Maximum Power Tracking Control for a Wind Turbine ... - CiteSeerX

IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 24, NO. 3, SEPTEMBER 2009

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Maximum Power Tracking Control for a Wind Turbine System Including a Matrix Converter S. Masoud Barakati, Member, IEEE, Mehrdad Kazerani, Senior Member, IEEE, and J. Dwight Aplevich, Member, IEEE

Abstract—This paper focuses on maximum wind power extraction for a wind energy conversion system composed of a wind turbine, a squirrel-cage induction generator, and a matrix converter (MC). At a given wind velocity, the mechanical power available from a wind turbine is a function of its shaft speed. In order to track maximum power, the MC adjusts the induction generator terminal frequency, and thus, the turbine shaft speed. The MC also adjusts the reactive power transfer at the grid interface toward voltage regulation or power factor correction. A maximum power point tracking (MPPT) algorithm is included in the control system. Conclusions about the effectiveness of the proposed scheme are supported by analysis and simulation results. Index Terms—Matrix converter (MC), maximum power tracking, wind turbine.

NOMENCLATURE a Ar B Cp fi , fo ii , ij Ir J JT , JG KVF , kW Ks Li , Ri , Ci Lo , Ro ngear PGrid , QGrid Pm ech loss Popt PT q, qrated rs , rr

Parameter for adjusting matrix converter (MC) input displacement power factor (PF). Area covered by wind turbine rotor (Ar = πR2 ). Damping coefficient. Performance coefficient (or power coefficient). Input and output frequencies of MC. MC input and output currents (i = a, b, c and j = A, B, C). Rotor current of induction generator. Total shaft moment of inertia. Rotor inertia of wind turbine and generator. Constant V /f coefficients. Stiffness coefficient. MC input filter inductance, resistance, and capacitance. MC output inductance and resistance. Gearbox gear ratio. Grid active and reactive powers. Mechanical losses. Maximum power or optimal power. Wind turbine mechanical power. MC output-to-input voltage gain and its rated value. Stator and rotor resistances.

Manuscript received April 1, 2008. First published June 16, 2009; current version published August 21, 2009. Paper no. TEC-00196-2008. The authors are with the Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada (e-mail: [email protected]; [email protected]; aplevich@ ece.uwaterloo.ca). Digital Object Identifier 10.1109/TEC.2008.2005316

Fig. 1.

Block diagram of the proposed wind energy conversion system.

R Sij T G , TC TT , Topt vi , vj Vs Vw β λ ρ ωG , ω T ωe , ωe rated ωP o p t ωr ωr o p t ωs ωs o p t

Turbine rotor radius. Switching function (i = a, b, c and j = A, B, C). Torque and counter torque of generator. Turbine torque and optimal turbine torque. MC input and output voltages (i = a, b, c and j = A, B, C). Generator terminal voltage. Wind velocity. Rotor blade pitch angle in radian. Tip-speed-ratio (= ωT × R/Vw ) Air density in kilogram cubic meter. Generator and turbine shaft speeds. Stator angular electrical frequency and its rated value. Angular speed at the maximum power. Shaft speed on high- or low-speed gearbox side. Rotor angular speed frequency at maximum power. Synchronous speed. Synchronous frequency at maximum power. I. INTRODUCTION

VARIABLE-SPEED wind-turbine configuration including an induction generator and a matrix converter (MC) was proposed in [1] and [2] by the authors of this paper. The system consists of a wind turbine, a gearbox, a squirrel-cage induction generator (SCIG), and an MC, as shown in Fig. 1. The SCIG is a low-cost and robust electric machine, and the industry has much experience with it. In addition, the induction generator has high reliability and good mechanical properties for wind turbines, such as slip and a degree of overload capability. These are the main reasons for choosing this type of generator in the proposed system. The wind turbine is followed by a gearbox that steps up the shaft speed, since an induction generator has a low efficiency at low speeds.

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Fig. 2.

IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 24, NO. 3, SEPTEMBER 2009

Block diagram of the overall wind turbine system model and the interactions between different components.

The MC, as an electronic power converter, interfaces the SCIG with the grid and implements shaft speed control. In the proposed system, the MC input is connected to the grid and the generator terminals are connected to the MC output. MC provides four-quadrant direct ac/ac conversion, and is considered to be an emerging alternative to the conventional two-stage ac/dc/ac converter. An MC is highly controllable and allows independent control of the output voltage magnitude, frequency, and phase angle, as well as the input power factor. Compared with the dc-link ac/ac converter system, the main advantage of an MC is elimination of a dc-link, including bulky capacitors [3]. However, the following drawbacks have been attributed to matrix converters: the voltage gain is limited to 0.866, the input filter design is complex, and because of the absence of a dc-link capacitor, ride-through capability and decoupling between input and output do not exist [3], [4]. A more detailed comparison of MCs with a conventional two-stage ac/dc/ac converter can be found in [5]. The closed-loop controller adjusts the MC control inputs in order to improve the system’s steady-state and transient performances. The controller implements a maximum power point tracking (MPPT) method to control the shaft speed and maximize the power captured from the wind. To design a controller for the proposed scheme, a dynamic model of the system is required. An overall dynamic model of the system that describes aerodynamic power conversion, drive train, MC, and SCIG was developed in [6]. This paper focuses on a maximum wind power extraction algorithm for the proposed wind energy conversion system. A literature survey has identified three common MPPT techniques, namely, wind speed measurement (WSM) [7], perturbation and observation (P&O) [1], and power signal feedback (PSF) [8]. In the WSM method, both wind velocity and shaft speed should be measured. Also, the ratio of the turbine blade speed to the wind velocity (tip-speed-ratio) must be determined. There are two drawbacks of implementing the WSM method [9]. First, obtaining accurate value of the wind velocity is complicated and increases the system cost. Second, the optimal tip speed ratio is dependent on the wind energy system characteristics. The P&O method does not require prior knowledge of the maximum wind turbine power at different wind velocities and electric machine parameters [1], [10]. The P&O method is suitable for wind

turbines with small inertia, but not for medium- and large-inertia wind turbine systems, since the P&O method adds delay [9]. To implement PSF control, the controller should have the wind turbine maximum power curve (maximum power versus shaft speed). The maximum power is then tracked by shaft speed control. No wind velocity measurement is required in this method [8], [9], [11]. In this paper, a mechanical speed-sensorless PSF method is adopted for the wind turbine system and integrated into an output feedback controller. The method has the capability of providing a power reference for the controller corresponding to maximum power point without measuring the turbine shaft speed. In the next section, the wind turbine system model is introduced. Section III is dedicated to design of the closed-loop controller. Two maximum wind power extraction methods, i.e., P&O and speed-sensorless power signal feedback, are adopted for the system under study in Section IV. Finally, simulation results and conclusions are presented in Sections V and VI, respectively. II. WIND TURBINE SYSTEM DYNAMIC MODEL The overall structure of the wind turbine system model is illustrated in Fig. 2. The figure shows model blocks for wind speed, wind turbine aerodynamics, mechanical components, generator, matrix converter, and utility grid. In the following, the model will be briefly described; the details were presented in [2] and [6]. The aerodynamic model gives a nonlinear formula for the mechanical torque on the wind turbine shaft as follows: TT =

PT 1 = ρAr Cp (β, λ)Vw3 . ωT 2ωT

(1)

The power coefficient Cp can be expressed as a function of λ and β as follows [2], [6]: Cp (λ, β) = (0.44 − 0.0167β) sin (θC p ) − 0.00184(λ − 3) β (2) where θC p = π(λ − 3)/(15 − 0.3β). The mechanical system is essentially a two-mass model of shaft dynamics, consisting of a large and a small mass, corresponding to JT and JG , respectively (see Fig. 2). The low-speed shaft is modeled as inertia, a spring, and a damper, although normally infinite stiffness can be assumed. An ideal gearbox of gear

BARAKATI et al.: MAXIMUM POWER TRACKING CONTROL FOR A WIND TURBINE SYSTEM INCLUDING A MATRIX CONVERTER

Fig. 3.

Inputs, state variables, and outputs of the wind turbine model.

ratio 1:ngear is included between the low-speed and high-speed shafts. The drive train converts the aerodynamic torque TT on the low-speed shaft to the torque TG on the high-speed shaft (with generator shaft speed of ωG ). The dynamics of the drive train can be described by three differential equations [2], [6]. To model the induction generator, a commonly used method based on flux linkages can be employed [12]. The machine is described by four differential equations in the dq frame [2], [6]. A constant V /f strategy, which is applied to the speed control of the induction generator to avoid core saturation, is taken into account in the modeling. The MC topology is composed of an array of nine bidirectional switches connecting each phase of the input to each phase of the output, as shown in Fig. 2 [13]. The two circuits connected to the input and output terminals of the MC are operated at two different frequencies, fi and fo . An MC contains no energy-storage elements and thus has no dynamics. However, the impedances of connecting wires and input filters should be considered in a complete dynamic model. A filter must be used at the input of the MC to reduce the switching harmonics in the input current. In this paper, a simple LC filter is used, which is the best solution for MC from the viewpoints of cost and size [3], [14]. The dynamic model of the MC can be described by six nonlinear differential equations [6], [13]. Note that in Fig. 2, the wind model is not a component of the dynamic system, and the wind turbine output power calculation requires knowledge of instantaneous wind speed [6]. By combining the state equations of the building blocks of the wind turbine system (excluding the wind speed model), the overall model of the system can be described by 11 nonlinear equations. Fig. 3 shows the structure as well as the input and output variables of the dynamic model. The model is characterized by six inputs u ¯, two outputs y¯, and 11 state variables x ¯. Four out of six input variables, i.e., ωe , q, a, and αo are the electrical set points of the MC [2]. The parameter a is used to construct the transformation matrix of the MC from the weighted sum of two matrices containing cosine of sum and difference of input and output frequencies [2], [12]. This allows for the adjustment of the input displacement power factor. The MC output voltage angle (αo ) is not used as a control variable due to the existence of sufficient control variables for the intended operations. Wind

Fig. 4.

Wind turbine small-signal model.

Fig. 5.

Block diagram of the wind turbine closed-loop system.

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velocity Vw is an uncontrollable input. Pitch angle, which is used for stall control against wind gust, is assumed constant in this study. The active and reactive powers injected into the grid, PGrid and QGrid , are chosen as the output variables for the model. As mentioned before, the terminal voltage and frequency of the induction generator are usually controlled according to a constant V /f strategy to avoid flux saturation. The constant ratio can be defined as follows: qrated . (3) KVF = ωe rated To take the constant V /f strategy into account, the state equations of the overall model are modified using (3), and the resulting dynamic model is used in closed-loop control design. For controller design, the nonlinear dynamic equations of the model are linearized around an operating point given in the Appendix. Small-signal analysis, based on the small-signal model of Fig. 4, shows that the linearized model is stable at the operating point. The open-loop step response of the model shows undershoot that is attributed to nonminimum-phase behavior. III. CLOSED-LOOP CONTROLLER The controller design objective is to track reference signals for active and reactive powers delivered to the grid. A sequential loop closure (SLC) method is used to design a controller for the system [15]. In the first stage of the SLC method, the system transfer function is converted to a triangular form. From small-signal analysis, it was noticed that there is a weak coupling between the second input ∆a and the first output ∆PGrid . By ignoring the input2–output1 cross-channel coupling, the multipleinput–multiple-output (MIMO) transfer function of the system in Fig. 4 can be written as follows: 


G22 u2 G12 y2 = . (4) y1 G21 ≈ 0 G11 u1 Using the SLC method, two controllers C11 and C22 should be designed for the system with the transfer function (4), as shown in Fig. 5. The SLC controller design starts with focusing on the first channel’s transfer function G11 . The open-loop step response of the first channel is similar to that of a second-order system for which a proportional-integral (PI) controller is a suitable choice. The PI controller will eliminate the steady-state

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Fig. 7. P&O method. (a) Turbine power versus shaft speed and principle of the P&O method. (b) Block diagram of the P&O control in wind turbine.

Fig. 6.

where ωP o p t is given by [6]   15 − 0.3β Vw ωP o p t = cos−1 R π    0.00184β(15 − 0.3β) + 3 . (8) π0.5ρ2 VW2 (0.44 − 0.0167β

Wind turbine mechanical output power versus shaft speed.

step error. The transfer function of controller C11 is chosen as C11 =

(6.83s − 6.2) × 10−4 . s

(5)

In the next stage of the SLC method, controller C22 is designed for the transfer function G22 . The influence of the first feedback loop must be considered as a disturbance for this feedback loop. The objective in designing C22 is to have a good tracking performance and disturbance rejection. To achieve this, the controller must have a high gain at the frequencies, where tracking the reference and rejecting the disturbance are desired. However, a high-gain controller magnifies the sensor noise and causes poor stability robustness at the frequencies with significant uncertainty [15]. Tracking and disturbance rejection should be considered at low frequencies, and noise rejection and stability robustness at high frequencies. The C22 controller is designed using the MATLAB SISOTOOL toolbox environment. The transfer function G22 has a zero in the right-half plane that imposes an upper limit on the control-loop bandwidth. The C22 controller includes an integrator to get perfect steady-state step tracking. The transfer function of controller C22 is chosen as C22 =

40s − 3920 . s(s2 + 16900s + 1.94 × 108 )

(6)

IV. MAXIMUM POWER POINT TRACKING A. Wind Turbine Mechanical Maximum Power Curve The wind turbine mechanical output power PT is affected by the ratio of the turbine shaft speed and the wind velocity, i.e., tip speed ratio (λ = RωT /VW ). As a result of variations in wind velocity, the turbine shaft speed ωT (or generator shaft speed ωG ) and wind turbine power PT will change. Fig. 6 shows a family of typical PT versus ωr curves for different wind velocities for a typical system. As seen in this figure, different power curves have different maximum power, or optimal power Popt , which can be calculated as follows: Popt = PT (ωP o p t )

(7)

Optimal operating conditions can be achieved by employing an MPPT method. In the following section, two MPPT methods are adopted for the wind turbine under study. B. Perturbation and Observation Method The P&O or hill-climb searching (HCS) method is based on perturbing the turbine shaft speed in small steps and observing the resulting changes in turbine mechanical power [1], [9]. The concept and schematic diagram of the P&O method are shown in Fig. 7. The details of the P&O method are presented in [1]. To implement the P&O method, one can check the signs of ∆ωT and ∆PT /∆ωT . The shaft speed is either incremented ∆ωT > 0 in small steps as long as ∆PT /∆ωT > 0, or decremented ∆ωT < 0 in small steps as long as ∆PT /∆ωT < 0. This is continued until the maximum power point is reached, i.e., ∆PT /∆ωT = 0. If incrementing the shaft speed results in ∆PT /∆ωT < 0 or decrementing shaft speed results in ∆PT /∆ωT > 0, the direction of shaft speed change must be reversed [1]. The advantage of the P&O method is that it neither requires prior knowledge of maximum wind turbine power at different wind velocities, nor electrical machine parameters [1], [16]. However, the P&O method is suitable for systems with small inertia (small time constant) [9], such as solar energy conversion systems with no inertia, or low-power, low-inertia wind turbine systems [17]. For medium- and large-inertia wind turbine systems, the turbine speed cannot follow changes in wind velocity quickly, so the P&O method (without any other controller) will not be able to control the wind turbine system properly. C. PSF Control Method The block diagram of a wind energy system with PSF control is shown in Fig. 8. In this method, first, the maximum power curve of the wind turbine (see Fig. 6) is obtained from experimental results. Then, the wind turbine speed and maximum output power data are recorded in a lookup table [9], [18]. The PSF method is independent of the wind velocity measurement. However, the difficulty of obtaining the maximum power curve of the wind turbine is a barrier. Moreover, measuring the mechanical shaft speed and wind turbine output power is

BARAKATI et al.: MAXIMUM POWER TRACKING CONTROL FOR A WIND TURBINE SYSTEM INCLUDING A MATRIX CONVERTER

Fig. 8.

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Block diagram of a wind energy system with PSF control.

Fig. 10.

Wind turbine torque versus shaft speed at different wind velocities.

Fig. 9. Block diagram of mechanical shaft speed-sensorless PSF control system, “M” at I.G. terminals represents the power measurement instrument.

another drawback of the PSF method. In the following, a mechanical speed-sensorless PSF method is implemented in the wind turbine system to overcome the mechanical shaft speed measurement requirement. D. Mechanical Speed-Sensorless PSF Control The mechanical speed-sensorless PSF method has the capability of providing a power reference for the controller of Fig. 5 corresponding to maximum power point without measuring the turbine shaft speed. This is the significant advantage of this method [8], [19]. Fig. 9 shows the block diagram of a mechanical shaft speedsensorless PSF control system. In this method, a lookup table containing synchronous speeds of the induction generator (ωs ) corresponding to the optimal generator powers (Pgen opt ) is used. As the wind velocity keeps changing with time, the wind turbine must keep adjusting its speed to track the optimum wind turbine speed. In the following, the details of the mechanical sensorless PSF method are presented. In the system under study, the generator is connected to the turbine through a gearbox with gear ratio ngear . Based on the turbine power versus turbine shaft speed (PT versus ωT ) curves of Fig. 6, the torque versus shaft speed on the generator side (Tg versus ωG ) characteristics are shown in Fig. 10. In this figure, the quadratic optimal torque curve, Topt versus ωG , is drawn based on the following: Topt =

Popt . ωP o p t

(9)

The dynamic behavior of the turbine and the induction generator can be described as follows: dωr (10) T T − Tc = J dt where TC (= −TG ).

Fig. 11. Maximizing captured wind power by shifting T C –ω r curve with respect to T T –ω r curve.

Maximum power production for any wind velocity is achieved when the generator’s counter torque equals the optimal turbine torque (Topt ). The shaft speed at equilibrium can be found graphically as the intersection of turbine torque–speed curve with generator torque–speed curves, as illustrated in Fig. 11. In this figure, the PT –ωr and TT –ωr curves of the wind turbine, as well as a family of Tc –ωr curves for the induction generator for different generator synchronous speeds (ωs ) are shown. By varying the output frequency of the matrix converter ωe , and thus, the induction generator synchronous speed ωs , the Tc –ωr curve can be shifted to the right or left with respect to the wind turbine torque–speed curve to obtain a wide range of possible steady-state operating points defined by the intersections of the two curves. Obviously, one of the operating points corresponds to maximum power. To move from one operating point to another, ωe is changed in steps (small enough to maintain generating mode), and the difference between the wind turbine torque TT and the new generator counter torque Tc at the operating speed will accelerate or decelerate the shaft according to (10) until the new steady-state operating point is reached.

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a) Accelerating Shaft Toward Maximum Power Point: In Fig. 11, OPopt is the operating point corresponding to maximum power captured from the wind at the wind velocity VW . At this point, PT = 1 per unit (p.u.), TT = 1 p.u., and ωr = ωr o p t = 1 p.u. Assuming the present operating point to be OP1 , corresponding to ωs1 , the shaft should speed up so that the operating point OPopt can be reached at. This can be achieved by increasing ωs from ωs1 to ωs o p t through an increase in the induction generator terminal frequency. The frequency adjustment is performed in steps small enough for the induction machine to keep operating as a generator throughout the transition period. This action makes TT − Tc > 0 and accelerates the shaft according to (10) toward maximum power point. b) Decelerating Shaft Toward Maximum Power Point: Assuming the present operating point to be OP2 , corresponding to ωs2 , the shaft should slow down so that the system assumes the operating point OPopt . This can be accomplished by decreasing ωs from ωs2 to ωs o p t through a decrease in the induction generator terminal frequency and voltage according to the constant V /f strategy, in steps small enough to restrict operation within the stable generating region. This action makes TT − Tc < 0 and decelerates the shaft according to (10) toward maximum power point. E. Finding the Lookup Table in the Speed-Sensorless Method In the following, a formula for Popt versus ωs curve will be derived and the corresponding data of the curve will be entered in the lookup table of Fig. 9. The generator torque is a function of its terminal voltage Vs , terminal frequency ωs , and rotor angular speed ωr

Fig. 12.

Stages of finding the lookup table.

the system mechanical speed sensorless, because there is no need to measure the mechanical speed ωr . The lookup table of Fig. 9 is the data of Pgen opt versus ωs o p t curve, which can be obtained easily from Topt versus ωs o p t curve. The optimal turbine power is Popt (ωr o p t ) = Topt (ωr o p t )ωr o p t . Finally, Pgen

opt

(15)

can be calculated as

In order to satisfy the constant V /f strategy, the voltage magnitude of the induction generator should be varied linearly with synchronous frequency as follows:

− 3rs Is2 − 3rr Ir2 (16) where 3rs Is2 and 3rr Ir2 are copper losses in the stator and rotor, respectively. It is worth noting that the currents Is and Ir can be obtained from the induction machine equivalent circuit. The flowchart of Fig. 12 shows the stages of finding the lookup table for implementing the speed-sensorless PSF method.

Vs (ωs ) = kW ωs

V. SIMULATION RESULTS

TG = f (Vs , ωs , ωr ).

(11)

(12)

where kW can be found from the steady-state induction machine equivalent circuit. Substituting (12) in (11), the generator torque can be written as a function of ωs and ωr TG = f (ωs , ωr ).

(13)

At the shaft speed ωr , the optimal torque corresponding to maximum power can be found from the Topt versus ωr curve of Fig. 6. The system is at the maximum power point if the induction generator counter torque is equal to Topt (ωr ) = −TG = −

3rr |Ir |2 . ωs − ωr

(14)

Using (14), for a given optimal turbine torque and mechanical shaft speed (ωr = ωr o p t ), the corresponding generator synchronous speed (ωs = ωs o p t ) can be determined. In other words, by solving (14), it is possible to plot the Topt versus ωs o p t curve. Employing this curve instead of Topt versus ωr o p t curve makes

Pgen

opt (ωs o p t )

= Popt (ωr o p t ) − Pm ech

loss

A. Implementing the P&O Method for a Small Wind Turbine System Including a Matrix Converter To evaluate the P&O method, a low-inertia version of the wind turbine system under study is considered. The system parameters for a small wind turbine are shown in the Appendix. To assess the capability of the P&O method for MPPT at varying wind velocity, a step change is applied to the wind velocity. The system is first operating at the wind velocity Vw 1 = 8 m/s. At this velocity, the optimal power is 37 kW. At t = 1.8 s, the wind velocity is decreased to 6 m/s. The optimal power corresponding to this velocity is 15 kW. Again, at t = 2.5 s, the wind velocity is increased back to 8 m/s. Fig. 13 illustrates successful tracking of maximum power using the P&O method following the changes made to the wind velocity. Fig. 14 shows the variations in the MC output frequency set point that result in the necessary changes in the induction generator terminal frequency and thus the shaft speed, in attempt to track the maximum power point. It has to be noted that the magnitude of the induction generator terminal

BARAKATI et al.: MAXIMUM POWER TRACKING CONTROL FOR A WIND TURBINE SYSTEM INCLUDING A MATRIX CONVERTER

Fig. 15. Fig. 13.

PT

o p t (ω s )

and P G rid

o p t (ω s )

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curves.

Maximum power point tracking control with the P&O method. TABLE I PARAMETERS OF THE WIND TURBINE SYSTEM AT THE OPERATING POINT

TABLE II MAXIMUM POWER AT DIFFERENT WIND VELOCITIES

Fig. 14. Frequency set point variations during maximum power point tracking with the P&O method.

voltage has been varied with frequency according to the constant V /f strategy. B. Implementing the Mechanical Speed-Sensorless PSF Method on the Wind Turbine System Under Study In this section, simulation results of the wind turbine system under study including the mechanical speed-sensorless PSF controller are presented. The parameters of the wind turbine system are given in the Appendix. In the wind turbine system under study, it is easier to measure the grid power instead of power at the generator output terminals. Therefore, for implementing the speed-sensorless PSF method on the system, the grid optimal power PGrid opt should be entered in the lookup table. The PGrid opt (ωs ) curve can be calculated based on subtracting MC active losses from Pgen opt at each ωs . Fig. 15 shows the PT opt versus ωs and PGrid opt versus ωs curves for the system under study. The system is originally stable at an operating point with the wind velocity of 10 m/s before applying the MPPT method. Table I shows the input and output parameters of the system at

the operating point. Positive sign for power implies that power flows toward the grid. In the following simulation, the mean wind velocity is changed to evaluate the MPPT method adopted. Table II shows the maximum mechanical wind power and the grid active power reference for three different wind mean velocities. The controller should follow the maximum power at each wind mean velocity. In Table II, the discrepancy between the wind turbine and grid maximum power values is because of the total system losses. Fig. 16 depicts the response of grid active power to step changes in wind velocity. Originally, the MMPT algorithm has stabilized the system at a maximum power point corresponding to wind velocity of 10 m/s. Mean wind velocity is then increased to 12 m/s at t = 30 s, decreased to 11 m/s at t = 60 s, and finally decreased to 10 m/s at t = 90 s. The wind turbine system successfully tracks the maximum power corresponding to different wind velocities. At the same time, the grid reactive power is kept constant by the MC at QGrid ref , as shown in Fig. 17. Fig. 18 illustrates the synchronous speed of the generator that is adjusted by the MC in response to the wind velocity variations. In the previous simulations, the wind velocity was considered to be a constant signal with step changes. In the following,

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Fig. 16.

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Tracking P G rid

opt

corresponding to different wind velocities.

Fig. 19. Evaluating the system equipped with speed-sensorless PSF control using the instantaneous wind model.

figure, the mean value of the instantaneous wind velocity is increased from 10 to 11 m/s at t = 20 s. In each instance, the system follows the wind velocity variations, and the controller leads the system toward the maximum power point based on the mean wind velocity. The simulation results show the capability of the mechanical speed-sensorless PSF control method in tracking the maximum power point at different wind velocities. However, accuracy of the method depends on the accuracy and resolution of the data obtained for the lookup table. Fig. 17.

Grid reactive power during the maximum power point tracking.

VI. CONCLUSION An MPPT method for the wind turbine system including an MC is presented in this paper. The controller equipped with the MPPT algorithm controls the shaft speed to maximize the power captured from the wind. This is possible by adjusting the MC output frequency according to the constant V /f strategy. The controller also adjusts the MC variables to control the reactive power transfer at the grid interface to regulate the power factor. Two MPPT methods, P&O and PSF, are explained. The P&O method is suitable only for low-inertia wind turbine systems, and the PSF method relies on the measurement of shaft speed. An improved power signal feedback method, called mechanical speed-sensorless PSF, is proposed for the wind turbine system under study that neither requires a wind velocity sensor nor a shaft speed sensor. Simulation results show successful tracking of maximum power at varying wind velocities.

Fig. 18.

Induction generator terminal frequency.

the speed-sensorless PSF control method is evaluated using an instantaneous wind velocity model. The wind velocity signal (VW ) and the grid active response (PGrid ), as well as the optimal synchronous speed, are depicted in Fig. 19. As shown in this

APPENDIX Parameters of the Main Wind Turbine System Wind turbine: JT = 100 kg·m2 , Ks = 2 × 106 N·m/rad, B = 5 × 103 N·m/rad/s, ngear = 20, ρair = 1.25 kg/m3 , R = 10 m. Induction generator: 500 hp, 2.3 kV, 1773 r/min,

BARAKATI et al.: MAXIMUM POWER TRACKING CONTROL FOR A WIND TURBINE SYSTEM INCLUDING A MATRIX CONVERTER

TB = 1.98 × 103 N·m, IB (ab c) = 93.6 A, rs = 0.262 Ω, Xls = 1.206 Ω, XM = 54.02 Ω, Xlr = 1.206 Ω, rr = 0.187 Ω, J = 11.87 kg·m2 , P = 4 Poles, Pm ech loss = 1%Prated . MC and grid: Ri = Ro = 0.1 Ω, li = llo = 1 mH, C = 0.1 mF, VG = 4 kV, fe = 60 Hz. Wind model: VW = 10 m/s, L = 180 m, σ = 2, τ = 0.4 s. Parameters of the Small Wind Turbine System Wind turbine: JT = 10 kg·m2 . Induction generator: 0.4 kV, 60 Hz, rs = 0.294 Ω, Ls = 1.39 mH, LM = 41 mH, Lr = 0.74 mH, rr = 0.156 Ω, J = 4 kg·m2 , P = 6 Poles, Pm ech loss = 1%Prated . MC and grid: Ri = Ro = 0.0001 Ω, li = llo = 0.01 mH, C = 0.001 mF, VG = 0.4 kV. The other parameters have been defined in the main wind turbine. REFERENCES [1] S. M. Barakati, M. Kazerani, and X. Chen, “A new wind turbine generation system based on matrix converter,” in Proc. IEEE PES Gen. Meet., 2005, pp. 2083–2089. [2] S. M. Barakati, J. D. Aplevich, and M. Kazerani, “Controller design for a wind turbine system including a matrix converter,” in Proc. IEEE PES Gen. Meet., 2007, pp. 1–8. [3] P. W. Wheeler, J. Rodr´ıguez, J. Clare, L. Empringham, and A. Weinstein, “Matrix converters: A technology review,” IEEE Trans. Ind. Elctron., vol. 49, no. 2, pp. 276–289, Apr. 2002. [4] P. W. Wheeler, J. C. Clare, M. Apap, L. Empringham, C. Whitley, and G. Towers, “Power supply loss ride-through and device voltage drop compensation in a matrix converter permanent magnet motor drive for an aircraft actuator,” in Proc. Power Electron. Spec. Conf. (Conf. PESC 2004), vol. 1, pp. 149–154. [5] L. Helle, K. B. Larsen, A. H. Jorgensen, S. Munk-Nielsen, and F. Blaabjerg, “Evaluation of modulation schemes for three-phase to threephase matrix converters,” IEEE Trans. Ind. Electron., vol. 51, no. 1, pp. 158–171, Feb. 2004. [6] S. M. Barakati, “Modeling and controller design of a wind energy conversion system including a matrix converter,” Ph.D. dissertation, Dept. Electr. Comp. Eng., Univ. Waterloo, Waterloo, ON, Canada, 2008. [7] T. Thiringer and J. Linders, “Control by variable rotor speed of a fixedpitch wind turbine operating in a wide speed range,” IEEE Trans. Energy Convers., vol. EC-8, no. 3, pp. 520–526, Sep. 1993. [8] W. Lu and B. T. Ooi, “Multiterminal LVDC system for optimal acquisition of power in wind-farm using induction generators,” IEEE Tran. Power Electron., vol. 17, no. 4, pp. 558–563, Jul. 2002. [9] Q. Wang and L. Chang, “An intelligent maximum power extraction algorithm for inverter-based variable speed wind turbine systems,” IEEE Trans. Power Electron., vol. 19, no. 5, pp. 1242–1249, Sep. 2004. [10] E. Koutroulis and K. Kalaitzakis, “Design of a maximum power tracking system for wind-energy-conversion applications,” IEEE Trans. Ind. Electron., vol. 53, no. 2, pp. 486–494, Apr. 2006. [11] R. Chedid, F. Mard, and M. Basma, “Intelligent control of a class of wind energy conversion system,” IEEE Trans. Energy Convers., vol. EC-14, no. 4, pp. 1597–1604, Dec. 1999. [12] B. Ozpineci and L. M. Tolbert, “Simulink implementation of induction machine model-a modular approach,” in Proc. Elect. Mach. Drives Conf. (IEMDC 2003), vol. 2, pp. 728–734. [13] S. M. Barakati, M. Kazerani, and J. D. Aplevich, “An overall model for a matrix converter,” in Proc. IEEE Int. Symp. Ind. Electron. (ISIE 2008), pp. 13–18. [14] P. Wheeler, H. Zhang, and D. Grant, “A theoretical and practical consideration of optimized input filter design for a low loss matrix converter,” in Proc. Inst. Electr. Eng. PEVD Conf., Sep. 1994, pp. 363–367. [15] D. Davison, Multivariable Control Systems, Course Notes-Part B. Waterloo, ON: Univ. Waterloo, 2005. [16] T. Thiringer and J. Linders, “Control by variable rotor speed of a fixedpitch wind turbine operating in a wide speed range,” IEEE Trans. Energy Convers., vol. EC-8, no. 3, pp. 520–526, Sep. 1993.

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[17] E. Koutroulis, K. Kalaitzakis, and N. C. Voulgaris, “Development of a microcontroller-based, photovoltaic maximum power point tracking control system,” IEEE Trans. Power Electron., vol. 16, no. 1, pp. 46–54, Jan. 2001. [18] R. Chedid, F. Mard, and M. Basma, “Intelligent control of a class of wind energy conversion system,” IEEE Trans. Energy Convers., vol. EC-14, no. 4, pp. 1597–1604, Dec. 1999. [19] G. Poddar, A. Joseph, and A. K. Unnikrishnan, “Sensorless variable-speed controller for existing fixed-speed wind power generator with unity-powerfactor operation,” IEEE Trans. Ind. Electron., vol. 50, no. 5, pp. 1007– 1015, Oct. 2003.

S. Masoud Barakati (S’04–M’08) received the B.Sc. degree from Ferdowsi University of Mashhad, Mashhad, Iran, in 1993, the M.Sc. degree from Tabriz University, Tabriz, Iran, in 1996, and the Ph.D. degree from the University of Waterloo, Waterloo, ON, Canada, in 2008, all in electrical engineering. From 1996 to 2003, he was a Lecturer in the Department of Electrical Engineering, S&B University, Iran. He is currently a Postdoctoral Fellow in the Department of Electrical and Computer Engineering, University of Waterloo. His current research interests include power electronic circuits, control systems, and renewable energy.

Mehrdad Kazerani (S’88–M’96–SM’02) received the B.Sc. degree in electrical and electronics engineering from Shiraz University, Shiraz, Iran, in 1980, the M.Eng. degree from Concordia University, Montreal, QC, Canada, in 1990, and the Ph.D. degree from McGill University, Montreal, in 1995, both in electrical engineering. From 1982 to 1987, he was with the Energy Ministry of Iran. He is currently an Associate Professor in the Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, Canada. His current research interests include power electronic circuits and systems design, power quality/active power filters, matrix converters, distributed power generation, utility interface of alternative energy sources, battery electric, hybrid electric and fuel cell vehicles, and Flexible AC Transmission Systems (FACTS). Dr. Kazerani is a Registered Professional Engineer in the province of Ontario.

J. Dwight Aplevich (M’69–LM’09) received the B.E. degree in electrical engineering science from the University of Saskatchewan, Saskatoon, SK, Canada, in 1964, and the Ph.D. degree in communications and electronics from Imperial College, London, U.K., in 1968. He is currently a Professor Emeritus with the University of Waterloo, Waterloo, ON, Canada, where he was a Professor of electrical and computer engineering, and also the Associate Dean of the Faculty of Engineering and the Associate Dean of Graduate Studies. He has held extended visiting positions at the Imperial College London, the Universit´e Paul Sabatier Toulouse, Lund University, the Ecole Polytechnique de Montr´eal, the University of Texas, Arlington, and the Vancouver Innovation Centre of the National Research Council. His current research interests include the theory of implicit system models, identification, computational aspects of control theory, and applications. Prof. Aplevich is a Registered Professional Engineer in the province of Ontario.