Multivariable control algorithm for laboratory experiments in wind energy conversion

Renewable Energy 83 (2015) 162e170

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Renewable Energy journal homepage: www.elsevier.com/locate/renene

Multivariable control algorithm for laboratory experiments in wind energy conversion A. Merabet a, *, Md.A. Islam a, R. Beguenane b, A.M. Trzynadlowski c a

Division of Engineering, Saint Mary's University, Halifax, NS, B3H 3C3, Canada Department of Electrical Engineering, Royal Military College, Kingston, ON, K7K 7B4, Canada c Department of Electrical Engineering, University of Nevada, Reno, USA b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 10 September 2014 Accepted 10 April 2015 Available online

Advanced experimentation with wind energy conversion systems is described. The real time multivariable control of a wind turbine is designed for investigation of theoretical concepts and their physical implementation. The control system includes a speed controller and a disturbance estimator for enhanced robustness of the control system. In order to provide students with deeper understanding of wind energy and energy extraction, a maximum power point tracking algorithm is developed and integrated into the control system. The multivariable control system is implemented in a small wind turbine laboratory system. A power electronic interface is based on two DCeDC converters: a buck converter for control of the speed and a boost converter controlling the load voltage. Experimental results demonstrate effectiveness of the multivariable control system for a wind turbine providing maximum power extraction. The experiment can be reconfigured for teaching various control concepts to both undergraduate and graduate students. © 2015 Elsevier Ltd. All rights reserved.

Keywords: Multivariable control Wind turbine DC generator Speed control Maximum power extraction

1. Introduction In modern power systems, the power generation based on wind energy enjoys significant interest, which has caused considerable increase in the related education and research [1e4]. Because it is difficult to use a real wind turbine in laboratory environment, a small turbine that can be used indoors is the best tool for implementation and demonstration of control strategies [5,6]. Wind turbine emulators, involving motor-generator set, variable load, and control system, which operate with the power-speed characteristics of a wind turbine are frequently used for research and teaching purposes due to their simplicity, low power, and low cost design [5]. However, neglecting the real wind effects represents an important flaw, especially when dealing with control strategies whose robustness need to be verified under realistic operating conditions [7]. Laboratory experiments in the wind energy area including hardware-in-the loop (HIL) and advanced control systems are important for education of future engineers and researchers.

* Corresponding author. Tel.: þ1 9024205712; fax: þ1 9024205021. E-mail address: [email protected] (A. Merabet). http://dx.doi.org/10.1016/j.renene.2015.04.031 0960-1481/© 2015 Elsevier Ltd. All rights reserved.

Developing a control system from the model of the wind turbine, and its practical realization would bridge the gap between theory and practice. It would allow the students to implement theories of advanced control by analysing the major components of a wind turbine system and extracting mathematical models needed for the design of a model-based control system. One major requirement in the considered wind energy conversion system (WECS) is controlling the generator speed and the load voltage in order to maximize wind energy extraction. As well known, the optimum turbine speed is a function of wind speed [1e3]. Variable speed WECS are increasingly common. Typically, at high wind speeds, the WECS use aerodynamic control in combination with power electronics to regulate torque, speed, and power, and prevent the turbine from damage. However, the aerodynamic control using variable pitch blades is usually expensive and complex. It ca also cause an unnecessarily high activity of the pitch actuator due to small fluctuations of power during the steady state operation [7]. Control systems implemented in the power electronic interface represent an efficient means to operate a wind turbine at the maximum power extraction. The control is not always aimed at capturing as much energy as possible. Power generation is limited during high wind speeds or when the load demand in an isolated system is low. Model based control strategies, such as feedback,

A. Merabet et al. / Renewable Energy 83 (2015) 162e170

predictive, and sliding mode, can be employed for speed control in WECS. Quality of control strategies depends on the accuracy of mathematical model of the system, which is usually not high [8,9]. For accurate speed tracking, the controller must maintain high performance when facing parameter variations and uncertainties of the system [10e15]. In this paper, a feedback speed control strategy is developed from the mathematical model of a generator connected to a wind turbine. Information about the turbine and wind speeds is assumed to be unavailable and their variations will be compensated using a torque estimator integrated in the controller. Performance of the proposed controller will be tested under multivariable control conditions with a maximum power point tracking (MPPT) algorithm and load voltage control. A Quanser's five-blade wind turbine is employed in an experimental setup equipped with a power electronic interface. The setup allows to verify efficacy of the proposed control system and to investigate its behaviour with real wind [16]. The rest of the paper is organized as follows: In Section 2, a description of the experimental system of wind turbine system is given. The proposed feedback control method for speed tracking is detailed in Section 3 followed by the robustness and stability analysis in Section 4. The MPPT algorithm, generating the speed reference needed for maximum extraction of power from wind, is described in Section 5. The experimental setup is described in details in Section 6 and experimental results and their discussion are given in Section 7. 2. Wind turbine experimental system 2.1. Wind turbine The wind turbine, manufactured by Quanser Inc., is installed in a wind tunnel. It has five blades and drives a DC generator through a gearbox of ratio 1:1. The gearbox converts rotation of the horizontal-axis turbine to that of the vertical-axis generator. The generator is connected to the load via a power electronic interface allowing control of the shaft speed and load voltage. The power delivered by the turbine shaft (neglecting losses in the drive train) is given by

Pt ¼ 0:5prCp ðlÞr 2 v3w

(1)

where r denotes the air density, r is the length of the turbine blade, vw is the wind speed, and l is the ratio of blade tip speed to wind speed, that is

l¼

ur vw

(2)

where u is the angular velocity of the turbine. The power coefficient Cp depends on speeds of the turbine and wind, and its relation to l is shown in Fig. 1. The power coefficient reaches maximum at a specific optimum value lopt. In order to extract maximum power from wind, the turbine speed should be so controlled as to maintain l at the optimum level. In some wind turbines, the optimum tip speed ratio may be unknown or not well defined and subject to change. Therefore, instant locating of the maximum Cp during the operation of wind turbine is very important. An MPPT algorithm based on the variation of the generated power and the shaft speed is proposed, in Section 3. The torque at the turbine shaft produced by the wind is given by

Tt ¼ 0:5prCt r 3 v2w

(3)

163

Fig. 1. Power coefficient of the wind turbine versus tip-speed ratio.

where Ct ¼ Cp/l is the torque coefficient. Here, the mathematical model of the mechanical structure of wind turbine system is assumed to be unknown. This uncertainty is dealt with in the proposed control system. 2.2. DC generator The armature of the DC generator is modeled as an RLE circuit, with E representing the back emf (speed voltage). Denoting the generated voltage as V, the electrical and mechanical equations of the generator can be written as

di R K 1 ¼ iþ bu V dt L L L

(4a)

du K B 1 ¼  i i  u þ Tt dt J J J

(4b)

where i is the armature current, Kb is the machine constant, u is the rotational speed of the generator, V is the generator voltage, J is the rotor inertia, B is the viscous-friction coefficient, and Tt is the unknown turbine torque. 3. Feedback control for speed tracking 3.1. Feedback controller development From the electrical and mechanical Equation (4) of the DC machine, a linear state-space equation can be derived as

x_ ¼ Fx þ g1 V þ g2 Tt

(5)

where,

2

x ¼ ½i

T

u ;

R  6 L 6 F¼6 4 K  i J

3 Kb L 7 7 7; B5  J

2

3 1 6 L 7 g1 ¼ 4 5; 0

2 3 0 6 7 g2 ¼ 4 1 5 J

The controlled output is the rotational speed u, the input is the voltage V and the disturbance is the turbine torque Tt. In order to find a relationship between the output u and the input V, the mechanical Equation (4b) is differentiated, using Equation (4a), which yields

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K B 1 € ¼  i i_  u_ þ T_ t u J J J     Ki R Kb B K B K B  i i  u þ i V  2 Tt  iþ u  ¼ L J J J L J JL J

k2 > (6)

The dynamic of the wind turbine is more sluggish than the electric energy conversion system. Therefore, according to [10], it can be assumed that

T_ t ¼ 0

(7)

The objective of the control law is minimization of the speed tracking error expressed by the second-order equation

€ eu þ k2 e_u þ k1 eu ¼ 0

(8)

where, eu ¼ u  uref The following control law is proposed

     JL K B k1 u  uref þ k2  i i  u  u_ ref V ¼ Ki J J       Ki R Kb B K B € ref  ii u u  iþ u  þ  L J J J L J  1 B þ k2 Tt  2 Tt J J (9) Implementation of this law requires precise knowledge of parameters of the system and the turbine torque, which is not easily available in the majority of practical wind energy systems.

B J

(15)

Thus, the stability of the torque observer is guaranteed. b t , the control law (9) becomes Using the observed torque T

     JL K B k1 u  uref þ k2  i i  u  u_ ref V ¼ Ki J J       Ki R Kb B K B € ref  ii u u  iþ u  þ  L J J J L J  1b Bb þ k2 T t  2 T t J J (16) If Equations (13), (14) and (16) are substituted in (11), a new form of the torque observer is produced

       b_ t ¼ p k u  u _  u_ ref þ u € u € ref T 0 1 ref þ k2 u

(17)

Integrating (17), the torque observer becomes

 Z       bt ¼ p k u  uref dt þ k2 u  uref þ u_  u_ ref T 0 1 (18) The torque observer has a PID structure, which helps the feedback controller (9) to enhance its capability of speed tracking and compensation of uncertainties resulting from the lack of detailed knowledge of wind turbine parameters. 4. Robustness and stability analysis

3.2. Robust control based on torque estimation 4.1. Robustness analysis In this work, the development of a robust controller to deal with parameter variations and unknown turbine torque is based on a torque observer. It is derived from the state space model of the DC generator, the control law, and the speed tracking error of the wind energy conversion system. From the model (5), the torque variable is defined as

g2 Tt ¼ x_  Fx  g1 V

(10)

Using the torque Equation (10) an observer can be defined as

b b_ t ¼ Pg T T 2 t  Pðx_  Fx  g1 VÞ

(11)

where P, of size 1  2, is the observer gain to be determined. From (7), (10) and (11), it can be found that the error dynamic of the observer is given by



bt b_ t ¼ Pg Tt  T e_ ¼ T_ t  T 2



(12a)

e_ þ Pg2 e ¼ 0

(12b)

It is exponentially stable if the term Pg2 is a positive constant. Based on (4), (5) and (6), the observer gain P can be defined as



P ¼ p0

Ki J



 B þ k2 ½ 0 J



1

(13)

Pg2 ¼ p0

 B 1  2 þ k2 J J

which is positive if the control gain k2 is such that

a. Structured (parametric) uncertainties characterized by a dynamical model of the system with parameter variations. b. Unstructured uncertainties characterized by omitted quantities, unknown torque, and external disturbances. The rotor dynamic Equation (6) can be rearranged to

€ ¼ ai þ bu þ cV þ dTt þ x u  where

a ¼ KJ i

R L

(19)

   2 þ BJ ; b ¼ 1J KiLKb  BJ ; c ¼ KJLi ; d ¼ JB2 ; and x

represents the effects of the omitted quantities of the electric/power electronics circuit, load, and any external disturbance. Now, the Equation (19) can be modified to include parameter uncertainties D($) and external disturbance x to

€ ¼ ða þ DaÞi þ ðb þ DbÞu þ ðc þ DcÞV þ ðd þ DdÞTt þ x u

(20)

Equation (20) is now reorganized to include all uncertainties in a common term as

€ ¼ ai þ bu þ cV þ dðTt þ hÞ u

(21)

where

where p0 is a positive constant. From (5) and (13), the term Pg2 is given by



The dynamics of the wind turbine is an uncertain system, where the uncertainties include:

h¼ (14)

1 ðDai þ Dbu þ DcV þ Dd Tt þ xÞ d

The uncertainties term, h, includes parametric uncertainty, omitted quantities, and external disturbances in the system.

A. Merabet et al. / Renewable Energy 83 (2015) 162e170

A general form of the torque Tu, which includes the torque Tt and the uncertainties h, is

Tu ¼ Tt þ h

(22)

The torque observer (18) can be generalized and used to compensate the effect of the turbine torque, parametric uncertainties, omitted quantities, and external disturbances, by replacing Tt by Tu as the new disturbance variable. Then,



bu ¼ p k T 0 1

Z 

    u  uref dt þ k2 u  uref þ u_  u_ ref

 (23)

2

0 A ¼ 4 k1 0

The closed loop system consists of the wind turbine-generator model (4), the controller (16), and the observer (11). The control law (16) is substituted into the speed dynamics (6) to yield

Stability of the error system (29) requires that as t/∞ then x(t) /0 From (27), the state is

xðt Þ ¼ xð0ÞeAt

€ ¼ k1 u  uref u

1 u_ zfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflffl{ B K C B 1 1b B C € ref C  k2 T  k2 B i i  u þ Tt  u t @ J A J J J

1 Bb B € ref þ k2 Tt þ 2 T t  2 Tt þ u J J J (24) Equation (24) is rearranged to describe the error dynamics, as



     € u € ref þ k2 u_  u_ ref þ k1 u  uref u    1 b t  B Tt  T bt ¼ k2 Tt  T 2 J J

€ eu þ k2 e_u þ k1 eu ¼ k3 e

(25a) (25b)

s 6 detðsI  AÞ ¼ det4 k1

1 B k3 ¼ k2  2 J J Now, from (25b) and (12b), the error dynamics of the closed loop system can be expressed as

e_ þ p0 k3 e ¼ 0

(26)

The involved errors as the state vector are defined as

3 2 3 eu x1 x ¼ 4 x2 5 ¼ 4 e_u 5 x3 e 2

(27)

(28)

where

3

s þ k2

k3

7 5

0 s þ p0 k3 

2 ¼ ðs þ p0 k3 Þ s þ k2 s þ k1

(31)

¼ ðs  l1 Þðs  l2 Þðs  l3 Þ where, the eigenvalues li (i ¼ 1, 2, 3) are

8 l ¼ p0 k3 > > > 1 > qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > > > > k2 þ k22  4k1 < l2 ¼ 2 > > qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > > > > k2  k22  4k1 > > : l3 ¼ 2

(32)

It can be seen that eigenvalues li satisfy the condition Re (li) < 0. Therefore, x(t) / 0 as t / ∞ for all x(0), and the stability is guaranteed. 5. Maximum power point tracking algorithm

uref ¼

lopt vw r

(29)

(33)

However, practical implementation of the MPPT algorithm based on (33) requires measurement of the wind speed and knowledge of the wind turbine characteristics. It makes this algorithm unreliable due to inaccuracies of the wind speed determination and flaws in modelling the wind turbine. Here, an MPPT method based on the variation of the generated power P and the turbine-generator speed u is proposed. The variation of the speed reference uref is given by

(34)

where the generated power is found from measurements of the voltage and current at the generator, that is,

P ¼ Vi

State space model for the error dynamics, in a matrix form, is given by

x_ ¼ Ax

0

0

duref dP ¼ a,u, dt dt

From (26) and (27), the state space representations are

8 x_ ¼ x 2 < 1 x_2 ¼ k1 x1  k2 x2 þ k3 x3 : x_3 ¼ p0 k3 x3

1

For maximum power extraction, if the wind turbine characteristics are available, the speed reference profile is derived from (2) using the optimum tip speed ratio lopt such that

where,

€ eu þ k2 e_u þ k1 eu ¼ k3 e

(30)

where, x(0) is the initial state vector of the errors. Thus the stability can be guaranteed if eAt / 0 when t / ∞ and it can be verified through eigenvalues of the matrix A. The characteristic polynomial of A is,

0



0 k3 5 p0 k3

2

4.2. Closed loop stability analysis



1 k2 0

165

3

(35)

and a is a constant. Correct choice of a will improve speed tracking at both high and low wind speeds and fast convergence of the algorithm. Implementation of (34) has been carried out numerically using a discretisation method as fellows

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uref ðkDtÞ ¼ uref ððk  1ÞDtÞ þ a$uðkDtÞ$½PðkDtÞ  Pððk  1ÞDtÞ

Wind Turbine

Blowerr

(36)

vw

where, Dt is the sampling time and k is an integer.

Tunnel

ω 6. Wind turbine experimental setup The wind turbine experimental setup consists of a five-blade wind turbine and a DC generator, as shown in Fig. 2. The generator provides power to a set of LEDs, which form a variable load. Control of the turbine speed and of the load voltage is realized through a power electronic interface between the generator and load. The interface consists of two DCeDC converters as shown in Fig. 3. The DCeDC buck converter controls the rotational speed of the generator and the DCeDC boost converter controls the load voltage. Such a cascade of two DCeDC converters would be impractical and in a commercial system. However, it allows independent manipulations, valuable for teaching purposes. A detailed description of the interface exceeds the scope of this paper and more information can be found in Ref. [17]. The variable electronic load, based on LEDs and shown in Fig. 4, consists of six parallel equal banks of two LEDs in each bank in series with a resistance. The load banks can be switched automatically ON/OFF from Matlab/Simulink, through the real-time data acquisition board Q2-USB [16], by sending a signal to the MOSFET gates of the banks. The load side converter control system is used to regulate the voltage across the load in order to maintain a proper functioning of the LEDs load. The PI voltage controller produces signal U* given by

Z     VL  VL* dt U * ¼ kp VL  VL* þ ki

(37)

The output of the voltage controller is the firing signal to be delivered to the gate of the MOSFET in the DCeDC buck converter as shown in Fig. 3. Rotational speed is measured by an encoder mounted on DC generator rotor shaft. Voltage and current sensors are available to measure the armature current and the generator and load voltages. The measurements are calibrated and sent to the computer (PC) through a real-time data acquisition board Q8USB, to be analysed by using the software package QUARC with MATLAB/Simulink. QUARC is a powerful rapid control prototyping tool that significantly accelerates control system design and implementation [16].

G

i P

MPPT

Robust Feedback Speed Control

VL* _ +

Voltage Control

V*

DC-DC Buck DC-DC Boost Converter

U*

VL

Fig. 3. Multivariable control strategy for the experimental wind turbine-generator system.

The wind is generated by a DC blower motor. An incremental encoder mounted on blower rotor shaft measures the motor speed, which is proportional to the wind speed. The advantage of the proposed control system is that it does not require knowledge of the wind speed for evaluation of the turbine torque. 7. Experimental results Experiments were carried out to validate the proposed control strategy under different scenarios of operation. The choice of the feedback controller gains (k1 and k2), the estimator gain (p0) and the load controller (kp and ki) were determined by trial and error to achieve high-quality performance. Voltage and current sensors (VS and CS) are available in the experimental setup, as shown in Fig. 3, to provide measurements of voltages of the generator, the buck converter, and the load, as well as the generator and load currents. The measurements are delivered to the computer (PC) through a real-time data acquisition board Q8-USB. The results were analysed using software packages Quarc with Matlab/Simulink. Quarc is a rapid control prototyping tool, which significantly accelerates the control system design and implementation [16]. Test 1: A random wind speed, shown in Fig. 5, was generated by changing the blower speed in order to test the MPPT algorithm and

G1 Fig. 2. Experimental set-up of the wind energy conversion system.

+

ωref _

DC Generator G

G2

Fig. 4. Variable electronic load.

G6

A. Merabet et al. / Renewable Energy 83 (2015) 162e170

167

Fig. 5. MPPT based speed tracking for fixed load.

the rotor speed tracking. The experimental wind turbine system was operating with maximum power extraction, nominal values of the parameters of the model (4), and fixed load (all banks were ON). It can be seen that the speed reference generated from MPPT and the rotor speed follow the variation of the wind speed. Estimations of the extracted power and torque are illustrated in Fig. 6. The estimators enhance the control, which results in a zero steady-state

speed error. The voltage regulation does not affect the speed tracking response. Test 2: The wind turbine and control system were tested with a variable load, the banks being turned ON at different time intervals as shown in Fig. 7. It can be observed in Fig. 8 that speed tracking and voltage control are accurate in spite of the varying wind and load. This high performance is attained by precise torque

Fig. 6. Estimated torque, extracted power and load voltage regulation.

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A. Merabet et al. / Renewable Energy 83 (2015) 162e170

Fig. 7. Variable load banks.

estimation, which allows compensation of external disturbances arising from the wind and load variations. The generated power and current follow the wind speed, as shown in Fig. 9, proving that the turbine extracts the maximum power from wind. The calibrated control input signal shown in Fig. 10 makes the turbine to operate within a safe region. Test 3: The experimental wind turbine system was tested with mismatched parameters. The perceived values of generator parameters had been increased by 10% and the load was varying

again. The results of speed tracking and torque estimation are shown in Fig. 11. The performance is still satisfactory, demonstrating robustness of the developed controller. 8. Conclusions A robust feedback control strategy has been proposed to track a speed profile, generated by an MPPT algorithm, to operate a laboratory wind energy system based on a DC generator. Information

Fig. 8. MPPT based speed tracking for variable load.

A. Merabet et al. / Renewable Energy 83 (2015) 162e170

169

Fig. 9. Generated power and current, and load voltage regulation.

about the wind turbine and wind speed is not needed in the implementation of this strategy, as their effects are compensated through a torque estimator integrated into the controller. Parameter, wind, and load variations, and component omitted in the mathematical model, such as the power electronics interface, do not significantly spoil the speed tracking performance.

Stability and robustness of the feedback controller have been analysed, and the developed control algorithm was tested in a small scale laboratory wind turbine system. The system will be used as an important tool for teaching control systems theory and training in the field of wind energy.

Fig. 10. Calibrated control input signal.

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Fig. 11. MPPT based speed tracking for variable load and mismatched generator parameters.

Acknowledgements This study was partially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) under the Engage Grant 432302-12. Appendix Wind turbine: r ¼ 14 cm, r ¼ 1.14 kg/m3 DC generator: R ¼ 3.705U, L ¼ 575 mH, Kb ¼ 10.575 mV/rpm, Ki ¼ 100.95 mNm/A, B ¼ 0.001833, J ¼ 165 g/cm2 Feedback controller and torque estimator: k1 ¼ 3.33  105, k2 ¼ 250, p0 ¼ 0.001. MPPT algorithm: a ¼ 0.5. PI voltage controller: Kp ¼ 20, Ki ¼ 0.5. References [1] Rubio JOḾ, Aguilar LT. Maximizing the performance of variable speed wind turbine with nonlinear output feedback control. Procedia Eng 2012;35:31e40. [2] Merabet A, Thongam T, Gu J. Torque and pitch angle control for variable speed wind turbines in all operating regimes. In: Proc 10th int conf. on environmental and electrical engineering; 2011. [3] Neammanee B, Sirisumrannukul S, Chatratana S. Development of a wind turbine simulator for wind generator testing. Int Energy J 2007;8:21e8. [4] Mayo-Maldonado JC, Salas-Cabrera R, Cisneros-Villegas H, Castillo-Ibarra R, Roman-Flores J, Hernandez-Colin MA. Maximum power point tracking control for a DC-generator/multiplier-converter combination for wind energy applications. In: Proc world congress on engineering and computer Sc; 2011. p. 1.

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