Model-based predictive direct power control of brushless doubly fed reluctance generator for wind power applications

Model-based predictive direct power control of brushless doubly fed reluctance generator for wind power applications

Alexandria Engineering Journal (2016) xxx, xxx–xxx H O S T E D BY Alexandria University Alexandria Engineering Journal www.elsevier.com/locate/aej ...

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Alexandria Engineering Journal (2016) xxx, xxx–xxx

H O S T E D BY

Alexandria University

Alexandria Engineering Journal www.elsevier.com/locate/aej www.sciencedirect.com

ORIGINAL ARTICLE

Model-based predictive direct power control of brushless doubly fed reluctance generator for wind power applications Maryam Moazen, Rasool Kazemzadeh *, Mohammad-Reza Azizian Renewable Energy Research Center, Electrical Engineering Faculty, Sahand University of Technology, Tabriz, Iran Received 13 January 2016; revised 7 June 2016; accepted 2 August 2016

KEYWORDS Brushless doubly fed reluctance generator; Predictive direct power control; Space vector pulse width modulation; Back to back converter; Fixed switching frequency; Wind power

Abstract In this paper, a predictive direct power control (PDPC) method for the brushless doubly fed reluctance generator (BDFRG) is proposed. Firstly, the BDFRG active and reactive power equations are derived and then the active and reactive power variations have been predicted within a fixed sampling period. The predicted power variations are used to calculate the required voltage of the secondary winding so that the power errors at the end of the following sampling period are eliminated. Switching pulses are produced using space vector pulse width modulation (SVPWM) approach which causes to a fixed switching frequency. The BDFRG model and the proposed control method are simulated in MATLAB/Simulink software. Simulation results indicate the good performance of the control system in tracking of the active and reactive power references in both power step and speed variation conditions. In addition, fast dynamic response and lower output power ripple are other advantages of this control method. Ó 2016 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction Nowadays, the brushless doubly fed reluctance generators (BDFRG) have been proposed as a potential alternative to the existing solutions for wind power applications [1–10]. The main reason of this increasing interest could be found in reasonable cost and high reliability of the BDFRG because of its brushless structure. On the other hand, its comparative performance with other generators such as wound and cage rotor induction generator, doubly fed induction generator * Corresponding author. E-mail address: [email protected] (R. Kazemzadeh). Peer review under responsibility of Faculty of Engineering, Alexandria University.

(DFIG) and brushless doubly fed induction generator (BDFIG) leads to consideration of the BDFRG as a suitable choice for wind power application [11,12]. Previously, the BDFRG couldn’t compete with its induction counterpart (BDFIG) because of low saliency ratio of reluctance rotor which caused lower torque in the BDFRG. However, recent developments in reluctance rotors with high saliency ratio, lead to more attention to the BDFRG [2]. The BDFRG needs partially-rated converter in wind power applications like other doubly fed generators [1–3,13]. In addition, the absence of rotor cage makes it more efficient [4] and easier to control [3] in comparison with the BDFIG. On the other hand, its brushless structure ensures high reliability and low maintenance of the BDFRG, which is especially important to off-shore plants [14].

http://dx.doi.org/10.1016/j.aej.2016.08.004 1110-0168 Ó 2016 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: M. Moazen et al., Model-based predictive direct power control of brushless doubly fed reluctance generator for wind power applications, Alexandria Eng. J. (2016), http://dx.doi.org/10.1016/j.aej.2016.08.004

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The BDFRG has two sinusoidal distributed three-phase winding in its stator in which the pole pairs and applied frequencies to these windings are different from each other [14,15]. The primary winding (power winding) is directly connected to the grid and the secondary winding (control winding) is connected to the grid through a back to back IGBT/Diode converter for bi-directional power flow which is shown in Fig. 1 [14]. Since the pole pairs of two stator windings are always different, so with a round rotor, there is ideally no magnetic coupling between them [2]. However, a reluctance rotor with Pr salient poles could make magnetic coupling between the primary winding with P1 pole pairs and the secondary winding with P2 pole pairs (supplied with angular frequencies xp and xs , respectively) by satisfying the following equations [2]: Pr ¼ P1 þ P2

ð1Þ

xr ¼ xp þ xs

ð2Þ

where xr is the electrical angular velocity of the rotor. Different methods have been proposed to control the BDFRG over the years. Field orientation control (FOC) [16–24] and vector control (VC) [3,19–26] are two similar methods that are presented to control the BDFRG. The FOC method is based on field orientation and the VC method is based on voltage orientation. Although orientation of voltage in the VC method is simpler, the FOC method has the advantage of inherent decoupled control of active and reactive power, which greatly facilitates the controller design [24]. In these control methods, accurate adjustment of current controller parameters is required to ensure adequate response and stability of system over the whole operating range. Direct torque control (DTC) method, which is based on decoupled control of flux and torque, has been applied to the BDFRG [27–31]. The absence of current control loops is one the advantages of the DTC method in comparison with the FOC method. Also, dynamic response of the DTC is faster than the FOC/VC. However, switching frequency of the DTC method is variable because of using hysteresis controller. In [32,33], an improved DTC method by combination of power controllers (PI controllers) and space vector modulation is proposed to reach a fixed switching frequency. However, it is required for accurate tuning of PI parameters. Direct power control (DPC) method, which is based on the DTC principles, is another method for control of the BDFRG [14,34]. Changing control parameters from flux and torque in the DTC to active and reactive powers in the DPC leads to simplicity and robustness of the DPC method (with similar

dynamic response). However, switching frequency of the DPC method is also variable because of using hysteresis controller. Variable switching frequency not only causes high output power ripple but also causes increase in harmonic filter cost. A comparative analysis of these control methods has been presented in [35]. In this paper, a predictive direct power control (PDPC) method is proposed to control the BDFRG. The proposed PDPC method has the advantage of fixed switching frequency, whereas its dynamic response is as fast as the DPC method. Fixed switching frequency leads to significant decrease in output power ripple of the proposed method in comparison with the DPC method. In addition, the proposed PDPC method does not need hysteresis controller and uses space vector pulse wide modulation (SVPWM) technique. In Section 2, the BDFRG model in an arbitrary reference frame is presented. Section 3 is dedicated to calculation of the BDFRG power equations. The basic principles of the PDPC strategy are outlined in Section 4. In Section 5, back to back converter control method is expressed. Finally, verifying simulation results for the BDFRG control system are presented in Section 6. 2. BDFRG model The space vector model of the BDFRG in an arbitrary reference frame rotating at x can be expressed as follows [36]: dkp þ jxkp dt

ð3Þ

dks þ jðxr  xÞks dt

ð4Þ

vp ¼ Rp ip þ

vs ¼ Rs is þ

kp ¼ Lp ip þ Lps is

ð5Þ

ks ¼ Ls is þ Lps ip

ð6Þ

where Rp, Rs, Lp, Ls and Lps are primary resistance, secondary resistance, primary inductance, secondary inductance and primary to secondary mutual inductance, respectively. xp and xs are the space vectors in a reference frame rotating at x, for the primary and secondary respectively. It should be noted that primary and secondary equations are expressed in two different reference frames: primary equation, (3), in reference frame x and secondary equation, (4), in reference frame xr  x. The reference frames that are used in the model are shown in Fig. 2 [5].

Grid

DC link

ωm

Converter

Converter

BDFRG

Figure 1

The connection of the BDFRG to the grid.

Please cite this article in press as: M. Moazen et al., Model-based predictive direct power control of brushless doubly fed reluctance generator for wind power applications, Alexandria Eng. J. (2016), http://dx.doi.org/10.1016/j.aej.2016.08.004

Model-based predictive direct power control

3 ksr ¼ Ls isr þ Lps ips

ð17Þ

Above Eqs. (14)–(17), are used to obtain the BDFRG power equations. The three-phase complex power of the BDFRG primary winding is obtained from (18). 3 Sp ¼ Pp þ jQp ¼ vps ips 2

ð18Þ

With substituting (14) into (18): Sp ¼

 3 Rp ips þ jxp kps ips 2

ð19Þ

By ignoring the copper losses of the primary winding, (19) is simplified as follows: Figure 2

The reference frames used for the BDFRG model.

3 Sp ¼ ðjxp kps Þips 2

ð20Þ

ips can be obtained from (16) and (17): Lps ksr kps  rLp rLp Ls

3. Power equations of BDFRG

ips ¼

In the previous section, the space vector equations of the BDFRG in an arbitrary reference frame rotating at x were expressed. Another reference frame is obtained by setting h ¼ 0 [5,36] which is suitable for power equations derivation. This leads to a stationary dq reference frame for the primary equation and a rotor reference frame for the secondary equation. In the following equations, sub-subscripts s and r indicate the stationary and rotor reference frames, respectively.

where r ¼ 1  L2ps =Lp Ls . With substituting ips from (21) into (20):    kps 3 Lps ksr Sp ¼ ðjxp kps Þ ð22Þ  rLp rLp Ls 2

vps ¼ Rp ips þ

dkps dt

dks vsr ¼ Rs isr þ r þ jxr ksr dt

ð7Þ ð8Þ

In steady state, if the angular frequency of the primary winding is xp , primary flux vector is rotating at a constant angular velocity of xp . In this condition, the primary flux vector is as follows: kps ¼ kp ejxp t

ð9Þ

With substituting (9) into (7): vps ¼ Rp ips þ jxp kps

ð10Þ

Similarly, the secondary flux vector in stationary frame can be written as follows: kss ¼ ks ejxs t

ð11Þ

Therefore, the secondary flux vector in the rotor reference frame is obtained as follows: ksr ¼ kss ejhr

ð12Þ

With substituting (12) into (8) [36]: vsr ¼ Rs isr þ jxs ksr

ð13Þ

So, the steady state equations of the BDFRG can be summarized as follows: vps ¼ Rp ips þ jxp kps

ð14Þ

vsr ¼ Rs isr þ jxs ksr

ð15Þ

kps ¼ Lp ips þ Lps isr

ð16Þ

So: Sp ¼

  3 xp 2 xp Lps j kp  j kps ksr 2 rLp rLp Ls

ð21Þ

ð23Þ

From Fig. 2, the primary and secondary flux vectors can be written as follows: kp ¼ kp ejap ¼ kp ejðhp hÞ

ð24Þ

kps ¼ kp ejhp ¼ kp ejðhþap Þ

ð25Þ

ksr ¼ ks ejas ¼ ks ejðhs þhhr Þ

ð26Þ

Since h ¼ 0, hence kp ¼ kps and consequently hp ¼ ap . So (23) could be rewritten as follows:   3 xp 2 xp Lps j kp  j kp ejap ks ejas ð27Þ Sp ¼ 2 rLp rLp Ls Finally, the three-phase complex power of the BDFRG primary winding is obtained as follows:   3 xp 2 xp Lps Sp ¼ ð28Þ kp  j kp ks ejðap þas Þ j rLp Ls 2 rLp So the three-phase active and reactive powers of the BDFRG primary winding are as follows: Pp ¼ RefSp g ¼

3 xp Lps kp ks sinðap þ as Þ 2 rLp Ls

ð29Þ

Qp ¼ ImfSp g ¼

3 xp 2 3 xp Lps k  kp ks cosðap þ as Þ 2 rLp p 2 rLp Ls

ð30Þ

Also kpss is defined as follows: kpss ¼

Lps  k Lp ps

ð31Þ

In addition, d ¼ ap þ as is the angle between kpss and ksr which is shown in Fig. 3.

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λsr

BDFRG. The proposed PDPC principles include the following aspects:

δ Figure 3

λps = s

L ps Lp

(a) Calculation of the required secondary winding voltage based on the developed predicted power model (i.e. (35) and (36)) within a fixed sampling period, Ts, directly. (b) Generation of proper voltage vectors within the fixed sampling period to approximate the calculated secondary winding voltage by SVPWM method.

λ*ps

The representation of kpss and ksr .

If d axis is fixed to kpss vector, then jkpss j ¼ kpsd . Therefore kpsd ¼

Lps kp Lp

ð32Þ

and ksd ¼ jks j cos d

ð33Þ

ksq ¼ jks j sin d

ð34Þ

So (29) and (30) can be expressed using d-q components: Pp ¼

3 xp kpsd ksq 2 rLs

3 xp Qp ¼ 2 rLs

ð35Þ

Lp Ls kpsd ksd þ 2 k2psd Lps

! ð36Þ

Thus, (35) and (36) indicate that the active and reactive powers of the stator primary winding can be controlled independently by adjusting ksq and ksd , respectively.

Suppose that, the active and reactive power errors are obtained from the following equations at the beginning of kth sampling period: dPp ðkÞ ¼ Pp ðkÞ  Pp ðkÞ

ð37Þ

dQp ðkÞ ¼ Qp ðkÞ  Qp ðkÞ

ð38Þ

The control objective within the following fixed sampling period is elimination of the active and reactive power errors at the end of the sampling period (the k + 1th sampling point), i.e. dPp ðk þ 1Þ ¼ Pp ðk þ 1Þ  Pp ðk þ 1Þ ¼ 0

ð39Þ

dQp ðk þ 1Þ ¼ Qp ðk þ 1Þ  Qp ðk þ 1Þ ¼ 0

ð40Þ

Thus, to satisfy (39) and (40), the variation of the active and reactive powers during Ts should be equal to the following: DPp ðkÞ ¼ Pp ðk þ 1Þ  Pp ðkÞ ¼ Pp ðk þ 1Þ  Pp ðkÞ þ dPp ðkÞ

4. PDPC for BDFRG PDPC method had been successfully applied to DFIG [37–39]. In this paper, a PDPC method is presented to control the

Figure 4

ð41Þ

DQp ðkÞ ¼ Qp ðk þ 1Þ  Qp ðkÞ ¼ Qp ðk þ 1Þ  Qp ðkÞ þ dQp ðkÞ

ð42Þ

The schematic block diagram of the system and the proposed PDPC method.

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Model-based predictive direct power control

Figure 5

5

The simulated system in MATLAB/Simulink software.

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M. Moazen et al. Table 1

DPp ðkÞ ¼

The parameters of the BDFRG.

Rated power Rated voltage Rated current Synchronous speed Poles J Rp Rs Lp Ls Lps

1.5 kW 415 V rms 2.5 A rms 750 rpm 6/2 0.1 kg m2 10.7 O 12.68 O 0.407 H 1.256 H 0.57 H

3 xp kpsd ðkÞDksq ðkÞ 2 rLs

DQp ðkÞ ¼ 

ð45Þ

3 xp kpsd ðkÞDksd ðkÞ 2 rLs

ð46Þ

The flux change of the secondary winding within Ts can be obtained with integrating from both sides of (8): Z Dksr ¼ ðvsr  Rs isr  jxr ksr Þdt ð47Þ Ts

For a short sampling period, (47) could be approximated in the d–q axes using Euler backward method as follows: Dksd ðkÞ ¼ ksd ðk þ 1Þ  ksd ðkÞ   ¼ vsd ðkÞ  Rs isd ðkÞ þ xr ðkÞksq ðkÞ Ts

ð48Þ

Dksq ðkÞ ¼ ksq ðk þ 1Þ  ksq ðkÞ ¼ ðvsq ðkÞ  Rs isq ðkÞ  xr ðkÞksd ðkÞÞTs

ð49Þ

Substituting (48) and (49) into (45) and (46), respectively, leads to required secondary winding voltage within the following sampling period:

Figure 6

vsd ðkÞ ¼ Rs isd ðkÞ  xr ðkÞksq ðkÞ þ

DQp ðkÞ 1 xp Ts  32 rL kpsd ðkÞ s

vsq ðkÞ ¼ Rs isq ðkÞ þ xr ðkÞksd ðkÞ þ

1 Ts

DPp ðkÞ kpsd ðkÞ

3 xp 2 rLs

ð50Þ

ð51Þ

By ignoring copper losses of secondary winding, (50) and (51) could be simplified as follows:

The speed curve of the BDFRG.

If ‘‘zero-order sample and hold” is used for reference values of the primary winding active and reactive powers, then Pp ðk þ 1Þ ¼ Pp ðkÞ and Qp ðk þ 1Þ ¼ Qp ðkÞ, and the required changes in active and reactive powers over k th sampling period are as follows: DPp ðkÞ ¼ dPp ðkÞ

ð43Þ

DQp ðkÞ ¼ dQp ðkÞ

ð44Þ

Consequently, the objective of the proposed control strategy is to generate required power changes, which is illustrated in (43) and (44), by applying correct voltage to the control winding. According to (35) and (36), and this fact that the flux of the primary winding is constant, the changes of the active and reactive powers over a small sampling period can be predicted as follows:

vsd ðkÞ ¼ xr ðkÞksq ðkÞ  vsq ðkÞ ¼ xr ðkÞksd ðkÞ þ

2rLs DQp ðkÞ 3Ts xp kpsd ðkÞ

2rLs DPp ðkÞ 3Ts xp kpsd ðkÞ

ð52Þ

ð53Þ

Therefore, the required voltage which should be applied to the secondary winding is given by the following: vsr ðkÞ ¼ jxr ðkÞksr ðkÞ 

2rLs DQp ðkÞ  jDPp ðkÞ 3Ts xp kpsd ðkÞ

ð54Þ

5. Control of back to back converter The control winding of the BDFRG is connected to the grid through a back to back converter. The duty of the grid side

Figure 7 The active and reactive output power of the BDFRG in speed variation operation: (a) the proposed PDPC method; (b) the DPC method.

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Model-based predictive direct power control

Figure 8 method.

7

The current of the BDFRG secondary winding in speed variation operation: (a) the proposed PDPC method; (b) the DPC

converter (GSC) is to charge DC link capacitor. GSC should be controlled with the purpose of setting the voltage of DC link to its reference value, while it has no reactive power transfer with the grid. In this paper, predictive direct power control method, which was presented by [40] to control a rectifier, is used to control GSC. Correspondingly, the task of the machine side converter (MSC) is to provide the required voltage of the BDFRG secondary winding. Therefore, the calculated voltage in (54) is set as a reference value for the controller of MSC. SVPWM technique [41] is used to control MSC which has constant switching frequency. The schematic block diagram of the system and the proposed PDPC are shown in Fig. 4. 6. Simulation results In this section, the performance of the proposed PDPC for the BDFRG has been evaluated. For this purpose, the BDFRG model and the proposed control method are simulated in MATLAB/Simulink software (Fig. 5). The simulated model consists of the following: (a) a 1.5 kW, 750 rpm, 6/2 poles BDFRG, (b) a three-phase back to back IGBT/Diode converter with 600 V DC link voltage and (c) a three-phase, 415 V, 50 Hz grid. The primary winding of the BDFRG is directly connected to the grid, but its secondary winding is connected, through the back to back converter. The BDFRG parameters can be seen in Table 1 [6]. The control system performance has been studied in both power step and speed variation conditions in the following subsections. For comparison, system response with original DPC method [14] is also tested. It should be noted that the BDFRG start-up period is not shown in the results.

6.1. Variable speed operation The active and reactive power tracking of the BDFRG primary winding in variable speed operation has been studied in this section. Fig. 6 shows the operational speed of the BDFRG in all synchronous (750 rpm), super-synchronous (950 rpm) and sub-synchronous (550 rpm) modes. The active and reactive power references have been respectively set to 400 W and 500 VAr where the negative sign of the active power indicates active power generation. The active and reactive power of the BDFRG with the proposed PDPC and DPC method has been illustrated in Fig. 7 which shows good power tracking for both mentioned methods. However, in the proposed PDPC method, output power ripple is very lower and precise control of both the active and reactive powers has been achieved. This is because of fixed switching frequency of MSC in proposed PDPC method. Fig. 8 shows the secondary current where its frequency changes with speed variation. In synchronous mode, the secondary current frequency is 0 Hz. By speed increase in supersynchronous mode, the secondary current frequency increases and by speed decrease, it decreases so that it reaches to 0 Hz at t = 5 s. The secondary current frequency decreases to negative value in sub-synchronous mode where the variation of its absolute value is proportional with speed deviation from synchronous speed. The primary current in speed variation operation has been shown in Fig. 9. The amplitude of the primary current with the proposed PDPC method is constant, because the primary active and reactive power references are constant. However with the DPC method, the amplitude of the primary current experiences fluctuations because of existing high ripples in the primary active and reactive powers. Fig. 10 shows the input

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Figure 9 The current of the BDFRG primary winding in speed variation operation: (a) the proposed PDPC method; (b) its extended view; (c) the DPC method; (d) its extended view.

Figure 10

The mechanical torque of the BDFRG in speed variation operation: (a) the proposed PDPC method; (b) the DPC method.

Figure 11 method.

The active and reactive output power of the BDFRG in power step condition: (a) the proposed PDPC method; (b) the DPC

mechanical torque to the BDFRG which leads to follow the speed curve of Fig. 6. The negative sign of the mechanical torque indicates the generation mode. 6.2. Power step condition In this section, the power tracking of the BDFRG and its dynamic response in power step condition have been evalu-

ated. Although this PDPC method is proposed for wind power application (generating state), it is also valid for motoring state. So, simulation is performed for both generating and motoring states (for comparison of proposed PDPC and DPC [14]). Initial reference values for the active and reactive powers are 400 W and 1400 VAr, respectively. Reactive power reference value changes to 700 VAr, at t = 1 s and active power reference value changes to 400 W at t = 2 s.

Please cite this article in press as: M. Moazen et al., Model-based predictive direct power control of brushless doubly fed reluctance generator for wind power applications, Alexandria Eng. J. (2016), http://dx.doi.org/10.1016/j.aej.2016.08.004

Model-based predictive direct power control

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Figure 12 The dynamic response of the BDFRG output powers during the following: (a) active power step with the proposed PDPC method; (b) active power step with the DPC method; (c) reactive power step with the proposed PDPC method; (d) reactive power step with the DPC method.

Figure 13 The current of the BDFRG primary winding in power step condition: (a) the proposed PDPC method; (b) its extended view; (c) the DPC method; (d) its extended view.

Negative and positive signs of active power respectively indicate power generation and consumption. The active and reactive power of the BDFRG with the proposed PDPC and the DPC methods is shown in Fig. 11. Fig. 12 illustrates the dynamic response of the BDFRG during active and reactive power step. From Figs. 11 and 12, it can be seen that dynamic

response of two methods is similar, but power ripple of the proposed PDPC method is lower. The primary current in power step condition has been shown in Fig. 13. There is a step change in the amplitude of the primary current at t = 1 s due to step change in the primary reactive power reference. At t = 2 s, only the sign of

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Figure 14

The mechanical torque of the BDFRG in power step condition: (a) the proposed PDPC method; (b) the DPC method.

Figure 15

The speed of the BDFRG in power step condition: (a) the proposed PDPC method; (b) the DPC method.

the active power reference changes. Therefore, the amount of the complex power is the same and the amplitude of the primary current does not change. The input mechanical torque to the BDFRG during test 2 has been shown in Fig. 14. Fig. 15 illustrates the BDFRG speed which is controlled to 800 rpm by less than 0.02% error. 7. Conclusion In this paper, a PDPC strategy for the BDFRG has been proposed. The active and reactive power variations of the BDFRG primary (power) winding have been predicted, which were used to calculate the required voltage of the secondary (control) winding to eliminate power errors. SVPWM approach was used to produce switching pulses. MATLAB/ Simulink software was utilized to simulate the BDFRG and the proposed control method. Furthermore, original DPC strategy was simulated for comparison. Result comparison of the proposed PDPC with DPC shows better performance of the proposed method in the BDFRG power control with fixed switching frequency and lower ripple in addition to fast dynamic response. References [1] R.E. Betz, M.G. Jovanovic, The brushless doubly fed reluctance machine and the synchronous reluctance machine – a comparison, IEEE Trans. Ind. Appl. 36 (4) (2000) 1103–1110. [2] R.E. Betz, M.G. Jovanovic, Theoretical analysis of control properties for the brushless doubly fed reluctance machine, IEEE Trans. Energy Convers. 17 (3) (2002) 332–339.

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Please cite this article in press as: M. Moazen et al., Model-based predictive direct power control of brushless doubly fed reluctance generator for wind power applications, Alexandria Eng. J. (2016), http://dx.doi.org/10.1016/j.aej.2016.08.004