DESIGN OF A CONTROL SCHEME FOR A MAXIMUM POWER

DESIGN OF A CONTROL SCHEME FOR A MAXIMUM POWER EXTRACTION IN LOW POWER WIND TURBINE-GENERATOR SYSTEM Elkin Henao-Bravo, Carlos Cuadros-Ortiz and Miguel Velez-Reyes Center for Power Electronics Systems, University of Puerto Rico at Mayag¨uez [email protected] - [email protected] - [email protected] ABSTRACT This paper presents modeling of a wind turbine-generator system and development of a control scheme for maximum power extraction. The system comprises a low-power variable speed wind rotor coupled to a squirrel cage induction generator through a gearbox. The generator delivers electrical energy to a DC load through a PWM three-phase rectifier whose control variables are duty-cycle and fundamental frequency of the modulated signal. The control scheme maintains a constant voltage/frequency relationship in the stator of the generator to operate the machine with constant air gap flux at its nominal value, thereby keeping low electrical losses in of the stator and rotor circuit. The controller is based on MPPT algorithms for determining the system operating point and achieving the proper mechanical shaft speed. Performance is evaluated through simulations and shows that this type of control is a good alternative for handling low-power wind turbine-generator systems effectively and efficiently. Index Terms— Wind turbine, Control scheme, MPPT, SCIG, PWM

force desired turbine operating conditions and to allow extraction of the maximum power available at any time [2]. According to characteristic curves such as wind power vs. rotating speed for a given wind turbine there is an optimum rotating speed that gets the maximum wind power at certain instant. Therefore a control scheme must be designed to find that optimal speed reference from power measurements or estimation in order to track the maximum power point. This work aims to design and simulate a maximum power extraction control scheme for a low power wind turbinegenerator system, based on low complexity control techniques (volts/hertz control) for induction generators. The system is shown in Fig. 1 and consists of a wind turbine rotor and a blade static model coupled through a drive train dynamic model for a squirrel-cage induction generator. The generator windings are connected to a PWM three-phase rectifier to feed a DC load and to track the maximum power R point. The simulations are being performed in Simulink and they make use of Wind Turbine Blockset [3] developed by Aalborg University and RIS∅ National Laboratory. 2. WIND TURBINE-GENERATOR SYSTEM MODEL

1. INTRODUCTION In the last decade, electricity generation from renewable energy sources has strongly increased due to efforts for diminishing harmful emissions and their global warming effects [1]. The energy contained in the flowing air is renewable and hence the use of wind turbines to convert part of this energy into electricity is being more necessary [2]. One of the major issues of this kind of renewable source is it randomness. Since the latter leads to uncertainty in the amount of wind power available at any instant and on the percentage of it that can be extracted in electrical form, wind turbine based systems should always be accompanied by storage and backup subsystems like battery banks and Uninterruptible Power Supply (UPS) among others. As a consequence, power converters are necessary to efficiently This work was supported by the ERC Program of the National Science Foundation under Award Number EEC-9731677 and UPRM.

A variable speed wind turbine with squirrel cage induction generator was selected to take advantage of the latter’s low cost and ease to produce its magnetic excitation field in low power and low budget isolated applications.

2.1. Wind Turbine Rotor and Blade Static Model The model used to represent the static behavior of the wind turbine rotor is given by equations 1 through 6, where PW is the power extracted from the airflow [W] and its characteristics are represented by the curves in Fig 2 for several wind speed values. ρ is the air density [Kg/m3 ], Cp is the performance coefficient or power coefficient, λ is the ratio between blade tip speed vT = Rωwt [m/s] and wind speed upstream the rotor vW [m/s] and usually called tip speed, β is the pitch angle (β = 0 in this case), AR is the area covered by the rotor [m2 ], R is rotor blade radius [m] and ωwt is wind turbine rotor speed [Rad/seg].

 Cp (λ, β) = c1

 −c5 c2 − c3 β − c4 e λi + c6 λ λi

1 1 0.035 = − 3 λi λ + 0.08β β +1

λ=

TM =

Rωwt vT = vW vW

(2)

(3)

(4)

1 2 ρCM AR vW 2

(5)

Cp λ

(6)

CM =

Fig. 1. Wind Energy System

Fig. 3. Characteristic Curve Cp vs λ

2.2. Mechanical Shaft Dynamic Model

Fig. 2. Characteristic Curve Power vs rotational speed

Equations 2 and 3 are an analytical approximation for this kinds of wind systems, where c1 = 0.5176, c2 = 116, c3 = 0.4, c4 = 5, c5 = 21 y c6 = 0.0068. It is thoroughly explained in [1, 4, 5] and its characteristics are represented by the curves in Fig 3 for several pitch angle values. The lower value of β yields the higher value of Cp , which means that more power can be extracted. PW =

1 3 ρCp (λ, β)AR vW 2

(1)

The dynamic model of the wind turbine in [6, 7, 8, 9] includes the drive train represented by two mass-spring-damper systems coupled through a gearbox, where high speed shaft and low speed shaft correspond to the generator dynamics and wind turbine rotor dynamics respectively. In this model, parameters are reflected from the low speed shaft side to the high counterpart as seen in 7, 8 and 9, where Jwt , ωwt and Twt are inertia, speed and torque of rotor wind turbine respectively, whereas Jwte , Wwte and Twte are their reflected values to the high speed shaft side with N as gearbox ratio. The wind turbine rotor damping factor (Bwt ) is also reflected to the high speed shaft by 10 where it is combined with the generator damping (Bg ) to define the equivalent damping factor . Equations 7 through 11 are casted in state space form in 12 and 13 where ωg is the generator speed and θg is the generator angular position.



Jwt Jwte = 2 N ωwte = ωg = N ωwt Twt Twte = N Bwt Beq = Bg + 2 N Jeq = Jg + Jwte

(7) (8) (9) (10) (11)

Jeq ω˙g = Twte − Tem − Beq ωg θ˙g = ωg

(12) (13)

Rs −ωe (Lls + Lm )  ωe (Lls + Lm ) Rs [R] =   0 (ωr − ωe )Lm (ωe − ωr )Lm 0  0 −ωe Lm  ωe Lm 0  Rr0 (ωr − ωe )(L0lr + Lm )  (ωr − ωe )(L0lr + Lm ) Rr0

Machine’s electromagnetic torque (Tem ), speed (ωr ) and rotor position (θr ) are given by 20, 21 y 22: Tem = Tg =

2.3. Squirrel Cage Induction Generator Model In this project the induction machine is modeled in a synchronous reference frame (ωe = 2 ∗ π ∗ F ). The electric model is given by:

3P 0 0 (Lm Idr Iqs − Lm Iqr Ids ) 22 ω˙r =

P ω˙g 2

θ˙r = ωr d[Iqdsr ] = [L]−1 [Vqdsr ] − [L]−1 [R][Iqdsr ] dt

(14)

Where [Vqdsr ], [Iqdsr ], [L], [L]−1 y [R] are defined in equations 15, 16, 17, 18 y 19. [Vqdsr ] =



Vds

Vqs

0 Vdr

[Iqdsr ] =



Ids

Iqs

0 Idr



Lls + Lm  0 [L] =   Lm 0

 −1

[L]

  =  

0 Lls + Lm 0 Lm

L0lr +Lm Lls L0lr +Lls Lm +L0lr Lm

0 −Lm Lls L0lr +Lls Lm +L0lr Lm

0 −Lm Lls L0lr +Lls Lm +L0lr Lm

0 Lls +Lm Lls L0lr +Lls Lm +L0lr Lm

0

0 Vqr

0 Iqr

T

T

(15)

(19)

(20)

(21)

(22)

P is the number of poles in the machine.

2.4. PWM Three Phase Rectifier Average Model The average model used for the PWM three phase boost rectifier (Vdc > Vm ) is shown in figure 4.

(16)

 0  Lm   0 L0lr + Lm (17)

Lm 0 L0lr + Lm 0

0

Fig. 4. PWM Three Phase Rectifier Average Model

L0lr +Lm Lls L0lr +Lls Lm +L0lr Lm

0

The equations for the average model of the rectifier are [10]:

−Lm Lls L0lr +Lls Lm +L0lr Lm

0



−Lm Lls L0lr +Lls Lm +L0lr Lm

    

0 Lls +Lm Lls L0lr +Lls Lm +L0lr Lm

(18)

→ − − d i l−l 1 → 1 → − = v L−L − d l−l · v dc dt 3L 3L −T → dv dc 1→ v dc − = d l−l · i l−l − dt C RC

(23) (24)

then  T → − v L−L = vAB vBC vCA  T → − v l−l = vab vbc vca  T → − i l−l = iab ibc ica  T → − d l−l = dab dbc dca

(25) (26) (27) (28)

A 250W wind turbine model is being coupled to a squirrel cage induction generator already available in the CPES laboratory at UPRM (for verification purposes) and whose parameters were obtained from [11, 8, 12]. Data for both wind turbine rotor and generator are shown in table 1 and 2 respectively. Table 1. Mechanical Parameters for the Turbine-Generator System Parameter R Jg Jr Bg Br Gearbox N

Value 0.73 0.00325 0.0306 0.0007022 0.0007022 4

Unit m Kgm2 Kgm2 Nms Nms

Fig. 5. Control Scheme 3.1. Constant Volts/Hz Control This control technique keeps the air gap flux (φm ) constant while the electric frequency of the stator or the load torque is varied [13]. According to the equivalent circuit of a squirrel cage induction machine, the phase voltage V a is given by: V a = (Rs + jωLls )I a + E ma

(29)

E ma = ωLm I ma

(30)

The air gap voltage Ema is given by equation 30 and neglecting the voltage drop across the stator impedance(Rs + jωLls ) gives [14]: E ma ∼ =Va

Table 2. Electrical Parameters for the Generator Parameter VLL HP Nm Rs Rr0 Lls L0lr Lm P

Value 230V 1/3hp 1725rpm 7.295Ω 5.890Ω 0.0230H 0.0148H 0.5866H 4

Explanation Line to line voltage Rated output power Rated speed Stator resistance per phase Rotor resistance per phase Stator leakage inductance Rotor leakage inductance Magnetizing inductance Number of poles

3. CONTROL SCHEME The control scheme (Fig 5) allows the system operate close to the maximum power point. The scheme is based on keeping constant air gap flux. Frequency and magnitude of stator voltage are changed to control the angular speed of the mechanical shaft to track the maximum power point determined by the MPPT algorithms. The design considers conditions at system start up as well as field weakening if necessary, and PWM boost rectifier limitations.

(31)

The air gap flux by phase (φma ) is defined in [13]: φma = Lm I ma

(32)

using 32 in 30 and taking into account 31 leads to: Va ∼ = E ma = φma ω

(33)

Given ω which is the stator electrical angular frequency (ω = 2πF ), equation 33 shows that V a is proportional to F . With φma given by 34 it can be seen that varying the stator voltage and electric frequency it is possible to keep the air gap flux constant. Va (34) φma ∼ = 2πF Since the controller must be efficient in power management, losses must be minimize for different values of shaft speed and electromagnetic torque [13]. Losses in the rotor are given by 35 whilst the electromagnetic torque is given by 36.

Pr,loss = ωslip Tem

(35)

Tem = ktω φ2m ωslip

(36)

3.3. Starting Considerations ωslip

Tem = ktω φ2m

Tem = kT ω ωslip

(37)

(38)

From 35 it can be seen that for different electromagnetic torque (Tem ) values the slip speed (ωslip ) can operate at low values and this can minimize losses due to rotor resistance [13]. Solving for ωslip from 36 gives 37. This shows that to minimize slip speed value, air gap flux(φm ) must be at its maximum possible value, i.e. nominal value for which the machine was designed (φm,rated ). With the air gap flux constant, the electromagnetic torque only depends on slip speed as shown by 38 where kT ω = ktω φ2m,rated [13]. Since the proposed control scheme will keep the air gap flux at its nominal value, this value can be obtained by replacing nominal values for phase voltage and stator frequency in equation 34. This is shown in 39.

q

φma,rated

2 V Va 3 230 = = 0.4981 = 3.13W b = 2πF 2π60 rad/seg (39)

3.1.1. Field Weakening Should it be necessary to operate with an electrical frequency greater than the nominal value, the air gap flux will become smaller since the phase voltage stays at its maximum value. This phenomena is called field weakening and the air gap flux has an inverse relationship with frequency above the nominal frequency [13]. The flux as a function of frequency is defined by 40. ( φm =

V a,rated 2πFrated φm,rated Frated F

→ F < Frated → F > Frated

(40)

3.2. Duty Cycle Amplitude In steady state the average duty-cycles are sinusoidal signals whose frequency F which determines the synchronous speed in the generator and their amplitude D determines stator voltage amplitude. Assuming a constant v dc and according to the average model for the PWM three phase boost rectifier, the value D∗ is given by: D∗ =

√ Va 3 v dc

(41)

To avoid in-rush current values greater than twice the steady state value, a start up time of 4 seconds was heuristically determined. During this period of time the air gap flux is set to 10% of the nominal value, and using a lineal function (42) the flux increases up to 100%.

φstarting (t) =

φm,rated − 0.1φm,rated t + 0.1φm,rated 4 (42)

3.4. MPPT Algorithms Most algorithms for maximum power extraction determine either optimum rotation speed or optimum generator torque at which maximum power is extracted. They can be divided in 3 categories [15]: Customized [16, 6, 17] Refer to those that are preprogrammed with the characteristics of a particular wind turbine. They are fast and efficient but they must be reprogrammed for each wind turbine. These kinds of algorithms require data from the turbine such as radius, inertia, Cp − λ curves (Fig 3), pitch angle among others as well as wind speed. These data and equations 2, 4 y 5 are used to determine the value of λopt , which achieves the maximum value for Cp and therefore the maximum power operating point. Given λopt velocity or reference torque can be obtained for the generator controller. Such type of algorithm has two major weaknesses, i.e. it only work for the specific turbine it was designed and expensive elements for measuring the wind speed need be included. In addition some of these measurements are really estimations since the former are not actually performed on the turbine.

Continuous [18, 15, 19, 8] They continuously search for the optimum operating point, i.e. maximum point in the wind power vs. rotating speed characteristic curve (Fig 2), without previous knowledge of the wind turbine. One of the most commonly used algorithm to reach the maximum power point of the characteristic curve δPW = 0, and is also called Hill Climb is defined by δω wt Searching (HCS). It introduces a perturbation in the point of operation and observes the sign of the change in the output power to decide what action to take, i.e., to continue in the same direction if the sign is positive or to move in the opposite direction otherwise. These tasks continue indefinitely and eventually the output power oscillates around the maximum power point [15].

Adaptative [20, 21, 22, 15] This type of algorithm uses artificial intelligence techniques like neural networks and fuzzy logic to determine the rotational speed or torque reference.

and it can almost extract the maximum quantity of available power.

4. SYSTEM SIMULATIONS RESULTS Different tests were performed to analyze the system behavior for different wind conditions, with different MPPT algorithms. Furthermore a test in open circuit was conducted to analyze the natural response of the turbine due to fast wind changes. Simulations for a step change in wind conditions and random wind conditions were also run. Fig. 7. Generator mechanical speed 4.1. Open Circuit test The objective of this test is to analyze the system behavior when no control structure is used. In Fig 6 the speed reference signal has fast changes due to the wind ”profile”, but the measured speed shows slow changes because of the turbinegenerator low-pass dynamics.

Fig. 6. Mechanical Speed of the Turbine and Generator 4.2. Constant Wind Speed To verify controller performance, different tests were done with constant wind speed plus a step change perturbation. Figure 7 shows angular speed reference for the generator shaft (red line), rate-limited version (blue line) to avoid in-rush current. Generator shaft mechanical angular speed (green line) follows very close by the rate-limited reference. Fig 8 shows output power and power losses in several system components. This test verifies that the controller track its reference value

Fig. 8. Output power and power losses: Step Change. (blue line) Wind turbine maximum power . (green line) Generator active power. (red line) DC load power. (light blue line) Wind turbine friction losses. (violet line) Generator friction losses. (yellow line) Rotor electrical losses. (black line) Stator electrical losses. 4.3. Customized MPPT Algorithm Test Results for output power and losses when the system sees a randomized wind profile under the customized MPPT algo-

rithm are shown in Fig 9.

Fig. 9. Output power and power losses: randomized wind profile. (blue line) Wind turbine maximum power . (green line) Generator active power. (red line) DC load power. (light blue line) Wind turbine friction losses. (violet line) Generator friction losses. (yellow line) Rotor electrical losses. (black line) Stator electrical losses.

4.4. Continuous MPPT Algorithm Test Results when using the HCS MPPT algorithm, are shown in Fig 10.

Fig. 10. Power Extracted and Power Losses: randomized wind profile. (blue line) Wind turbine maximum power . (green line) Generator active power. (red line) DC load power. (light blue line) Wind turbine friction losses. (violet line) Generator friction losses. (yellow line) Rotor electrical losses. (black line) Stator electrical losses.

5. SUMMARY A control scheme to extract the maximum power in a wind turbine-squirrel cage induction generator system was developed. For all the cases the system efficiency is around 80%. Both types of MPPT algorithms were able to extract the same amount of power (Fig 11), but for low power applications the HCS algorithm is more suitable because it does not need reconfiguration or anemometer.

connected pmsg wind generation system,” in IEEE Industrial Electronics, IECON 2006 - 32nd Annual Conference on, Nov. 2006, pp. 4248–4253. [9] B. Beltran, T. Ahmed-Ali, and M.E.H. Benbouzid, “Sliding mode power control of variable speed wind energy conversion systems,” in Electric Machines and Drives Conference, 2007. IEMDC ’07. IEEE International, May 2007, vol. 2, pp. 943–948. [10] Silva Hiti, Modeling and control of three-phase pwm converters, Ph.D. thesis, Virginia Polytechnic Institute and State University, July 1995.

Fig. 11. Comparison of Power Drawn by the MPPT Algorithms 6. REFERENCES [1] Siegfried HEIER, Grid integration of wind energy conversion systems, Wiley, Chichester, 1998, Includes bibliographical references and index. [2] E.B. Muljadi P.W. Carlin, A.S. Laxson, “The history and state of the art of variable-speed wind turbine technology,” Tech. Rep., National Renewable Energy Laboratory, February 2001. [3] Poul Sorensen Frede Blaabjerg Florin Iov, Anca Daniela Hansen, Wind Turbine Blockset in Matlab/Simulink, Aalborg University and RIS∅ National Laboratory, March 2004. [4] Joanne Hui, “An adaptive control algorithm for maximum power point tracking for wind energy conversion systems,” M.S. thesis, Queen’s University, December 2008. R [5] The MathWorks, Matlab R2007a, The MathWorks, January 2007.

[6] H. Camblong, I. Martinez de Alegria, M. Rodriguez, and G. Abad, “Experimental evaluation of wind turbines maximum power point tracking controllers,” Energy Conversion and Management, vol. 47, no. 18-19, pp. 2846 – 2858, 2006. [7] M. Orabi, F. El-Sousy, H. Godah, and M.Z. Youssef, “High-performance induction generator-wind turbine connected to utility grid,” in Telecommunications Energy Conference, 2004. INTELEC 2004. 26th Annual International, Sept. 2004, pp. 697–704. [8] Rou-Yong Duan, Chung-You Lin, and Rong-Jong Wai, “Maximum-power-extraction algorithm for grid-

[11] Roberto II Ovando Domnguez, “Emulador de turbina elica para banco de pruebas de generacin eolo-elctrica,” M.S. thesis, CENIDET, 2006. [12] Wee Liam Fung Ng, “Implementation of a sensorless induction motor drive,” M.S. thesis, University of Puerto Rico, Mayaguez (Puerto Rico), United States – Puerto Rico, 2001. [13] N. Mohan, Electric Drives An Integrative Approach, MNPERE, 2003. [14] Ramu Krishnan, Electric Motor Drives Modeling Analysis and Control, Prentice Hall, February 2001. [15] Joanne Hui and Alireza Bakhshai, “A fast and effective control algorithm for maximum power point tracking in wind energy systems.,” . [16] G.D. Moor and H.J. Beukes, “Maximum power point trackers for wind turbines,” Power Electronics Specialists Conference, 2004. PESC 04. 2004 IEEE 35th Annual, vol. 3, pp. 2044–2049 Vol.3, June 2004. [17] Tomonobu Senjyu, Yasutaka Ochi, Yasuaki Kikunaga, Motoki Tokudome, Atsushi Yona, Endusa Billy Muhando, Naomitsu Urasaki, and Toshihisa Funabashi, “Sensor-less maximum power point tracking control for wind generation system with squirrel cage induction generator,” Renewable Energy, vol. 34, no. 4, pp. 994 – 999, 2009. [18] Jia Yaoqin, Yang Zhongqing, and Cao Binggang, “A new maximum power point tracking control scheme for wind generation,” Power System Technology, 2002. Proceedings. PowerCon 2002. International Conference on, vol. 1, pp. 144–148 vol.1, Oct 2002. [19] R. Datta and V.T. Ranganathan, “A method of tracking the peak power points for a variable speed wind energy conversion system,” Energy Conversion, IEEE Transactions on, vol. 18, no. 1, pp. 163–168, Mar 2003.

[20] S. A. Papathanassiou, A. G. Kladas, and J. A. Tegopoulos, “Applications of artificial intelligence techniques in wind power generation,” Integr. Comput.-Aided Eng., vol. 8, no. 3, pp. 231–242, 2001. [21] Shuhui Li, D.C. Wunsch, E.A. O’Hair, and M.G. Giesselmann, “Using neural networks to estimate wind turbine power generation,” Energy Conversion, IEEE Transaction on, vol. 16, no. 3, pp. 276–282, Sep 2001. [22] M.G. Simoes, B.K. Bose, and R.J. Spiegel, “Design and performance evaluation of a fuzzy logic based variable speed wind generation system,” Industry Applications Conference, 1996. Thirty-First IAS Annual Meeting, IAS ’96., Conference Record of the 1996 IEEE, vol. 1, pp. 349–356 vol.1, Oct 1996.