2015_pitch-controlled[1]_ieee.pdf

Ouput Power Smoothening of Variable-Speed Wind Turbine Systems by Pitch Angle Control Tan Luong Van

Dong-Choon Lee

Dept. of Electrical Engineering Yeungnam University 214-1, Daedong, Gyeongsan, Gyeongbuk, 712-749, Korea

Dept. of Electrical Engineering Yeungnam University 214-1, Daedong, Gyeongsan, Gyeongbuk, 712-749, Korea

E-mail: [email protected]

E-mail: [email protected]

On the other hand, the pitch angle control has been employed for smoothening the power fluctuations. To control the pitch angle, the proportional-integral (PI) pitch controller has been often used for the power smoothening [3]. However, the strategy is based on the model of the wind turbines linearized at the operating points. Also, the controller provides the poor performances by highly nonlinear characteristic of the wind turbine. Also, a fuzzy logic controller has been used to guarantee the power smoothening reliably [4]. Also, a minimum variation controller for smoothening has been introduced in [5]. This method is effective to compensate for the influence of parameter variations. Moreover, the H∞ controller has been employed to achieve the robust stability [6]. In addition, a generalized predictive controller used together with a fuzzy reasoning corrector provides the stable operations during the rapid change of the wind speed in operating points [7]. However, the control methods partially smoothen the output power fluctuations, which results in a large drop in output power. A pitch angle control scheme based on the fuzzy logic control is proposed for the power smoothening in the low wind speed region for the variable-speed wind turbine system. With this method, the turbine power reference is calculated depending on the double exponential smoothening (DES) method. The superiority of the DES over other conventional smoothening techniques is that the DES can follow the wind speed quickly since it uses a current data as well as the prior estimated data for the next sampling period [8]. This method improves the performance of the power smoothening without any power compensation. The proposed method is verified by MATLAB/SIMULINK simulation results for a 2-MW PMSG wind turbine system.

Abstract—This paper proposes a new strategy of the output power smoothening for the variable speed wind turbine systems, which is based on the pitch angle control using the fuzzy logic controller. In this method, the turbine power and its reference are used as control input variables for the fuzzy logic controller (FLC), in which the turbine power reference is determined depending on the double exponential smoothening (DES) method. This method is effective to smoothen the generator output power without any need of the power compensation by the energy storage system. The effectiveness of the proposed method is verified by simulation results for a 2-MW PMSG wind turbine system. Keywords - Fuzzy logic control, pitch angle, power smoothening, wind turbine.

I.

INTRODUCTION

In recent years, there has been a great growth in the wind power system due to the environmental advantages and the economic benefits of the fuel savings. The turbine output power is proportional to the cube of the wind speed, which causes the generated power to be fluctuated much. This can lead to the frequency and voltage stability problems when the penetration of the wind turbines into the electrical power grid is high [1]. The pitch angle control is necessary for the variable-speed wind turbine system. In the wind speed regions higher than its rated value, the generator output power and speed are controlled at the rated values by controlling the pitch angle. On the contrary, in low wind speed regions, the maximum energy extracted from the wind turbine is obtained by controlling the turbine speed. As a result, the power conversion efficiency of the turbine is significantly increased with the increase of the power ripples. The pitch angle control can also be applied for smoothening the output power fluctuations. A few methods have been suggested to smoothen the generator output power in the variable-speed wind turbine system. In one category, the energy storage system has been used to absorb the power fluctuations [2]. This strategy is very effective when the power quality issues are related to the high sensitive loads. However, it is not efficient in term of the economic view point.

978-1-4673-4584-2/12/$31.00 ©2012 IEEE

II.

WIND TURBINE SYSTEMS

A. Blade modeling The output power of wind turbines ( PWT ) is determined as [1] 1 PWT = ρπ R 2 C p ( λ , β ) vw3 (1) 2 where  is the air density [kg/m3], R is the radius of blade [m],

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IPEC 2012

vw is the wind speed [m/s], and C p (λ , β ) is the power conversion coefficient which is a function of the tip-speed ratio ( λ ) and the pitch angle ( β ). The turbine power is determined by the power conversion coefficient and the tipspeed ratio if the swept area, air density, and wind speed are constant. The power conversion coefficient and the tip-speed ratio depend on the aerodynamic characteristics of the wind turbine. The tip-speed-ratio λ is defined as [1] Rωt λ= (2) vw

where ωt is the rotor speed of turbines. The power conversion coefficient is expressed as 1 1 (3) C p (λ , β ) = c1 (c2 − c3 β − c4 β c5 − c6 ) exp(−c7 ) Λ Λ where

1 1 0.035 = − Λ λ + 0.08β 1 + β 3

Fig. 1. Block diagram of the pitch control system.

β = −

1

τc

β+

1

τc

β ref

(6)

which is subject to

β min ≤ β ≤ β max where  and ref are the actual pitch angle and pitch angle reference. The time constant of the servo system is normally selected to be 0.25 sec for the fast acceleration of the servo system [1]. Also, a rate limiter (d/dt) is added to obtain a realistic response since the pitch actuation system cannot respond instantly. Moreover, the pitch rate is limited at the maximum value of ±10 deg/sec. To decrease the risks of the fatigue damage, the limit is not reached during the normal operation of the wind turbine.

(4)

and c1-c7 are the constants [9]. From (1) and (2), the turbine torque can be expressed as Cp (λ, β ) 2 1 Tt = ρπ R 3 vw . (5) 2 λ

III.

B. Control of PMSG Systems The control structure of the line-side converter (LSC) consists of the outer DC-link voltage control and reactive power control loops, and the inner current control loops [2]. For the generator-side converter (GSC), a cascaded control structure composed of an inner current control loops and an outer speed control loop is employed. To obtain the maximum power at the minimum current, the d-axis reference current component is set to zero and then q-axis current is proportional to the active power, which is determined by the speed controller. The maximum power point tracking method is applied for the wind turbine control, which gives the speed reference of the PMSG [1].

C. Pitch System There are two operating modes in wind turbine systems according to the wind speed. Below the rated wind speed, the blade pitch angle is fixed to give the maximum output power. In this region, the characteristic curve reflects the basic law of power conversion, in which the power is proportional to the cube of the wind speed [1]. At the wind speeds which exceed the rated value, the blade pitch angle is controlled to protect the turbines, where the output power is limited at the rated value. The block diagram of the typical pitch control loop is shown in Fig. 1, in which the pitch servo system is included. The pitch servo is modeled as the first-order delay system, with a time constant ( τ c ). The dynamic behavior of the pitch servo is described as [1]

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EXISTING POWER SMOOTHENING METHODS

For smoothening the wind generator output power, the most important part is to determine the turbine power reference (Pref ), which is the pitch controller input. The types of the average values are evaluated to ensure the effectiveness of the proposed controller.

A. Average Signal (AVG) The average signal value is calculated after every specified number of periods. For twenty measurements from D1 to D20, the successive four-period average values, for example, are calculated as follows [8]:

AVG4 = ( D4 + D3 + D2 + D1 ) / 4 AVG8 = ( D8 + D7 + D6 + D5 ) / 4 . . AVG20 = ( D20 + D19 + D18 + D17 ) / 4

(7)

B. Simple Moving Average (SMA) The simple moving average value is calculated after every four specified number of periods. If the twenty measurements, D1 through D20, are available, then the simple moving averages for successive four periods are calculated as follows [8]: SMA4 = ( D4 + D3 + D2 + D1 ) / 4

SMA8 = ( D5 + D4 + D3 + D2 ) / 4 . .

SMA20 = ( D20 + D19 + D18 + D17 ) / 4

(8)

C. Single Exponential Smoothening (SES) The single exponential smoothening method is calculated as [8] st = kxt + (1 − k ) st −1 (9) where xt is the current value, st-1 is the previous period of the SES, and k is the weighting factor. For a period-based SES, the k can be calculated as: 2 k= (10) 1+ N

Fig. 2. Calculation of smoothened value using SES and DES methods.

Power

PWT

where N is the specified number of the periods. IV.

PWT PWT

Pref

PROPOSED METHOD FOR POWER SMOOTHENING

To smoothen the generator output power, the turbine power reference in the pitch controller (Pref ) is determined by the double exponential smoothening. Then, the fuzzy logic controller is designed to control the pitch controller. A. Double Exponential Smoothening (DES) The single exponential smoothening is not good when there is a wind profile in the data in the next period of time. The exponential smoothening with a trend works similarly to the SES. However, two components of the level and the trend have to be updated at every period. The level and trend components are the smoothened estimates of the data and average growth at the end of each period, respectively. The formula for the DES are expressed as [8] st′ = α xt′ + (1 − α )( st′−1 + bt −1 )

(11)

bt = β ( st′ − st′−1 ) + (1 − β ) bt −1

(12)

Time (s)

Fig. 3. Concept of grid power smoothening.

where x0′ and x1′ are is the values of the DES at the time, t=0 and t=1, respectively. Fig. 2 shows an example of calculating the smoothened value using SES and DES methods. With the given current value, xt, the smoothened values (st , Ft+m ) using the SES and DES methods are obtained, as illustrated in Fig. 2, respectively. As can be seen, the smoothened value using the DES method gives the better performance than that of using the SES one, due to the additional estimated value, bt. The concept of the output power smoothening for the wind turbine system is shown in Fig. 3. The following steps describe how to generate the power reference for the pitch controller. a. The turbine power, PWT, can be obtained as: PWT =

where xt′ is the current value of the DES, st′ represents the smoothened value, bt is the best estimate of the trend, α is the data smoothening factor (0<α<1), and  is the trend smoothening factor (0<  <1). To obtain the smoothened value, in this work, α and  are selected to be 0.095 which approximates 20 periods of the average value. It means that only 9.5% weight is considered for current value ( xt′ ), and smoothened value ( st′ ) of the present and previous periods, while the remaining 90.5% of weight is used for its smoothened value and estimated value of the previous period. The output of the algorithm depicting the estimate of the value, x, at the time (t+m) is expressed as

(14)

b0 = x1′ − x0′

(15)

(16)

b. The average turbine power, PWT can be calculated from (13). c. The standard deviation of the turbine output power can be calculated from the following equation: t

³ (P

WT

PWT σ =

t −T

− PWT ) dt 2

T

(17)

d. Finally, the input power reference of the controller, Pref, can be obtained as

Ft + m = st′ + mbt (13) The initial values for the st′ and bt can be set as follows: s0′ = x0′

1 ρπ R 2 vw3 C p ( λ , β ) 2

Pref = PWT − PWT σ

(18)

B. Design of Fuzzy Logic Controller For variable-speed wind turbine systems, the performance of the PI pitch controller is limited, especially due to the nonlinearities of the wind turbine characteristics. Another pitch angle controller using a fuzzy logic control has been

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proposed for output power smoothening when the wind speed is lower than the rated value [7]. In this method, three types of the average value for the turbine power have been used for generating the turbine power reference. However, this method is not effective when the wind speed changes rapidly. In the proposed method, the turbine power reference, which is the pitch controller input, is calculated from the turbine output power by using the DES method. Then, the error between the turbine power reference and the turbine output power, PWT, is sent to the fuzzy logic controller (FLC) to generate the pitch angle reference for the mechanical servo system. The proposed fuzzy logic controller is shown in Fig. 4. To find the pitch angle reference ( β ref ), the design process

Fig. 4. Block diagram of the pitch controller.

for a fuzzy logic controller consists of determining the inputs, setting up the rules and designing a method to convert the result of the rules into the output signal. It is known as a defuzzification. To design the proposed FLC, the error of the turbine power, ΔP , and variation of the power error, δ (ΔP) are considered as the controller inputs. For convenience, the inputs and output of the FLC are scaled with the coefficients of kΔ , kδ , and k β , respectively.

0.5w

 β

N

i =1

i =1

PS

PM

PL

NS

ZE

PS

PM

PL

NS

ZE

PS

PM

PL

βref [deg ree]

Fig. 5. Membership functions of fuzzy logic controller for (a) Error of turbine power (P). (b) Variation of power error (δP). (c) Pitch angle (ref ). Table I: Fuzzy rules of pitch controller.

δP

ref

(19)

= ¦ μi Ci / ¦ μi (20)

NM

NL

P

the width, m is the co-ordinate of the point at which the grade of the membership is 1, and x is the value of the input variable. The fuzzy mapping of the input variables to the output is represented by IF-THEN rules. The entire rules consisting of the operation regions are given in Table I. In this work, the fuzzy logic with the Mamdani-type is applied for the inference mechanism [9]. The pitch angle reference, β nref , is calculated as follows: N

ZE

δΔP [ pu]

where μ ( x ) is the value of the grade of the membership, w is

ref n

NM

NL

respectively. The triangular membership functions with the overlap used for the fuzzy sets of the inputs and output are illustrated in Fig. 5, in which the linguistic variables are represented by NL (Negative Large), NM (Negative Medium), NS (Negative Small), ZE (Zero), PS (Positive Small), PM (Positive Medium), and PL (Positive Large). The grade of the input membership functions is obtained from the following equation:

x−m

NS

ΔP[pu]

These scaling factors can be constants or variables which play an important role in the FLC design to achieve a better response in both transient and steady states. In this work, for the simplicity of the controller design, these scaling factors are empirically selected to be constant by a trial and error. These values of the kΔ , kδ , and k β , are chosen as 1, 2000, and 100,

μ ( x) = 1−

NM

NL

NL NM NS ZE PS PM PL

NL NL NL NM NM NS NS ZE

NM NL NM NM NS NS ZE PS

NS NM NM NS NS ZE PS PS

ZE NM NS NS ZE PS PS PM

PS NS NS ZE PS PS PM PM

PM NS ZE PS PS PM PM PL

PL ZE PS PS PM PM PL PL

where N is the total number of the rules, μi is the membership grade for the i-th rule and Ci is the coordinator corresponding to the respective output or consequent membership function. The actual pitch angle reference is obtained from multiplying β nref by k β . V.

SIMULATION RESULTS

To verify the validity of the proposed method, simulation has been performed using MATLAB/SIMULINK for 2-MW PMSG wind power system. The simulation condition is shown

169

in Table II and III. Fig. 6(a) and (b) show the wind speed and output power reference, respectively. As can be seen, the turbine power, its average value, and the reference value of the turbine power are obtained. Fig. 7 shows the simulation results of the pitch angle control, employing the conventional method ( β = 0 ) and the fuzzy logic controllers using the SES and DES, respectively. As can be seen in Fig. 7(a), in the low wind speed regions, the maximum power is extracted from the wind turbines. For the conventional method, however, the generated power is much fluctuated due the wind speed variations. In this case, the wind power is proportional to the cube of the wind speed. With the proposed FLC, the generator output power in the method using

the DES is more smoothened than that of in the method using the SES for the same pattern of the wind speed. The variations of the pitch angle for the conventional method and the FLCs using the SES and DES, respectively, are illustrated in Fig 7(b). The performance of the generator output power is evaluated by the maximum energy function and the smoothening functions which are expressed, respectively, as M

Pg max = ¦ Pgi ⋅ Δt

(21)

i

M

Pgsmooth = ¦ Pgi ⋅ Δt / ¦ Δti i

(22)

i

where Pgi is the generator output power at the sampling time ti, t is the sampling period, and M is the number of sampling. Compared with the conventional method, the generator output power is decreased in this case. If the Pgsmooth is low, the fluctuations of the generator output power are low. In the low wind speed region, since the pitch angle is fixed at zero, the Pgmax will be the maximum. At this fixed pitch angle, the Pgsmooth will be increased since the generator torque cannot be controlled. As seen from Fig. 7(c), the maximum power obtained by the FLC methods using the SES and DES are approximately 76MWh and 78-MWh, respectively. With the same pattern of the wind speed, the smoothening functions for the FLC method using the SES and DES are 12.9% and 11.2%, compared with the conventional PI controller. Thus, the method using the DES gives the better performance of the power smoothening than that of in the case of the SES.

(a) Generator power (pu)

Fig. 6. Wind speed and turbine power. (a) Wind speed. (b) Turbine power, average value and deviation component.

VI.

CONCLUSION

(c) Energy (MWh)

(b) Pitch angle (degree)

In this paper, a fuzzy pitch control scheme has been proposed to smoothen the power fluctuations during the low speed regions. The proposed fuzzy pitch control is based on the average turbine power, power deviation, and controller input power reference. The average turbine power generated from the exponential smoothening can follow the wind speed profile well. Compared with the conventional method, the proposed method using the single and double exponential smoothening produces 12.9% and 11.2% lower output power of the generator, respectively. However, the proposed method can alleviate the power fluctuation and improve the system performance without any need of the power compensation by the energy storage device.

APPENDIX

Fig. 7. Performance comparison of different pitch control methods. (a) Generator power. (b) Pitch angle. (c) Energy.

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The parameters of wind turbine and generators used for simulation are shown in Tables II and III, respectively.

[2]

TABLE II PARAMETERS OF WIND TURBINE FOR SIMULATION Rated power Blade radius Air density Max. power conv. coefficient Cut-in speed Cut-out speed Rated wind speed Blade inertia

2 [MW] 45 [m] 1.225[kg/m3] 0.411 3[m/s] 25[m/s] 10.6[m/s] 6.3x106[kg.m2]

TABLE III PARAMETERS OF 2 [MW] PMSG FOR SIMULATION Rated power Grid voltage Stator voltage/frequency Stator resistance d-axis inductance q-axis inductance

2 [MW] 690 [V] 690[V]/60[Hz] 0.008556[Ω] 0.00359[H] 0.00359[H]

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