Improved direct torque control of an induction

ISA Transactions 52 (2013) 525–538

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Research Article

Improved direct torque control of an induction generator used in a wind conversion system connected to the grid Radia Abdelli a, Djamila Rekioua a,n, Toufik Rekioua a, Abdelmounaïm Tounzi b a b

Laboratoire de Technologie Industrielle et de l'Information, Bejaia University, 06000, Algeria Laboratory of elctrotechnics and Power Electronics of Lille, L2EP, France

art ic l e i nf o

a b s t r a c t

Article history: Received 22 July 2012 Received in revised form 26 March 2013 Accepted 26 March 2013 Available online 21 April 2013 This paper was recommended for publication by Dr. Ahmad B. Rad.

This paper presents a modulated hysteresis direct torque control (MHDTC) applied to an induction generator (IG) used in wind energy conversion systems (WECs) connected to the electrical grid through a back-to-back converter. The principle of this strategy consists in superposing to the torque reference a triangular signal, as in the PWM strategy, with the desired switching frequency. This new modulated reference is compared to the estimated torque by using a hysteresis controller as in the classical direct torque control (DTC). The aim of this new approach is to lead to a constant frequency and low THD in grid current with a unit power factor and a minimum voltage variation despite the wind variation. To highlight the effectiveness of the proposed method, a comparison was made with classical DTC and field oriented control method (FOC). The obtained simulation results, with a variable wind profile, show an adequate dynamic of the conversion system using the proposed method compared to the classical approaches. & 2013 ISA. Published by Elsevier Ltd. All rights reserved.

Keywords: Induction generator (IG) Modulated hysteresis direct torque control (MHDTC) Direct torque control (DTC) Field oriented control method (FOC) Wind conversion system Modulated hysteresis controller

1. Introduction Actual strategies for sustainable energy development have, as a prior objective, the gradual replacement of fossil-fuel-based energy sources by renewable energy ones. Among them wind energy conversion systems currently carry significant weight in many developed countries [1,2]. Besides, nearly all wind turbines use either induction or synchronous generators [3–6]. Induction generators are widely used in wind energy conversion systems (WECs). Doubly fed induction generators were presented, modeled and controlled in several works [7–12]. Dual stator and polyphase induction generators were also studied [13,14]. Other papers [15–22] deal with self excited induction generators (SEIG) whose main advantages are ruggedness, low cost and ease to connect either to electric grid [15–18] or to use them in standalone operations [19– 21]. In the latter case, the main control objective is to be insensitive to the generator and load parameter variations and to provide good performance despite the wind disturbances. On the other hand, in the case of grid connected systems, constant magnitudes and frequencies of currents and voltages, with a unit power factor, as well as a week harmonic distortion of these variables are required to supply the grid.

n

Corresponding author. Tel.: +213 34 21 50 90; fax: +213 34 21 51 05. E-mail address: [email protected] (D. Rekioua).

Therefore, the generator control has to take into account these constraints while being robust towards wind speed variations. To improve the use of SEIG in grid connected WECs, several papers investigated different methods to control the generator. In [17], a sensorless indirect vector control was applied to the statorside converter in order to reduce the sensitivity to the machine parameters and wind speed variations. A fuzzy logic supervisor, based on Takagi-Sugeno controllers, has been studied in [16]. It is inserted in a fixed speed WECs to smooth the generated active and reactive powers and to regulate the stator voltage. Many other research have studied the grid connected WECs involving doubly fed induction generators DFIG. Hence, direct torque/power control (DTC/DPC) were highly detailed and improved in [7,8,10]. Authors in [8,10] have investigated an improved DPC method based on the discrete space vector modulation (DSVM) allowing low THD of stator and rotor currents with fast transient response and less sensitivity to parameter variations. In [7], DTC scheme associated to the space vector modulation (SVM) theory was used. A comparative study with classical VC and conventional DPC strategies was carried out. Simulation results have shown that the proposed method maintains both transient and steady-state performances similar to those obtained by DPC and VC strategies. The use of DTC to control SEIG in WECs was not very attractive due to the low quality of current (harmonic distortion) and power

0019-0578/$ - see front matter & 2013 ISA. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.isatra.2013.03.001

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R. Abdelli et al. / ISA Transactions 52 (2013) 525–538

supplied to the grid. However, the cost and robustness of the SEIG and the simplicity of DTC compared to classical methods as FOC and VC (sensorless, simple implementation and no need of PI regulators) make the research of new strategies to improve DTC for SEIG very interesting. For decades, several control strategies of induction machines have been developed [23–30], among them, direct torque control (DTC) has been considered as a solution to many problems of classical methods such as vector control (VC) and field oriented control (FOC). Indeed, the main problem of FOC methods is the constant gains of the PI controllers which cannot compensate or reject neither machine parameter nor wind speed variations. In the case of DTC, the use of hysteresis controllers instead of classical PI regulators leads to good performances despite machine parameter or load variations. The major drawback of DTC lies in the important current distortions and torque ripples due to the variable switching frequency. In order to overcome these problems, different solutions have been proposed for motor drives [23,25–33]. Hence, in [26], authors have applied a fuzzy control strategy to the voltage vector selection in the DTC of an induction machine to improve its torque and dynamic behavior. Other works deal with the use of artificial intelligence techniques in the same context as in [27] where an adaptive neuro-fuzzy controller was used instead of the two classical flux and torque hysteresis controllers. Recently, a simple control strategy, called modulated hysteresis direct torque control (MHDTC), was applied to induction machine drives [25]. It is based on the modulated hysteresis technique to ensure a constant switching frequency [31] which leads to minimize the torque ripples and improve the current waveform. The principle of MHDTC is to superpose to the torque reference a triangular signal with an appropriate frequency and magnitude in order to ensure a fixed switching operation mode. Conventional methods of control which are based either on the use of PI regulators (FOC) or direct controls (DTC, DPC) are unable to ensure all of the grid requirements in the same time (unit power factor, sinusoidal current, less power losses, robustness towards wind perturbations, constant periodic frequency); improving some performances deteriorates the other ones. In the other papers, authors proposed solutions to just one problem without analyzing the other grid requirements. In order to gather all good performances for better control of the WECs connected to the grid, the MHDTC strategy, which was verified by simulation and experimentation, is applied in our work to control directly a SEIG in WECs connected to the grid. It allows supplying a sinusoidal current, with minimized direct voltage variations and a unit power factor, to the electrical grid.

Simulation results under Matlab/Simulink are presented and compared for three different methods (DTC, FOC and MHDTC). The remainder of this contribution is organized as follows. In Section 2, the model of the WECs is given taking into account all parts of the system starting by the turbine till the electrical grid. Section 3 introduces the FOC strategy then the DTC and MHDTC schemes with a detailed calculation of the MHDTC's parameters. Simulation results are presented, compared and analyzed in Section 4 in order to demonstrate the effectiveness of the proposed method. The paper ends with some conclusions and guidelines for further work.

2. Wind conversion system model The studied system is presented in (Fig. 1).

2.1. Wind turbine model Considering a wind average velocity v and a multiplier gain G, supposed without losses, the mechanical torque of the generator can be expressed, in a classical way, as follows: Tg ¼

1 v3 C p ðλÞρS 2 Gωt

ð1Þ

Cp-max

CP

λ

λopt

Fig. 2. Characteristic CP (λ).

Fig. 1. Wind generator based on an induction generator [32].


527

Fig. 3. Wind turbine model with the MPPT algorithm.

where S is the turbine section (S ¼ πR2 ), ρ represents the air density, Cp(λ) is the performance coefficient, λ is defined as: λ¼

The basic principle of dynamics gives:

ωt R v

ð2Þ

where λ is the tip-speed ratio, ωt (rad/s) is the turbine angular speed and R is the blade radius. The characteristic CP (λ), given by the turbine manufacturer, is of a parabolic form for the pitch angle β¼0 with a maximal value CP−max for λopt. The generator speed is then controlled thanks to an algorithm allowing the maximum extraction of the power (MPPT: Maximum Power Point Tracking [33,34]). This one requires the measure or estimation of the wind speed knowing that to a given wind speed v corresponds an optimal tip-speed ratio λopt and then a maximal power (Fig. 2). In this case, the electromagnetic torque reference Te−ref can be expressed as: T e−ref ¼

2.3. Transmission elements model

C P−max ρ R5 2 π :ωm λ3opt 2 G3

ð3Þ

where ωm is the mechanic generator speed

2.2. Speed multiplier model The speed multiplier is used to adapt the turbine rotation speed ωt to the generator one. It is described by the two following equations: Tt ¼

Tg G

ð4Þ

ωt ¼

ωm G

ð5Þ

where Tt and Tg are respectively the turbine and generator torques.

T e−ref −T g ¼ J

dωm þ f ωm dt

ð6Þ

where f and J are the friction coefficient and the system moment of inertia respectively. Fig. 3 presents the model of the mechanic system composed of the wind turbine and the speed multiplier with the MPPT algorithm: 2.4. Induction generator model The model of the induction generator, expressed in d−q frame, is given by the following voltage system equations: 8 > V ds ¼ Rs ids þ dϕdtds −ωs ϕqs > > > > > < V qs ¼ Rs iqs þ dϕqs þ ωs ϕds dt ð7Þ > 0 ¼ Rr idr þ dϕdtdr −ωr ϕqr > > > > > : 0 ¼ Rr iqr þ dϕqr þ ωr ϕ dr dt where Rs,Rr,ωs,ωr are phase resistances and electrical variable pulsations respectively. (Vds,Vqs)(ids,iqs)(idr,iqr)(Фds,Фqs)(Фdr,Фqr) represent the park components of voltages, currents and fluxes along d and q axes respectively. The subscripts s and r are related to the stator or rotor quantities. The flux equations are given by: 8 ϕds ¼ ℓs ids þ midr > > > > < ϕqs ¼ ℓs iqs þ miqr ð8Þ ϕ ¼ ℓr idr þ mids > > > dr > : ϕqr ¼ ℓr iqr þ miqs ℓs and ℓr are the stator and rotor phase leakage inductances respectively, m is the stator-rotor mutual inductance.

528


Fig. 4. Direct bus and power control.

and

2.5. Rectifier model and control The AC/DC rectifier model is expressed by the two following equations: 0 1 0 10 1 Va Sa −2 1 1 V BV C CB C dc B ð9Þ @ bA¼ @ 1 −2 1 A@ Sb A 3 Vc Sc 1 1 −2

in ¼ F 1 in1 þ F 2 in2 þ F 3 in3

ð13Þ

F1, F2, F3 are logic functions according to the switch states given by the grid link control (Fig. 5) and in1, in2, in3, are the three phase currents supplied to the grid.

2.7. Inverter and grid link control idc ¼ Sa ia þ Sb ib þ Sc ic

ð10Þ

With Vdc and idc are the direct bus voltage and current respectively. (Sa,Sb,Sc)are the logic functions according to the switch states obtained by the application of either vector control, DTC or the proposed method. 2.6. Direct bus voltage model The instantaneous change in direct bus voltage Vdc is given by the capacitive current ic integration. Z 1 ic dt V dc ¼ ð11Þ C with: ic ¼ idc −in

ð12Þ

The inverter is modeled in the same manner as the previous rectifier: 0 1 0 10 1 V in1 F1 −2 1 1 B V C V dc B CB F C 1 −2 1 ð14Þ @ in2 A ¼ @ A@ 2 A 3 V in3 F3 1 1 −2 where Vin1, Vin2, Vin3 being the three phase voltages of the DC/AC inverter. Then the filter, constituted of Rn and Ln, links these voltages to E1, E2, E3, which are the three phase voltages of the grid, through the following relation: 0

1 0 1 0 1 0 1 V in1 E1 in1 in1 dB BV C Bi C C B C @ in2 A ¼ Rn @ n2 A þ Ln @ in2 A þ @ E2 A dt V in3 E3 in3 in3

ð15Þ


529

Fig. 5. Direct bus and power control.

The control scheme of the inverter is presented in Fig. 5. The grid link control consists in adjusting the active power supplied to the grid to its reference value Pref and the reactive power Qref to zero in order to fix the power factor at the unit. The active power reference is deduced by controlling the direct bus voltage with a proportional integral corrector generating the current reference ic−ref to the capacity (Fig. 4). Hence, we can express Pref as: P ref ¼ V dc :ðidc −icref Þ

ð16Þ

ð19Þ

Q ref ¼ Eq indr ef −Ed inqr ef

ð20Þ

Then, multiplying Eq. (19) by Ed and Eq. (20) by Ed, the addition and subtraction of the two resulting equations give the reference current value according to active and reactive power ones by:

ð17Þ inq−ref ¼

with: icref ¼ PI:ðV dc−ref −V dc Þ

P ref ¼ Ed indr ef þ Eq inqr ef

ind−ref ¼

thus: P ref ¼ P dc −P cref

The reference active and reactive powers are given by the following equations:

ð18Þ

P ref Ed þ Q ref Eq E2d þ E2q P ref Eq −Q ref Ed V 2d þ V 2q

where Ed, Eq are the Park components of E1, E2, E3.

ð21Þ

ð22Þ

530


Fig. 6. Field oriented control strategy.

Fig. 7. Basic concept of the modulate hysteresis.

Fig. 9. Selection of the voltage vector according to the zone (i¼ 1). FD: flux decrease, FI: flux increase, TD: torque increase, TI: torque increase.

Table1 Switching table. ET

Fig. 8. Determination of the switch states.

EФ

N 1

2

3

4

5

6

ET ¼ 1

EФ¼ 1 EФ¼ 0

V2(110) V6(101)

V3(010) V1(100)

V4(011) V2(110)

V5(001) V3(010)

V6(101) V4(011)

V1(100) V5(001)

ET ¼ 0

EФ¼ 1 EФ¼ 0

V3(010) V5(001)

V4(011) V6(101)

V5(001) V1(100)

V6(101) V2(110)

V1(100) V3(010)

V2(110) V4(011)


531

3. Different AC/DC control strategies 3.1. Field oriented control strategy The field oriented control (FOC) strategy is based on the following considerations: Фrd ¼ Фr and Фrq ¼ 0

Fig. 10. Determination of the triangular signal parameters.

ð23Þ

then, from the power or torque reference, this strategy generates the three phase reference currents which are applied to PWM control of the AC/DC inverter. The FOC control principle is depicted in Fig. 6.

Fig. 11. Conversion system control with MHDTC method.

532


3.2. DTC and MHDTC methods

and (29)), the two slopes of the torque are given by: (subscript k is omitted):

Fig. 7 The use of FOC strategy with a PWM (Fig. 6) leads to a high quality of current and power factor supplied to the grid. This is not the case of the DTC because of the variable switching frequency of the used hysteresis controllers which lead to current distortions. To overcome this problem, we applied a PWM technique to the classical DTC scheme by superposing to the constant torque reference a triangular signal with an appropriate frequency. The modulated reference torque is then compared to the estimated one using a hysteresis controller as in the classical DTC (Fig. 7-8). The new torque reference T neref is defined by:

þΔT e Rs Rr 3p m þ ¼ −T e þ −V sα ϕrβ þ V sβ ϕrα −ωm ðϕsα ϕrα þ ϕsβ ϕrβ Þ 4 sℓs ℓr T tr sℓs sℓr

ð30Þ

−ΔT e Rs Rr 3p m ¼ −T e þ ωm ðϕsα ϕrα þ ϕsβ ϕrβ Þ − 4 sℓs ℓr T tr sℓs sℓr

ð31Þ

T ne−ref ¼ T e−ref þ T tr

ð24Þ

where Te−ref is the reference torque and Ttr is the triangular signal. In DTC and MHDTC methods, decoupled control of the stator flux modulus and torque is achieved by acting on the radial and tangential components respectively of the stator flux-linkage space vector in its locus. These two components are directly proportional to the components of the same voltage space vector in the same directions. Fig. 9. shows the possible dynamic locus of the stator flux, and its different variation depending on the VSI states chosen. The possible global locus is divided into six different sectors signaled by discontinuous line. In accordance with Fig. 9, the general Table 1 can be written. The appropriate voltage vector is chosen according to the output of flux and torque hysteresis regulators and the locus of the stator flux vector (N). The condition to impose a switching frequency is that the estimated torque variation during a half period should not exceed the difference between the maximum of the upper limit (T ne−ref þ BH ) and the minimum of the lower one (T ne−ref −BH ) (Fig. 10). Where BH is the hysteresis bandwidth, Atr and ftr are the triangular signal amplitude and frequency respectively. Then, according to the stator and rotor flux, the electromagnetic torque Te is given by the following equation: Te ¼

3p m Im Фs Фr 4 sℓs ℓr

Rr Lm Rr ϕsk þ jωm − ϕ T tr sLs Lr sLr rk

dT e 2BH 4 dt min T tr

ð33Þ

The torque dynamic ðdT e =dtÞ is equivalent to the current dynamic and so, it is fixed by the machine parameters. We can easily estimate ðdT e =dtÞmin and ðdT e =dtÞmax by replacing the parameters in Eq. (30) with their values (we scan all possible Table 2 Wind turbine parameters. Parameters

Values

Rated power Radius Rated speed Multiplier gain

10 KW 3.5 190 rd/mn 8.48

ð25Þ

where (s ¼ 1−m2 =ℓs ℓr ) is the leakage coefficient. Stator and rotor flux are provided respectively by Eqs. (26) and (27) in a discrete form with a small sampling period giving the flux value at sampling instant (k+1)Ttr as a function of its value at the instant kTt. −Rs Rs Lm ϕsk þ ϕrk þ V sk T tr ð26Þ ϕsðkþ1Þ ¼ ϕsk þ sLs sLs Lr ϕrðkþ1Þ ¼ ϕrk þ

Thus, the condition for setting the switching frequency equal to the applied triangular signal one is to fix the number of intersections points between the triangular signal and the hysteresis band limits to 2 during each half sampling period (Ttr/2). These 2 points determinate the switching times where the non zero and zero voltage vectors are selected. To satisfy this condition, the maximal and minimal torque dynamic values must verify the two following conditions according to the triangular signal amplitude Atr and frequency ftr and the hysteresis band width BH: dT e ¼ 4f tr ðAtr þ BH Þ ð32Þ dt max

ð27Þ

Table 3 Generator parameters. Parameters

Values

Rated power Rated voltage Number of pole pairs Stator leakage inductance Rotor leakage inductance Stator-rotor mutual inductance Stator resistance Rotor resistance grid frequency

5.5 KW 220/380 V 2 0.0112 H 0.0148 H 0.0101 H 1.196 Ω 1.263 Ω 50 Hz

By replacing ϕs(k+1)and ϕr(k+1)by their expressions given by above in the discrete form of Eq.25, the torque increment +ΔTe by nonzero voltage vector Vmk and the torque decrement −ΔTe by the zero voltage vector during time duration Ttr at the (k+1)th sampling instant can be obtained as (the square of Ttr is neglected): þΔT eðkþ1Þ Rs Rr 3p Lm ¼ −T ek þ ImðV mk ϕrk −jωm ðϕsk ϕrk ÞÞ≡f 1 þ 4 sLs Lr T tr sLs sLr ð28Þ −ΔT eðkþ1Þ Rs Rr 3p Lm ¼ −T ek þ Imðjωm ðϕsk ϕrk ÞÞ≡f 2 − 4 sLs Lr T tr sLs sLr

ð29Þ

Taking into account the two components of the vector voltage (Vs ¼Vsα+jVsβ) and simplifying the two previous equations (Eq. (28)

Fig. 12. Wind profile.


533

Fig. 13. Phase current supplied to the grid under the three control schemes. (a) FOC method, (b) DTC method and (c) MHDTC method.

combinations of torque, flux and voltage), we find ðdT e =dtÞmax and ðdT e =dtÞmin and we set the value of the desired triangular signal. By substituting ðdT e =dtÞmax and ftr by their values in Eq. (32), we find the condition about (Atr+BH) given in the case of this work by: 1 dT e ≥0:317 ð34Þ ðAtr þ BH Þ≥ 4f tr dt max From Eq. (33) we can find the following condition giving the limit to the hysteresis bandwidth BH: BH ≺0:275

ð35Þ

Atr and BH values must be selected so that Atr should not be too high otherwise, the new torque reference will be far from its real value (T ne−ref ⪢T e−ref ). It should not be too small as well otherwise the method will be the same as the classical DTC (T ne−ref ≃T e−ref ). The best ratio between Atr and BH is that: 2≤

Atr ≤4 BH

ð36Þ

Note: The triangular signal frequency is three times the desired switching one because during each period of the triangular signal, only one switch operates. Therefore, ftr ¼3n3.3 KHz ¼10 KHz.

534


Fig. 14. Electromagnetic torque obtained by the three control strategies. (a) FOC method, (b) DTC method and (c) MHDTC method.

Fig. 15. Stator flux and its trajectory. (a) DTC method and (b) MHDTC method.

To operate with a fixed switching frequency of 3.33 KHz, the following relations have to be satisfied: 8 f tr ¼ 10 KHz > > > < Atr þ BH ≥0:317 ð37Þ > BH ≺0:275 > > : 2BH ≤Atr ≤4BH The control of the wind conversion system under the proposed scheme is depicted in Fig. 11.

4. Simulation results Fig. 16. Direct bus voltage under the three control strategy.

The system studied is constituted of a wind turbine, an induction generator and a rectifier/inverter connected to the grid. The parameters of the turbine and the induction machine are given in Tables 2 and 3.

The control strategies presented in the previous paragraph are then introduced in the MATLAB SIMULINK environment to study the performance of the WEC system. They are tested in the case of


variable wind speed whose profile is given in Fig. 12. The limits of the wind speed profile (7 m/s–13 m/s) are selected corresponding to the second zone (zone II) of the wind energy conversion system operation. For the MHDTC method, we take the following parameters: BH ¼ 0.15, Atr ¼0.35, ftr ¼10 KHz The phase current supplied to the grid by the conversion system under the three control methods is presented in Fig. 13. We can note that the current waveform obtained using the MHDTC strategy is more sinusoidal than that under conventional DTC and is relatively close to that obtained with FOC method.

535

Fig. 14 shows the electromagnetic torque waveforms obtained by the three control strategies. Whatever the approach adopted, the torque follows the reference given by the control. As expected, the torque ripples are low in the case of FOC while they are important in classical DTC method due to the hysteresis controller. The proposed MHDTC allows us to reduce these ripples by about 56%. The stator flux trajectory for the classical DTC and MHDTC are presented in Fig. 15. In both cases, the stator flux is kept constant around its reference. The direct bus and AC phase voltages are also compared when using the three approaches (Fig. 16 and 17). We can notice that,

Fig. 17. Phase voltage under the three control strategies. (a) Phase voltage under FOC, (b) Phase voltage under DTC and (c) Phase voltage under MHDTC.

536


1

Power factor

0.8

1

1

0.98

0.6

0.98

0.96

0.4

0.94 70

0.96 80

90

100

510

515

520

525

0.2 FOC

0

0

100

DTC

200

MHDTC

300 Time (s)

400

500

600

Fig. 18. Power factor under three control methods.

600

Power losses (W)

500 400

250

200

200

150

150

100

100 100

DTC FOC MHDTC

510

101

513

300 200 100 0

0

100

200

300 Time (s)

400

500

600

Fig. 19. Total losses under the three methods.

100 90

Effeciency (%)

80 70

95.5

97

60 94.5

50

96

40

93.5

30

92.5 108

20

109

110

10 0

DTC

0

100

200

95 551

MHDTC

300

553

555

557

FOC

400

500

600

Time (s) Fig. 20. Efficiency under the three methods.

under MHDTC and DTC, the DC voltage bus is kept around its reference (465 V) with less oscillation than under FOC. This can be highlighted by Fig. 17 where the phase voltage under FOC method has variable rms (Fig. 17a). This variation follows the wind speed

perturbation which confirms the limited robustness of the method. The power factor for the three methods was also calculated. We note that the latter is around the unity whatever the control


537

strategy. However, in the case of DTC, it is variable and slightly higher than that of FOC and MHDTC methods (Fig. 18). In steady-state, the total losses can be written as: " # ðRs þ Rf s Þ 2 Rs þ ðRr =ð1 þ sr Þ2 Þ þ ððsr :Rf s Þ=ð1 þ sr ÞÞ 2 −2 P loss ¼ :ϕr þ :T e :ϕr m2 ½p:ð1−sÞ:ð1 þ sr Þ2

one simple control which is impossible with the classical control methods (FOC and DTC).

ð38Þ

A study of an improved direct torque control strategy applied to an induction generator used in a wind conversion system has been presented in this paper. This method, based on a combination of DTC and the PWM technique, takes the advantages of the classical direct torque control while overcoming its main drawbacks in terms of high THD and variable frequency. Hence, it permits to the conversion system to supply sinusoidal currents to the grid with constant periodic frequency, a unit power factor and a constant rms of the phase voltage. The proposed strategy presents attractive features such as constant periodic frequency and energy saving than other proposed methods (FOC and DTC). The effectiveness of MHDTC has been highlighted by simulation. The main objective of the proposed method MHDTC is to obtain a constant frequency, we found 49.97 Hz with an error of 0.06% which is an acceptable tolerance level in practice. For the implementation, compared to the DTC method, there's no more complexity. We have just added one comparator, which eliminates low frequencies. The work has been validated in motor operating. And it will be interesting to do it in future with the overall system in generator operating.

And then, efficiency η is given by the well known expression: η ¼ 1−

P loss P loss ¼ 1− P in vds :ids þ vqs :iqs

ð39Þ

Using the expressions above, we present, in Fig. 19, the waveform, with respects to time, of the total losses calculated in the case of the three control strategies. We can note that the losses in the case of MHDTC have been reduced compared to that under classical DTC method, which leads, obviously, to a better efficiency. Fig. 20 below shows the waveforms of the efficiency given by relation (29). Besides, we present, in Fig. 21, the frequency of the phase current supplied to the grid in the case of the three control strategies. We can notice that, when using the MHDTC approach, the frequency is almost constant with a mean value of 49.97 Hz which is better than what is obtained by FOC or DTC. Finally, in Table 4, the three control strategies are compared in terms of total harmonic distortion (THD), power factor, power losses and efficiency. As expected, FOC strategy provided better results than DTC in terms of THD but its implementation is complex as it needs the use of PI regulators and mechanical sensors. Moreover, it leads to greater power losses. Using our proposed strategy (MHDTC), the current supplied to the grid is much improved, compared with the case using DTC, with less THD, a constant frequency around 50 Hz (Fig. 21) and a unit power factor (Table 4). Furthermore, the total losses decrease leading to the best efficiency among the three approaches (Table 4). We can conclude that the MHDTC strategy gathers all good performances for better control of the WECs connected to the grid (unit power factor, sinusoidal current, less power losses, robustness towards wind perturbations, constant periodic frequency) with great simplicity of implementation (sensorless method without PI regulators), all these performances are ensured with only

Frequency (Hz)

52 51 50 49 48 47

MHDTC

0

100

200

DTC

300 Time (s)

FOC

400

500

600

Fig. 21. Frequency of the current supplied to the grid under the three methods.

Table 4 Comparison between the different studied methods. Control methods used

THD (%)

Cos(ϕ)

PLoss(W)

η (%)

FOC method Classical DTC method MHDTC method

10.94 64.89 30.57

0.9997 0.9711 0.9993

126.7 121.42 117.21

92.07 92.13 92.82

5. Conclusion

References [1] Ouammi A, Dagdaoui H, Sacile R, Mimet A. Monthly and seasonal assessment of wind energy characteristics at four monitored locations in Liguria region (Italy). Renewable Energy Reviews 2010;14(7):1959–68. [2] Marchenko OV, Solomin SV. Efficiency of wind energy utilization for electricity and heat supply in northern regions of Russia. Renewable Energy 2004;29 (11):1793–809. [3] Singh GK. Modeling and analysis of six-phase synchronous generator for stand-alone renewable energy generation. Energy 2011;36(2011):5621–31. [4] Margato E, Faria J, Resende MJ, Palma J. A new control strategy with saturation effect compensation for an autonomous induction generator driven by wide speed range turbines. Energy Conversion and Management 2011;52: 2142–2152. [5] Miao Z, Fan L. The art of modeling and simulation of induction generator in wind generation applications using high-order mode l. Simulation Modelling Practice and Theory 2008;16(9):1239–53. [6] Zaragoza J, Pou J, Arias A, Spiteri C, Robles E, Ceballos S. Study and experimental verification of control tuning strategies in a variable speed wind energy conversion system. Renewable Energy 2011;36:1421–30. [7] Hu J, Yuan X. VSC-based direct torque and reactive power control of doubly fed induction generator. Renewable Energy 2012;40:13–23. [8] Kazemi MV, Yazdankhan AS, Kojabadi HM. Direct power control of DFIG based on discrete space vector modulation. Renewable Energy 2010;35:1033–42. [9] Kassem AM, Hasaneen KM, Yousef AM. Dynamic modeling and robust power control of DFIG driven by wind turbine at infinite grid. Electrical Power and Energy Systems 2013;44:375–82. [10] Gao Z. From linear to nonlinear control means: a practical progression. ISA Transactions 2002;41(2):177–89. [11] Qian W, Panda SK, Xu JX. Periodic speed ripples minimization in PM synchronous motors using repetitive learning variable structure control. ISA Transactions 2003;42(4):605–13. [12] Pourjafari E, Mojallali H. Predictive control for voltage collapse avoidance using a modified discrete multi-valued PSO algorithm. ISA Transactions 2011;50(2):195–200. [13] Bekka H, Rekioua D, Taraft S, Bacha S. Power Control of a Wind generator connected to the network in front of Strong winds. IREC Conference Sousse, Tunisia 2012:1–6. [14] Singh GK, Kumar AS, Saini RP. Performance analysis of a simple shunt and series compensated six-phase self-excited induction generator for stand-alone renewable energy generation. Energy Conversion and Management 2011;52: 1688–1699. [15] Tunyasrirut S, Wangsilabatra B, Charumit C, Suksri T. Grid connected based six-pulse converter applied a self-excited induction generator for wind turbine applications. Energy Procedia 2011;9:128–39. [16] Wan Tan DWW. A simplified type-2 fuzzy logic controller for real-time control. ISA Transactions 2006;45(4):503–16. [17] Idjdarene K, Rekioua D, Rekioua T, Tounzi A. Vector control of autonomous induction generator taking saturation effect into account. Energy Conversion and Management 2008;49(10):2609–17.

538


[18] Ouhrouche M. Transient analysis of a grid connected wind driven induction generator using a real-time simulation platform. Renewable Energy 2009;34: 801–806. [19] Bouzid AM, Benghanem M, Hamane B, Belabbes A, Bouhamida M, Draou A. Current control of the isolated self-excited induction generator using shunt active filter. Energy Procedia 2012;18:349–58. [20] Rahim AHMA, Alam MA, Kandlawala MF. Dynamic performance improvement of an isolated wind turbine induction generator. Computers and Electrical Engineering 2009;35:594–607. [21] Khezami N, Benhadj Braiek N, Guillaud X. Wind turbine power tracking using an improved multimodel quadratic approach. ISA Transactions 2010;49 (3):326–34. [22] Sawetsakulanond B, Kinnares V. Design, analysis and construction of a small scale self-excited induction generator for a wind energy application. Energy 2010;35:4975–85. [23] Lazim MT, Al-Khishali MJM, Al-Shawi AI. Space vector modulation direct torque speed control of induction motor. Procedia Computer Science 2011;5:505–12. [24] Iplikci S. A support vector machine based control application to the experimental three-tank system. ISA Transactions 2010;49(3):376–86. [25] Abdelli R, Rekioua D, Rekioua T. Performances improvements and torque ripple minimization for VSI fed induction machine with direct control torque. ISA Transactions 2011;50(2):213–9. [26] Gao Y, Wang J, Qiu X. The improvement of DTC system performance on fuzzy control, 3rd international conference on environmental science and information application technology. Procedia Environmental Sciences 2011;10:589–94.

[27] Areed FG, Haikal AY, Mohammed RH. Adaptive neuro-fuzzy control of an induction motor. Ain Shams Engineering Journal 2010;1:71–8. [28] Arnanz R, Miguel LJ, Peran JR, Mendoza A. A modified direct torque control with fault tolerance. Control Engineering Practice 2011;19:1056–65. [29] Zhang BT, Pi Y, Luo Y. Fractional order sliding-mode control based on parameters auto-tuning for velocity control of permanent magnet synchronous motor. ISA Transactions 2012;51(5):649–56. [30] Idjdarene K, Rekioua D, Rekioua T, Tounzi A. Performance of an isolated induction generator under unbalanced loads. IEEE Transactions on Energy Conversion 2010;25(2):303–11. [31] Nejad MA, Pierfederici S, Martin JP, Meibody-Tabar F. Study of an hybrid current controller suitable for DC–DC or DC–AC applications. IEEE Transactions on Power Electronics 2007;22(6):2176–86. [32] Zheng X, Li L, Xu D, Platts J. Sliding mode MPPT control of variable speed power system, In procedding of APPEEC 2009. IEEE Conference 2009:1–4. [33] Rekioua D, Matagne E. Optimization of photovoltaic power systems: modelization, simulation and control. Edition springer; 978-1-4471-2403-0 /http://www.springer.com/engineering/energy+technology/book/978-1-44712348-4S. [34] Rekioua D, Rekioua T. DSP-controlled direct torque control of induction machines based on modulated hysteresis control. In: Proceedings of the International Conference on Microelectronics, ICM, Art. no. 5418603; 2009 pp. 378–381.