Speed Control of Doubly Fed Induction Motor

Available online at www.sciencedirect.com

ScienceDirect Energy Procedia 74 (2015) 575 – 586

Speed control of doubly fed induction motor S. Lekhchinea*, T. Bahib, I. Aadliab , Z. Layateb, H. Bouzeriac a*

Department of Electrical Engineering, 20 August 1955-Skikda University,Skikda 21000, Algeria b LASA and LEE, Badji Mokhtar University , BP 12, Annaba 23000, Algeria c Department of Electrical Engineering, Hadj Lakhdar University, Batna 05000, Algeria

Abstract

In this work the performance comparison study of the proportional integral and fuzzy logic speed controllers which used for the speed control of doubly fed induction machine is presented. For a long time, electromechanical systems used the squirrel-cage induction motors, as main actuators, however, doubly fed induction motors, present of estimable advantages at variable speed drive. From that, the performances of conventional speed controllers are sensitive to parameter variations of the motor. So, in this paper, the analyze of performances of speed fuzzy logic controller is presented. The simulation results showed that the fuzzy logic controller ensure the best dynamic performances in rotor resistance and load variations. © 2015 by by Elsevier Ltd.Ltd. This is an open access article under the CC BY-NC-ND license © 2015The TheAuthors. Authors.Published Published Elsevier (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Euro-Mediterranean Institute for Sustainable Development (EUMISD). Peer-review under responsibility of the Euro-Mediterranean Institute for Sustainable Development (EUMISD)

Keywords: Doubly fed induction machine; variable speed; performances, fuzzy logic controller; simulation.

1. Introduction The electric motors of industrial systems operate generally at variable speed. Since, the induction motors are often used because they are unquestionably an advantage over to the machine the DC machine [1, 2]. But, the coupling between the flux and torque of IM present a serious problem for its control. For this purpose, the vector control theory [3] has long since been applied successfully for three phase induction motors. However, the performances of the speed control are sensitizes at motor parameters variations [4, 5].

* Corresponding author. Tel.: +213-0781-66-24-27. E-mail address: [email protected]

1876-6102 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4 .0/). Peer-review under responsibility of the Euro-Mediterranean Institute for Sustainable Development (EUMISD) doi:10.1016/j.egypro.2015.07.758

576

S. Lekhchine et al. / Energy Procedia 74 (2015) 575 – 586

Consequently, it is interesting to use the modern control techniques more towards for the high power in the energy renewable applications. Notably, fuzzy logic aims to study and representation of imprecise knowledge and approximate reasoning [6]. The description of imprecise or uncertain situations may contain the fuzzy expressions such as: big, medium, small, etc…These «linguistic" expressions are subject to membership functions [7-8]. Currently, fuzzy logic is used in many fields, such as, management, medicine and control systems. It is also used to match the degree of truth to a variable that can be linguistic. This scaling in the membership of an element has a situation that allows the modeling of man observation expressed in linguistic form [9, 10]. She allows you to translate a control strategy of a qualified set of easily interpretable linguistic rules and to treat linguistic variables whose values are sentences in natural language [11, 12]. In this works, doubly fed induction motor (DFIM) is used because he offers the opportunity to modulate power flow into and out the rotor winding in order to have, at the same time, a variable speed in the characterized supersynchronous or sub-synchronous modes in motor or in generator regimes [13-15]. The DFIM can be controlled from the stator or rotor by various possible combinations and the strategy of the flux orientation can to transform the non linear and coupled DFIM-mathematical model to a linear model leading to one attractive solution as well as under generating or motoring operations [15-17]. The paper is organized as follows. In section 2, modelling of doubly fed induction motor, the field oriented control and inverter are developed. The methodology approaches of the conventional and fuzzy logic controllers are presented, in section 3. The simulation results and their discussion are presented in section 4. Finally, conclusion is presented in last section.

2. Modeling system An easy way to comply with the conference paper formatting requirements is to use this document as a template and simply type your text into it. 2.1. DFIM model The structure of DFIM is very complex. Therefore, in order to develop a model, it is necessary to consider the following simplifying assumptions [16, 19]: the machine is symmetrical with constant air gap ; the magnetic circuit is not saturated and it is perfectly laminated, with the result that the iron losses and hysteresis are negligible and only the windings are driven by currents; the mmf created in one phase of stator and rotor are sinusoidal distributions along the gap. By this means, the DFIM state equations [20, 21] are described as follow: .

­. ° x Ax  Bu ® °¯ y Cx

(1)

With,



x

>ids u

iqs

>Vds

idr

iqr

@T

Vqs Vdr

is the state vector ;

Vqr

@ T is input vector.

577

S. Lekhchine et al. / Energy Procedia 74 (2015) 575 – 586

Where,  Rs ª « VLs « « (1  V )Z  Z s « V A « RL s m « « VLs Lr « LmZ « VLr ¬«

B

C

ª 1 « VL s « « 0 « « L m « « VLs Lr « « 0 ¬

ª1 «0 « «0 « ¬0

LmZ º (1  V )Z  Z s Rr Lm V VLs Lr VLs » »  Rs LmZ Rr Lm » VLs VLs Lr VLs Lr »  Lm Z  Rs VZ s  Z » » V » VLr VLs  Rs » R s Lm Z  VZ s » VLs Lr V VLs ¼» 0

 Lm VLs Lr

1

VLs

0

0

VLr

1

Lm

VLs Lr

0

(2)

º » »  Lm » VLs Lr » » 0 » » 1 » » VLr ¼ 0

(3)

0 0 0º 1 0 0»» 0 1 0» » 0 0 1¼

(4)

The dynamical equation and electromegnetical torque are given by (5) and (6), respectively:

J

d: dt

Tem

Tem  Tl  k f :

(5)

p.Lm (iqs .idr  ids .iqr )

(6)

The vector control aimed to ensure control decoupled of the flow and torque [3]. In the synchronous reference frame whose axis d is aligned with the rotor flux vector Φ dr= Φ*and Φqr= 0. Fig. 1 shows the vector representation of vector control.

q

d

)r )rd

is

Ts

isd

isq

Rotor axis

Tr T

0 Fig. 1. Rotor orientation

Stator axis

578

S. Lekhchine et al. / Energy Procedia 74 (2015) 575 – 586

) qr

Lr iqr  Lm (iqs  iqr )

0

(7)

So

Lmiqs

iqr

(8)

Lr  Lm

And,

) dr

) *r ,

Zs  Zr

d) dr dt Rr iqs

0

(9)

( Lr  Lm )ids

(10)

However, using the torque equation can be expressed as:

Te

K m ) dr iqr

(11)

Where Km is torque constant. So, if the rotor flux

) dr

) *r is considered as constant, the quadrature stator current component (iqs)

control the torque and the rotor flux can be controlled with direct component of stator current (ids). The dynamical equation is given by:

J d Zr p dt

K) dr iqr  Tl 

kf p

Zr

(12)

Thus, the transfer function will be expressed by the speed:

wr ( P)

K m ) * iqr ( P) Tl ( P)  Kf J Kf J  P  P p p p p

(13)

The block diagram of the speed loop regulation is in Fig. 2:

Tl

Zr*

+-

Speed Controller

,qr*

Ke

+ 7em*

Fig. 2. Speed loop

-

1 Kf J p +pP

Zr

579

S. Lekhchine et al. / Energy Procedia 74 (2015) 575 – 586

2.2. Inverter model The inverter is composed of six (6) switches supposed idealized. A KiK function that links between the sizes of input and output is defined for each switch. Expressions of currents and voltages are written as following:

­ ° I IK ® ° ¯V IK

K IK I IK (14)

(1  K IK )V IK

With, KiK= 0 if the switch is open and KiK = 1 if he is closed.

I  ^a, b, c`, k  ^p, n` Ilk: Load phase current and lk: Supply voltage. Table 1. Inverter Output Voltages Sequence Ki1 Ki2 1 0 1 2 1 0

Ci -1 1

Vi0 -Udc/2 +Udc/2

Where the structure of the two levels inverter is represented in Fig. 3. Ka1

D1

Kb1

D2

Kc1

D3

isa

Udc /2 Udc

isb

isc

Udc /2 Ka2

D4

Kb2

D5

Kc2

D6

Fig. 3. Structure of the two levels inverter

The functions of cell connections must satisfy the following condition: Fip+Fin=1. The functions relating to each of these connections are:

ªVab º ª 1  1 0 º ª Fap º « » «V » V « 0 1  1»» « Fbp » pn « « bc » «¬Vca »¼ «¬ 1 0 1 »¼ «¬ Fcp »¼

(15)

And,

ªVa º «V » « b» «¬Vc »¼

ª 2  1  1º ª Fap º 1 « » V pn «« 1 2  1»» « Fbp » 3 «¬ 1  1 2 »¼ «¬ Fcp »¼

(16)

580

S. Lekhchine et al. / Energy Procedia 74 (2015) 575 – 586

The PWM triangular-sinusoidal strategy is to compare two signals. The first signal is a sine wave where its frequency is the frequency of output desired, it is usually called the reference wave. The second signal is a triangular carrier frequency which must be enough large from the frequency of the sinusoid.

Fap

1 if Vm ! V p and Vm ! 0

(17)

Fan

1 if Vm  V p and Vm  0

(18)

3. Speed Controllers 3.1. PI conventional controller The classic numerical Proportional and Integral ( PI) regulator is well suited to regulating the speed Ω , to the



 and I term K i

desired values Ω* as it is able to reach constant reference, by correctly both the P term K p

winches are respectively responsible for error e sensibility and for the steady state error. The dynamic model of speed induction motor drive with PI is significantly simplified, and can be reasonably represented by the bloc diagram shown in Fig. 4.

Fig. 4. Speed control loop with PI controller

Lm * .M r . Lr Where the speed controller is a proportional integral (PI), the proportional action (P) ensures the performance criteria required by speed loop. So the integral action (I) cancel the error in study state. By neglecting, the load torque (Tl=0), the transfer function is [22, 23].

With, K e

Zr Z r*

p.

K PZ1 P 1 K iZ 1 J .P 2  p.K iZ1

K PZ1  K iZ1

Kf p

P 1 .

(19)

Where:

K pZ1 K pZ K e , K iZ1

K iZ K e and K e

K m )*

581

S. Lekhchine et al. / Energy Procedia 74 (2015) 575 – 586

By identification with the canonical form: G(s)

Zr Z r*

1 1

2

Zn2

P 

2[ P 1 Zn

(20)

We obtained: ­ ° K iZ ° ° ° ® °K ° P: ° ° ¯

JZ n2 p.K e k · § ¨ 2[ K iZ  f ¸ p ¸ 1 ¨ ¸K ¨ Zn ¸ e ¨ ¸ ¨ ¹ ©

We chose the coefficients for

[

1 and response time (Trep=20ms) at 5%.

3.2. Fuzzy logic controller In this section, we focus on the application of fuzzy logic for adjusting the speed of DFIM. Fig. 5 shows the block diagram of a fuzzy logic controller (FLC). e

Fuzzy control rules

Ge

Wrréf+

Fuzzification -

Wr

Computation of 'e

'e

G'e

'u Defuzzification

G'u

ʃ

Inférence

DFIM Fig. 5. Scheme of speed control using FLC

The FLC is made up of parameters such as rule base database membership functions, input and factor scaling output (SF). SF is a very important parameter because it is directly related to the stability control system etc ... [2427]. For this study, the membership functions of the error, the error and variation of the output are shown by Fig 6. NB

-1

-0.6

NM

-0.4

NS

-0.2

EZ

PS

PM

0

0.2

0.4

PB

0.6

1

e , 'e et 'u

Fig. 6. membership functions of "e", "de" and “du”

The linguistic variables are identified by symbols: NB: Negative Big , NM: Negative Medium, NS: Negative Small, EZ: About Zero; PS: Positive Small, PM: Positive Medium, PG: Positive Big .

582

S. Lekhchine et al. / Energy Procedia 74 (2015) 575 – 586

The fuzzy rules define the controller output based on input [28]. The "Table2" presents the rules adopted in this work. Table1. Matrix Inference de

e

NB

NM

NS

EZ

PS

PM

PB

NB NM

NB NB

NB NB

NB NB

NB NM

NM NS

NS EZ

EZ PS

NS ZE

NB NB

NB NM

NM NS

NS EZ

ZE PS

PS PM

PM PB

PS

NM

NS

EZ

PS

PM

PB

PB

PM

NS

EZ

PS

PM

PB

PB

PB

PB

EZ

PS

PM

PB

PB

PB

PB

4. Simulation results The proposed FLC controller for the DFIM drive is tested under Matlab/Simulink. The scheme system represented on Fig. 7 consists of the following elements: three-phase DFIM, two voltage-source inverters.

Zr* +

-

FLC

7e*

,qr*

1

+

Km )dr

Zr

,dr*

PI

-Lr

+

,qs*

LM

Field weakeping

)dr*

-

-

Decoupling and Current regulation

-

1 ,ds + LM *

,qr

,dr +

Vd-q*

,qs

Vabc*

PWM

DFIM

Vd-q* Vabc*

,ds Fig. 7. Scheme of control

The structure of Fig. 7 has been programmed, using the environment MatLab Simulink, in the aim to carry out comparative analysis of the performance of the PI conventional and fuzzy logic speed controllers. Therefore, the motor is simulated starting followed for reversing the direction of rotation at time 4s. As shown in the Figures 8.a and 8.b , for each rotation, the motor is subjected to constraint for load variation and motor resistance. Figure 9 shows the evolution of input and output of the FLC, the speed, electromagnetic torque and flux components are represented respectivly by figures 10, 11, 12 and 13. Each of them, represents of zooms on moments of constraint changes. We note that, the performance provided by a fuzzy controller is better in response time and rejection of the load disturbance. Moreover, the electromagnetic torque (Fig. 11) and the flux ploted on figures 12 and 13 , show that thanks to the fuzzy logic controller the decoupling between the torque and flux is maintained despites changes considered.

583

S. Lekhchine et al. / Energy Procedia 74 (2015) 575 – 586

10

Load torque

8 6 4 2 0 0

1

2

3

4 Time(s)

5

6

7

8

5

6

7

8

3 Rr=Rn+50%Rn

Rotor resistance

2.8 2.6 2.4 2.2 2 1.8 1.6 0

Rr=Rn 1

2

3

4 Time(s)

Fig. 8. Load and resistance variations

Fig. 9. Input and output fuzzy logic controller

584

S. Lekhchine et al. / Energy Procedia 74 (2015) 575 – 586

200 195 190 185 180 0.15

0.2

0.25

0.3

0.35

0.4

300

0.5

0.55

Motor speed with PI Reference speed Motor speed with FLC

200 100 0 -100 -200 -300 0

1

2

3

4 Time(s)

5

6

7

8

210 205 200 195 190 1.5

2

2.5

3

Fig. 10. Speed motor

20

10

15

8 6

10

4

5

2 0

0 0

0.05

0.1

0.15

0.2

0.25

0.3

1.6

30

Motor torque (N.m)

Motor speed (rad/s)

0.45

1.8

2

2.2

2.4

2.6

Load torque

20

Motor torque with FLC Motor torque with PI

10 0 -10 -20 -30 0

1

2

3

4 Time(s)

5

Fig. 11. Electromagnetic torque

6

7

8

585

S. Lekhchine et al. / Energy Procedia 74 (2015) 575 – 586

1.5

phird with FLC

1

phird with PI 1.202 1.201 1.2

0.5

1.199 1.198 1.197 1.196 1.195 1.45

0 0

1.5

1

1.55

2

1.6

3

1.65

4 Time(s)

5

6

7

8

Fig. 12. Components d and q direct flux

0.3

Phirq with FLC

0.25

Phirq with PI 0.015

0.2

0.01 0.005 0

0.15

-0.005 -0.01 -0.015

0.1

-0.02 1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

0.05 0 -0.05 -0.1 0

1

2

3

4

5

Fig. 13. Components d and q indirect flux

6

7

8

586

S. Lekhchine et al. / Energy Procedia 74 (2015) 575 – 586

5. Conclusion This work exposed a study which aimed to investigate the improvement obtained using fuzzy logic controller of the doubly feed induction motor drive. The results show the proposed controller which offers regulated responses in terms of fast tracking, small overshoot, and zero steady-state errors with good obtained control performance related to robustness and adaptability. Another important advantage of the proposed intelligent controller is its easy relatively to tune the gain parameters of the controllers effectively and efficiently for high-performance. So, the intelligent technique can be easily adopted for industrial applications.

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28]

Seyoum D, Granthan C. Terminal voltage control of a wind turbine driven isolated induction generator using stator oriented field control. IEEE transaction on industrial application; 2003 .p. 846-852. Hubert R. Variable speed induction machine 2, sensors, models, control and diagnostic. Hermes. Lavoisier; 2006. Blaschke E. The principle of field orientation as applied to the new trans vector closed-loop control system for rotating field machine. Siemens Review; 1972, Vol. 34 .p. 217-220. Sathiakumar S, Betz R E, Evans R J. Adaptive field-oriented control of an IM using predictive control. IEEE Trans. Aero. Elec. Syst; 1990, Vol. 26, No. 2. Lekhchine S, Bahi T, Soufi Y. Fuzzy logic control for rotor field oriented control of a dual star induction machines. International Conference on Power Engineering.Energy and Electrical Drives. 978-1-4673-6392-1/13/$31.00 © IEEE; 2013 .p. 1723-1728. Siva G M, Jagan Mohana R M. Direct Torque Control of Induction Motor with Fuzzy Controller: A Review. International Journal of Emerging Trends in Electrical and Electronics (IJETEE – ISSN: 2320-9569); 2014, Vol. 10, No. 3. Aissaoui A, Abid M, Abid H, Tahour A and Zeblah A. A Fuzzy logic controller for synchronous machine. Journal of Electrical Engineering; 2007, Vol. 58, No. 5 .p. 285-290. Fnaiech M A, Fnaiech F, Betin F, and Capolino G A. Comparison between fuzzy logic and sliding mode control applied to six phase induction machine positioning. Int. Conf. on Elec. Machines. IEEE; 2008 .p. 1-6. Zadeh L A. Fuzzy Sets. Information and Control; 1965, Vol. 8, No. 338. Zadeh L A. A Rationale for fuzzy control. J. Dynamic Syst., Meas and Control; 1972, Vol. 94, Series G 3. Zadeh L A. Making the computers think Like People. IEEE Spectrum; 1994. Yan J, Ryan M, Power J. Using fuzzy logic. Prentice Hall International UK; 1994. Vicatos M S, Tegopoulos J A. A doubly-fed induction machine differential drive model for automobiles. IEEE Transactions on Energy Conversion; 2003, Vol. 18, No. 2 .p. 225–230. Yuan L, Feng-you H, Zong-bin Y. Study on sliding mode speed control with fuzzy approach for doubly-fed induction motor. IEEE International Conference on Control and Automation, Christchurch, New Zealand; 2009 .p. 2171-2175. Datta R, Ranganathan V T. A simple position sensorles algorithm for rotor side field oriented control of wound rotor induction machine. IEEE Trans. Ind. Electron; 2001, Vol. 48 .p. 786–793. Kelber C, Schumacher W. Control of doubly fed induction machine as an adjustable motor/generator. Euro-pean Conference of Variable Speed in Small Hydro (VSSHY), in Grenoble; 2000. Longya X, Wei C. Torque and reactive power control of a doubly fed induction machine by position sen- sorless scheme. IEEE Transactions on Industry Applications; 1995, Vol. 31, No. 3 .p. 636–642. Peresada S, Tilli A, Tonielli A. Indirect stator flux-oriented output feedback control of a doubly fed induction machine. IEEE Trans. On Control Systems Technology; 2003, Vol.11 .p. 875–888. Salloum G, Mbayed R, Pietrzak DM, Fornel B. Mixed sensitivity HĞ control of doubly fed induction motor. ISIE, IEEE International Symposium on Industrial Electronics, Vigo, Spain; 2007 .p. 1300-1304. Boudjemaà Z, Bounadja M, Yahdou A, Belmadani B. Nonlinear feedback state control of doubly fed induction motor by PI-fuzzy controller. Journal of Science and Technology –RST; 2010, Vol.1, No. 2 .p. 1-13. Ben Attous D, Bekakra Y. Speed control of a doubly fed induction motor using fuzzy logic technique. International on Electrical Engineering and Informatics; 2010, Vol. 2, No. 3 .p. 179-189. Tapia G, Tapia A, Ostolaza J X. Proportional-integral regulator-based approach to wind farm reactive power management for secondary voltage control. IEEE Transactions on Energy Conversion; 2007, Vol. 22, No. 2 .p. 488-498. Rahman MF, Tang L. A novel proportional-integral (PI) stator resistance estimator for a direct torque controlled interior permanent magnet synchronous machine drive, Electric Machines and Drives Conference. IEMDC'03. IEEE International; 2003, Vol.1 .p. 382-388. Aissaoui A, Abid M, Abid H, Tahour A and Zeblah A. A fuzzy logic controller for synchronous machine. Journal of Electrical Engineering; 2007, Vol. 58, No. 5 .p. 285-290. Jagadish H, Pujar and Kodad S F. Robust sensorless speed control of induction motor with dtfc and fuzzy speed regulator. International Journal of Electrical and Electronics Engineering; 2011. Mudi R K, Pa1 N R. A robust self-tuning scheme for PI- and PD-type fuzzy controllers. IEEE Trans, Fuzzy Systems; 1999, Vol.7, February .p. 1-16. Masiala M, Vafakhah B, Salmon J and Knight A. Fuzzy self-tuning speed control of an indirect field-oriented control induction motor drive. in Proceedings of IEEE Ind. Appl. Soc. Ann. Meet IAS; 2007.p. 1008-1014. Jihong Lee. On methods for improving performance of PI-type fuzzy logic controllers. IEEE Tran.Fuzzy Systems; 1993.p. 298-301.