MPPT turbinas

AbstractOn the basis of explaining the wind turbines operating characteristics and analyzing the relationship between the wind speed and the power extracted by a wind turbine system with variable speed constant frequency, an on-off control method is investigated for the maximum power point tracking (MPPT) of a wind energy conversion system. In this paper, a mathematic model of a squirrel-cage induction generator control system is established, a decoupling method is employed to achieve the purpose of MPPT, and simulation studies are made with Matlab/Simulink to verify the effectiveness of the purposed algorithm, and the simulation results show that the efficiency of the control strategy.

Index TermsWind turbine; Maximum power point tracking; On-Off control

I. INTRODUCTION n today's human survival and development, energy and environment are the pressing problems to be solved. Wind

power, as one source of inexhaustible, clean and pollution-free power, it is prospective of large-scale development and utilization, and is to an effective form by harnessing the wind. At present, the main power generation system of wind driven generator is VSCF (Variable Speed Constant Frequency) wind power generation system for grid. The greatest advantage of it is that the output of the power generator can be changed with variable wind speed, the power and wind speed are closely related to the rotor speed of the generator, and there is an optimal speed point at certain rotation speed to make the output power reaches a maximum. As for wind power systems, how to control generator speed from the wind speed variation to capture to the largest wind power has considerable influence with the overall efficiency

Manuscript received March 10, 2012. This work was supported in part by the Ministry of Housing and Urban-Rural Development, China, under Grant 2008-K2-18 and Department of Education of Liaoning Provincial Government, China, Grant 2009A603.

Feng Zhang is with the Faculty of Information and Control Engineering, Shenyang Jianzhu University, 9 Hunnan East Road, Hunnan New District, Shenyang, 110168 China. (Tel: 0086-24-2469-0672, Fax: 0086-24-2469-0042, eMail:[email protected]).

Honhguang Lan is with the Faculty of Information and Control Engineering, Shenyang Jianzhu University, 9 Hunnan East Road, Hunnan New District, Shenyang, 110168 China.

Feng Qiao is with the Faculty of Information and Control Engineering, Shenyang Jianzhu University, 9 Hunnan East Road, Hunnan New District, Shenyang, 110168 China

Shuang Sun is with the Faculty of Information and Control Engineering, Shenyang Jianzhu University, 9 Hunnan East Road, Hunnan New District, Shenyang, 110168 China.

Xueyang Sun is with the Faculty of Information and Control Engineering, Shenyang Jianzhu University, 9 Hunnan East Road, Hunnan New District, Shenyang, 110168 China.

of wind power generation system. Thus, the maximum wind power tracking strategy remains a hot spot of VSCF wind power control system research field [1, 2].

At present, the maximum wind power tracking control mainly involves the optimal tip speed ratio method, power feedback method and hill climbing method. How to get the optimal tip speed ratio in the wind power system was studied in [3] with double PWM converter control algorithm, and with the auto-tuning fuzzy PI control strategy, it proposed a feasible control scheme for the optimal tip speed ratio control. But the optimal tip speed ratio method need real-time accurately measure of the wind speed, which is more difficult in practice. Maximum wind power tracking can be achieved with the power feedback method by adjusting the rotor of the generator excitation amplitude and frequency to change the generator speed. This method needs to set a wind turbines optimal tip speed ratio according to the practical situation in advance. Hill climbing method is to tracking maximum output power points by measuring real-time wind turbine speed and output power. It tracks maximum output power points by classical mathematical optimization method. The optimal DC current control was adopted in [4] to adjust the input DC current to follow the optimal reference current. The existing three algorithms were analyzed and studied in [5] to capture maximum wind power, it points out that the mountain climbing method avoids the problem of measuring the wind speed, but it needs to real-time measure the output power and the rotor speed of the wind turbine, and the measuring time often affect control precision. So a maximum wind power capture strategy was proposed in this paper which not only depends on wind velocity measured but also has high control precision. On the basis of the analysis of VSCF wind power system structure, according to the dynamics of the wind turbine, a model of the induction generator is established for the induction generator power to realize the rotor current decoupling so as to adjust generator speed. Through the calculated electromagnetic torque, the expected electromagnetic torque of the On-Off control is compared with to adjust the rotor current for the adjustment of the generator speed. This method avoids the problem of real-time measuring wind speed, and it responses quickly to the low frequency wind speed change. It can realize capture of the maximum power with higher accuracy.

On-Off Control of Wind Turbine for Maximum Wind Power Point Tracking

Feng Zhang, Hongguang Lan, Feng Qiao, Xueyang Sun, and Shuang Sun

I

Proceedings of 2012 International Conference on Modelling, Identification and Control, Wuhan, China, June 24-26, 2012

963

II. DYNAMICS OF AIR WIND TURBINE According to Betz theory, the mechanical power harvested

by a wind turbine aP is expressed as:

),(21 32 pa CVRP (1)

where R is the blade radius of the wind turbine, is the air mass density, V is the wind speed, is the tip speed ratio, is the pitch angle, pC is the wind turbine energy coefficient with the maximum of 59.3% Betz limit.

The tip speed ratio is defined as:

VRm (2)

where m is a wind turbine rotor speed. In fact, pC is the efficiency of transforming the wind

power to mechanical power by the wind turbine, and it is the function of tip speed ratio and pitch angle of blades. It is shown in (1) that in the certain wind speed circumstances, the captured mechanical power by the wind turbine will only depend on wind power conversion coefficient. Adjusting blades pitch angle to manipulate the operation of a wind turbine belongs to mechanical regulation. Generally, for the electrical adjustment, the pitch angle of blade is kept to a constant. So pC is only the function of , the relation curve between them is one of basic characteristics of a wind turbine.

For a given , wind turbine pC curve is as shown in

Fig. 1. It can be seen that for a certain wind turbine, when is certain, there is always an optimal tip speed ratio opt corresponding to the maximal power coefficient

maxpC , now

the wind turbine conversion efficiency is the highest. In other words, for a particular wind speed v , wind turbine has the highest wind energy conversion efficiency only when it runs on a specific speed .

From the Fig. 2, it can be seen that under different wind speed the output power of wind turbine changes as the rotor speed changes [6]. In different variable wind speed, there is a

maximum output power point, which corresponds to the maximum wind energy conversion coefficient

maxpC .

Connecting each maximum output power points under different wind speeds, we can get the optimal curve maxP of wind turbine mechanical power output [7, 8]. To make wind power operated on this curve, it must adjust rotor speed timely when the wind speed changes to maintain the optimal tip ratio and wind turbine can capture the maximum wind power. At the same time, the maximal mechanical power will be captured. This paper starts from the stator vector formula under the synchronization reference frame. According to the characteristics of the stator-flux orientation, deduce the relationship between generator speed and the rotor current. Using On-Off control to output the reference electromagnetic torque, compared with the actual generator torque, we can get the reference rotor current to achieve the purpose of controlling the generator speed.

III. BUILD A WIND TURBINE CONTROL MODEL

A. On-Off Control System The purpose of the MPPT (Maximum Power Point

Tracking) control strategy is to use the characteristics of static power-speed curve to make wind power conversion system running nearby the maximum power point. At this moment, the wind capture rate is the optimal.

From (1), we can see that the input power aP of the wind turbines is decided by wind speed and conversion efficiency as the wind speed is constantly changing. So that, the wind energy conversion efficiency pC should be kept at its

optimal to get the maximum power harvest. As pC is the function of both blades pitch angle and the ratio of the tip , if is constant, there is always an optimal tip speed ratio

opt corresponding to the maximal power coefficient maxpC and at this time the wind turbine conversion efficiency is the highest. In other words, for a particular wind speed V , wind turbine has the highest wind energy conversion efficiency only when operating at a specific speed . And can be controlled by electromagentic torque to adjust through the practical electromagnetic torque and the expectations of the

Fig. 1. The relation graph of pC

Fig. 2. The power characteristics of the wind turbine


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electromagnetic torque and ultimately to achieve the purpose of the speed control. The electromagnetic torque can be obtained by the On-Off control.

The On-Off control strategy is commonly used in wind energy conversion system under rated wind speed, meeting the requirements of the system to make rapid response to low frequency wind speed changes [9]. In order to ensure the optimal energy conversion, we should make the system operating steadily in the optimal condition characteristics. To achieve this goal, On-Off control is adopted to make actual tip speed ratio to track the optimal one.

Here, the difference between the optimal tip speed ratio and actual tip speed ratio is defined as

opt (3) where opt is the optimal tip speed ratio under which the maximum power can be captured with

maxppCC .

The control objective is to design the On-Off control algorithm to regulate the rotor speed according to the wind speed to make the tracking error as small as possible.

The output of the design On-Off controller u is [16]: Neq uuu (4)

where equ is equivalent control which is a smooth component, corresponding to the optimal operating point (at opt ) defined as:

223 )(21

sopt

optpseq KVN

CVRu

(5)

here opt

optp

NC

RK )(

21 3 , N is the gear box ratio; and Nu

is a high-frequency switching component, varying between two values defined as:

)sgn( Nu (6) here is a constant, Nu switching between and . ( )sgn( is a sign function of : when 0 ,

1)sgn( , when 0 , 1)sgn( .) The equivalent control equ makes the system operated in the optimal point, and the switching control Nu makes the system worked stably nearby the optimal operating point. Fig. 3 shows the structure of the On-Off controller. In the figure, the function of the Zero-Order Holder is to limit switch frequency GT is the time constant of generator.

In Fig. 3, the wind energy conversion system (WECS) converts wind power into electrical power, the wind acts on the blades of the wind turbine to drive the rotor, the wind speed is measured as well as the speed of the rotor. Then, the actual tip speed ratio can be obtained according to (2), and the optimal tip speed ratio opt can be obtained with the maximum conversion coefficient

maxpC and the measured

wind speed. Then the proposed On-Off controller can be designed with (3) to (6).

In order to gets the actual electromagnetic torque, a

mathematical model of a Squirrel-Cage Induction Generator (SCIG) in d-q rotating coordinate system is established.

B. Mathematical Model of SCIG The rotor of the squirrel-cage asynchronous generator is

short circuit. So in the rotor field-oriented conditions, 0dru , 0qru , rdr , 0qr [10-15]. So in the d-q rotation

coordinate system, the voltage equation of the squirrel-cage asynchronous generator is as follows:

qr

dr

qs

ds

rrm

rrm

mmsss

mmsss

qs

ds

iiii

RLLpLRpL

pLLpLRLLpLLpLR

uu

ss

11

11

000

00

(7)

The flux equations of stator are as follows:

qr

dr

qs

ds

rm

rm

ms

ms

qr

dr

qs

ds

iiii

LLLL

LLLL

0000

0000

(8)

The torque equations of vector controlling are as follows:

rsqr

mpe iL

LnT (9)

sdr

mr ipT

L1 (10)

sqrr

ms iT

L (11)

where r is the rotor flux, 1 the stator electricity angular velocity, s is the slip angular velocity, sL is stator inductance, rL is the rotor inductance, mL is the excitation circuit reactance. In the expression of components and rotor flux, rrr RLT / . In (10), the rotor flux r only has a relationship with sdi which is the excitation component of stator current, and has nothing to do with sqi which is the stator current torque component. When the rotor flux r is constant, the generator torque eT is only for the stator current torque component to decide. So through the control of sqi , we can control the electromagnetic torque of the generator. The

opt

][vK

1sT1

G WECS SVR

Nu

equ sv

u *eT

Fig. 3. The On-off controller structure


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key to decoupling the stator current is the observation of the position of the rotor flux, the turning slip frequency s and the measured angular velocity r adding together can get stator frequency 1 , then we can get the needed rotor flux angle after integral, finally use the current tracking control methods to control inverter. In a word, because the decoupling between two components of the stator current, sdi and sqi only decided by r , sqi only affect the torque, they correspond to the exciter current and armature current of DC generator, so this greatly simplifies the multi variably strong coupling problem of asynchronous generator.

The converter adopts the rotor flux oriented vector control as shown in Fig. 4, which consists of electric circuit and speed outer ring. The direction of the stator current in d-axis, sdi determines the direction of r , that is to say, the generator

torque eT is controlled by sqi , realizing decoupling of the magnetic flux and torque. The expected electromagnetic torque *eT is generated by the output of reference electromagnetic torque of the On-Off control, according to the torque and flux, we can get the given torque current of q-axis, according to the given magnetic flux value of the field current in d-axis. The output of torque current loop and exciter current loop regulator, which achieves the aim of controlling the generator by control procedures by coordinate transformation (2r/3s) and Space Vector Pulse Width Modulation (SVPWM) control converter working, and realize wind energy extraction and maximum power tracing. In Fig. 4, the function of the slip calculation is to get the slip angular velocity s , and the rotor flux calculations function is to get the rotor flux r .

I. SIMULATION STUDIES In order to verify effectiveness of the On-Off control

designed for a WECS with squirrel-cage asynchronous generator, simulation studies were carried out with Matlab/Simulink.

The parameters of the wind turbine are selected as: the air density 3 /m1.29kg , the blade radius of the wind turbine

mR 5.2 ,the maximum wind power conversion coefficient 0.45

maxpC , the optimal tip speed ratio 8opt , the

generator parameters: the gearbox speed ratio 4N , the rated voltage 220V, the rated frequency 50Hz, the stator winding resistance 1.160sR , the rotor winding resistance

1.233rR , the stator winding self-inductance 0.1352mHrL , the transformer between the stator winding

and equivalent rotor winding 0.1292mHmL , the rotor inertia 23kgmJ .

The simulation results are shown in Figs. 5-9.

The simulation of the wind speed is stochastic wind, with

the maximum wind speed 8m/s, the minimum wind speed 5m/s. Fig. 5 is the rotor power coefficient pC . In Fig. 5, it can

0 5 10 15 20 25 30 35 40 45 500

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

t/s

cp

Cp

Fig. 5. The power coefficient pC

PI

PI

2r/3s SVPWM

Torque Calcula

tion

Rotor flux Calculation

Slip Calculation 3s/2r

M

*eT

r

sqi

1 s

r

*r

eT

*sdi

*sqi

*sAi

*sBi

*sCi

sCi

sBi

sAi

sqi

sdi

On-off control torque

Calculation

Fig. 4. Diagram of vector control of SCIG


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be seen that when the system is stable, pC is stable down, it is located basically in 0.45. The value is steady.

Fig. 6 is the actual tip speed ratio . From Fig. 6, it can be

seen that the tip speed ratio controlled by the On-Off control algorithm is closed to its optimal value 8opt .

0 5 10 15 20 25 30 35 40 45 50-20

-15

-10

-5

0

5

t/s

emT r

ef

Reference electromagnetic torque

Fig. 7. Reference electromagnetic torque

Fig. 7 is the reference electromagnetic torque and Fig. 8 is

the actual electromagnetic torque eT . From Figs. 7-8, it can be seen that the electromagnetic torque can kept up with reference value quickly by the vector control mainly, so as to achieve the speed control.

Fig. 9 shows the generator speed, from this figure, it can be seen that the generator speed is more stable through continuous adjusting the electromagnetic torque, making the speed under the control of the tip speed ratio to achieve the optimal ratio.

II. CONCLUSIONS Based on the analysis of the maximum power point

tracking (MPPT) principle in wind turbine systems, a mathematical model is established, in this paper, for a wind energy conversion system with SCIG, and an On-Off controller is designed to tackle the problem of MPPT for wind power extraction in WECS.

In this paper, in order to verify the effectiveness of the proposed On-Off control strategy, the simulation studies were made with Matlab/Simulink, and the simulation results show the desirable MPPT under rated wind speed.

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0 5 10 15 20 25 30 35 40 45 50-20

-15

-10

-5

0

5

t/s

emT

Electromagnetic torque

Fig. 8. Actual electromagnetic torque

0 5 10 15 20 25 30 35 40 45 500

2

4

6

8

10

12

t/s

lam

Tip speed ratio

Fig. 6. Actual tip speed ratio 0 5 10 15 20 25 30 35 40 45 50

0

50

100

150

200

250

t/s

Om

gh

Generator speed

Fig. 9. Generator speed


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[9] T. Meng, T. X. Shen, Z. C. Ji, Two frequency loop optimal control for wind energy conversion system based on on-off and H state feedback, Journal of Southeast University ( Natural Science Edition), Vol.39, Sup(I), Sept. 2009.

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