Where Ts is the Switching period of the PWM rectifier. H(s) is the delay link of speed detecting. The aerodynamic torque is not only the source power to drive the wind turbine operating, but also the strong disturbance of affecting the system stability. In this paper, the use of the disturbance observer for aerodynamic torque estimation and compensation was presented, which is to eliminate the unstable factors in the system itself and make the system into a stable linear system.

Fig.1 The RT-LAB model of the system

Fig.2 Torque coefficient curve

Fig.3 Block diagram of speed control system

III PRINCIPLE OF DISTURBANCE OBSERVER

The disturbance observer (DOB) puts the difference between the actual output and the output of the reconstruction model as an equivalent disturbance to apply to the reconstruction model. The basic structure of disturbance observer is shown in Fig.3. Where u is the system input; d is the disturbance signal. is the output of system. G(s) is the real mode of control object. Gn(s) is the nominal model [9–10].

The structure of DOB which is shown in Fig.3 can not be achieved in practice. There are several reasons as follow: (1) The inverse of the system [G(s)]-1 can not be achieved; (2) The real model G(s) can not be obtained, and there are always some difference between real mode G(s) and nominal model Gn(s).

Some improved methods are adopted to overcome the above shortcomings: (1) Add low pass filter Q(s) to the DOB. (2) The inverse of the nominal model [Gn(s)]-1 replaces the inverse of the real mode [G(s)]-1; the realizable structure of disturbance observer applied to wind turbine is shown in Fig 5.

Where Tm is the aerodynamic torque; Te is the electrical torque of the generator; r is the measurement noise.

The system output can be obtained from the Fig 5

)())()(()()()()(

)())()(()())(1)(()()(

)())()(()()()()(

)()()()()()()(

3

2

1

3121

sQsGsGsGsQsGsG

sQsGsGsGsQsGsG

sG

sQsGsGsGsGsG

sG

srsGsTsGsTsGs

nn

nn

n

nn

n

me

(7)

Where G1(s) is the transfer function from the electrical torque to the rotor speed. G2(s) is the transfer function from the aerodynamic torque to the rotor speed. G3(s) is the transfer function from measurement noise to the rotor speed.

Equation (7) shows that, at low frequency, if |Q(j )| 1, then G1(s)=Gn(s), G2(s)=0. So the system has a strong robustness to the disturbance signal. At high frequency, if |Q(j )| 0, then G3(s)=0. The measurement noise is suppressed by the disturbance observer. The above analysis shows that the key of DOB designed is to choose the proper low pass filter Q(s). Taking into the effect of the electrical torque loop account and guaranteeing that Q(s)[Gn(s)]-1 can be achieved in practice, this paper adopt second order filter as follow:

1)(2)(

1)( 2 sssQ (8)

Where is the filter time constant, [10 15]T, T is the sampling time of discrete system.

Fig.4 The basic structure of disturbance observer

Fig.5 The realizable structure of disturbance observer

Based on the compensation of DOB, the unstable factors in the system are eliminated and the system becomes a stable linear one. So the open-loop transfer function of the system is

)))(13/(()()( sck BJssTsGsG (9)

Because the speed control loop need fast tracking ability, the speed controller is designed according with typical 1 type system. The transfer function of speed controller is

ssTK

sG ip )1()( 1

c (10)

Where T1=J/B and Kip=B/ (6Ts)

IV EXPERIMENT RESULTS

Permanent magnet synchronous motor parameters is as follow: Rated Power: PN=10KW, Stator Inductance: La=Lb=Lc=5mH, Resistance Rs=0.6 , Rotor Magnetic Potential f =0.57, Rated Rotor Speed: =16rad/s, Pole Pairs P=8, Rated Wind Speed v=10m/s, Radius R=4m, Maximum power coefficient Cpmax=0.364, Rated Power of Wind Turbine Pm=10KW.

When wind speed is 6m/s, the output power of wind turbine is 2.5KW. After 0.1s, the wind speed becomes 16m/s. Because of the limitation of the output voltage of RT-LAB simulation system, the waveform in Fig. 6 and Fig.7 have been normalized. For example, when the wind speed v is 6m/s, the output voltage observed from the oscilloscope is as follow:

maxmax

Uv

vU (11)

Where v is the temporary wind speed, vmax is the maximum wind speed, vmax=24m/s and Umax is the maximum output voltage according with vmax, Umax=10V. So when the wind speed v is 6m/s, the output voltage observed from the

oscilloscope is 2.5V. The other parameters of the waveform are as follow:

TABLE I PARAMETERS

Maximum output Maximum output voltage

rotor speed 16 rad/s 10 V

electrical torque 1000 N*m 10 V

Output power 10 KW 10 V

Power coefficient 0.37 10 V

The operating region of the wind turbines can be divided into three regions: constant power coefficient CP region, constant rotor speed region, constant power region. Fig.6 and Fig 7 show that in the constant power coefficient region, the wind turbine speed varies linearly with the wind speed. The power coefficient is kept constant at 0.36 (10V). And the output power of wind turbine is increasing fast. With wind speed increasing, the wind turbine speed reaches its limit 16m/s (10V), although the rated power has not been reached yet. In this region, the wind turbine speed is kept constant as the wind speed increases. The power increases until the rated power 10KW (10V) is reached. While the power coefficient is reduced as the wind speed increased.

(20 /div)

(4/d

iv)

(4

/div

)(4

/div

)

Fig.6. Electromagnetic torque (upper), generator speed (middle),

and wind speed (lower)

Fig.7. Power coefficient (upper), the rotor speed (middle) and aerodynamic

power (lower)

As the output power reaches the rated power of the wind turbine, the power is kept constant, although the wind speed is increasing still. In this region the system is unstable; the wind turbine can not operate stably without some special control. In this paper, the use of disturbance observer for aerodynamic torque estimation and compensation was presented, which is to eliminate the unstable factors in the system itself and make the system into a stable linear system. So the speed of wind turbine is reduced to limit the output power of wind turbine, when the output power reaches its rated value. The output power is kept at 10KW (10V). Fig 6 shows that when wind speed exceeds a certain value, the decrement of the rotor speed doesn’t change obviously. Because the stall characteristics of the wind turbines play a major role, so the rotor speed need not change too much to limit the output power of wind turbine.

V CONCLUSION

Based on the small signal model of the wind turbine, the unstable factors are found out. Then the use of disturbance observer for aerodynamic torque estimation and compensation was presented, which is to eliminate the unstable factors in the system itself and make the system into a stable linear system. Finally the speed control system was designed based on RT-LAB real time simulation system. Experimental results show that the fixed-pitch variable speed wind turbines can be operated stably in all operating wind speed and the speed control system have good at tracking changing wind velocity,

which indicated that fixed-pitch variable speed wind turbine can be operated not only for MPPT in low wind speed but also for constant power control in high wind speed.

ACKOWLEDGMENT

This work was supported by National Basic Research Program of China (973 Program) (No.2007CB210303).

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