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Back-to-back converter state-feedback control of DFIG (doubly-fed

induction generator)-based wind turbines

F.E.V. Taveiros

*

, L.S. Barros, F.B. Costa

Federal University of Rio Grande do Norte (UFRN), Natal, Brazil

a r t i c l e i n f o

Article history:

Received 17 December 2014 Received in revised form 4 May 2015

Accepted 9 June 2015 Available online 14 July 2015 Keywords:

Wind energy

DFIG (doubly-fed induction generator) State-feedback

Internal model control

VS-MRAC (variable-structure model reference adaptive control)

MPPT (maximum power point tracking)

a b s t r a c t

Control of DFIG (doubly-fed induction generator) is traditionally based on PI (proportional-integral) controllers and recently many papers have proposed sliding-mode based controllers. However, such controllers may excite unmodeled high-frequency system transients due to chattering, resulting in os-cillations or even in unforeseen instability. In order to overcome these drawbacks, this paper proposes a internal model state-feedback control strategy for regulation of rotor direct and quadrature currents for wind driven DFIG, which can keep the smooth control signal of the classical PI controller and, at the same time, provides robustness to external disturbances. The currents are controlled in order to accomplish reactive power support to the grid and MPPT (maximum power point tracking). The proposed state-feedback control strategy as well as the classical PI and the VS-MRAC (variable-structure model refer-ence adaptive control) sliding-mode strategy were discretized and implemented in a digital signal processor in order to interact with a real-time digital simulation of the DFIG-based wind energy con-version system. The proposed control structure achieved the fastest and the most robust dynamic response without stressing the converters or deteriorating the power quality.

© 2015 Elsevier Ltd. All rights reserved.

1. Introduction

Nowadays, there is an effort to minimize the environmental impact of electricity generation and, therefore, the search for a clean and renewable energy has received much attention throughout the world. The main advantages of renewable energy sources are neutrality with respect to greenhouse gas emissions and the infinite availability of the input energy that is converted into electricity. Among the renewable energy, wind energy pre-sents the highest growth and technological development in installed capacity and penetration in modern power systems[1]. Wind power generation already compete economically with traditional sources of generation in many sites, comparing with coal, fuel or gas-based plants, and in many other, it is likely to be competitive in the short term. Therefore, reliability and efficiency of wind turbines become important topics in research and industry. Accordingly, reliable and powerful control strategies are needed for wind energy conversion systems to achieve maximum performance.

Power control of wind turbines allows the MPPT (maximum power point tracking), which seeks to extract maximum power from the wind energy source[2,3]. The wind turbine harnessing is highly influenced by the rotor speed, therefore, modern wind tur-bines operate in the variable-speed mode, whose benefits include maximum power extraction and mechanical stress reduction[4]. Appropriate control of back-to-back converter scheme allows DFIG (doubly-fed induction generator)-based wind turbines to operate in the variable-speed mode[5,6]. The control schemes for DFIG are generally based on vector control concept associated with classical PI (proportional-integral) controllers[7]. This control technique has the limitations that its performance largely depends on the tuning of the PI parameters, the accuracy in machine parameters and the connected grid voltage conditions[8e10]. One of the main issues in any realistic control system is its robustness with respect to per-turbations and variations of its parameters. Therefore, aiming to reduce parametric dependence and disturbance rejection, papers have presented different control schemes for DFIG such as smart control or adaptive algorithms[8e16]. As advantages, these control strategies do not require the knowledge of the parameters of the system to be controlled, which reduce parametric dependence and remove cross-coupling compensation. These control structures achieve fast and robust dynamic response and are not sensitive to

* Corresponding author.

E-mail addresses:filipe.taveiros@ect.ufrn.br(F.E.V. Taveiros),lsalesbarros@dee. ufrn.br(L.S. Barros),flaviocosta@ect.ufrn.br(F.B. Costa).

Contents lists available atScienceDirect

Energy

j o u r n a l h o me p a g e : w w w . e l s e v i e r . c o m/ l o ca t e / e n e r g y

http://dx.doi.org/10.1016/j.energy.2015.06.027 0360-5442/© 2015 Elsevier Ltd. All rights reserved.

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parametric uncertainties. However, many of these strategies pro-duce high frequency control signal which may increase harmonic distortion, mechanical stresses and high heat losses in power cir-cuits due to chattering.

Considerable amount of work has been done on chattering is-sues in past and researchers are still working in this domain to get a chattering free controller. One effective technique to alleviate chattering is to introduce a boundary layer around the sliding surface. As a result, a continuous function around the sliding sur-face neighborhood is obtained as used in Ref.[10]. One algorithm that uses this technique is the VS-MRAC (variable-structure model reference adaptive control) sliding-mode strategy, originally pro-posed by Ref.[17]. It allows to reduce switching in the control signal, however, the controller performance is still limited by the power converters in mediumehigh power turbines, where the device switching frequency is normally below 1 kHz[18]. The above difficulties have been motivating the search for a robust control strategy that does not produce control signals of high frequency.

To overcome adaptive control limitations and still suppress disturbances, this paper proposes an internal model state-feedback approach to control the DFIG currents, which can keep the smooth control signal of the classical PI controller and, at the same time, provides robustness to external disturbances automatically, elimi-nating the need of disturbance compensation. Many studies have stated this technique presents better performance than classical PI,

[19e23]. The proposed state-feedback control strategy as well as the classical PI and the VS-MRAC sliding-mode strategy were dis-cretized and implemented in a digital signal processor, in order to interact with a real-time digital simulation of the DFIG-based wind energy conversion system. Real-time simulation can be used to get realistic behavior of the system and it is becoming an essential simulation environment for engineering design, especially in po-wer systems. A wind speed profile measured in a high wind po-tential site was used to evaluate the control systems under various realistic conditions. The proposed control structure achieved the fastest and the most robust dynamic response without stressing the converters or deteriorating the power quality.

The paper is organized as follows: Section2presents an over-view of the DFIG-based WECS (wind energy conversion system) and the basics of WECS power control. Section 3 presents the electrical models of the system, the classical control strategy and a sliding-mode control strategy. Section 4 presents the proposed state-feedback control technique. Section 5 presents the result assessment of the proposed control strategy in comparison with the classical control by means of real-time simulations. Section6

concludes the paper.

2. DFIG-based wind energy conversion system

Nowadays, commercial WECS based on the DFIG are the most used for ratings equal or greater than 1 MW[1]. The topology of WECS under consideration in this paper is depicted inFig. 1. The stator windings are connected direct to the grid bus, whereas the

rotor windings are connected to the RSC (rotor side converter). The GSC (grid side converter) is connected to the grid bus trough a line filter to reduce harmonic content injection. The RSC and GSC are connected to each other by a DC link, forming the back-to-back scheme. The appropriate synthesizing of the RSC and GSC volt-ages allows control of many machine variables, such as active and reactive power injected into the grid or electromagnetic torque and speed. In this paper, the control is focused on tracking the maximum power point of the active power delivered to the grid and reactive power supply.

2.1. Power control

The fraction of power extracted from the wind by a wind turbine is usually referred by the symbol Cp, standing for the coefficient of

performance or power coefficient. The actual mechanical power output Pmof a wind turbine is given by Ref.[6]

Pm¼1

2rpR

2V3

wCpðl; bÞ; (1)

where

r

is the air density, R is the blades length, Vwis the wind

speed,

b

is the blade pitch angle and

l

is the TSR (tip speed ratio), which is defined as

l ¼uTR

Vw ; (2)

whereuTis the turbine rotational speed.

Theoretically, a maximum of 59.3% of the wind power can be harnessed and converted by a turbine. However, actual turbines have maximum power coefficient around 35e45%[24,25]. As stated in (1), the power coefficient is a parcel of the TSR and the pitch angle, which means that the harnessing of the turbine can be controlled by means of

l

and

b

.

Variable-speed wind turbines are designed to achieve maximum aerodynamic efficiency over a wide range of wind speeds. However, this degree of freedom requires a power control scheme in order to track the maximum power available and to limit the captured power when the wind speed exceeds a certain level. All wind turbines are designed with some sort of power control. For variable-speed wind turbines, there are two types of power control: aerodynamic and generator control. Aerodynamic control aims to limit the power in very high winds in order to avoid damage to the wind turbine. The more commonly used form of aerodynamic po-wer control is to adjust the attack angle of the turbine blades accordingly to the wind speed, often realized by pitch angle control. On the other hand, generator control is realized by adjusting its speed in order to capture the energy from the wind in an optimal way. Any change in the rotor speed induces change in the turbine power capture.

Fig. 2depicts the ideal maximum power curve of a wind turbine with MPPT[26]in dependence of the wind speed Vw. The wind

turbine operation is considered in four-speed bands. In thefirst band (I), which goes from zero to the minimum speed of generation (cut-in), the wind speed is usually below 3 m/s. Up to this limit, the power generation just supplies the friction losses. Therefore, the turbine is shut down. In band II, the turbine operates with fixed-pitch and variable-speed, which the generator speed is controlled in order to obtain the maximum power available from the wind (MPPT operation).

Ideally, aerodynamic control only starts to operate when the generated power achieves its rated value, which characterizes the beginning of band III. In the third band, i.e., for wind speeds above rated, the turbine speed and power must be limited to its rated

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value in order to prevent mechanical damages. Therefore, the operation with MPPT is no longer applied. The pitch mechanism works in order to aerodynamically reduce power capture with the increase of the wind speed, that allows the turbine to work even with wind speeds above rated until a certain limit. In the fourth band (IV), the wind speed is considered too high and the turbine is shut down. The association of generator control and pitch control comprises the MPPT, limited to rating values of turbine and generator. Fig. 3 illustrates the combination of generator and aerodynamic control to form the MPPT through several wind speeds[18]. The values of the wind speed and turbine power are represented in per unit for simplicity.

For each wind speed, there is an optimal turbine rotational speed which takes the maximum power from wind. The pair tur-bine speed uT and mechanical power Pm form, therefore, the

operation point of the turbine. In other words, MPPT consists in maintain the operation point along the maximum power trajectory presented inFig. 3by means of variable-speed control. To achieve variable-speed operation, a back-to-back converter is placed be-tween the generator and the grid. The power converter will apply voltages of variable frequency and amplitude to the generator in order to control the rotor currents, which in turn allows control of the generator torque and speed.

3. System model and control

In order to control the DFIG speed, it is necessary to control the rotor currents by means of the rotor side converter. A model of the machine in Park dq frame is used to design the controller.

3.1. DFIG model

Referred both stator and rotor variables to the stator flux reference Park frame, the d-component of the statorflux is equal to the totalflux, whereas the q-component of the stator flux is null. In this approach, decoupled control between the stator active and reactive power is obtained. Therefore, referring to the chosen frame, the equations which describe the machine electromagnetic torque, stator active and reactive power are given by

Tem¼ PLLm s  fsirq  ; (3) Ps¼ LLm s vsqirq; (4) Qs¼ Vsq  Vsq usLs Lm Ls Ird  ; (5)

respectively, where Lsis the stator inductance, Lmis the mutual

inductance, v, i,

f

, and us are voltage, current,flux, and stator

electrical angular speed, respectively. The subscripts s and r denote stator and rotor variables, respectively, and the subscripts d and q denote direct and quadrature components, respectively.

For a strong gridvsqandfsare constant in steady-state.

There-fore, (3) and (4) shows that the electromagnetic torque and stator power can be directly controlled by the quadrature component of the rotor current irq, and (5) shows that the reactive power is

directly controlled by ird. The plant of control loop for irdand irqare

expressed as follows vrd¼ Rrirdþ a d dtird ausrirqþ Lm Ls d dtfsd; (6) vrq¼ Rrirqþ adtdirqþ ausrirdþ usrLLm sfsd; (7)

where Rrand Lrare the rotor resistance and inductance

respec-tively,

s

is the leakage coefficient of the machine, usr is the slip

speed anda ¼ sLr.

3.2. Classical PI control

The third terms of (6) and (7) are called cross-coupling terms. From the control point of view, the third and fourth terms are considered perturbations since they depend on variables external to the loop.Fig. 4depicts the classical control loop for irdand irq

with PI controllers and compensation of cross-coupling terms[6]. This strategy tries to compensate known perturbations in each control loop, which are the cross-coupling terms. The other per-turbations proportional to the stator flux and its derivative are expected to be small and compensated automatically by the PI controller. However, the compensation as presented inFig. 4 is often not used because it does not provide much improvement, once it is not robust. Although it works in steady-state for well-known parameters of the machine, this is not the case during a voltage dip or during a wind gust. In order to track the maximum power point efficiently, it is necessary a robust control system to

Fig. 2. Ideal power curve for wind turbines.

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ensure reference tracking despite parameters uncertainties and transients.

3.3. VS-MRAC sliding mode control

The VS-MRAC structure is depicted inFig. 5and is summarized as follows: A reference model M (s) is designed to describe the desired plant closed-loop dynamics, which in the case of DFIG control are the rotor dq currents. Nominal gainsqn and q2n are

introduced to the reference and to the plant output. These gains are obtained with some nominal model of the plant G (s) to match the reference model and, together, they form the nominal input Unom.

One effective technique to alleviate chattering is to introduce a boundary layer around the sliding surface. As a result, a continuous function around the sliding surface neighborhood is obtained as used in Ref.[10]. In the VS-MRAC, the discontinuous control signal Udis implemented by a modified relay with a linear boundary

re-gion around the sliding surface, given by

Ud¼ 8 < : Keo D ; jeoj  D K$sgnðeoÞ; jeoj > D (8)

whereD is the linear region width, K is the relay amplitude and eois

the error between the model currents im;dqand the generator

cur-rents ir;dq.

When the error lies inside the linear region, a PI controller is introduced to produce a smooth control signal and this alleviate chattering. To avoid deterioration of the transient behavior of the system, the PI compensator is saturated with an anti-reset-windup technique.

4. The proposed state-feedback control

The IMC-SF (internal model control state-feedback) approach is proposed in this paper in order to control the DFIG, which keeps the smooth control signal of the classical PI controller and, at the same time, provides robustness to external disturbances automatically, eliminating the need of feed-forward compensation.Fig. 6depicts the IMC-based state-feedback control structure.

The basic state-space equation is written as

_x ¼ Ax þ Bu þ Bd;

y¼ Cx; (9)

where A, B and C are the system, input, and output matrixes, respectively, x is the state vector, u and y are the system input and output, respectively, and d is the disturbance in the plant input. Robustness with respect to perturbations of the plant polynomial can be represented by a redundant internal model[22,23]. This can be done introducing an augmented state vector xa, which dynamic

behavior is given by the plant output error (e¼ r e y), as follows

_xa¼ e: (10)

Appending this new state as an internal model to (9) and introducing a state-feedback control law from the new state vector as follows u¼ ½ k ke  x xa  ; (11)

yields the augmented closed-loop system

Fig. 4. Current control loop with compensation of the cross terms.

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 _x _xa  ¼ Aa  x xa  þ  0 1  rþ  B 0  |ffl{zffl} Ba d; y¼ ½ C 0  |fflfflfflffl{zfflfflfflffl} Ca  x xa  ; (12) where Aa¼  Aþ Bk Bke C 0  : (13)

Namely, Aa, Ba and Caare the augmented system, input, and

output matrices, respectively. Recall that, if the modes of the closed-loop system in (12) are stable, the system transients will rapidly decay to practically zero. Thus, _xa¼ 0 and y ¼ r, therefore,

the tracking is achieved. The feedback gains are designed to this end.

If the pair (A,B) is controllable and the plant transfer function has no zero at s¼ 0, then all eigenvalues of the A-matrix in (12) can be assigned arbitrarily by selecting a feedback gain½ k ke[22].

Therefore, choosing stable eigenvalues for the closed-loop system, the disturbance is suppressed at the output both asymptotically and robustly. This robust tracking still holds for large parameter variations due to changes of load or aging. A better dynamic response is expected when a system is controlled by state-feedback control laws, in comparison with the classical control approach

[23], and, by feed-back of the system states and a IMC-based augmented state, it is possible to control a non-linear plant satis-factorily, whereas the classical control cannot accomplish this task

[21].

Applying the proposed control structure to the DFIG model, the state-variables are the rotor direct and quadrature currents idqand

the integral of error with respect to each reference:

x¼ 2 4Zirdq edq 3 5: (14)

Therefore, the fundamental control law for the dq components is vrdq¼ kdq ke 2 4Zirdq edq 3 5: (15) 5. Performance assessment

A real-time digital simulation of the DFIG-based wind energy conversion system described inTable 1was built on FPGA real-time

hardware-in-the-loop digital simulation developed with NI-RIO (National Instruments re-configurable I/O technology) in order to evaluate the controllers in a realistic set-up. The proposed IMC-SF strategy, the classical PI and VS-MRAC sliding-mode strategies were discretized and implemented in a DSP (digital signal proces-sor) in order to interact with the real-time digital simulations. The sampling frequency used was 1 kHz.

The controllers were designed to attain same dynamic perfor-mance in order to compare the results in the same scale. The pa-rameters of the controllers used for the rotor and grid sides are presented inTable 2, where Kp and Kiare the proportional and

integral gains of the PI controller, respectively,D and K are the linear region width and relay amplitude of the VS-MRAC controller and k is the feed-back gain vector of the proposed controller.

The wind speed time series profile shown inFig. 7was used to evaluate the control systems under various conditions. This wind profile was measured in one of the states with the highest wind potential of Brazil. The performance results are related to the 300 s highlighted inFig. 7, which describes a situation where the turbine was operating in nominal conditions, and then subjected to severe wind variations, which will require the controllers to maintain optimal power extraction and reactive power supply during those transients.

5.1. MPPT assessment

The rotor quadrature current was controlled to set the machine stator power according to the MPPT strategy presented inFig. 3, and the rotor direct current was controlled to provide reactive power according to the reference. In response to the wind speed sequence inFig. 7, which starts around the rated power speed of the turbine,

Fig. 6. Robust state-feedback control.

Table 1

DFIG-based WECS parameters.

Parameter Value

Rated power at Vw¼ 15 m=s 500 kW

Electrical frequency 60 Hz

Rated speed 1800 RPM

Rated line-to-line stator voltage 400 V

Poles 2

Base voltage 231 V

Base current 722 A

Base impedance 0.32U

Base inductance 849mH

Stator resistance 0.0625 p.u.

Stator leakage inductance 0.24 p.u.

Rotor resistance 0.0625 p.u.

Rotor leakage inductance 0.24 p.u.

Magnetizing inducante 4.95 p.u.

Lumped inertia 16.42 kg m2

Converter switching frequency 1500 Hz

DC-link capacitor 10 mF

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the active power of the machine stator is near to 1 p.u. during the first 50 s, as the wind speed remains bounded to the nominal value. The reactive power is controlled to provide 0.4 p.u. to the grid. Between t¼ 100 s and t ¼ 200 s, the wind presented speed varia-tions of high inclination below the rated wind speed, which means the generator control must act in order to capture the highest available power according to MPPT strategy. At t ¼ 120 s, the reactive power reference is lowered to provide 0.2 p.u. to the grid, returning to 0.4 p.u. at t¼ 220 s. Between t ¼ 200 s and t ¼ 250 s, the wind speed presents minor variations, and after that again high variations below the rated speed.

Regarding the maximum power tracking, the three controllers presented similar good results as the operation point trajectory is narrow to the optimal curve, as depicted inFig. 8(a)e(c). This is the expected result as the controllers were designed equally. However, the control variables of the generator results are very different. The resulting stator active and reactive power delivered to the grid, the rotor direct/quadrature voltage and currents are depicted in

Figs. 9e11 for classical PI, VS-MRAC and the proposed IMC-SF controllers, respectively. The PI and IMC-SF controllers presented smooth rotor direct/quadrature voltage signals, and the rotor direct/quadrature currents followed the references accordingly. In theory none of the controllers are designed to track ramp reference

signals, which happens specially in the case of the rotor quadrature current. Therefore, the quadrature current tracks the overall trend of the reference in the case of PI and IMC-SF controllers. On the other hand, the VS-MRAC sliding-mode results reveal a rotor quadrature current much more tied to the reference. This result can be numerically stated by means of RSME (root mean squared error) between the controlled variable and the reference, which is pre-sented inTable 3for the simulation with nominal values.

The VS-MRAC better tracking result comes with the price of chattering appearance in the rotor voltage control signals, as illustrated in Fig. 10. While in the case of the rotor quadrature current the switched control signal provided a better tracking, in the case of the rotor direct current it presented the opposite result. Fast switching may generate unexpected chattering, which may excite unmodeled high-frequency system transients and even result in unforeseen instability. It appears to be what happened in the case of direct current control, where chattering in the rotor direct voltage excited high oscillations in the direct current and reactive power waveforms.

In addition to the aforementioned need for robustness regarding the parametric variation in the case of DFIG control, another issue is the power converter limitations and constraints. The power con-verters have limited bandwidth and increased heat losses are un-desirable. Chattering issue limits sliding-mode applicability in practical applications, because the switching frequency of the po-wer converter limits the control signal bandwidth[8]. It therefore limits the power of action of many adaptive control strategies, which are often based on switching control laws. In some of the sliding-mode proposing papers, the back-to-back converters are carried out as ideal voltage sources. Nevertheless, previous studies have also not considered the chattering phenomenon of the sliding-mode control [27], which may increase mechanical and thermal stresses in the converters and in the generator[28].

Chattering phenomenon in power waveforms has already been reported in Ref.[10], where the boundary layer around the sliding surface was proposed to remedy this problem. However, the results in this paper revealed the problem still exists in the reactive power waveform. In the case of VS-MRAC algorithm, it similarly depends on a commitment relationship between the sliding-mode discon-tinuous control signal and the PI regulator, regarding the linear region widthD. The lower D, higher robustness and dynamic per-formance is achieved, however, higher chattering may be excited. The higherD, smoother control signals are generated and conse-quently less chattering. However, the controller may result acting as PI regulator most of the time. In this paper, the linear region widthD was extensively tuned by trial and error in order to attain the lowest chattering levels while keeping the sliding-mode controller characteristics. It resulted in a chosen value of

Table 2

Controllers parameters.

Classical PI VS-MRAC Proposed IMC-SF

Kp¼ 0:04 D ¼ 0:68 p.u. k¼ ½ 0:04 2 

Ki¼ 2:05 K¼ 1:4 p.u.

Fig. 7. Wind speed profile, courtesy of the Brazilian National Institute for Spatial Research (INPE).

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D ¼ 0:68 p.u., which means that the controller will lie in the linear boundary ifjeoj  490 A.

5.2. Power quality assessment

Chattering depreciates not only power and current waveforms, but most importantly, power quality. The harmonic distortion is heavily increased every time chattering dynamics are excited. In

Fig. 12is presented the measured THD (total harmonic distortion) for each 10 cycles of the fundamental frequency of the stator cur-rents. During periods of high wind power availability, the THD re-mains below 5% level. On the other hand, during period 120 t  200, the wind power captured is lower and, therefore, the harmonic distortion is more expressive. While IMC-SF and PI controllers presented almost the same results, the sliding-mode

controller presented high THD levels during all period of simula-tion due to chattering, even during high wind power availability. Despite chattering effects not being visually present in the stator active power and rotor quadrature currents waveforms inFig. 10, the harmonic distortion analysis clearly reveal its presence. This directly impacts negatively the power quality delivered to the grid.

5.3. Robustness assessment

The results presented inFigs. 9 and 11show that PI and IMC-SF controllers played quite similar performance. RMSE values in

Table 3 reveal a slight difference between them. However, the impact of DFIG parameters variation on MPPT and reactive power control performance was also carried out. Since the leakageflux magnetic path is mainly air in the generator, the variations of the

Fig. 9. PI controller results.

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stator and rotor leakage inductances during operation are insig-nificant. However, mutual inductance variation needs to be considered due to possible variation of the magnetic permeability of the stator and rotor cores under different operating conditions. Besides, variations of stator and rotor resistances should also be taken into account[10]. Therefore, a situation considering errors of50% in the machine resistances and in the mutual inductance was simulated and the results are presented inFigs. 14e16for the PI, VS-MRAC and IMC-SF, respectively.

Performance deterioration in PI controller is immediately revealed in the rotor quadrature current waveform, which is pre-sented enlarged between t¼ 120 s and t ¼ 200 s to enhance visi-bility. Low robust tracking to PI controller specially in the case of ramp reference is now evidenced. MPPT highly depends on the rotor quadrature current control and, since the control was not able

to robustly track the reference, MPPT performance is compromised. This result is presented in the MPPT trajectory depicted inFig. 13(a), where it deviates from the optimal trajectory. The stator reactive power also shows depreciation, due to the presence of high noise in the rotor direct current it also reflects in the reactive power waveform. The noise presented in those waveforms is exactly the effect of the external disturbances in (6) and (7), which are not robustly rejected.

The VS-MRAC sliding-mode controller in turn, maintained its optimal performance keeping track of rotor quadrature current reference. MPPT trajectory still tied to the optimal as depicted in

Fig. 13(b). However, chattering issue still present in reactive power waveform. It is always a concern that, in a sudden change of the DFIG operation mode for example, the controller may loose the ability to control the reactive power, causing instability or damage to the system.

Even in the presence of parameter mismatch, the proposed IMC-SF controller was able to track the rotor quadrature current refer-ence efficiently. MPPT trajectory is very narrowed to the optimal as depicted in 13(c). In addition, the rotor direct current presented much less noise, and consequently the reactive power. It arises as a consequence of the controlled variables being controlled faster, and the disturbances present in the control loop being robustly sup-pressed. As result, the rotor quadrature current tracks the reference faster, robustly and less responsive to the disturbances.

Fig. 17 presents the disturbance rejection impact on MPPT by means of the power coefficient Cp. It is depicted the normalized

value of Cp over time for the three controllers, where 1 means

maximum power extraction. The proposed IMC-SF and VS-MRAC controllers presented similar results, keeping track of at least 97% of available power. On the other hand, PI controller presented levels as low as 93%. It means that during wind speed gusts, the proposed IMC-SF and sliding-mode based controllers are able to capture more power than classical PI controller.

The aforementioned results reveal that the proposed IMC-SF controller presented better performance, as it robustly suppresses the disturbances in the plant input and converges faster to the reference. It showed better reliability to keep track of MPPT and to recover in case of a disturbance or parameter mismatch. In addi-tion, the proposed controller does not produce high-frequency

Fig. 11. Proposed IMC-SF controller results.

Table 3

Root mean squared error (p.u.) in rotor quadrature current.

Nominal parameters Parameter variation

Classical PI 0.0334 0.0515

VS-MRAC 0.0270 0.0279

Proposed IMC-SF 0.0337 0.0330

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control signals. It also comes as a result of the faster disturbance rejection, which allows the control loops to be controlled more smoothly. Hence, it produces lower voltage steps and less switch-ing, which requires less effort from the power converters. It makes the proposed IMC-SF strategy a suitable alternative to control the WECS as it presents good performance, disturbance rejection and robustness without producing high frequency control signals.

Table 4 summarizes the performance and features of the three compared controllers.

6. Conclusion

This paper presented a regulatory state-feedback design method that automatically reject disturbances at the input of the plant. This method was applied to the DFIG-based wind energy conversion

system in order to optimally control the rotor quadrature current, which provides control of the stator active power injected into the grid, and the rotor direct current, which provides control of the reactive power injected into the grid. The proposed IMC-SF strategy along with the classical PI and the VS-MRAC sliding-mode strategy were discretized and implemented in a digital signal processor interacting with a real-time digital simulation of the DFIG-based WECS, and actual wind data were utilized.

The state-feedback controller presented the best performance, as it robustly suppresses the disturbances in the plant input and converges fastest to the reference. It showed the best reliability to keep MPPT at optimal trajectory and to recover in case of a disturbance or parameter mismatch. It also did not produce high-frequency control signals and therefore was chattering-free. Random disturbances that exist in the wind speed along with

Fig. 13. MPPT Trajectory with parameter variations.

Fig. 14. PI controller results with parameters variation.

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electromechanical transients are important factors influencing the controller performance in the WECS. The assessment showed that the proposed state-feedback controller deals better with such conditions and is a suitable alternative to the conventional control structure of DFIG-based WECS.

Acknowledgment

This work was supported by the Brazilian National Research-Council (CNPq).

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[20] Harnefors L, Nee H-P. Model-based current control of ac machines using the internal model control method. IEEE Trans Industry Appl 1998;34:133e41. [21] Pradeepkannan D, Sathiyamoorthy S. Design and modeling of state feedback

with integral controller for a non-linear spherical tank process. Int J Emerg Technol Adv Eng 2012;2.

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[26] Sim~oes G, Farret F. Alternative energy systems: design and analysis with in-duction generators, power electronics and applications series. CRC Press; 2008. Fig. 16. Proposed IMC-SF controller results with parameters variation.

Fig. 17. Normalized power coefficient. Table 4

Controllers performance and features.

Feature PI VS-MRAC IMC-SF

Greater parametric dependence ✓

Less sensitiveness to disturbances ✓ ✓

Smoother control signal ✓ ✓

Faster control of inner loops ✓ ✓

Higher resiliency ✓ ✓

Full dq decoupling ✓ ✓

More suitable for DFIG control ✓

Reduced computational cost ✓ ✓ ✓

All plant states must be known ✓

Control reading only the output of the plant ✓ ✓

(11)

[27] Liu Y, Zhang Q, Wang C, Wang N. A control strategy for microgrid inverters based on adaptive three-order sliding mode and optimized droop controls. Electr Power Syst Res 2014;117:192e201.

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Referências

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