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Power control for wind power generation and current harmonic ﬁltering with doubly fed induction generator Adson B. Moreira a, b, *, Tarcio A.S. Barros b, Vanessa S.C. Teixeira a, b, Ernesto Ruppert b a b

, Campus de Sobral - UFC, Brazil Federal University of Ceara University of Campinas - UNICAMP, Brazil

a r t i c l e i n f o

a b s t r a c t

Article history: Received 12 July 2016 Received in revised form 5 January 2017 Accepted 27 January 2017 Available online 31 January 2017

This paper describes a wind power system which controls the active and reactive generated powers as well as it performs the function of ﬁltering the harmonic components of the grid currents. From the grid side converter, the harmonic ﬁltering is achieved by an algorithm proposed by compensation of harmonics. This technique ensures the improvement of power quality. The machine side converter controls the active and reactive powers that are delivered to the electric grid by the stator ﬂux oriented control. The design methodology of the controllers used is presented. This paper is distinguished by three key contributions. The ﬁrst contribution of this article is the tutorial character, it should assist in the development of future work. The second is the analysis of the harmonic ﬁltering behavior for some operating points of the DFIG/APF system. The third is the application of the precise model of the DC link voltage dynamics, allowing verifying the stability of the system control for each DFIG/APF (active power ﬁlter) operating point. Simulation and experimental results conﬁrm the effectiveness of the proposed research. © 2017 Elsevier Ltd. All rights reserved.

Keywords: Active power ﬁlter Back-to-back converter Controllers design DFIG Harmonic ﬁlter Power generation

1. Introduction Energy quality is an important aspect not only of wind power installation, but of all that use electronic power converters connected to the grid. The increase in applications of electronic devices such as variable speed drives, computer power source, among other things, they result in harmonic injection of current on the grid. This harmonic pollution distorts voltage and current waveforms in the grid with the presence of harmonic components, providing low power factor, possible warming, reactive power ﬂuctuating, ﬂicker, swell, among others. Active power ﬁlter is a solution for reducing harmonics of electric current. The active power ﬁlter (APF) detects the harmonic electric current of nonlinear load and injects a compensation of electrical current to mitigate the harmonic components that go into the grid [1]. Applications on APF have been performed by means of changes in DFIG (Doubly Fed Induction Generator) converter control, which can improve the quality of electric power supplied and compensate

, Campus de Sobral - UFC, * Corresponding author. Federal University of Ceara Brazil. E-mail address: [email protected] (A.B. Moreira). http://dx.doi.org/10.1016/j.renene.2017.01.059 0960-1481/© 2017 Elsevier Ltd. All rights reserved.

the most harmonic currents [1e7]. Reference [2] proposes a control strategy by rotor side converter (RSC) that achieves reactive compensation and active ﬁltering of harmonics grid currents of 5th. and 7th. orders. While [3] shows a similar system in Ref. [2], however the system manages the priority between the maximum power point tracking (MPPT) and improvement at power quality. The works [1,4e6] propose a system that controls the active and reactive powers and performs compensation of harmonic current, by modifying the RSC control using the sliding mode controller type. In these studies [1,6], the current references for harmonic compensation are determined from the load current, calculated by the instantaneous power PQ theory [8]. Paper [4] proposes a wind power system and the mitigation of grid harmonic currents, using current controllers by hysteresis with constant switching frequency. It was obtained THD bigger than in Ref. [5], that used current controller by hysteresis with variable switching frequency. The authors, in Ref. [7], show the DFIG running with control delivery power to the electric grid, by using sensorless vector control, MPPT and mitigating grid harmonics currents. Research on mitigation of grid harmonic currents from RSC control [1e7], using the harmonic currents injection in DFIG, and the electric machine is not designed for it, which increases losses and leads to a not adequate operation, which can cause a reduction

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in its useful life. Recently, other studies have implemented the current harmonic compensation based on grid side converter (GSC) [9e11]. In Ref. [10], the currents reference for harmonic current compensation are determined from the load current, calculated by the instantaneous power PQ theory [8]. In Refs. [10,11], the reference currents are determined using synchronous reference Frame (SRF) theory is based on the transformation of currents in synchronously rotating dq frame [12]. In the literature, most of the studies addressing the simulation results. Few studies present the experimental results [7,11]. The authors in Ref. [7] implement the functions of the system DFIG/APF using an experimental setup developed with microcontroller to include the ﬁltering function from RSC control. However, the authors did not determine the THD of grid current, making the strategy analysis difﬁcult. In Ref. [11], the operation of DFIG/APF system is implemented on the dSPACE system (DS1103). It is sold on the market and has a high cost. The authors present the simulation and experimental results of THD of grid current before and after ﬁltering through GSC control, using a control technique with current controllers hysteresis. The researches do not discuss the behavior ﬁltering for the operation of the DFIG with grid current harmonics ﬁltering in the literature, either for RSC control or for GSC control. In this research, we propose a control strategy for a wind-power system with DFIG, shown in Fig. 1. Besides the power control, the proposed system improves the energy quality by using the converter connected to the grid to perform active ﬁltering in the point of common coupling (PCC) of the electric grid in the presence of three-phase full bridge rectiﬁer with LiL feeding a resistive load. The control of active and reactive powers of the generator is accomplished through ﬁeld vector control by stator. The active ﬁltering function is performed by the grid side converter, using dq reference frame. The power control and ﬁltering function occur simultaneously. In harmonic identiﬁcation, the extraction of the fundamental component is based on the SRF theory. Also, this paper presents a design methodology of the controllers employed in these techniques. The proposed control of DFIG/APF improves the electric power quality in the electric grid. Simulation and experimental results are presented to demonstrate the idea of this study. The paper contributions are: (1) the tutorial character, assisting in the development of future researches; (2) the analysis of the harmonic ﬁltering behavior for some operating points of the DFIG/ APF system; (3) the application of the precise model of the DC link voltage dynamics, allowing evaluating the stability of the system control for each DFIG/APF operating point. The paper is organized as follows: Section 2 describes the

P s, Qs

is

RSC Ce

GSC

2. Power control of the doubly fed induction generator - DFIG The generator is controlled in the reference of synchronous rotation with the stator ﬂux directed along the axis d. Thus, the active and the reactive powers of the stator are decoupled. The mathematical model of a DFIG in the d-q reference frame is described from (1) to (6) [13],

djsd ue jsq dt djsq þ ue jsd ¼ rs isq þ dt

(1)

djrd usl jrq dt djrq þ usl jrd ¼ rr irq þ dt

(2)

vsd ¼ rs isd þ vsq

vrd ¼ rr ird þ vrq

usl ¼ ue ur

(3)

jsd ¼ Ls isd þ Lm ird jsq ¼ Ls isq þ Lm irq

(4)

jrd ¼ Lr ird þ Lm isd jrq ¼ Lr irq þ Lm isq

(5)

p Te ¼ 3 Lm isq ird isd irq 2

(6)

where vsd, vsq and vrd, vrq are stator and rotor voltages in the d-q reference frame, rs and rr are the stator and rotor per phase electrical resistances, isd, isq and ird, irq are stator and rotor currents in the d-q reference frame, jsd, jsq and jrd, jrq are stator and rotor ﬂuxes in the d-q reference frame, Ls, Lr and Lm are stator, rotor and magnetizing per phase inductances, ue and ur are the synchronous and rotor speeds, Te is the electromagnetic torque, and p is the number of poles. The speed generator is given by (7):

idfig

is

DFIG

studied the power control of the generator. Section 3 contains the technique proposed of harmonic current ﬁltering. Section 4 and 5 contain the design methodology of the controllers. Section 6 shows simulation results and Section 7 shows experimental veriﬁcations. Section 8 presents stability analysis of the system and Section 9 presents feasible application of the wind turbine converter in range of MVA up to 15 kHz. Conclusions are summarized in Section 10.

PCC

P g , Qg ig

Electric grid

Lg

L LiL

ir ωm

RSC control

Ps* Qs*

Vdc

iL

GSC control iLhdq

Vdc*

RL Non linear load

Harmonic isolator

Fig. 1. Proposed DFIG/APF operation diagram.

A.B. Moreira et al. / Renewable Energy 107 (2017) 181e193

2 p

um ¼ ur

(7)

The dynamic of the mechanic system is expressed by (8):

J

d um ¼ Tm Te Bum dt

(8)

where: J is the moment of inertia and B is the coefﬁcient of viscous friction of the system and Tm is the load torque. The magnetic ﬂux in the stator in d and q axis is determined by (9):

jsq

djsq ¼0 ¼ 0 and dt

js ¼ jsd ¼ Lm ims

(9)

djsd ¼0 and dt

From (4), (5) and (9), the components of the electric current of dq quadrature of stator can be obtained by (10) and (11):

isq ¼

isd ¼

Lm irq Ls

js Ls

Lm i Ls rd

From (13) into (15), one observes that the active and reactive powers can be controlled by the quadrature components of rotor current, considering the constant voltage. Fig. 2 shows the block diagram for the rotor side converter (RSC). The control diagram is obtained from (1) to (15). The converter controls the active and reactive powers of the DFIG stator, where s ¼ 1 - L2m/LsLr and ims is the magnetizing current. The PLL (Phase Locked Loop) block is responsible for the synchronization between the grid voltage and the one produced by the converter, generating a q angle in phase with grid voltage. In Fig. 2, the control scheme, qsl is slip the angle calculated by (16),

qsl ¼ qe qr ;

(10)

Pref ¼

i 3h * vd id þ vq i*q 2

(17)

(11)

Qref ¼

i 3h vd i*q þ vq i*d 2

(18)

Since vq ¼ 0, (17) and (18) can be simpliﬁed as (19) and (20):

3 v i þ vsq isq 2 sd sd

(12)

Substituting (10) into (12) and considering vsd ¼ 0, the active power is given by (13):

3 Lm Ps ¼ vs irq 2 Ls

2 P 3vd ref

(19)

2 i*q ¼ Q 3vd ref

(20)

3. Active power ﬁlter in the GSC

3 vsq isd vsd isq 2

(14)

Similarly to the calculation of the active power, replacing (11) into (14), thus the reactive power of the stator can be deﬁned by (15):

Qs ¼

i*d ¼

(13)

The stator reactive power is given by (14):

Qs ¼

(16)

where qr is the electrical angle of the rotor. The GSC block diagram (Fig. 3) uses current loops to id and iq, having i*d as reference from the DC link. Since i*q ¼ 0, the converter operates at a unity power factor. The reference signal generator (Fig. 3) produces the current reference (i*d, i*q), from (17) and (18):

The stator active power is deﬁned by (12):

Ps ¼

183

3 Lm vs vs ird 2 Ls ue Lm

(15)

The presence of a non-linear load in the PCC should distort the grid current, then the use of active ﬁlter can reduce the distortion of the current ﬂowing through the electric grid. The control structure of the grid side converter is modiﬁed with the inclusion of iLhd in the loop id and iLhq in the loop iq, as shown in Fig. 4. These modiﬁcations maintain the DC link voltage and allows mitigate harmonic currents in the electric grid, as shown in the control algorithm, Fig. 4. New reference currents for harmonic compensation, ird and irq,

σLrωslirq Qs*

ird*

Eq. 13

Ps*

Eq. 15

irq*

PI(z)

ird

PI(z)

rr 0.5.Vdc rr

/

dq PWM

/

irq

θsl

σLrωslirq + (1-σ)Lrωslims ir

abc

θsl

dq

θe

θ π /2

θsl Fig. 2. Control scheme of rotor side converter.

RSC

abc

PLL

vs θr

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Vd - iqLω

id id*

PI(z)

dq

/

iq

/

PI(z)

iq

abc θ

Vq + idLω

Vdc* Vdc

Pmax Pref

PI(z)

X

GSC

PWM

0.5.Vdc

*

vs

id*

Reference signal generator

Pmin Qref

X

PLL

iq*

Fig. 3. Control scheme of grid side converter (GSC).

id* iLhd

idr

iLhq

r

PI(z)

0.5 Vdc

iq

Vdc

iq

X

/

dq

/

PI(z)

iq* Vdc*

Vd - iqLω

id

θ

Vq + idLω Pmax Pref

PI(z)

Pmin Qref

X

PWM

GSC

abc

Reference signal generator

vs

PLL

id* iq*

Fig. 4. Proposed control scheme of active power ﬁlter (APF) in the GSC.

are given by (21):

ird ¼ i*d þ iLhd irq ¼ i*q þ iLhq

(21)

where iLhd and iLhq are harmonic current components of nonlinear load in the d-q reference frame, id and iq are currents of the grid side converter in the d-q reference frame. Electric current ﬁltering in the PCC is obtained from current measurement of the three-phase nonlinear load and extraction of the desired components. The measured components are transformed in the d-q reference frame (iLd, iLq) by (22).

2

iLd iLq

¼

26 6 cos q 6 3 4 sinq

2p cos q 3 2p sin q 3

3 2p 2 3 cos q 3 7 iLa 74 5 ; i 7 5 Lb 2p iLc sin q 3 (22)

where iLd and iLq are nonlinear load currents in the d-q reference

frame. The currents of the three-phase nonlinear load (iLd, iLq) are measured and processed by low-pass ﬁlters to extract the fundamental component. The fundamental component of current is drawn from the total load current, and then the harmonic current components are isolated from (23). The cutoff frequency of the ﬁlter is 12 Hz.

iLhd ¼ iLd iLfd iLhq ¼ iLq iLfq

(23)

where iLfd and iLfq are fundamental components of nonlinear load, iLhd and iLhd are the other harmonic components of nonlinear load, in the d-q reference frame. Harmonic components identiﬁed in Fig. 5 are added to the reference currents produced by the reference signal generator in Fig. 4. 4. Current and dc link voltage control The dynamics of the three-phase voltage source converter (VSC)

A.B. Moreira et al. / Renewable Energy 107 (2017) 181e193

iLa iLb iLc

iLhd

iLfd

abc

iLd

dq

iLq

iLhq

Fig. 5. Proposed harmonic current identiﬁer.

Gp2(s) PI ( s )

G (s)

idq

G p (s)

Fig. 6. Control block diagram of a current-controlled VSC system.

connected to the grid with L ﬁlter, in Fig. 6, is represented by blocks: PI(s) controller, G(s) represents the PWM dynamic of the VSC, Gp(s) is the plant of the VSC with L ﬁlter [13]. The transfer function Gp(s) is given by (24):

Gp ðsÞ ¼

1 Ls þ R

(24)

where: L is ﬁlter of the VSC; R is ﬁlter resistance, Gp2(s) is G(s) in cascade with Gp(s). The controllers design of GSC and RSC is done through frequency response method, it considers the dynamics of the PWM of the VSC, which is represented by a time delay, G(s) (25) [14]:

GðsÞ ¼

1 s T4s

jPIðjuÞj$ Gp2 ðjuÞ ¼ 1

(31)

Therefore, substituting (27) into (31) and isolating kp, a second condition for controller design is determined by (32):

iLfq

θ

idq*

185

1

kp ¼

Gp2 ðjuc Þ $j1 j=uc Ti j

(32)

According to [16,17], a well-designed control system should have a gain margin (GM) higher than 6 dB and a phase margin (PM) between 30 and 60 . Thus, the values of kp ¼ 95.56 and Ti ¼ 0.0126 of GSC current controllers were calculated by GM > 6 dB and PM of 60 , for gain crossover frequency of 16,000 rad/s, Fig. 7. Dynamic of the DC link voltage controller of the VSC in Fig. 8 is represented by: PI controller, Gi(s) is closed-loop of the GSC current and Gv(s) represents DC link voltage dynamic, Gv2(s) is Gi(s) in cascaded with Gv(s). In the technical literature, the instantaneous power of the interface reactors is often neglected [18e20], thus the simpliﬁed model transfer function Gv(s) described with details in Ref. [13] is given by:

2 1 ; Gv ðsÞ ¼ C s

(33)

where C is an equivalent capacitance of the VSC. This model has no dependence on the operating point. However, the precise model considers the instantaneous powers of the reactors and the transfer function Gv(s) to according [13] and becomes (34):

(25)

1 þ s T4s

The design methodology of the controller is described in (26) to (32). The transfer function of the PI controller is given by (26):

1 PIðsÞ ¼ kp 1 þ Ti $s

(26)

for s ¼ ju, it results:

PIðjuÞ ¼ kp 1 þ

1 Ti $ju

1 :PIðjuÞ ¼ arctan Ti $u

(27)

(28)

The desired phase margin for the controlled system is calculated by (29) [15]:

MFd ¼ p þ :Gp2 ðjuc Þ þ :PIðjuc Þ;

(29)

where uc is the gain crossover frequency. Substituting (28) into (29) and isolating Ti, it obtains a design condition (30):

1 Ti ¼ uc $tan p þ :Gp2 ðjuc Þ MFd

(30)

As the magnitude of the open-loop transfer of control system is unit at the crossover, it has (31):

Fig. 7. Open-loop frequency response controller of id and iq of GSC.

v*dc 2

Gv2(s) − PI ( s)

Gi ( s )

Gv ( s )

vdc 2

Fig. 8. Block diagram of DC-link voltage control loop.

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Gv ðsÞ ¼

2 1 ts þ ; C s

(34)

2LP t ¼ exto 2 3Vsd

(35)

where Pexto is active power. Equation (35) indicates that t is proportional to the active power ﬂow between source and converter. In the case of converter operating mode, Pexto > 0 and t > 0 and in the rectiﬁer operating mode, Pexto < 0 and t < 0. Equation (33) can be consider a particular case of (34), when t ¼ 0. The values of kp ¼ 0.0646 and Ti ¼ 0.0106 of the DC link voltage controller were obtained for GM > 6 dB, PM of 60 and gain crossover frequency of 150 rad/s, Fig. 9. In the rectifying mode of operation, where Pexto is negative, t is negative and results in reduction in the phase of Gv(s). The phase drops further as the absolute value of Pexto becomes larger. Based on (33), the plant zero is given by z ¼ 1/t. Therefore, a negative t corresponds to a zero on the right-half plane (RHP). Consequently, the DC link voltage dynamics is a non-minimum-phase system in the rectifying mode of operation [21]. This non-minimum-phase property has a detrimental impact on the system stability and must be accounted for in the control design process [21].

5. RSC current control The current dynamic of the voltage source converter connected to the DFIG, in Fig. 10, is represented by: PI controller, G(s) represents the PWM dynamic of the VSC and Gm(s) is DFIG plant. The transfer function Gm(s) matches (35) [13]

Gm ðsÞ ¼

1

sLr s þ Rr

;

(36)

where s is 1 - (L2m/LsLr). As the adopted controller for RSC control is PI controller, it was used the same design criteria for DC link voltage controller [14]. The values of kp ¼ 6.9 and Ti ¼ 0.0028 of RSC current controller were obtained for GM > 6 dB, PM of 60 and gain crossover frequency of 5000 rad/s, Fig. 11. 6. Simulation results The system shown in Fig. 1 was modeled and simulated in the Matlab/Simulink® associated with SimPowerSystem toolbox to analyze the control strategy proposed by DFIG/APF system. The circuit shown consists of DFIG, converters, a balanced three-phase source, a three-phase full bridge rectiﬁer with LiL feeding a R load and the DFIG. The parameters used in the simulation are shown in Appendix. The stator terminals are connected to electric grid and rotor terminals are connected to grid through back-to-back converter bridge. The RSC controls active and reactive power, while GSC keeps DC link voltage constant and can realize function of active ﬁltering. The PWM modulation strategy was used to carry out converter switching logic, which makes the power converter to behave like a controlled voltage, the voltage source converter. Control algorithms RSC (Fig. 2) and GSC (Fig. 4) were modeled in Simulink. A transformation dq-abc was used to obtain the current references in these algorithms. The current references to the GSC and RSC were used to implement the PWM modulation on both converters. The simulation used discrete models and the controllers were discretized from Tustin method with sampling frequency equal to 30 kHz, while the switching frequency of the converters is 15 kHz. Two cases of system operation were studied. In case 1, the generator delivers active power to the non-linear load. In case 2, the generator delivers active power and performs active ﬁltering of grid current in the presence of the same load. 6.1. Case 1 In the ﬁrst case, the doubly fed induction generator operates in

Fig. 9. Open-loop frequency response of DC link voltage controller of GSC.

irdq*

PI ( s )

G (s)

Gm ( s )

Fig. 10. Block diagram of the rotor current-control loop.

irdq

Fig. 11. Open-loop frequency response controller of ird and irq of DFIG.

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187

the traditional mode, providing power. The components idr and iqr follow the references i*dr and i*qr, Fig. 13, controlling the power Ps and Qs, Fig. 14. The DC link voltage (Vdc) is set to 400 V, Fig. 12. The generated power remains stable without showing overshoot. The waveforms of the grid voltage, generator, load and electric grid currents are obtained for the system running in generator mode, partially feeding a nonlinear load for the generator speed of 177.93 rad/s (Fig. 15). In order to evaluate the harmonic content of current, the total harmonic distortion (THD) is considered. The calculation of the THD is given by:

THDð%Þ ¼ 100

qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ P∞ 2 h¼2 I h I1

(37)

where I1 is fundamental and Ih are others harmonics components of grid current. The non-linear load current and its harmonic spectrum are shown in Fig. 16. The waveform of the load current is distorted and

Fig. 12. Response of control loop of the dc link voltage.

Fig. 14. Response of active (Ps) and reactive (Qs) power delivered to the electric grid.

Fig. 15. Waveforms of grid voltage, DFIG, load and electric grid currents for the system running in generator mode.

shows a total harmonic distortion (THD) of the load current of 19.45%. The current waveform at the PCC is distorted and shows THD of 16.55% at 177.93 rad/s, in Fig. 17, well above the value required by the main rules governing the connection of generators to the low voltage electric grid [22]. This current distortion in the electric grid can cause a distorted voltage to other consumers connected to the PCC. The current spectrum of the electric grid shows that among the main harmonics that contribute to this distortion are the oddorder harmonics (5th. and 7th.). 6.2. Case 2

Fig. 13. Response of control loop of the rotor current controllers ird and irq.

In the second case, the generator provides powers and acts with active ﬁltering function. The behavior of the power control is similar to Figs. 13 and 14, due to the RSC control algorithm is the same in both cases. Fig. 18 shows the waveforms of the generator, load, active ﬁlter and electric grid currents, which are obtained from the system running with active ﬁltering function, feeding a nonlinear load, in Fig. 16, for the generator speed of 177.93 rad/s.

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A.B. Moreira et al. / Renewable Energy 107 (2017) 181e193

Fig. 16. Harmonic spectrum of load current.

Fig. 17. Harmonic spectrum of the grid current without ﬁltering at speed of 177.93 rad/ s.

Fig. 18. Waveforms of DFIG, load, active ﬁlter, electric grid currents for system running in APF mode.

Fig. 19. Harmonic spectrum of the grid current with ﬁltering at speed of 177.93 rad/s.

The waveform of the current grid has sinusoidal behavior, unlike the current shown in Fig. 15, due to harmonic current compensation produced by the generator in the active ﬁlter mode. The THD value obtained is suitable to the main rules governing the connection of generators of low-voltage grid. The spectrum of the grid current before (case 1) and after the active ﬁltering (case 2) shows THD of the electric grid that is reduced from 16.55% to 3.26% at 177.93 rad/s. Comparing the spectrum harmonic of the grid current in case 1 with one in case 2, we veriﬁed that the odd harmonic components are attenuated (Figs. 17 and 19). 7. Experimental results The experimental setup has been designed and assembled and consists of: DFIG coupled to a squirrel cage induction controlled by converter, working as the wind turbine in Fig. 20. Routines in C language were developed for the measured

Fig. 20. Experimental setup of the tests DFIG.

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189

variables (speed, electric currents and voltages), protection, drive relays and generation of PWM pulses. A software was developed in Labview to get the data and supervises the system. In the control of DFIG RSC, the rotor speed is set to 1700 r/min. Both the RSC and GSC control strategies were implemented on the same DSP TMS320F28335, and the driver for IGBT is SEMIKRON SKHI20OPA. The switching frequency is 15 kHz with a sampling frequency of 30 kHz. 7.1. Case 1 In this case, the system runs at traditional mode. The DC-link voltage is set to 400 V, Fig. 21, it is observed the response of the rotor currents following the reference currents (Fig. 22) and controlling the powers (Fig. 23). The value reference current irq is modiﬁed from 4 A to 8 A, while ird is zero, the reactive power is provided by the electric grid. The active power was changed from 350 W to 700 W, while the reactive power kept 1,300VAr. In the presence of a nonlinear load three-phase in PCC, the waveforms of the generator, load and grid currents, in Fig. 24, show similar behavior to Section 5. The load and electric grid currents are distorted with THD of 21.09% (Fig. 25) and 17.46% (Fig. 26).

Fig. 23. Experimental results of the response of active (Ps) and reactive (Qs) power delivered to the electric grid.

7.2. Case 2 In this case, the generator provides electric power and GSC works as APF in the presence of a three-phase nonlinear load in

Fig. 24. Experimental results of the waveforms of DFIG, load and electric grid currents, for system running in generator mode.

Fig. 21. Response of control loop of the DC link voltage.

Fig. 25. Experimental result of the harmonic spectrum of load current.

Fig. 22. Experimental results of the response of control loop to rotor currents controllers ird and irq.

PCC. The current ird remains at zero while irq is changed from 4 A to 8 A. Thus, the active and reactive powers show similar behavior to

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A.B. Moreira et al. / Renewable Energy 107 (2017) 181e193

Fig. 26. Experimental result of the harmonic spectrum of the current in the electric grid without ﬁltering at speed of 177.93 rad/s.

Section 6.1. The waveforms of the generator, load, active ﬁlter and electric grid currents obtained when the system running in APF mode, Fig. 27, are similar to the ones shown by the numerical simulation (Section 6.2). The electrical grid current is sinusoidal with THDi of 6.42% (Fig. 28). It was veriﬁed the reduction of components 5th., 7th., 11th. and 13th. orders over the previous situation, Fig. 26. The components 5th. and 7th. orders show greater reduction in magnitude. Comparing the experimental results with the simulation, differences were veriﬁed in THD of grid current because the not ideals conditions presented in the tests, as THD of the grid voltage was 3%, errors accumulated in the calibration of the sensors and noise that were not modeled and calculated during the simulation. Experimental tests were performed for different conditions in which the generator delivers power to the electric grid and performs harmonic ﬁltering with its THD, Table 1. For smaller active powers, the ﬁltering of harmonic currents has shown greater efﬁcacy. Initially, the power grid provides all the current the load requires, it changes when the generator injects active power and also it performs harmonic ﬁltering simultaneously. The generator

Fig. 27. Experimental results of the waveforms of grid, load and DFIG currents, operating in APF mode.

Fig. 28. Experimental result of the harmonic spectrum of the current in the grid with ﬁltering at speed of 177.93 rad/s.

Table 1 Power control simultaneous.

operation

and

harmonic

ﬁltering

of

DFIG/APF

Active power (W)

THD of grid current (%)

0 350 700 1000

5.43 5.89 6.42 6.70

injects active power, the load requires less fundamental current by the grid. The active ﬁlter provides the harmonics that the load requires without including the fundamental current. The fundamental load current is supplied in part by the grid and generator. The THD of the grid current increases when power delivered by DFIG increases because the fundamental component of the grid current is reduced. The other harmonic components remain the same, thus the active ﬁlter realizes to ﬁltering harmonics identiﬁed. The magnitude of the fundamental grid current is reduced, then from (35) veriﬁes that the THD increases.

Fig. 29. Power delivered to the DFIG (Ps) and power processed by GCS (Pexto) for the operation DFIG/APF system.

A.B. Moreira et al. / Renewable Energy 107 (2017) 181e193

8. Stability analysis of the system control Unlike other controls in the GSC shown in the literature, it was used the precise model of the DC link voltage dynamics described in Ref. [13]. This model allows evaluating the stability of the system control for each DFIG/APF operating point. The frequency response of the converter control depends on the system operating point for both rectiﬁer and inverter mode. For each operating point, the DC link voltage dynamics transfer function is modiﬁed in accordance with the new active power, Pexto. An operating point for the converter GSC is determinated for each operating point of the DFIG/APF system. Neglecting the converter losses, Pexto can be the obtained by (38):

Table 2 Frequency response of DC link voltage controller for operation points of DFIG/APF system. Operating point

Active power (W)

Pexto of GSC (W)

GM (dB)

PM( )

1 2 3 4

0 350 700 1000

17 43 74 114

45.5 44.9 44.1 43.1

57.3 57.3 57.3 57.2

191

3 Pexto ¼ vd id 2

(38)

After the calculation of Pexto, the power is ﬁltered by a low pass ﬁlter of the second order and cutoff frequency is 12 Hz. Thus, the GSC operating points are showed in Fig. 29. In the operating point 1, the GSC acts as a rectiﬁer and active ﬁlter with Pexto ¼ 17, Table 2. Thus, it considers the same current and DC link voltage controllers obtained in Section 4, then the new transfer function of the dynamic DC link voltage control (Gv(s)) is calculated by (33) and (34) for this GSC operating point. In the operating point 1, the GSC acts as a rectiﬁer and active ﬁlter with Pexto ¼ 17, Table 2. The new transfer function of the dynamic DC link voltage control (Gv(s)) is calculated by (33) and (34). Considering the new transfer function Gv(s), for the same current and DC link voltage controllers obtained in Section 4, the frequency response was calculated: GM of 45.5 dB, PM of 57.3 , for gain crossover frequency of 150 rad/s, Fig. 30a). The converter also acts as a rectiﬁer and active ﬁlter for other operating points (2, 3 and 4). The same procedure applied in the operating point 1 is used to determine the system frequency response for other cases, Fig. 30b), c) and d). Table 2 summarizes the DC link voltage controller frequency response for each operating point of the DFIG/APF system with data

(a)

(b)

(c)

(d)

Fig. 30. Frequency response of dc link voltage controller for a) operating point 1, b) operating point 2, c) operating point 3 and d) operating point 4.

192

A.B. Moreira et al. / Renewable Energy 107 (2017) 181e193

extracted from Figs. 29 and 30a), b), c) and d). The margin gain and phase margin of GSC control are a bit reduced in the new GSC operating points e Table 2. However, the MG follows the designed control system requirements: MG > 6 dB and 30 < PM < 60 . The GSC performs as a rectiﬁer and active ﬁlter simultaneously and it runs stable because it follows the control design criteria. The current dynamic of the voltage source converter connected to the DFIG doesn’t change, thus the generator control are also stable.

9. Application of the wind turbine converter in range of MVA up to 15 kHz The use of Silicon Carbide (SiC) in the development of semiconductors is a promising technology. Commercial SiC power switches are already available in the market and allow to process large power at frequencies higher. Simulations results implemented on SemiSEL software indicate that the use of SiC devices in wind power converters are technically feasible in applications, which present the range of MVA for the switching frequency up to 15 kHz. In order to demonstrate a comparative between losses of Si and SiC converter technology it was developed two simulations. The parameters of two level voltage source converter (Fig. 31) used in the simulation are: Vdc ¼ 800 V, Vout ¼ 480 V, Iout ¼ 1050 A, Pout ¼ 873 kW, fout ¼ 60 Hz. The switches available in the market used in simulation are: SKM500MB120SC (SiC technology) and SKM600GB126D (Si technology). Table 3 shows the losses for a grid side converter of fundamental ﬁxed frequency in the range of MW with technology Full SiC (DMOS þ schottky diode) and the loss for the converter with IGBT NPT fast diode ultrafast coplanar Si. The Si converter runs with switching frequency of 2.4 kHz while SiC converter runs with switching frequency of 15 kHz. It observes that the converters losses are similar to the same output power, considering the same cooling system. The operating temperatures of the switches in Table 3 respect the maximum junction temperature, it should be less than 150 C to Si technology and 175 C to SiC technology. This analysis is implemented to the PWM modulation. If it was chosen the modulation space vector pulse width modulation (SVPWM), the converters losses could be smaller.

Note that the wind turbine converter in range of MVA is achievable to 15 kHz with SiC switches. In applications with DFIG, the converters do not operate at rated machine power. The converters design in the back-to-back topology is limited to 30% of the machine rated power. Thus, the DFIG/APF system can be implemented technically with the switching frequency of 15 kHz. Some characteristics must be considered in designing an L ﬁlter, such as current ripple, ﬁlter size and switching ripple attenuation. The ﬁlter should not be large but sufﬁcient to avoid the high frequency components which are the switching frequency components generated by the converter. The L ﬁlter design depends on the parameters: line-to-line rms voltage (Vll), peak phase voltage (Vpp), rated active power (Pout), DClink voltage (Vdc), switching frequency (fs) and maximum current ripple (DiLmax). The L input ﬁlter is designed with details in Ref. [23] and calculated by (39):

L¼

Vdc 6fs DiLmax

(39)

The typical L ﬁlter values for systems with large power are in range of 125 mH up to 300 mH as in Refs. [24] and [5], but the maximum current ripple is an important criteria which will determine the inductor, this is adopted by the designer and obtained by (40) and (41).

DiLmax ¼ k$ILmax

(40)

pﬃﬃﬃ Pout 2 ILmax ¼ pﬃﬃﬃ 3Vll

(41)

where k is the percentage of the maximum current, ILmax, the maximum current. The DC-link voltage is determinated by (42) according to [13]:

Vdc 2$Vpp ;

(42)

where Vpp is the peak phase voltage. The GSC converter compensates components identiﬁed of the load (iLhd and iLhq) by harmonic current identiﬁer. Depending on the magnitude of iLhd and iLhq, the DC-link voltage can be increased to improve the compensation of harmonic currents. 10. Conclusion

fsw TR1

TR3

TR5 Vout

Vd

fout

TR2

TR4

TR6

Iout

Fig. 31. Three phase voltage source converter.

Table 3 Losses and junction temperature to Si and SiC converter. Technology

Switching frequency (kHz)

Losses (W)

Maximum junction temperature (o)

Si Converter SiC Converter

2.4 15

7795 8674

125 137

This research investigated a wind-power system with DFIG in the traditional mode of power generation (case 1), and the system working with power control and current harmonic ﬁlter grid (case 2). Both in case 1 as in case 2, the power generation through DFIG remains the same. Thus, the technique of stator ﬂux oriented control to power control of the generator is satisfactory. Comparing the harmonic spectrum of the grid current before the harmonic compensation with the compensated grid current spectrum, with simulation or experimental results, we veriﬁed that the THD was reduced. Thus, the harmonic compensation strategy incorporated into a wind generator with DFIG improves power quality. The controllers of the wind power generation system were calculated and implemented by the methodology presented. The work developed an experimental setup with conditioning the measurement signals and a central control board that does not require high investment cost of a dSPACE with processing of 1 GHz. The developed control board has the TMS320F28335 microcontroller (processing of 150 MHz) that achieves good results with the

A.B. Moreira et al. / Renewable Energy 107 (2017) 181e193

inclusion of the active ﬁltering function in DFIG operation. The proposed new control strategy was veriﬁed and discussed in simulations and experiments conﬁrming the effectiveness of the technique, and it’s a strategy with technical viability among the works in the presented literature. The controllers of the wind power generation system were calculated and implemented by the methodology presented. Simulations with converter design software indicate that wind turbine converter applications in range of MVA are also feasible for the switching frequency up to 15 kHz using silicon carbide power semiconductor switches. Thus, applications such as those described in this article are technically feasible. It was established that the THD of the grid current rises with the increase of the power delivered to the grid by the generator for the strategy adopted. This increasing of THD is assigned to the reduction of the grid current fundamental component when the generator delivers more active power. The residue of the harmonic components compensated are still present in the electric grid. Unlike other controls in the GSC shown in the literature, this research presents as contribution the application of the precise model of the DC link voltage dynamics, allowing evaluating the stability of the system control for each DFIG/APF operating point. The DC link voltage controller design contemplates the nonminimal phase property, in the rectifying mode of operation, which it has a detrimental impact on the stability of the system. One of the contributions of this article also is the tutorial character, it should assist in the development of future work. Acknowledgements This work was supported by FAPESP grant number 2015/032489. Appendix Parameters of DFIG: Pn ¼ 2.25 kW, n ¼ 1750 rpm, 60 Hz, 220 V, Lm ¼ 144.14 mH, Llr ¼ 11.53 mH, Lls ¼ 11.53 mH, Rs ¼ 0.47 U, Rr ¼ 1.31U; Irotor ¼ 20.2 A; Istator ¼ 8.8 A. Parameters of the nonlinear load: RL ¼ 34, LiL ¼ 10 mH. Parameters of the converter and inductive ﬁlter: Ce ¼ 1020 mF, L ¼ 7.5 mH, R ¼ 0.31 U. Parameters of the electric grid: Vgrid ¼ 220 V, 60 Hz, Lg ¼ 2.85 mH. References [1] M. Boutoubat, Selective harmonics compensation using a WECS equipped by a DFIG, in: IECON 2012-38th Annual Conference on IEEE Industrial Electronics Society, 2012, pp. 745e750. [2] D. Kairus, R. Wamkeue, B. Belmadani, M. Benghanem, Variable structure control of DFIG for wind power generation and harmonic current mitigation,

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