The research paper published by IJSER journal is about Direct Torque Control of Permanent Magnet Synchronous Motor 1

ISSN 2229-5518

Direct Torque Control of Permanent Magnet Synchronous Motor

Nitin Kelkar, V.A.Joshi,

Abstract— Due to the features such as high efficiency and high power density Permanent Magnet Synchronous Motors (PMSM) are becoming attractive. In high performance servo applications a rapid and accurate torque control is desired preferably without the use of motion state sensor. The use of PMSM combined with Direct Torque Control (DTC) scheme offers many opportunities to achieve this. This paper describes theoretical aspects of Direct Torque Control for PMSM drives. It is mathematically proven that the increase in electromagnetic torque in a PMSM is proportional to the increase in the angle between stator and rotor flux linkages and ther efore fast torque response can be obtained by adjusting the rotating speed of stator flux linkages as fast as possible. It is also shown that zero voltage vectors should not be used and stator flux linkages should be kept moving with respect to rotor flux linkages all the time.

Index Terms— Direct Torque Control, Permanent Magnet Synchronous Motor, Stator flux linkage, Voltage Space Vector.

—————————— ——————————

irect Torque Control is one of the high performance control strategies designed for AC machines in 1980s. the DTC is implemented by selecting proper voltage space

vector (VSV) according to the switching status of the inverter which depends upon the error values between the reference flux linkage and torque with their measured real values ob- tained from calculations in stationary reference frame by means of simply detecting the motor voltage and currents. The DTC scheme has already been realised successfully in induc- tion motor drives and nowadays for Permanent Magnet Syn- chronous Motor also [1]. Therefore there are lots of questions and techniques needed to and deserved to be investigated further in this aspect. Aiming at the DTC of PMSM drives this paper illustrates the theoretical basics of DTC in PMSM drives firstly and then explains the application of DTC to PMSM for the purpose of utilizing the successful and matured technique of DTC to solve the problems in implementation of DTC in PMSM**.**

Following equations are used to derive the mathematical model of PMSM. [4]

(1) (2) (3)

(4)

where & are voltages, & are the currents, , & are the inductances, & are the flux linkages of the d and q axes respectively, p is the number of pole pairs

, is flux through stator windings and is the electromag-

netic torque.

A. Coordinate transformation

Using the coordinate transformation concept, the voltage, flux linkage and current can be transformed from one reference frame to another. Therefore, the torque equation in the syn- chronous speed reference frame can be written as [5]

(6) Above equation indicates that the torque is directly propor- tional to the y –axis component of the stator current if the am- plitude of the stator flux linkage is constant.

B. The generation of voltage vectors

The switches of the voltage source inverter are in 180° con- ducting mode means only three switching signal Sa, Sb and Sc are needed to uniquely determined the status of six switches. Assuming that the VSV is located in the a-axis of the a, b, c reference frame with phase a voltage Va applied alone, then the inverter output VSVs under different switching states can be expressed as[3]

(5)

C. Control of the stator flux linkage.

(7)

The stator flux linkage of a PMSM expressed in the stationary reference frame is,

(8) Neglecting the stator resistance, the stator flux linkage can be

directly defined by the integration of the voltage vector.

Nitin Kelkar is currently pursuing masters degree in power systems in Pune

University, India. E-mail: niteenvk@yahoo.co.in

Dr.Mrs.V.A.Joshi is professor in Dept of Electrical Engg. At PVG’s COET,

Pune University, Pune, India.

(9) Equation (9) explains that the movement of the end of the sta- tor flux linkage has the same direction with the given voltage vector and therefore, it is possible to control the amplitude, moving direction and moving speed of the stator flux linkage

IJSER © 2012

The research paper published by IJSER journal is about Direct Torque Control of Permanent Magnet Synchronous Motor 2

ISSN 2229-5518

by selecting proper voltage vectoris the initial stator flux

C o ntinuo us p o we rg ui

linkage at the instant switching.

1

phi _ref

Sp_ref

Te*

phi_ref

Te_ref

T l oad

Switc hing Table

Invr_and_PMSM

Load

M

<Stator current is_q (A)>

Torque1

Theta

D. The control of the rotation of stator flux linkage.

Speed_ref

Sp_act

Subsystem 1

Te_ac t S

phi_ac t

hySte re SiS bloc k

FI_beta

Se c t_Se ln

S P ulseS

Gate

<Stator current is_d (A)>

<<RRototor angle tthetam (rad)>

Iq I_alpbeta

Id

Subsystem3

The torque of a PMSM with DTC could be effectively con-

Stator

FI_alpa

FI_alp

Sec tor

Sec tor Sabc

<<RRototor sspeed wwmm (rad/ss)>

FI_bet

Sabc

<<Electtromagneticic ttorque TTee (N**mm)>

trolled by adjusting the rotating speed of the stator flux lin-

Flux

Psi _Q Vs Psi _D

FI_S Ialpbeta

Flux_ESt

I_alp

kage under the condition of keeping its amplitude invariant,

T_e

I_beta

FI_alp

while the amplitude and rotating speed of the stator flux lin- kage are both controlled by selecting the proper voltage vec- tor.

FI_beta

T e_Cal n

The transformation of three-phase variables is into dq axes variables are done with following matrix [2]:

The selection of VSV for the DTC of PMSM should be in such a way that when the torque is less than the reference, the VSV which could make the stator flux linkage vector rotate in its original direction should be selected. Due to the mechanical inertia of the rotor, the instantaneous velocity of the stator flux linkage could be much faster than that of the rotor flux lin- kage. An inverter-switching table can be arranged as shown in table I, where ‘Ф’ and ‘τ’ represent the outputs of flux linkage and electromagnetic torque hysteresis-loop controller, respec- tively; ‘θ(1)-θ(6)’ denote the section of the space vector plane where the present flux linkage vector is located; V is the VSV to be selected.[1]

(10)

where *f *represents the stator currents, voltages, and flux linkages.*f*0 is zero for symmetrical stator wind- ings. The three phase voltage are transformed into dq axes variables depending upon the values of switching signals Sa, Sb and Sc using

(11)

θ

Ф τ

Ф=1

Ф=0

1 2 3 4 5 6

τ=1 V2(110) V3(010) V4(011) V5(001) V6(101) V1(100) τ=0 V6(101) V1(100) V2(110) V3(010) V4(011) V5(001) τ=1 V3(010) V4(011) V5(001) V6(101) V1(100) V2(110) τ=0 V5(001) V6(101) V1(100) V2(110) V3(010) V4(011)

The schematic diagram of DTC for PMSM is as shown in figure 2

The reference torque is obtained from the output of the speed

Tref

Psiref

Te

Psist ator

Hysteresis

Controller

Hysteresis

Controller

Sa

Switching Sb

Table

Sc

0

Flux and Torque

Estimator

Va

Vb

Inverter

Vc

PMSM

controller and is limited at a certain value, with respect to a given reference flux linkage, which guarantees the stator cur- rent not to exceed the limit value. The main advantage of DTC is that it is independent of motor parameters except stator re- sistance, which affects only the low-speed performance of the

drive and can be compensated. The inductances and back EMF

constant, which change with the saturation and temperature,

respectively, are not used in the controller, and, therefore, there is no need to compensate for the saturation and back

IJSER © 2012

The research paper published by IJSER journal is about Direct Torque Control of Permanent Magnet Synchronous Motor 3

ISSN 2229-5518

EMF constant variation.

The system shown in figure 2 is simulated using Matlab soft-

ware. A motor with pole saliency is considered for verification

of the DTC concepts explained in earlier parts. A randomly varying is load torque is considered with an assumption that the rotor position at starting is zero. This assumption elimi- nates the need of encoder in the simulation.

6

4

2

0

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Ti me (Se conds)

6

4

2

0

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Ti me (Se conds)

1000

500

0

-500

-1000

1000

800

600

400

200

0

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Ti me (Se conds)

The theoretical concepts related to DTC are explained. It has been mathematically proved that the increase of electromag- netic torque in a permanent magnet motor is proportional to the increase of the angle between the stator and rotor flux lin- kages, and, therefore, the fast torque response can be obtained

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Ti me (Se conds)

1

0.8

0.6

0.4

0.2

0

-0.2

-0.4

-0.6

-0.8

-1

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Phi A (Wb)

0.812

0.811

0.81

0.809

0.808

0.807

0.806

0.805

0.804

0.803

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Ti me (Se conds)

by adjusting the rotating speed of the stator flux linkage as fast

as possible. The implementation of DTC in the permanent

magnet motor is discussed. The simulation results verify the proposed control and also show that the torque response un- der DTC is much faster than the one under current control.

REFERENCES

*1+ R. Krishnan, ‚Permanent Magnet Synchronous and Brushless DC Mo-

tor Drives‛.CRC Press, 2010.

*2+ Dr. P. S. Bhimbhra, ‚Generalised theory of Electrical Machines‛, Kha n- na Publishers, Delhi.

[3] I. Takahashi, T. Noguchi, *“A new quick response and high efficiency Control strategy of an Induction motor”*, *IEEE transactions on industry applications*, Vol.4A-22, No.5 Sept/Oct 1986.

*4+ L. Wang, Y. Gao, ‚*A Novel Strategy of Direct Torque Control for PMSM*

drive Reducing Ripple in Torque and Flux”, Electric Machines and Drives Confe- rence 2007, IEMDC’07, IEEE International, Vo1.1, No.5, pp.403-406, 3-5

May 2007.

[5] Wang Chengyuan, Zhou Minwen, Guo Qingding, ‚Vector Control AC

Servo Drive,‛ *Machinery industry press, *1995.

*6+ G. S.Buja, Kazmierkowsli, ‚ Direct Torque Control of PWM fed AC

motor- A Survey‛, IEEE transaction on Industrial Electronics, Vol. 51, No.

4, pp. 744-757, Aug. 2004

*7+ M. Pacas and J. Weber, ‚Predictive direct torque control for the PM

synchronous machine,‛ IEEE Trans. Ind. Electron., vol. 52, no. 5, pp.1350 –

1356, oct. 2005.

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International Journal of Scientific & Engineering Research Volume 3, Issue 8, August-2012 4

ISSN 2229-5518

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