An improved sliding mode control for reduction of harmonic currents in grid system connected with a wind turbine equipped by a doubly-fed induction generator Текст научной статьи по специальности «Электротехника, электронная техника, информационные технологии»

UDC 621.3

https://doi.org/10.20998/2074-272X.2022.2.08

S. Bouraghda, K. Sebaa, M. Bechouat, M. Sedraoui

An improved sliding mode control for reduction of harmonic currents in grid system connected with a wind turbine equipped by a doubly-fed induction generator

Introduction. The implementation of renewable energy resources into the electrical grid has increased significantly in recent years. Wind power is one of the existing resources. Presently, power electronics has become an indispensable tool in wind power plants. Problem. However the associated control usually has an impact on increasing the harmonic distortion, especially on the output voltage. Goal. This paper proposes a new sliding mode control strategy, applied on a rotor-side of a doubly-fed induction generator. The main goal is to meet the electrical power requirements, while responding to the power quality issues. Methodology. The wind energy conversion system must be able to not only track the maximum power point of the wind energy, but also to mitigate the harmonic currents caused by the non-linear loads. To achieve this goal, the power converters are driven by the proposed sliding mode control strategy. The corresponding two gains of the sliding surface are well selected using a particle swarm optimization algorithm. The particle swarm optimization algorithm solves a constrained optimization problem whose fitness function is a prior formulated as the sum of two mean square error criterions. The first criterion presents the tracking dynamic of the reference active power while the second one presents the tracking dynamic of the reference reactive power. The novelty lies in the implementation of the particle swarm optimization algorithm in conventional sliding mode control strategy, in which the proposed-improved sliding mode control strategy is developed. The wind energy conversion system control uses the principal of the vector oriented control to decouple the control of the active power from that of the reactive power. Results. The improved sliding mode control strategy is applied to control separately theses powers in the presence of non-linear loads. The energy assessment of this strategy is analysed using the wind energy conversion system model based on SimPower software. Originality. The obtained simulation results confirm the superiority of the proposed-improved sliding mode control strategy in terms of reference tracking dynamics and suppression of harmonic currents. References 23, tables 2, figures 11.

Key words: doubly-fed induction generator; wind energy conversion system; bidirectional converter; particle swarm optimization; sliding mode control.

Вступ. Використання вiдновлюваних джерел енергп в електричнш мережi остантми роками значно зросло. Енергiя eimpy - один Í3 iснуючих pecypcie. Hmi силова електротка стала незамтним тструментом втряних електростанцш. Проблема. Проте, вiдnовiднe управлтня зазвичай мае вплив на збтьшення гармоншних спотворень, особливо у вихiднiй напрузь Мета. У цт cтаттi пропонуеться нова cтpатeгiя управлтня ковзним режимом, що застосовуеться на боц ротора асинхронного генератора з подвшним живленням. Основна мета - задовольнити вимоги до електроенергп, виршуючи вiдповiднi проблеми з яюстю електроенергп. Методологш. Система перетворення енергп втру повинна мати можливicть не тыьки вiдcтeжyвати точку максимальноi потyжноcтi втру, але й пом'якшувати гармоншт струми, викликаш нелтшними навантаженнями. Для досягнення цei мети cиловi пepeтвоpювачi керуються запропонованою cтpатeгiею управлтня ковзним режимом. Вiдповiднi два коефщенти посилення поверхт ковзання добре вибираються з використанням алгоритму оптимiзацii рою частинок. Алгоритм оптимiзацii рою частинок виршуе задачу оптимiзацii з обмеженнями, функщя пpидатноcтi яmi заздалeгiдь сформульована як сума двох критерпв cepeдньоквадpатичноi похибки. Перший критерш репрезентуе динамк вiдcтeжeння eталонноi активноi потyжноcтi, а другий - динамк вiдcтeжeння eталонноi peактивноi потyжноcтi. Новизна полягае в peалiзацii алгоритму оптимiзацii рою частинок у традицшнш стратеги управлтня ковзним режимом, в якт розроблена запропонована покращена cтpатeгiя управлтня ковзним режимом. Управлтня системою перетворення енергп втру використовуе принцип вeктоpно-оpieнтованого управлтня, щоб вiдокpeмити управлтня активною потужтстю вiд управлтня реактивною потужтстю. Результати. Удосконалена cтpатeгiя управлтня ковзним режимом застосовуеться для роздыьного управлтня цими потужностями за наявноcтi нелтшних навантажень. Енергетична оцтка цiei стратеги аналiзyeтьcя за допомогою модeлi системи перетворення енергп втру на оcновi програмного забезпечення SimPower. Оригтальтсть. Отримат результати моделювання тдтверджують перевагу запpопонованоi yдоcконалeноi стратегп управлтня ковзним режимом з точки зору eталонноi динамт стеження та придушення гармоншних cтpyмiв. Бiбл. 23, табл. 2, рис. 11.

Ключовi слова: асинхронний генератор Í3 подвшним живленням; система перетворення енергй BÍTpy; двонаправлений перетворювач; оптимiзацiя рою частинок; керування ковзним режимом.

Abbreviations

APF Active Power Filter PRC Proportional Resonance Control

BTB Back-To-Back PSO Particle Swarm Optimization

DFIG Doubly-Fed Induction Generator PWM Pulse-Width Modulation

DPC Direct Power Control RSC Rotor-Side Converter

DTC Direct Torque Control SMC Sliding Mode Control

GSC Grid-Side Converter THD Total Harmonic Distortion

HSF High Selectivity Filter VCS Vector Control Scheme

MPP Maximum Power Point VOC Vector Oriented Control

MSE Mean Square Error WECS Wind Energy Conversion System

NLL Non-Linear Loads WPP Wind Power Plants

PMSG Permanent Magnet Synchronous Generator WT Wind Turbine

Introduction. The incorporation of renewable energy resources into the electrical grid has increased significantly in recent years. Among of them, the wind

energy is one of the existing resources whose potential demand has increased due to domestic and industrial

© S. Bouraghda, K. Sebaa, M. Bechouat, M. Sedraoui

necessities. This growth is mainly due to the advanced technology used in the design of WECS, reducing the cost of producing electrical energy and enabling it to be competitive with other traditional sources such as fossil fuels, petroleum, natural gas, and so on. A lot of research has focused on DFIG systems in their structures. These have several advantages, including speed control, current harmonic reduction and four-quadrant active and reactive power control. As its rotor speed can be operated at any wind speed, the DFIG system is therefore able to deliver high mechanical power and, in economic terms, it becomes more attractive than other existing conversion systems, thanks to its conversion rate, which is generally around 30% of the nominal power, allowing thus to generate the electrical energy at a lower cost [1].

Currently, power electronics has become an indispensable tool in WPPs to ensure such required specifications such as steady state stability, high energy efficiency, regardless of changing wind conditions. In fact, these tools are often providing many important functionalities to WTs, including the control of several electrical quantities such as stator terminal voltage and frequency, active and reactive power and so on. Nevertheless, the associated control effort usually has an impact on increasing the harmonic distortion, especially on the output voltage of existing converters. As a result, the occurrence of inadequate harmonics has unfortunately become the main issue for the majority of wind energy designers as well as the company managers [2]. The attenuation of the effect of such harmonics on the DFIG system can be performed through proper regulation of the existing converters in the control loop. Similarly, the power quality problem can also be posed of serious challenges where its remedy has been discussed by several researchers [1, 2]. On these grounds, many control strategies have been proposed to overcome these drawbacks. Among them, a control strategy was published in [3] where the WECS is designed to operate partially as an active filter. Also, another control strategy that can be employed to simultaneously generate active and reactive power where an extra active filter is incorporated into a DFIG wind system having a variable speed [1]. Similarly, a modulation technique was proposed in [4] for shunt active filter operation, in which the existing harmonics in the WECS output current are well mitigated. The corresponding feedback control system incorporates a PMSG as well as an AC/DC current converter. Also, a PWM control strategy including a five-leg converter was proposed in [5] where the given performances are compared by those provided by the conventional six-leg topology. The main shortcoming, compared to the six-leg BTB converter, lies in the restriction of increasing the DC link voltage for the same operating point. In parallel, a PRC strategy was developed in [6] for a stationary reference frame to mitigate, as much as possible, the existing harmonics in the rotor current and in torque pulsations. In the same direction, a VCS was suggested in [7, 8] for rotor-side control of a stand-alone generator based on a wound rotor induction machine. The main aim of the proposed control scheme is to keep a constant terminal voltage with stationary frequency at the generator output. In the same way, the

full harmonic component compensation technique of the grid current was adopted in [9]. The corresponding RSC control structure is modified, in which a filtering task is incorporated. Also, an efficiency assessment of the electrical part of the WECS was reported in [10] where the two BTB-PWM inverters, which are supplied with voltage and connected between the stator and rotor, are used to improve the bidirectional power flow. Accordingly, the second inverter, which is disposed on the grid side, serves as an active power filtering to remove the harmonics, generated by the nonlinear load, while providing the required active and reactive power to the DFIG rotor.

Different alternative control strategies have been developed for wind power generation in the electrical grid. Among them, the VOC and the two direct control strategies such as the DTC and the DPC are becoming the most widely used in real world applications [11]. Furthermore, some other nonlinear control strategies have been proposed in the literature where the best known is the SMC, which has proven to be the most attractive during the last decades. This is due to its inherent properties to overcome complex challenges that are caused by the presence of unmolded dynamics, the neglect of high frequency dynamics, the presence of model uncertainties, the variation of model parameters, the presence of load disturbances, and the persistence of the effect of sensor noise. To this purpose, it is important to emphasize that the SMC-based synthesis of a robust controller, taking into account all the previous obstacles, is crucial for the active and reactive power control of the DFIG equipped with a wind turbine [12]. Nevertheless, this control strategy has the capacity to provide good reference tracking dynamics, high robustness in the presence of the preceding factors, and a good tradeoff between the two preceding targets. However, it also presents various misfunctions when strict specifications are considered. Among them, the undesired phenomenon known as «chattering» occurs during the operation of the WECS near its operating point. The drawback that results from this phenomenon is often associated with improper selection of sliding surface gains where trial and error selection is typically performed, leading thus to control inaccuracy, dramatic performance degradation and high thermal loss in power devices. To overcome this problem, the PSO algorithm is introduced in the conventional-SMC-based synthesis where their gains are properly optimized. This can be done by solving the constrained optimization problem whose fitness function is perfectly minimized. The manner of the incorporation of the PSO algorithm in conventional SMC strategy constitutes therefore the main contribution of this paper.

Goal. In this paper, the actual behavior of WECS is primarily modelled near its operating point. Then, the VOC principal is used for decoupling the active power control from the reactive power one. Finally, the improved-SMC-based synthesis is applied to ensure the proper reference tracking dynamics where the suppression of harmonic currents is considered.

System description. The WECS is mainly composed by a DFIG equipped with a wind turbine. Its stator is connected to the grid while the BTB PMW

converter is connected between the DFIG rotor and the grid. The grid-side converter GSC is used to provide bidirectional power flow that is generated from the rotorside converter RSC, stabilizing thus the DC link voltage and achieving unity power factor. Figure 1 shows the block diagram of a grid-connected DFIG wind turbine.

Gear box

= DFIG'<

Ps , Qs

Grid

RSC (APF) GSC

Converter

NLL

Ig=IL -Ih ; Ih =Is - Ic •

(1) (2)

ILa =ILqf+ILah ; ILß =ILßf + ILßh

reference active and reference reactive powers requires prior modeling of all parts involved in the actual WECS behavior, such as wind-turbine part, the rotor-side and stator-side of the converter.

Fig. 1. Block diagram of the grid connected DFIG wind turbine in the presence of NLL

In general, the NLL often unfortunately injects harmonic current into the grid where the desired controller for active and reactive power regulations must be operated as an active filter, in which the existing harmonic currents and voltages are well absorbed. Also, from Fig. 1, the node law imposes that:

Fig. 2. Harmonic isolation of the whole load harmonic current

Modeling of actual WECS behavior. Modeling of wind turbine. A wind turbine collects the wind through its blades and transmits it to the rotor hub. The kinetic energy of the wind is accordingly converted into mechanical power, generating thus a mechanical torque. Also, the rotor shaft generates an electrical energy and transmits it to the grid. Since the wind energy is found in the form of kinetic energy where its amplitude depends on the air density and the wind speed [12, 13]. The power of the wind Pv being found in the form of kinetic energy when it crosses at the speed Vv, air density p and the surface area S. It can be expressed by:

1 3

Pv= - • P • S • Vv3.

(5)

The stator current Is of the DFIG is assumed to have a non-sinusoidal waveform close to that of the NLL current IL. The converter is designed to supply a pure sinusoidal current Ic. Then, the harmonic current Ih thus represents the current that the APF (rotor converter) must generate. Therefore, and in accordance with (1), the grid current Ig will be clear of unwanted harmonic components. To be in agreement with these assumptions, the suggested WECS must generate the same harmonic components as the non-linear current but with opposite phases. This may be performed by investigating the correct control circuit of the rotor converter. Keep in mind that this control circuit may also be used to achieve decoupled control of active and reactive power. The NLL currents must be measured. Following that, the measured load currents (ILa, ILb, ILc) are converted using the abc to a-P (stationary reference frame) transformation. The NLL current is equal to the sum of the fundamental frequency and various harmonics, as shown below:

(3)

The wind turbine can usually only recuperate a part of the preceding power Pv, resulting thus the power Pt that is expressed by:

Pt= \ • p • n • R2 • Vv3 •

(6)

where R is the radius of the wind turbine; Cp is the corresponding power coefficient, which is given as a function of the wind speed, the rotation speed and the pitch angle.

Also, Cp is often given as a function of the tip speed ratio A, which is defined by:

X = , (7)

V r v

where Qt is the angular speed of the rotor.

Furthermore, the wind power Pt and the power extracted by the wind turbine Pv are expressed in terms of the power coefficient Cp. Hence, one can obtain:

Pt=1 • Cp (l, ß )•

2

P • S • Vi

(8)

(4)

where (ILah, IL/3h) and (ILaf, hf are the NLL current's harmonic and fundamental constituents.

Based on (3), (4) and by deducting the load current from its fundamental component, the harmonic components of the NLL current can be expressed. The approach depicted in Fig. 2 can be utilized to distinguish the harmonic of NLL. In this figure, the Park transformation is applied to convert the a-f current components to d-q (synchronous) reference frame. The HSF is used to extract the fundamental component from a-f components. The HSF is a band pass filter as in Fig. 2 [8].

It should be noted that the design of the controller design based on the SMC strategy for tracking both

where the coefficient Cp(X,p) has a theoretical limit, called BETZ limit. It is defined by:

X X ~C5

Cp (l, ß) = Ci •

C2 - C3 • ß - C4

Ai

e A +C6•A. (9)

(10)

The numerical values of the parameters Ck are experimentally given by:

C1 = 0.5176; C2 = 116; C3 = 0.4; C4 = 5; C5 = 21; C6 = 0.0068, while the parameter A is expressed by:

■1=, 1 ,-0331. (11)

A (A + 0.08 • p) p3 +1

It is worth noting here that the power conversion coefficient Cp is expressed as a function of the tip speed

ratio A and the pitch angle [ of the rotor blades. Their evolution, depending on A for different values of [, is illustrated in Fig. 3 [14].

iiSl elm

Fig. 3. Evolution of Cp as a function of 1 for different Rvalues

From Fig. 3 it seems that the power conversion coefficient Cp reaches its maximum when the pitch angle ß is zero and the tip speed ratio 1 becomes optimal. Therefore, the corresponding curve is shown in Fig. 4.

C u

cp

0 5 ii' ir

Fig. 4. Extraction of the curve defining the maximum power

conversion coefficient C

pmax

Also, the rotor torque Tt can be computed from the received power Pt and the speed of rotation Qt of the turbine. Therefore, the simplified equation that defines the rotor torque is given by:

_ _p • * • R3 • V2

2

(12)

Vsd = Rs

• lsd

dV sd dt

• V sq •

77 p • sq ,

Vsq=Rs * lsq+—7- + œs ' V sq •

Vrd = Rr • lrd

dt dV rd dt

-™r • Vrq ;

V = R • I

rq r rq

, dV rq

+-+ a>r ■ Vrd ;

dt

'r lrd + Lm

I + T • I •

r Lrq ^m lsq >

• lsd •

V rd = L

V rq = L Vsd = Ls • lsd + Lm • lrd • Vsq = Ls • lsq + Lm ' lrq •

(15)

(16)

(17)

Also, the electromagnetic torque is expressed by:

Tem= —' ^sd ' 'sq ~ Vsq ' >sd ) (18)

2

and both active and reactive powers are expressed by:

Ps= — -ksd-isd+Vsq • isq ); (19)

Qs =

• sd ' lsq Vsq ' lsd ) '

(20)

where V and i are the voltage and current, respectively; R and L are the resistance and inductance, respectively; y/ and co are the flux and angular speed of the DFIG, respectively; P and Q are the active and reactive powers, respectively.

Also, from (14)-(20), the indexes d and q represent respectively, the electrical components, which are located in the d-axis and the q-axis, while the indexes r, s and m represent respectively the values of the rotor, the stator and the magnetization.

Design controllers for DFIG wind turbine. Design controller for GSC. The proposed control for this converter is the VOC strategy, which employs a rotational reference frame (d-q) oriented to the space vector of the grid voltage (Fig. 5). Thanks to this kind of strategy, it is possible to achieve the two main targets of the converter on the grid side, i.e., the control of the DC bus voltage as well as the power transmission performed by the converter using the controlled reactive power transmission.

where Ct indicates the torque coefficient, which depends heavily on the power conversion coefficient Cp according to the following equation:

Cp (l) = 1 • Ct (¿). (13)

Using the adequate model that resulting from momentum theory requires a priori knowledge of both expressions Cp(A) and Ct(A). Indeed, these two last ones depend essentially on the geometrical characteristics of the blades. Therefore, they are adapted to particular characteristics such as the site where the WECS is located, the desired nominal power, the control type such as pitch or stall, and the WECS operation in variable or fixed speed.

Modeling of DFIG. The DFIG design model is determined by applying the conventional modeling in the Park reference frame. Therefore, the corresponding voltage and flux equations are expressed by [12, 15]:

Vbus

Regulator

n * w

r^l Regulator

l19 *

lqg Regulator 4

Fig. 5. Control loop performed in the grid-side converter (g subscript demonstrates grid-side components)

Accordingly, the difference between the reference

*

DC voltage Vbus and the measured DC voltage Vbus

becomes the input of the Vbus regulator. Indeed, the idg regulator is used to remove the discrepancy that is

- œ

PWM

occurred between the reference current i*g and the

current idg. It allows to regulate the active power Pg of the grid. Similar, the iqg regulator is used to control the reactive power Qg of the grid, in which the difference

qg

- iqg is removed [16].

eqf

■ L

■fmiqg

edf = ms ■ Lf ■ idg

For better performance in the dynamic responses, there is additionally one coupling component in each equation that is best incorporated in the control as a feedforward term, as illustrated in Fig. 5 (at the output of the current controllers) [16]:

r , y, f-1 if S(x) < 0;

■"^H if S(x->0. (25)

According to the SMC principal, the control law U" has often stabilized the WECS behavior, in which the given power conversion becomes maximal and the corresponding speed ratio reaches its optimal point Aopt. This closed-loop stability requires often to satisfy the Lyapunov condition that is expressed by:

S (x )• S (x)< 0, (26)

(21) (22)

Design controller for RSC The rotor-side converter is designed to control the DFIG output power to grid. It is also used to control the power factor across the DFIG [1]. The stator active and reactive powers serve as the control inputs of the RSC. As mentioned previously, the aim is to operate the DFIG as an APF. The SMC strategy is used for the RSC where the block diagram of RSC is shown in Fig. 6.

where S (x)=

d,S' (x ) dt

denotes the derivative of the sliding

surface, which is expressed as a function of the variable to be controlled (x). This last will be considered as either the active power or the reactive power that is delivered by the WECS.

The goal is first to decouple the control of the active power Ps from that of the reactive power Qs. Then, the desired controller based on the conventional SMC

strategy should keep good track of both reference powers

* *

Ps and Qs , in which a proper suppression of all harmonics occurring in the duty currents should be taken into account. These requirements need detailing some equations such as the rotor currents and their derivatives as well as the sliding surfaces and their derivatives. Furthermore, the relationships between reference stator powers and the reference rotor currents are given by:

I

-L,

rq

K ■ Lm

■ Ps -1 Lqh;

I

K

rd

o)s ■ Lm

K ■ L

■ Q* -1

Ldh

(27)

(28)

Fig. 6. Control loop performed in the rotor-side converter

Assuming that a reference frame is rotating synchronously with the stator flux and we suppose that the network is stable, the stator flux ^¡a is becoming constant and equal to y/s. On the other hand, the stator flux ysq becomes zero, i.e., \f/sd = ys; yqq = 0. Also, for the generators utilized in the wind turbine the stator resistance Rs may be ignored, resulting in Vsd = 0 and Vq = Vs = a y/sq.

Conventional SMC strategy The SMC strategy is a very powerful nonlinear tool that has been widely employed by researchers, especially in the last decades [15, 17]. It consists in moving the system behavior along a predetermined sliding surface, where a numeric control signal is applied [12]. Moreover, the state trajectory of the closed-loop system must be oriented towards the sliding surface S(x) = 0 and maintained constantly around this surface using the switching logic function U". In general, the basic SMC law is commonly expressed by [18, 19]:

Uc=Ueq+U", (23)

where Ueq is the equivalent control law that is applied when the existing states of the system are located in the slip plane.

The control law U" is alternated between -k and +k where k > 0. It is defined by:

U"=k • sg4S (x)] . (24)

Also, the sigmoid function occurred in (24) is defined by:

Noted here, that the reference reactive power Q* is

*

set to zero and the reference active power Ps can be

expressed is related to the synchronous speed cos, and the electromagnetic torque Tem can be expressed by:

P* = • Tem . (29)

Moreover, the derivative of rotor currents, in J-axis and g-axis, are expressed by:

dI

rq dt"

1

Lr ■ a

Vrq - Rr ■ Irq - g ■ ws ' Lr 'a ' Ird - g ' ws

L ■V

rns ■ Ls j

(30)

dI

TT =T"- (Vrd - Rr ■ lrd+g ■ ws ■ Lr ■ ° ■ Jrq\ dt Lr ■o

where g and a are respectively the slip and dispersion coefficient.

In general, the active power becomes directly proportional to the rotor current in q-axis, while the reactive power becomes proportional to the rotor current in d-axis. Accordingly, the control surface of each power is expressed by:

..........(31)

(32)

Knowing that the appropriate reference tracking dynamics necessitates that all sliding surfaces as well as their derivatives must be equal to zero, i.e., S(P) = 0, S(Q) = 0, S(P)= 0 and SQ) = 0 . These require that the

S (P ) = I*q - Irq ;

S (Q ) = Ird - Ird .

L

s

plot of Ps (with respect to Qs) is exponentially converged to the one of the corresponding reference powers Ps*

(with respect to Qs* ). Therefore, all previous sliding

surfaces necessarily become attractive and invariant, where the key to the success of the SMC strategy strongly depends on respecting the attractivity relationship of Lyapunov [17], given by (26).

Control law used for active power control This part focuses on finding the two parts of the control law

Vq (equivalent control vector) and V"q (switching part

of the control) that constituting the rotor voltage Vrq, given in q-axis. Accordingly, the derivative of the sliding surface S(p) is computed using (30)-(32), which yields also (33) as follow:

S (P ) =

-Ls

L ■¥

V - Rr'Irq - g-Vs'Lr-C Ird - g- m s

(33)

From (33) the control law Vrq is determined and then decomposed into the two control laws Vq and Vq ,

where Vrq = Vq + V,"q . The resulting rotor voltages in q-axis are given by:

Vrq = Ls Lr °-1 Ldh +Rr -Irq +g-ms 'Lr ' Jrd +

rq

L -V

+g-Lmf^+Lr-a - vvsgn{s(p)] L

Veq _ Ls ' Lr ' a ~

rq

L -V

j^m ' s

-Ps -1 Lqh +Rr -Irq +

Lm Vs

+g-ms-Lr-a-Ird+g- mT s;

(34)

(35)

Vrnq=Lr -a-vrsgn[S(P)]. (36)

Control law used for reactive power control

Similarly, the derivative of the sliding surface S(Q) is

first computed and the control law Vrd is then extracted as follows:

s (Q)=

Vs

Lm-ms LmVs

-Q* -1

Ldh

Lr a

— (d - Rr '1 rd +g-ms -Lr -a-Irq )

(37)

Vrd=Lr-o I-—s----—S—'Qs -1 Ldh I +Rr ' Ird -

,Lm Lm ' Vs ) (38)

-g-Lr-O-Irq+Lr' v2 •sgn['S (Q)]

According to (38), the two control laws V^ and Vn are expressed by:

Ve]=Lr-a

V.

L -m L -V

^j-j m ^m ' s

-Q* -1

Ldh

+ Rr -Ird - g-ms -Lr -a-Irq;

V?d=Lr -a-v2-sgn[[(Q)].

(39)

(40)

The block diagram that explains the SMC implementation for active and reactive power controls of the DIFG equipped with a wind turbine is given in Fig. 6.

From (38), (40), it is obvious that the desired reference tracking dynamic requires the proper interaction of all states of the system toward the switching surfaces, i.e., S(P) = 0 and S(Q) = 0. This still leads to the occurrence of the chattering problem due to the existing

of the sigmoid function in both control laws Vrnq and

Vr

rd

in which the control law Vrnq can either have the

gain -v1 or +v1. In the other hand, the control law Vq can either have the gain -v2 or +v2. To overcome this challenge, the implementation of the PSO algorithm to optimize the two gains appearing in the two preceding control laws becoming an indispensable key in the design phase of the controllers. This enables to highlight the improved version of the SMC strategy whose details are discussed in the next part.

Improved SMC strategy In this study, the main contribution lies in the selection of the two optimal gains

v1 and v2 involved in the two control laws Vq and Vq

respectively. The corresponding bounded optimization problem includes the fitness function J(X), expressed as the MSE criterion. It consists of the sum of the two squared errors e1 and e2, produced by the simultaneous

tracking of the two reference powers Ps* and Qs* . Accordingly, the optimization problem can be expressed by:

min

J(X) =

min

Xmn<X<XmJ NT

-L £ [X)+e2(X)

(41)

i=l

where both tracking errors e1 and e2 are defined by

e^X )=Ps (X)-P* and e2 (x)=Qs (x)-Q*

respectively, X = (X1,X2) denotes the design vector to be optimized where their components are constrained by -v1 <X1 <+v1 and -v2 <X2 ^+v2 , N and T denote the total number of samples and the sampling time.

The PSO algorithm is implemented in a classical SMC strategy to avoid the fast switching of the two gains v1 and v2 from their positive to their negative values. In fact, there is a multitude of unknown gains found between the two positive and negative bounds for each gain of the sliding surface. The objective is therefore mainly to focus on finding the optimal gains during the tracking process of the two reference powers. These optimal gains lead to finding two feasible optimal commands, in which the chattering problem of the SMC strategy is well solved. The optimization process by the PSO algorithm is carried out as follows: The PSO algorithm uses a swarm made up of particles npeN to know in search of the sub-optimal solution X eNqx1 which minimizes the objective function, called J(X)eR. The position and velocity of particle vectors ith are given respectively by

Xi = (a,X,2,...,X,q) and V- = ((,1,V,2,-,V,q) .

They are determined by the following iterative expressions [20-22]:

- Ps -1 Ldh -

LmV

1

Lr -a

s

Xmin<X <Xmix

s

L

s

+

V+ = CO ■ Vl+cx ■ -(xfestJ - Xl )+

+ C2 ■ r2 i

X+1 = xli+v}+1,

Functional value

I xbest,l - xl 'x swarm x i

(42)

Vopt r rq

and

VoPt rd

using

optimal rotor voltages

(34), (38), respectively.

Simulation results and discussion. The previous system (Fig. 1) was modelled and simulated using SimPower System Demo, MATLAB/Simulink. The proposed control strategy is applied to a WECS equipped with a 2MW DFIG. The system parameters are presented in the Appendix 1. The optimal values obtained are V = 1550.05211 and V2 = 525.0299 as shown in the fitness plots (Fig. 7) provided by the algorithm during the extraction process for 20 execution of the code.

Figure 8 is the simulation results for active and reactive power response in case of sliding mode control. In this case study, simulation results show clearly the improvement of active and reactive power demand obtained by applying sliding mode control in term of time response and good reference tracking accuracy.

ni-A'.m J.if.nv

where l is the number of iterations previously provided by the user; c0, c1 and c2 are respectively the inertia factor, the cognitive (individual) and social (group) learning

relationships; r(j and are random numbers evenly

distributed over the interval [0, 1], Xhiest l and x\lstalm are respectively the best position obtained previously by the particle and the best position obtained in the whole of the swarm at the current iteration l. In summary, the PSO algorithm can consist of the following steps [21-23]:

• Step 1: initialize the "p particles with positions chosen at random and which should previously be contained in the lower and upper bound vector Xmin and Xmax;

• Step 2: evaluate the fitness function for each position;

• Step 3: determine the initial solutions Xbest'0 and

xbest,0 , X swarm ;

• Step 4: check the stop condition. If it is satisfied, the algorithm then converges to the desired optimal gains

v<pt and vOpt. Otherwise, go to the next step;

• Step 5: assign the new values obtained to all particles (updates);

• Step 6: go back to step 2.

It should be noted that the PSO algorithm is

achieved by obtaining the two optimal gains v<pt and

v2pt . They are multiplied by the constant value Lr- o and then used for computing the two optimal commands

opt opt

V"q and V" . Knowing that the two equivalent

commands such as Vreqq and Vredq are a priori computed

using (35), (39), respectively. The resulting four preceding optimal commands are used to compute the two

Iteration .-.■ J.'-

Fig. 7. The obtained fitness curve through PSO

xio" Active Power, W_ _ xlf/ Reactive Power, W

The most significant harmonic components which will spread in the grid side with a THD as depicted in Fig. 9. After implementing the active filtering technique on the rotor current control loop, the waveform became greatly improved with better harmonic spectrum as displayed in Fig. 10. Referring to the results obtained, THD values are put in the table below (Table 1). The grid side inverter gives an active and reactive power needed by the rotor of DFIG.

Table 1

THD of the grid current

THD without filtering, % THD after filtering, %

26.22 2.45

Grid current wave form before filtering

Fundamental (50 Hz) = 16.59, THD = 26.22 %

14.12 14.14 14.16 14.18 14.2

Fig. 9. Grid current wave form and his harmonic spectrum before filtering

Grid current wave form after filtering

Fundamental (50 Hz) = 1114, THD = 2.45 %

f, Hz

Fig. 10. Grid current wave form and his harmonic spectrum after filtering

The reference harmonic compensating currents is shown in Fig. 10. Concerning Vdc regulation, the obtained result is satisfying. In fact, as illustrated in Fig. 11, after a transient state, VcC follows perfectly its reference (Vref = 1190 V).

Voltage, V

Fig. 11. DC-bus voltage wave form

Conclusions.

In this article, a study concerning a wind turbine based on a doubly-fed induction generator connected to the grid has been elaborated. The goals were to implement a rotor current control loop that would eliminate harmonic currents generated from a coupled nonlinear load using an active filtering concept, while also permitting independent regulation of power flow from and to the generator. For this reason, rotor converter was used as an active power filter. The response was conclusive given the improvements (an almost sinusoidal shape) obtained in the network current. Where we

have found that the total harmonic distortion decrease from 26.22 % (before filtering) to 2.45 % (after filtering).

In addition, the other goal was to regulate the common DC bus voltage between the rotor converter and the grid converter. In this study, we discovered that the simulation results show clearly the improvement of active and reactive power demand obtained by applying sliding mode control in term of time response and good reference tracking accuracy.

In summary, the following characteristics of the proposed wind energy conversion system are highlighted in the following points:

1. Possibility to recover the maximum quantity of power from the input wind speed.

2. Using an active power filter to reduce the harmonic currents.

Finally, in order to complete the suggested investigation, the power factor must be corrected. Additionally, the system should be implemented on a real machine in order to explore the impact of the saturation effect on the performance of the generator. These considerations will be investigated in future work.

Conflict of interest. The authors declare that they have no conflicts of interest.

Appendix 1

System parameters [16]

Parameter Value Parameter Value

Turbine Radius, m 42 DFIG Speed range, rpm 900-2000

Nominal wind speed, m/s 12.5 Pole pairs 2

Optimum tip speed ratio Àovt 7.2 Magnetizing inductance Lm, mH 2.5

Maximum power coefficient Cpmax 0.44 Rotor leakage inductance Lr, ^H 87

Air density p, kg/m3 1.1225 Stator leakage inductance Ls, ^H 87

Inertia J, kg • m2 127 Rotor resistance Rr, mQ 26

Friction D, N • m • s/rad 0.001 Stator resistance Rs, mQ 29

DFIG Nominal stator active power, MW 2 Grid Grid inductance Lg, mH 0.4

Nominal torque, N • m 12732 Grid resistance Rg, mQ 0.02

Stator voltage, V 690 Grid frequency f Hz 50

Nominal speed, rpm 1500 Grid voltage Vg, V 690

t, s

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Received 12.01.2022 Accepted 14.02.2022 Published 20.04.2022

Skander Bouraghda1, PhD, Assistant Professor, Karim Sebaa1, Professor,

Mohcen Bechaoua2,3, PhD, Associate Professor, Moussa Sedraoui3, Professor,

1 Laboratory of Advanced Electronic Systems (LSEA), University of Medea, Algeria,

e-mail: [email protected] (Corresponding Author), [email protected]

2 Automatic & Electromechanic Department, University of Ghardaia, Algeria,

e-mail: [email protected]

3 The Telecommunications Laboratory,

8 Mai 1945 - Guelma University, Alegria, e-mail: [email protected]

How to cite this article:

Bouraghda S., Sebaa K., Bechouat M., Sedraoui M. An improved sliding mode control for reduction of harmonic currents in grid system connected with a wind turbine equipped by a doubly-fed induction generator. Electrical Engineering & Electromechanics, 2022, no. 2, pp. 47-55. doi: https://doi.org/10.20998/2074-272X.2022.2.08