AMELIORATE DIRECT POWER CONTROL OF STANDALONE WIND ENERGY GENERATION SYSTEM BASED ON PERMANENT MAGNET SYNCHRONOUS GENERATOR BY USING FUZZY LOGIC CONTROL Текст научной статьи по специальности «Электротехника, электронная техника, информационные технологии»

UDC 621.3

doi: 10.20998/2074-272X.2020.6.09

R. Lebied, R. Lalalou, H. Benalla, K. Nebti, I. Boukhechem

AMELIORATE DIRECT POWER CONTROL OF STANDALONE WIND ENERGY GENERATION SYSTEM BASED ON PERMANENT MAGNET SYNCHRONOUS GENERATOR BY USING FUZZY LOGIC CONTROL

Purpose. Electricity is a basic energy for life and its consumption increased so we need the discovery of new sources of energy such as wind energy .for this ameliorate the quality of generated wind energy by using the intelligent artificial control, this control is made to optimize the performance of three-phase PWM rectifier working. Methodology. These strategies are based on the direct control of the instantaneous power, namely: the control direct power control (DPC) with classic PI regulator and direct power control with fuzzy logic regulator. The fuzzy characterized by its ability to deal with the imprecise, the uncertain has been exploited to construct a fuzzy voltage regulator. The simulation of these methods was implemented using Matlab/Simulink Results. A comparison with the results obtained by the classic PI showed the improvement in dynamic performance. This makes the fuzzy controller an acceptable choice for systems requiring quick, precise adjustments and less sensitive to outside disturbances. Originality. The proposed this control strategy using for to obtain a performance adjustment of the DC bus voltage and sinusoidal currents on the network side. Practical value. Fuzzy logic is proven to be effective in terms of reducing the harmonic distortion rate of the currents absorbed, correct adjustment of the active and reactive power and DC voltage and unit power factor operation. References 26, tables 6, figures 15.

Key words: direct power control, fuzzy logic control, permanent magnet synchronous generator (PMSG), PWM technique, wind energy system.

Мета. Електроенерпя e основною енергieю для життя, i и споживання збтьшуеться, тому нам Heo6xidHO sidKpummn нових джерел енерги, таких як енерля eimpy. Для полтшення якостi енерги eimpy, що генеруеться за допомогою управлння на основi штучного ттелекту, таке управлння призначене для оптимiзацií продуктивностi роботи трифазного Ш1М випрямляча Методологя Данi стратеги засноват на прямому управтнш миттевою потужнстю, а саме: пряме управлння потужнстю з класичним П1-регулятором i пряме управлтня потужнстю регулятором з нечiткою логжою. Нечтшсть, що характеризуешься и здатнстю справлятися з неточнстю, невизначетстю, була використана для створення нечткого регулятора напруги. Моделювання цих методiв було реалЬовано за допомогою Matlab/Simulink. Отримаш результати. Порiвняння з результатами, отриманими за допомогою класичного П1-регулятора, показало полтшення динамiчних характеристик. Це робить нечiткий контролер прийнятним вибором для систем, що вимагають швидкоí i точноí настройки i менш чутливих до зовнiшнiх перешкод. Оригiнальнiсть. Запропоновано стратегю управлтня, що використовуе для отримання регулювання продуктивностi напруги шини посттного струму i сину^дальн струми на сторож мереж1 Практична щншсть. Доведено, що нечiтка логжа ефективна з точки зору зниження коефцента гармонШих спотворень поглинаються струмiв, коректного регулювання активноí i реактивно1' потужностi i постiйноí напруги, а також коефцента потужностi роботи блоку. Бiбл. 26, табл. 6, рис. 15.

Ключовi слова: пряме управлшня потужшстю, управлшня з неч^кою логжою, синхронний генератор з постшними магштами, метод Ш1М, впроенергетична система.

Introduction. The readily available renewable energy especially the abundant resources of solar energy and wind energy have led to a steady growth of interest concerning distributed generation units. As the adoption of system into the smart power grid is seen a tendency of becoming a new paradigm to sustainable energy, the integration of power converters to take control of the smart grid operation become one of the main research areas that require immense attention. The three phase grid connected voltage source converter which features Bidirectional power flow, nearly sinusoidal input currents, controllable power factor, and high quality DC output voltage have made it an increasingly important proportion in renewable energy system [1].

There are three type of renewable energy:

• mechanical energy (wind energy);

• electric energy (photovoltaic panels);

• energy in the form of heat (geothermal, solar [2]).

Wind energy, is one of the available non-conventional

energy sources, which is clean and an infinite natural resource. Wind power is still the most promising renewable energy in the year of 2013. The wind turbine system (WTS) started with a few tens of kilowatt power in the

1980s. Now multi-megawatt wind turbines are widely installed even up to 6-8 MW [3] (Fig. 1).

Fig. 1. Global cumulative installed wind power capacity from 1999 to 2020 [3]

Wind energy based power system operation is challenging under fluctuating nature of wind speeds and variable load conditions, particularly when the operation mode of the hybrid wind power system is stand alone. The changing wind speeds causes fluctuations in windturbine generator, which causes fluctuations in load

© R. Lebied, R. Lalalou, H. Benalla, K. Nebti, I. Boukhechem

voltage and frequency in the stand-alone wind-energy system. Variable speed wind-turbine systems are more advantageous when compared with the fixed speed wind turbine systems. They generate maximum amount of power and gives less mechanical stress, higher power quality and efficiency than fixed speed wind-turbine systems [4, 5]. Standalone wind energy conversion systems are electric energy alternative sources for isolated area. They usually supplies air conditioning mechanical loads, ventilation and water pumps [6]. Various control strategies have been proposed in recent works on this type of PWM rectifier. It can be classified for its use of current rent loop controllers or active/reactive power controllers. The well-known method of indirect active and reactive power control is based on current vector orientation with respect to the line voltage vector. It is called voltage oriented control (VOC) [7]. VOC guarantees high dynamics and static performance via internal current control loops. However, the final configuration and performance of the VOC system largely depends on the quality of the applied current control strategy. Over the last few years, an interesting emerging control technique has been direct power control (DPC), developed analogously with the well-known direct torque control (DTC) used for adjustable speed drives [8].Therefore, the wind generating system is found to be of a great potential as a very attractive supply option for industrial and domestic applications. Several electrical generators can be used to perform the electromechanical energy conversion. Permanent magnet synchronous generator (PMSG) offer significant advantages over conventional synchronous generators as a source of isolated supply. Brushless, absence of a separate DC source, and maintenance free are among the advantages. However the variable natural of wind and the fluctuation of load profiles lead to fluctuating torque of the wind turbine generator. This causes variation in the output voltage and frequency [9]. The relay control can be performed by selecting an optimum switching state of the converter, so that the active and reactive power errors can be restricted in appropriate hysteresis bands, which is possible by using a switching table and several hysteresis comparators. The latter is based on a calculation of the voltages for each switching state of the converter by detecting the line currents, and the calculation is performed by utilizing the active and reactive power as intermediate variables. Since this method deals with instantaneous variables in obtaining the voltages, it is possible to estimate not only a fundamental component [10]. Fuzzy logic control has found many applications in the past two decades. This is so largely increasing because fuzzy logic control has the capability to control nonlinear uncertain systems even in the case where no mathematical model is available for the control system [11]. This paper proposes a novel DPC for a three phase PWM rectifier, which makes it possible to achieve unity power factor operation by directly controlling its instantaneous active and reactive power without any power-source voltage sensors. In this situation, the DPC based on fuzzy logic control is used instead of DPC. This control technique greatly lowers the

fluctuations of the active and reactive power and the harmonic distortion rate THD [12].

This paper is organized into the following sections:

• Section I describes about the stand-alone wind energy system configuration with PMSG modeling;

• Section II represented different control strategies;

• Section III discusses about the simulation results;

• Conclusions.

Section I. Stand-alone wind energy supply system. The system consists of the following components (parameters are presented in Appendix in Tables A.1 -A.3):

• wind turbine;

• PMSG which is directly driven by the wind turbine without using a gearbox;

• uncontrolled rectifier PWM.

Profile wind turbine model. The first step necessary for a wind production project is the geographical choice of the site. The properties of wind are interesting for the study of the whole wind energy conversion system, since its power, under ideal conditions, is proportional to the cube of the wind speed. To know the characteristics of a site, it is essential to have measurements of the wind speed and its direction, over a long period of time. It is modeled by an addition of a number of harmonics and the wind speed variation is according to the following equation [13, 14]: V = 6.5 + (0.2sin(0.1074i) + 2sin(0.2665i) + sin(1.2930i) + + 0.2sin(3.6645i)).

Turbine modeling. The turbine is a device used to convert wind energy into mechanical energy. The mechanical power P of wind turbine extracted from the wind can be expressed as follows [15]

(1)

P = CpPm= 2 CPpn.R2V3

(2)

where CP is the power coefficient which is a function of the pitch angle of rotor blades 0 [deg] and of the tip-speed ratio 2; Pm is the dynamic force; p [kg/m3] is the air density; R [m] is the blade turbine radius; V [m/s] is the wind speed.

The dynamic force accessible:

1

Pa=2 psv3 = 2 p^v ■

The tip-speed ratio 2 is defined as

DR

1

23

2=-

V

(3)

(4)

where Q is the angular mechanical speed of the turbine rotor.

Modeling of PMSG. AC machines are generally modeled by non-linear equations (differential equation). This non-linearity is due to the inductances and coefficients of the dynamic equations which depend on the rotor position and time. A three phase - two phase transformation necessary to simplify the model (reduce the number of equations). In the PMSG, the rotor excitation is supposed constant. The electrical equation represented by [16, 17]:

Vd --RsId - L,

d_ dt~

-Id + 0)rLqIq

(5)

Vq - ~RsIq - L

d

qdtq

Iq -orLdId + orPf.

(6)

where Vd and Vq are the components of stator voltage; Rs is the stator resistance; Ld and Lq are the components of stator inductances; Id and Iq are the components of stator current; c/f is the permanent magnet flux; mr is the electric pulsation; np is the pole pair number.

The electrical rotation speed is given by:

we = np ■ w , (7)

where np is the pole pair number; w is the mechanical speed.

The electromagnetic torque Te represented by:

3

-■ np Vf ■ Iq . (8)

T -

1e

2

The equations for active power P and reactive power Q are provided by:

3

P - ~(Vd ■ Id - Vq ■ Iq ); 3

Q - "(Vq ■ Id - Vd ■ Iq).

(9) (10)

Uncontrolled rectifier PWM. The wind generator, which is based on a variable speed turbine and a PMSG, is connected to a DC bus by through a PWM power converter [18]. Since we have three phase line voltage and the fundamental line currents in:

(11) (12)

Ua - Em cos ot ;

2n

Ub - Em cos(ot H——) ;

2n

Uc - Em cos(ot - —) ;

ia - Im cos(ot + p) ;

2n

ib - Im cos(ot + -3- + p) ;

2n

ic - Im cos(ot —— + p),

(13)

(14)

(15)

(16)

where Em, Im are the amplitudes of the phase voltage and current respectively; a> is angular frequency; p is the phase shift.

Line to line input voltages of PWM rectifier can be described as:

Usa - - sb )'udc ; (17)

Usb -(sb-sc)udc; (18)

Usc-(sc - sa)udc , (19)

and phase voltages equations give by:

U - 2sa -isb + sc)

u sa

Usb -

Usc -

3

2sb - (sa + Sc )

3

2sc -(sa + Sb )

udc ;

3

udc ;

■ udc

(20) (21) (22)

where sa, sb and sc are the switching states of the rectifier and udc is voltage rectifier.

Section II. Generalized strategies control. DPC of PMSG. The objective of the proposed command is to control the DC voltage at the input of the

inverter udc. From the desired value of the DC voltage, it is possible to express that of the reference power by:

Pref = udc ■ ^dc ,

(23)

where idc is the rectifier output current.

The principle of DPC and it was later developed for several applications. The aim was to eliminate the modulation block and the internal loops by replacing them with a switching table whose inputs are the errors between the reference values and the measurements. Then, a similar technique was proposed for a rectifier control application (generator in our case). In this case, the quantities controlled are the instantaneous active and reactive powers, use this quantity as control variables and which does not need to use modulation blocks because the switching because the switching states are chosen directly by a switching table .

Figure 2 gives the DPC structure adopted for the application studied.

Qr„ = 0

Fig. 2. Diagram of DPC for the PMSG

Estimated instantaneous power. The instantaneous active power is defined by the dot product between the currents and the line voltages. Whereas, the reactive power is defined by the vector product between them [19, 20]:

S = U x I = P + jQ ; (24)

S = Ua ■ la + Ub ■ lb +Ucic + jA=[(Ub ~ Uc)'a +

V3 (25)

+ (Uc - Ua)ib + (Ua - Ub)ic], where U is instantaneous source voltage; I: is line instantaneous current; L is the line inductance

_L[3L( diLic + ic

■yJ3 dt dt + Sb (ic - ia ) + Sc (ia - ib ))]; dib . dic dt dt dt

The first parts of the two expressions represented above present the power in the line inductors, noting here that the internal resistances of these inductors are negligible because the active power dissipated in these resistors is in fact much lower compared to the power involved. Other parts represent the power in the converter.

Voltage estimation. The line voltage working area is required to determine the switching orders. In addition it is important to estimate the line voltage correctly, even with the existence of harmonics, its gives a high power

Q [3L(%ic +rjitia ) - Udc (Sa (ib - ic ) +

(26)

P - L^«

lib +—ric ) + udc (Saia + Sbib + Scic ). (27)

factor. The following expression gives the line currents i,

ib, ic in the stationary coordinates a - p ' — —

a - [2 1 2 2

pj-v 3 0 V3 —yj _ 2 2 We can write the expressions of the active and reactive powers as follows [21]:

(28)

P = F

(abc) ' l(abc)

= Voia+ Vßi ß

Q = V(abc) A i(abc) = Va ß ~ Vßii '

(29)

(30)

~Va Vß a

Q_ - VaVa_ iß_

The matrix writing of the expressions (29) and (30) is:

(31)

The matrix equation (31) can be rewritten, depending on the line current (measured) and the power (estimated), as follows:

(32)

Va 1 ia - iß ~P p

Vß_ i 2 + i2 ia +i ß iß ia Q_

Concordia's inverse transform of line voltages is written [22]:

1 0

Va " ¡2 -1 V3

Vb = J 7 2 2

Vc _ V3 -1 -V?

2 2

(33)

(AP = Pref - P; Uq =Qref -Q.

(33)

(35)

The hysteresis comparators provide two logic outputs dP and dQ. The state «1» corresponds to an increase in the controlled variable (P and Q), while «0» corresponds to a decrease

'i/AP > hp ^ dp -1;

i/AP x -hP ^ dP - 0; i/AQ > hQ ^ dQ -1; i/AQ < -hQ ^ dQ - 0,

where hP and hQ denote the hysteresis bands [21].

Switching table. The digital error signals SP and Sq and the working sector are the inputs of the switching table where the switching states Sa, Sb and Sc the PWM rectifier are stored. By using the table, the optimum switching state Of the converter can be chosen at each switching state according to the combination of the digital signals SP and SQ sector number, that is to say, that the choice of the optimum switching state is made so that the error of the active power can be restricted in a hysteresis

band of width 2H_p, and likewise for the error of reactive power, with a band of width [22].

The sectors can be numerically expressed as:

7 7

(n-2)—<en <(n-1)-), 6 6

(36)

where n = 1, 2, ... ,12.

By using several comparators, it is possible to specify the sector where the voltage vector exists. The digitized error signals SP and Sq digitized voltage phase are 6n input to the switching table in which every switching state of the converter is stored, as shown in Table 1. By using this switching table, the optimum switching state Sa, Sb and Sc of the converter can be selected uniquely in every specific moment according to the combination of the digitized input signals (Fig. 3). The selection of the optimum switching state is performed so that the power errors can be restricted within the hysteresis bands [23].

Table 1

Possible switching table

Hysteresis controller. The main idea behind the DPC method is to maintain the instantaneous active and reactive powers within a desired band. DPC consists of two hysteresis comparators whose inputs are the errors between the reference and estimated values of the active and reactive powers, respectively.

Sp Sq 01 02 03 04 05 06

0 0 V6 V1 V1 V2 V2 V3

1 V1 V2 V2 V3 V3 V4

1 0 V5 V6 V6 V1 V1 V2

1 V3 V4 V4 V5 V5 V6

Sp Sq 07 08 09 010 011 012

0 0 V3 V4 V4 V5 V5 V6

1 V4 V5 V5 V6 V6 V1

1 0 V2 v3 V3 V4 V4 V5

1 V6 V1 V1 V2 V2 V3

Fig. 3. The vector plane divided into 12 sectors

External voltage regulation loop. The external regulation loop maintains a load assimilated to a resistance R. The impedance thus formed is charged by the current idc from the PWM rectifier. The current idcre/ is the current from the PWM rectifier (Fig. 4). The product of the reference DC with the DC voltage gives the active power of reference. Capacitance voltage DC at a reference voltage is udcre/ . The capacity C is in parallel with load (resistance).

Fig. 4. DC voltage regulation

ß

Fuzzy logic control for DPC. Improving the quality of the currents absorbed by the PWM rectifier and maintaining of the DC voltage at the output around the of the DC voltage at the output around the reference requires voltage regulation and fast and robust currents[24]. For this reason presents a DPC operating with a fuzzy logic controller which replaces voltage in conventional commands. Figure 5 gives the block diagram of the proposed fuzzy logic controller for DPC of three-phase PWM rectifier.

• positive small noted PS;

• average positive noted AP;

Fig. 5.The block diagram e block diagram of fuzzy logic controller for DPC of three-phase PWM rectifier

The configuration of the voltage loop is illustrated in Fig. 6, it is composed of [25]:

• normalization factors relate to the error (e) and the variation of the command (Ae);

• a block of fuzzyfication of the error and its variation;

• rule of inference. The control strategy is presented by an inference matrix presented in table;

• a defuzzification block used to convert the fuzzy control variation into a digital value.

Ujrrof ________________________________ Pf.

Fuzzy logic controller Fig. 6. Diagram of the proposed fuzzy logic controller for DPC

Fuzzyfication. This step deals with the transformation of numeric values to inputs into fuzzy values or linguistic variables. The input variables which are the velocity error and its variation are subjected to a fuzzification operation and therefore converted to fuzzy sets. The normalized universe of speech of each variable of the regulator (the error, its variation and the variation of variation and the variation of the command) is subdivided into seven fuzzy sets; these are characterized by the following standard designations:

• large negative noted LN;

• average negative noted AN;

• small negative noted SN;

• about zero noted AZ;

• large positive noted LP.

For the membership functions we chose for each variable the triangular and trapezoidal shapes.

Inference rules. The rule base represents the control strategy and desired goal through linguistic control rules. It makes it possible to determine the decision or action at the output of the fuzzy controller and to express qualitatively the relationship that exists between the input variables and the output variable. From the study of the behavior of the system, we can establish the control rules, which connect the output with the inputs. As we mentioned, each of the two linguistic inputs of the fuzzy controller has seven fuzzy sets.

Fuzzy rules table (Table 2) showing change in control output [26].

Table 2

Fuzzy rules table

e Ae\ LN AN SN AZ PS AP LP

LN LN LN LN LN AN SN AZ

AN LN LN LN AN SN AZ PS

SN LN LN AN SN AZ PS AP

AZ LN AN SN AZ PS AP LP

PS AN SN AZ PS AP LP LP

AP SN AZ PS AP LP LP LP

LP AZ PS AP LP LP LP LP

The logic for determining this matrix of rules is based on a global or qualitative knowledge of the functioning of the system. As an example, consider the following two rules:

• if e is LP and Ae is LP then Au is LP;

• if e is AZ and Ae is AZ then Au is AZ.

They indicate that if the speed is too small compared to its reference (e is LP and Ae is LP), then a large torque demand (Au is PG) is needed (to bring the speed back to its reference). And if the speed meets its reference and settles (e is AZ and Ae is AZ) then keep the same torque (Au is EZ).

Deffuzzyfication. When the fuzzy output is calculated, it must be transformed into a numeric value. There are several methods to achieve this transformation. The most used is the center of gravity method, which we have adopted in our work. The abscissa of the center of gravity corresponding to the output of the regulator is given by:

AU -

J xy( x)dx Jy( x)dx

(37)

Section III. Discusses about the simulation results and discussion. Simulations and results of DPC are presented in Fig. 7-15. We present the wind turbine profile (Fig. 7); the stator voltages of PMSG (Fig. 8); the stator voltage and current of PMSG (Fig. 9); the rectified

voltage DPC (Fig. 10); the active (Fig. 11) and reactive Fig. 12) power for classic DPC and fuzzy DPC technique (Fig. 13-15).

Simulations and results of Fuzzy logic control for

2 3

Time(s)

Fig. 9. The stator voltage and current of PMSG

r

100L

1 2 3

Time(s)

Fig. 10. The rectified voltage DPC

jVf

1 2 3

Tlime(s)

Fig. 11. The active power DPC

200

100

CD o

á è o

-100

-200

12 3 4

Time(s)

Fig. 12. The reactive power DPC

DPC.

300 r

250 -

M >200 I

DÉ 1501

<D I

-C T

~ 100L

(D 3000

I

CL

<D ^2000

1000

CD

12 3 4

Time(s)

Fig. 13. Rectified voltage DPC fuzzy logic

1 1

112 3 4

Time(s)

Fig. 14. The active power DPC fuzzy logic

12 3 4

Time(s)

Fig. 15. The reactive power DPC fuzzy logic

During the transient response (Fig. 10) shows that there is an overshooting in the rectifier output voltage caused by PI parameters choice and the signal produced by the start of the PMSG, but at (t = 0.3 to 2.5 s), note that the direct voltage reaches its reference value (230 V) and (280 V), but for fuzzy logic the direct voltage reaches its reference value from (t =0 to 0.025 s) (Fig. 13), and the instantaneous powers (P, Q) followed by the reference power (P = 550 W) and (P =850 W) in the Fig. 11, and (q = 0 vAR) with a considerable presence of oscillations around the reference (Fig. 12), but for the DPC by PI regulator from (t = 0 to 0.3 s) the response very slow and from (t = 2.5 to 2.8 s) it there is a disturbance produced by the change of the reference voltage on the other hand fuzzy logic DPC instantaneous powers (P, Q) followed by the reference power from (t = 0.24 s) and response time speed very and the absence of disturbance produced by the change in the reference voltage (Fig. 14) and decrease in oscillations around the reference (Fig. 15), the voltage and current of the PMSG are in phase, and the line currents are sinusoidal (Fig. 9).

The active and reactive power responses follow their references perfectly, these results, show the superiority of fuzzy regulator compared to the conventional PI. With fuzzy regulators no overshoot is produced, fast response in transient conditions and the static error is nearly zero.

THD comparative study. The objective of this study is to show the contribution of each two methods presented throughout this work. The two criteria taken into account in evaluating the performance of these

controls are: the rate of distortion of the network currents (THD). Table 3 shows the THD values obtained in steady state for the two control modes. All of these commands give acceptable THD values of less than 5 %. We also notice the superiority of fuzzy logic regulator over the other control; in fact, it can reduce the THD to a low value of approximately 1.87 %.

Table 3

THD values

Control Classical regulator PI for DPC Fuzzy logic control for DPC

THD % (f = 12.8 Hz) 3.58 % 1.87 %

Conclusion.

The proposed control is simple, robust, not sensitive to the parametric disturbance and variation of the system, and with very good dynamic characteristics. For DPC fuzzy the value of rectified voltage is 0.025 s and very speed time response of disturbance produced by the change in the reference voltage 0.01 s. It can be said that the use of fixed PI regulators gives a robust control system and an acceptable response 0.3 s, but the conventional problems of the PI regulator such as the response time and the robustness against external disturbances have appeared, and to solve the problems mentioned above we will use the fuzzy control to establish a regulator robust.

The fuzzy logic adjustment gives a very programmatic approaches, allowing integrating the knowledge acquired by the operators.

Spectral analysis of line current shows that all low-order harmonics are well attenuated which gives a THD around to 3.6 %.

The fuzzy DPC simulation results obtained good performance in steady state and transient conditions especially for the case of current harmonic distortion rate which is good for other techniques; it is able to reduce the THD to a low value of around 1.87 % with better convergence of active power (P = 550 W and P =850 W), however reactive power (q = 0 vAR) towards their respective references.

APPENDIX

Table A.1

Wind turbine parameters

Parameter Symbol Value

Power P 7.5 kW

Radius R 3.24 m

Inertia J 7.5 kg -m2

Friction coefficient F 0.06 N- m- s/rad

Table A.2

PMSG parameters

Parameter Symbol Value

Direct stator inductance Ld 0.012 H

Stator quadrature inductance Lq 0.0211 H

Permanent magnet flux (f 0.9 Wb

Stator resistance Rs 0.895 a

Inertia J 0.00141 kg -m2

Number of poles n„ 3

Friction force F 0 N- m/rad- s

Table A.3

Rectifier parameters

Parameter Symbol Value

Line resistance R, 0.7 Q

Line inductance L 0.01 H

Filtering capacity C 0.0033 F

DC voltage reference Udcref 230 - 280V

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Received 05.09.2020 Accepted 19.10.2020 Published 24.12.2020

Ryma Lebied Ph.D.,

Rachid Lalalou1, Doctor of Electrotechnical, Hocine Benalla2, Doctor of Electrotechnical, Professor, Khalil Nebti2, Doctor of Electrotechnical, Ismail Boukhechem1, Ph.D.,

1 Electrotechnical Laboratory Skikda (LES), University 20 August 1955, Department of Electrical Engineering,

26 Road El Hadaiek 21000, Skikda, Algeria.

2 Electrical Engineering Laboratory of Constantine, LEC, Department of Electrical Engineering,

University of Constantine 1, 25000 Constantine, Algeria. e-mail: [email protected]; [email protected]; [email protected]; [email protected]; [email protected]