Optimal Speed Tracking for Wind Power

Generator via Switching Control

CHEN Yan, WANG Xiang-dong, LI Shu-jiang and KONG Li-xin

Shenyang University of Technology

Shenyang, China

Abstract—For the control target of capturing maximum power

for variable speed wind turbine when the wind speed is below the

rated wind speed, a switching “optimal” tracking controller of

the generator angular velocity is designed. First, the generator

optimal angular velocity is identified by using dynamic fuzzy

neural network. Then a generator angular velocity optimal

tracking controller is designed by using different system

parameters in different angular velocity range based on

switching control. The ideal of the control is by controlling the

voltage of the generator rotor to adjust the generator angular

velocity, so it can track the optimal angular velocity. By

simulation its result shows that the controller makes the system

track the optimal angular velocity, and so realizes maximum

wind power capture.

Keywords-wind power generator; maximum wind power

capture; angular velocity; switch control; dynamic fuzzy neural

network

I. INTRODUCTION

Wind energy is a kind of green energy. There are different optimal operating speeds for wind turbine to capture wind energy under different wind speed. The efficient of wind power captured is high on the optimal operating speed, and the stress added to wind turbine is minimum, so wind turbine should be controlled to run on the optimal speed. Because of the angular velocity of wind power generator can only be fixed on the synchronous speed for traditional constant speed wind turbine, the angular velocity of wind power generator will deviate from the optimal angular velocity when the wind speed changes, and this results in reduction of operating efficiency. This not only is a waste of wind resources, but also increases the wear of wind turbine. According to the goal of capturing maximum wind power, the angular velocity of generator should be adjusted to run at the optimal angular velocity when the wind speed changes for variable speed wind turbine, so it can improve the efficiency of wind turbine power system. Therefore, how to carry out variable speed control for capturing maximum wind power becomes a focus research of wind power technology [1].

Currently, there are three main aspects about the control of variable speed wind turbine: First, how to get the optimal angular velocity of generator to capture the maximum wind power. Some authors have reported several results, for example optimum tip speed ratio look-up table method [2] and hill climbing search method [3], and so on. But lookup table

method has a larger error; Hill climbing search method requires continuous tentative regulation to speed, which is easy to produce frequently torque ripple and increase the fatigue to transmission chain. Second, the generator control, this is mainly active and reactive power decoupling control [4]. Third, tracking the optimum speed, there are fuzzy control [5] and neural network control [6] and other intelligent control methods in this aspect. But their control algorithms are relatively complex.

In this work, some researches are done about the first and third aspects described above. Firstly, a network identification model for the optimal angular velocity of wind power generator is proposed. Secondly, an optimal tracking controller is designed by using switching control in different speed range. Finally, the effectiveness of the controller is showed by simulation.

II. VARIABLE SPEED WIND POWER GENERATOR MODEL

The structure of variable speed wind power system is shown in Figure 1.

Fig.1 Variable speed wind generation system block diagram

The stator side of generator uses generator convention and the rotor side of generator uses motor convention. A two axis d-q reference frame rotating at synchronous speed of the generator equations are depicted. The stator and rotor flux linkages equations can be written as [7]:

ds s ds m dr

qs s qs m qr

dr m ds r dr

qr m qs r qr

L i L i

L i L i

L i L i

L i L i

ψ

ψ

ψ

ψ

= − +

= − +

= − +

= − +

(1)

Sponsor: Foundation of Education Department of Liaoning Province (2008S159)

2283978-1-4244-8756-1/11/$26.00 c©2011 IEEE

The voltage equations can be written as:

1

1

ds s ds ds qs

qs s qs qs ds

dr r dr dr s qr

qr r qr qr s dr

u R i

u R i

u R i

u R i

ψ ωψ

ψ ωψ

ψ ω ψ

ψ ω ψ

= − + −

= − + +

= + −

= + +

(2)

The electromagnetic torque equation is given by

3 /(2 ( ))e p m qs dr ds qrT n L i i i i= − (3)

The motion equation is given by

/r e p m eJ n T Tω = − (4)

Where: the first letter of subscript d or q represents respectively d or q axis component in the synchronous rotating coordinates, and the second letter s or r represents respectively the stator or rotor side variable; ψ , I and u are respectively

flux linkage, current and voltage; Rs and Rr are respectively the stator and rotor resistance; Ls, Lr and Lm are the stator and rotor

self-inductance and their mutual inductance;1

ω , sω and rω are

synchronous angular velocity of motor, slip angular velocity and rotor angular velocity, and they have the relationship

1 1s r sω ω ω ω= − = , s is the slip rate; Je and np are respectively

the moment inertia of the motor and the number of pole pairs; Te and Tm are respectively the electromagnetic torque and mechanical torque.

The stator flux linkage sψ is oriented in the d-axis by

using the stator flux-oriented vector control,

then , 0ds s qsψ ψ ψ= = . Because the stator resistance is much

smaller than the generator stator winding reactance, it can be ignored, that is Rs =0. Because the stator voltage us is behind

the stator flux sψ 90°, us is in the q-axis negative direction,

then uds =0, uqs=-us. When the stator side incorporates into the ideal grid, us equals the stable grid voltage.

Put , 0ds s qsψ ψ ψ= = , uds=0, uqs=-us, and Rs=0 into the (1)

and (2), we can get

1 1

0ds ds s

qs ds s s

u

u u

ψ ψ

ωψ ωψ

= = =

= = = −(5)

Equation (5) shows that the stator flux linkage is constant

when the operation runs steadily, and its value is1

/s suψ ω= .

Put , 0ds s qsψ ψ ψ= = into (1), we can get

( ) /

/

ds m dr s s

qs qr m s

i L i L

i i L L

ψ= −

=(6)

Put (6) into (1), then into (2), we can get

dr dr dr qr

qr qr qr dr

u ai bi di

u ai bi di c

= + −

= + + +(7)

Where ,ra R=2 / ,r m sb L L L= − / ,m s s sc L Lψ ω=

2( / )r m s sd L L L ω= −

Put the (6) and (3) into (4), we can get

r qre fiω = − (8)

Where 2/ , 3 /(2 )p m m s p e se n T J f L n J Lψ= = .

idr iqr and r in (7) and (8) are chosen as state variables, udr

and uqr as control variables, r as output variables. The state space equation of double-fed wind power generator is described as

/ / 0 1/ 0 0

/ / 0 0 1/ /

0 0 0 0

[0,0,1][ , , ]

dr dr

dr

qr qr

qr

r r

T

r dr qr r

i a b d b i bu

i d b a b i b c bu

f e

y i i

ω ω

ω ω

−

= − − + + −

−

= =

(9)

Where ,ra R=2 / ,r m sb L L L= − / ,m s s sc L Lψ ω=

2( / )r m s sd L L L ω= −2/ , 3 /(2 )p m m s p se n T J f L n JLψ= =

The wind speed is not always constant in the actual wind farm. It will inevitably lead Tm and r to change when the wind

speed changes, then lead to c d e in (9) change, so the system of (9) is a system of variable parameters. To solve this problem, the actual parameters are used to design controllers by using switching control theory when the parameters change. Therefore, the control problem of double-fed wind power generation system (9) is formed as follows: We needs to design a number of optimum tracking controllers: udr

*, uqr* in some

operating points, so that the actual output of the system r can quickly track the desired optimal angular velocity r

* when the wind speed changes, ultimately realize maximum wind energy capture.

III. OPTIMUM ANGULAR VELOCITY IDENTIFICATION

A. Building Generator Optimum Angular Velocity

Identification Model

According to the principle of maximum wind power capture, there must be an optimal angular velocity under a certain wind speed, which making the wind turbine capturing maximum wind power [8]. This paper identifies the generator optimal angular velocity when the system is in the optimal operation. The method of identification is to build dynamic fuzzy neural networks. "Dynamic" in "dynamic fuzzy neural networks" means the structure of fuzzy neural network is not pre-configured. There are no rules before learning; the numbers of fuzzy rules are becoming increase or decrease in the process of learning. The most important feature of this method is, at the same time, that the parameters and the structure of the fuzzy neural networks are adjusted, and its learning speed is very fast. Using a neural network for system identification means that the input-output structure of the network is the same as the system identified. A serial and parallel identification model is used, and its structure is shown in Figure 2.

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v(t)Principle of Maximum

Wind Power Capture

q-1

q-1

ynq

−

Dynamic

Fuzzy

Neural

Networks

Y*(t)

Yr(t)

xnq

−

Fig.2 Serial-parallel structure of identification model

Where q-1 represents a unit delay operator, v(t) is wind speed signal, the actual output Y*(t) of the system to be identified represents the wind power generator optimum angular velocity, Yr(t) represents the output of the neural network model. Specific structure and learning algorithms of dynamic fuzzy neural network is explained in [9].

B. Simulation of Identification

Wind turbine parameters for simulation are as follows: blade radius R=2.3m, rated power P=2.2kW, air density =1.25kg/m3; the wind turbine and generator are connected by

a gearbox whose growth rate is N=7.846 [10].

Wind speed from 3m/s (cut in wind speed is 3m/s) gradient to 10.95m/s (under rated wind speed). The data of training is gotten according to the principle of maximum wind power capture by computation. The generator optimal angular velocity identified by dynamic fuzzy neural network and its identification error curve are shown in Figure 3 to 5.

Fig.3 Curve of gradient wind speed

Fig.4 Curve of generator optimal angular velocity identification

Fig.5 Generator optimal angular velocity identification error

Figure 4 and Figure 5 show that using dynamic fuzzy neural networks can well identify the generator optimal angular velocity, and the precision is very high. The maximum identification error is less than 0.004.

In practice, whenever the wind speed is measured in real-time, the generator optimal angular velocity can be immediately gotten from the model. Thus a useful reference value is provided, which is used in optimum tracking control strategy designed as follows.

IV. SWITCHING CONTROL

A. Model Normalization

Since the form of (9) is not a standard state space form, the model needs to be standardized.

Order 1

2

3

dr

qr

r

i x

i x

xω

=1

2

dr

qr

u u

u u=

Do substitution by putting ' ' '

1 1 2 2 3 3, / ,x x x x e f x x= = − = to (9), we

obtain

' '

1 1

1' '

2 2

2' '

3 3

/ / 0 1/ 0 /( )

/ / 0 0 1/ / /( )

0 1 0 0 0 0

x a b d b x b de bfu

x d b a b x b c b ae bfu

x x

−

= − − + + − − (10)

Then do substitution by putting ' '

1 1 2 2/ , /u u de f u u ae f c= + = − −

to (10), we obtain

X AX BU

Y CX

= +

=(11)

Where:

'

1

'

2

'

3

x

X x

x

=

'

1

'

2

uU

u=

/ / 0

/ / 0

0 0

a b d b

A d b a b

f

−

= − −

−

1/ 0

0 1/

0 0

b

B b= [0,0,1]C = ; ,ra R=2 / ,r m sb L L L= −

/ ,m s s sc L Lψ ω=2( / )r m s sd L L L ω= − /p me n T J= ,

23 / (2 )m s p sf L n JLψ=

2011 6th IEEE Conference on Industrial Electronics and Applications 2285

Equation (11) is the standard model transformed.

B. Switching “Optimun” Tracking Controller

According to the generator angular velocity range, the generator angular velocity is divided into a number of stalls. Optimum tracking controller is designed by using different system model in different stalls. When the generator angular velocity is running to the appropriate stall, the controller is switched to the optimum tracking controller designed in this appropriate stall. This is the thought of switching control for this paper. Table 1 shows the generator angular velocity switching rules.

TABLE.1 GENERATOR ANGULAR VELOCITY SWITCHING RULES

Stalls of angular velocity

Switching system Optimum tracking

controller

[ r0 r1 ) Subsystem 1 (A1 B1) U1*

[ r1 r2 ) Subsystem 2 (A2 B2) U2*

… … …

[ r(n-1) rn ) Subsystem n (An Bn) Un*

Taking an example of any subsystem, assume the performance indicators as

0

1[( ( )) ( ( )) ( ) ( )]

2

ftT T

r rJ Y Y t Q Y Y t U t RU t dt= − − + (12)

Where: the terminal time tf is infinite, Yr is the given generator angular velocity tracking signal, Q is positive real constant, R is a 2×2 positive definite symmetric constant matrix. The optimal gain matrix of the system is:

1 1

1 2,T TK R B P K R B g− −

= − = (13)

The unique optimal control law is:

*

1 2( ) ( )U t K x t K= + (14)

In such case the following expression of the optimal trajectory are obtained:

* 1 * 1( ) ( ) ( )T Tx t A BR B P x t BR B g− −= − + (15)

Taking into account tf is large enough, P t is to a constant

matrix P, which is positive definite solutions matrix of Riccati matrix algebraic equation:

1 0T T TPA A P C QC PBR B P−+ + − = (16)

And the constant vector g is obtained from:

1 1( )T T T

rg PBR B A C QY− −≈ − (17)

Figure 6 shows the structure of optimal tracking system.

X

Fig.6 Structure of optimal tracking system

In practice, the optimal gain matrix K1 and K2 change according to the change of the given tracking signal Yr, so it can meet the change of the system parameters when the wind speed change.

C. Simulation of Optimum Tracking Control

In order to verify the correctness and effectiveness of the controller designed, the following three-phase winding induction generator parameters are selected [10]: number of pole pairs np=2, rated power Pe=2.1kW, rated voltage U=220V, rated frequency f=60Hz, the stator resistance Rs=0.435 , and its sef-inductance Ls=71.36mH, rotor resistance Rr=0.816 , and its sef-inductance Lr=71.36mH, mutual inductance Lm=69.31mH, moment inertia Je=0.089kg•m2.

Without loss of generality, the simulations are only taken on some operations of closed-loop system when the wind speed change within a period of time. There are two cases for simulation.

Assuming case 1: the wind speed increase as follows:

3m / s,0 5s

4m / s,5s 10s

5m / s,10s 15s

t

t

t

≤ <

≤ <

≤ ≤

Within this change of wind speed, we can get the ideal reference value of the optimal angular velocity by using the identification model designed previously. Then use the optimal angular velocity identified as the tracking signal, and use the switch “optimum” tracking controller to track it. Figure 7 shows the response of the generator angular velocity.

Fig.7 Generator output angular velocity and its tracking signal

Assuming case 2: the wind speed decrease as follows:

6m / s,0 5s

5m / s,5s 10s

3m / s,10s 15s

t

t

t

≤ <

≤ <

≤ ≤

Figure 8 shows the response of the generator angular velocity within this change of wind speed.

2286 2011 6th IEEE Conference on Industrial Electronics and Applications

Fig.8 Generator output angular velocity and its tracking signal

The following statements can be obtained from Figure 7 and 8: No matter the wind speed increase or decrease, the angular velocity r of the system can well track the optimal angular velocity r

*, with the regulation of this switch

“optimum” tracking controller. The time of regulation is very shot, and the error of tracking is nearly zero.

V. CONCLUSION

This paper has solved two issues of variable speed double-fed wind power generation, namely how to get the generator optimal angular velocity value and how to control the generator angular velocity to track the optimal value. The main conclusion of the paper can be summarized in the following points:

Firstly, the network identification model for generator optimal angular velocity is proposed using dynamic fuzzy neural network. The most important feature is that its learning speed is very fast and its identification error is very small. By study the model can give out the optimal angular velocity, so can provide a useful reference to the system to work in a high efficiency and low load way.

Secondly, aiming at the characteristics of the double-fed generator, the state space description of the wind power system is established, using the stator flux-oriented vector conversion technology, based on the introduction of the double-fed

induction wind turbine mode. The tracking controller designed by using switching “optimum” control technology can make the system track well the optimal angular velocity when the wind speed and the parameters of system change. And it has the advantage of easier to realize than other intelligent control methods. Computer modeling and simulation verify that the system control strategy proposed satisfy the goal of capturing maximum wind power, with the good dynamic and static performance.

REFERENCES

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[2] XU Hong-hua and NI Shou-yuan. “FD7-5kW wind turbine generator and its control utilizing claw-pole brushless self-excited generator”. Acta Energine Solaris Sinica, Vol.19, No.1, pp.163-168, 1998.

[3] Tanaka T and Toumiya T, “Output control by hill-climbing method for a small wind power generating system”, Renewable Energy, Vol.12, No.4, pp.387-400, 1998.

[4] ZHAO Dong-li, GUO Jin-dong and 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 Energine Solaris Sinica, Vol.27, No.2, pp.174–179, 2006.

[5] ZHANG Xin-fang and XU Da-ping. “Adaptive fuzzy control based on variable universe for variable speed variable pitch wind turbine”, Control Engineering, Vol.10, No.4, pp.342-345, 2003.

[6] Hany M.abr and Narayan C. Kar, “Neuro-fuzzy vector control for doubly-fed wind driven induction generator”, 2007 IEEE Canada Electrical Power Conference, pp.236-241, 2007.

[7] REN Li-na, JIAO Xiao-hong and SHAO Li-ping, “Robust control for doubly-fed induction generators(DFIG) with variable speed and constant frequency in wind power systems”, Control Theory and Applications,Vol.26, No.4, pp.377-382, 2009.

[8] YE Hang-zhi, Wind Turbine Control, 2nd ed., Beijing: Mechanical Industry Press, 2009.

[9] WU Shi-qian and XU Jun, Dynamic Fuzzy Neural Networks-Design and Application, Beijing: Tsinghua University Press, pp.27-68, 2008.

[10] J. LI Qi-hui, HE Yi-kang and ZHAO Ren-de. “The maximal wind-energy tracing control of avariable-speed”. Autormation of Electric Power Systems, Vol.27, No.20, pp.62-67, 2003.

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