Electrical Technology Department, Benha Higher Institute of Technology, Benha University., Egypt

Department of Electrical Engineering, Faculty of Engineering, Minoufiya University, Shebin El-Kom , Egypt.

F. A. Osman A. M. Osheiba F. M. El-Khouly M. M. Khatter

J. Electrical Systems x-x (xxx): x-xx

Regular paper

A DSP-Based Space Vector Modulation Direct Torque Control of IPM

Synchronous Machines

In this paper a new DTC scheme for interior permanent magnet synchronous machine (IPMSM) is proposed. The proposed DTC scheme having the advantages of low torque ripples as well as constant switching frequency. The increment in the switching frequency requires neither an increase of the sampling frequency nor high frequency dithering signal injection. Here in the proposed scheme, a model based observer is used to generate the optimal reference voltage vector. Furthermore, a well developed space vector modulation technique is applied to inverter control in the proposed scheme using a DSP-based hardware, thereby reducing the torque ripples and increasing the switching frequency which becomes constant. To illustrate the performances of the proposed control scheme, simulation and experimental results are presented.

Keywords: Permanent magnet synchronous motor, Direct torque control, torque ripple minimization, Digital signal processor applications.

1. INTRODUCTION

The basic concept of DTC of AC motor drives is to control both stator flux linkage and the electromagnetic torque of the machine simultaneously. Since a DTC-based drive system select the inverter switching states using switching table, neither current controllers nor pulse-width modulation (PWM) modulator is required, as shown in Fig. 1, thereby introducing fast torque dynamics response in comparison with the field oriented vector control technique. However, this conventional DTC approach has some disadvantages such as; high torque ripple and variable switching frequency, which is varying with speed, load torque and the selected hysteresis bands. On the other hand to reduce the torque ripple; the hysteresis torque and flux controller bands must be reduced to match the required torque performance, which requires reduction of the system sampling time and it is necessary to use a very fast processing controller. Although the system sampling frequency can be increased in the conventional DTC the inverter switching frequency is still low, approximately less than one third of the sampling frequency [1, 2, 3, 4]. The inverter switching frequency can be increased using a dithering signal, by adding a limited amplitude high frequency signal to the torque and flux error signals [5, 6]. Although the switching frequency is increased it is still variable for small error bands. Other research concerns with these disadvantages using multilevel inverter, there are more voltage space vectors available to control the flux and torque [7, 8, and 9]. However, these approaches require more power devices, which increase the cost of the system and make it more

complex. In [10, 11], discrete space vector modulation DTC approach is used to reduce the torque ripple. However, there is a complexity of selecting the additional hysteresis controllers. On the other hand, space vector modulation (SVM) modulator is incorporated with direct torque control for PMSM drives as described in [12, 13, 14], to provide a constant inverter switching frequency and low torque ripple. In [13] a deadbeat controller is used to generate the voltage command of SVM modulator, which requires on-line solution of very complex equations. In reference [12], a predictive controller is used to calculate the command voltage vector. However, the predictive controller has the same problem as the deadbeat controller.

Figure. 1 Conventional DTC of IPMSM drives system.

In this paper, a new and simple DTC algorithm with fixed switching frequency for IPMSM is proposed to reduce the torque ripples. The well-developed SVM technique is applied to inverter control in the proposed DTC-based IPMSM drive system, thereby dramatically reducing the torque ripples. The remaining sections of the paper are arranged as follows: Section II gives the requirements of a stable DTC IPM drive. Section III explains the proposed DTC scheme. Section IV contains the simulated and experimental results for both classical and proposed DTC schemes. The simulation results are carried out by modeling the drive systems using a Matlab/Simulink.

2. IPM MACHINE EQUATIONS

The voltage equations of the IPM motor in the rotor reference frame can be written as follows:

⎥⎦

⎤⎢⎣

⎡+⎥

⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡+

−+=⎥

⎦

⎤⎢⎣

⎡

pmeq

d

qsde

qeds

q

d

λ ω0

ii

L pRL ωL ωL pR

vv

(1)

The torque equation is,

] 2δSin )L(Lλ δSin L λ 2 [T dqsqpmL L 2λ P 3

eqd

s −−=

(2)

where:

Inverter

PMSM

3/2

Torque and Flux Estimator

iα,iβvα,vβvdc

s1,2,3

Switching Table

s1,2,3

θs

λ*

T* hys.

hys. - -

ibia

Vdc

vd, vq d and q axis stator voltages;

id, iq d and q axis stator currents;

Rs stator armature resistance per phase;

Ld, Lq direct and quadrature axes synchronous inductances;

ωe electrical rotor speed in rad/sec; Te electromagnetic torque, Nm; P number of pole pairs; δ angle between stator and rotor flux linkages; λs, λpm stator and rotor flux linkages. From equation (2), it is seen that the electromagnetic torque can have

fast dynamic response by changing δ as fast as possible. This is the basis of DTC for IPM motor drive system [1, 3].

3. PROPOSED DTC BY MEANS OF SVM

In the proposed DTC system, the same flux and torque estimator which is used for the conventional DTC is still used in the proposed DTC scheme as shown in Fig.2. Instead of the switching table and hysteresis controllers, an optimal voltage vector calculator is used to calculate the reference voltage vector as a function of the torque error. The applied voltage vectors and their duration times are selected and calculated using the SVM modulator. From the block diagram of the proposed DTC shown in Fig. 2, it is seen that the proposed scheme have the most important advantage of the conventional DTC, such as fast torque dynamics, by applying the conventional DTC during the step change in the torque command; then at steady state time of the torque response the SVM is applied to insure a ripple reduction occurring at the steady state torque response.

Figure. 2 Proposed DTC IPM drive.

Vi , Vdc

Torque & Stator flux Estimator

3/2

Switching Table

Switching

States Selector Inverter

θΦ

τ

Vdc

IPM

λs

T*

T

Optimal Voltage Vector Calculator SVM

Vs*

λs*

The proposed DTC scheme can be further explained as follows; at starting up or at the

instance of the load change, almost when the torque error is large, the switching state selector selects the switching states of the conventional DTC switching table to get a fast torque response at starting and at a step change in the load torque command. When the torque error is within the hysteresis band limits, the switching state selector, select the switching states generated by the SVM which guaranty that the switching frequency is fixed and the ripples at the steady state torque response are reduced.

3.1 Optimal Voltage Vector Calculator

The optimal voltage vector calculator (OVVC) is used to generate the reference voltage vector according to the torque error, which is the difference between the reference and estimated torque. The principal of operation of the optimal voltage vector calculator is based on the machine model. The effectiveness of each non-zero voltage vector on changing the stator flux linkage and torque is proportional to its amplitude. Thus when the amplitude of the non-zero voltage vectors increased, the dynamic response to the changes of stator flux and torque references become faster. However, the torque ripple amplitude in steady state operation grows. On the other hand, when the non-zero voltage vectors reduced, the dynamic response to the change of stator flux and torque references becomes slower. However, the amplitude of the torque ripple in steady state operation decreased. Fig. 3 explains the signal flow diagram for the optimal voltage vector calculator.

Figure. 3 Optimal voltage vector calculator (OVVC).

The electromagnetic torque equation can be written as follows,

qdqdpm2P 3

e i ]i )LL (λ [ T −+= (3)

Then, the torque differential with respect to id and iq can be obtained as:

} i d ] i )LL (λ [i d i )LL ( { dT qddqpmdqqd2P 3

e −−+−=

(4)

During each sampling period, Ts, the two current components, id and iq, can considered as constant values, so equation (4) can be approximated by:

q2d1e i d ai d adT += (5)

Where:

1/k2

λd

- λq

ωe

vd

vq dT +

+

] i ) LL (λ [ a

i ) LL ( a

ddqpm2P 3

2

qqd2P 3

1

−−=

−=

From equation (1), by neglecting the voltage drop across the stator resistance, we have;

dqedsd L / )λ ω v( Ti d += (6)

Lq / ) λ ω v( Ti d deqsq −= (7)

Substituting from equations (6, 7) into equation (5) one obtains,

3q2d1e K vK vKdT ++= (8)

Where:

) λ Kλ K ( ωK

L / T aK,L / T aK

d2q1e3

qs22ds11

−=

==

From equation (1), with respect to the direct voltage component, vd, at steady state and neglecting the drop across the stator resistance, the following equation can be obtain,

qed λ ωv −= (9)

Substituting from equation (9) into equation (8), yields:

de2eq λ ωK / dTv += (10)

From equations (9, 10) it is seen that we get the reference voltage vector components in the rotor reference frame, which are used to generate the required reference voltage vector. The switching states and its duration times are calculated using the SVM technique.

3.2 Space Vector Modulation (SVM)

As shown in Fig.4 the reference space vector Vs* defined by Vd*, Vq* and angle θr, can take any position in the x-y plane, while the inverter output takes only one of the six nonzero vectors V1, … , V6 and two zero vectors V0 & V7. The space vector Vs* is approximated by the two closest non-zero vectors and one of the two zero vectors. As an explanation example consider the case where Vs* lies in sector-0 where the two closest vectors are V1 and V2 as shown in Fig.4. The inverter output must give V1, V3 and V0 or V7 for times t1, t2 and t0 during each switching cycle T such as;

021 tttT ++= (11)

The times t1 and t2 are proportional to components Vj and Vk respectively which are given as follows;

2 / t ) α ( Cos VA t 2*s1 −=

(12)

) α (Sin V Bt *s2 =

(13)

T ) / π3 (BT ) π2 / 3 3 (A

==

Figure 4: The possible voltage vectors of inverter output

4. SIMULATION RESULTS

The system performance under the proposed DTC strategy is evaluated, and the results are compared with the results obtained by the conventional DTC. MATLAB/SIMULINK models were developed to examine the conventional and the proposed DTC algorithms. In simulation, the sampling time is 70 µs for both the conventional and proposed DTC schemes and the switching time for the proposed DTC is 140 µs. The switching table used in [1] is employed for the conventional DTC. The switching delays and the forward drop of the power switches, the dead time of the inverter and the non-ideal effects of the PM motor are neglected in the models. The torque dynamics performances of the conventional and proposed DTC schemes at 1000 rpm are compared as shown in Fig. 5 under the same operation conditions. It is seen that the torque ripple is reduced by more than 70 % at no-load and load conditions in the proposed DTC. Also the two algorithms have same torque response dynamics performance during start-up and load changes as illustrated in Fig. 6.

U2 ( 0 1 0 ) U3 ( 0 1 1 )

U4 ( 1 0 0 ) U5 ( 1 0 1 )

Fig. 2. 12 The Possible Space Vectors of Inverter Output.

SECTOR2 Uk Us*

U0 α U7 Uj

Sector 0

Sector 1

Sector 2

Sector 3

Sector 4

Sector 52Udc / 3

Udc / 3

U1 ( 0 0 1 )U6 ( 1 1 0 )

V1

V2V3

V4

V5 V6

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

500

1000S

peed

(rp

m)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

-2

0

2

4

6

Time (sec)

Tor

que

(Nm

)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

-2

0

2

4

6

Tor

que

(Nm

)

Classical DTC

Proposed DTC

Figure5: Torque and speed responses for both schemes.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

500

1000

Classical DTC

Spe

ed (rp

m)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

0

2

4

6

Tor

que

(Nm

)

0 0.005 0.01 0.015 0.02 0.025

0

2

4

6

Time (sec)

Tor

que

(Nm

)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

500

1000

Proposed DTC

Spe

ed (rp

m)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

0

2

4

6

Tor

que

(Nm

)

0 0.005 0.01 0.015 0.02 0.025

0

2

4

6

Time (sec)

Tor

que

(Nm

)

Figure6: Torque and speed responses for both schemes.

However, it is also seen that under the conventional DTC, the torque response has

reached the reference torque ± 5% of its value, while the torque under the proposed DTC can reach and settle down at the reference value. The speed response is also shown for the proposed DTC in Fig. 6. It can be seen from the figure that the proposed DTC has achieved a fast speed response than that for the conventional DTC, about 27 ms. Furthermore declaration is shown in Fig. 7 for speed dynamic response and their corresponding torque response for both algorithms. It is seen that the torque ripple reduction is still valid at low and high speed ranges. A speed reverse dynamics is carried out at two different speed references, ± 500 rpm and ± 1000 rpm, to indicate the validity of the controller operation at both speed directions. The simulation results for the speed reversing dynamics are shown in Fig. 8

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

250

500

750

1000

Spe

ed (

rpm

)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

-5

0

5

Tor

que

(Nm

)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

-5

0

5

Time (sec)

Tor

que

(Nm

)

Conventional

Proposed

Figure7: Speed and torque responses for both schemes.

0 0.5 1 1.5 2 2.5 3 3.5 4-750

-500

-250

0

250

500

750

Spe

ed (

rpm

)

0 0.5 1 1.5 2 2.5 3 3.5 4-7

-3.5

0

3.5

7

Time (sec)

Tor

que

(Nm

)

0 0.5 1 1.5 2 2.5 3 3.5 4-1200-1000-800-600-400-200

0200400600800

10001200

Spe

ed (

rpm

)

0 0.5 1 1.5 2 2.5 3 3.5 4-7

-3.5

0

3.5

7

Time (sec)

Tor

que

(Nm

)

Figure8: Proposed DTC torque response with speed reversal, at ± 500 and ± 1000 rpm.

Also a comparative simulation results between the proposed DTC algorithm and some other algorithms are shown in Fig. 9, where a reference speed of 1000 rpm is applied to the motor then, a load torque of 2 Nm is applied at t = 1.5 sec. The torque response for the classical DTC algorithm is given in Fig. 9 (a) and the Fig. 9 (b) show the torque response for the DTC algorithm with dithering signal. Fig. 9 (c) gives the torque response for the DTC algorithm where the flux linkage and electromagnetic torque estimator is carried out at the synchronous reference frame (rotor frame), and finally the proposed DTC algorithm torque response is given in Fig. 9 (d).

0 0.5 1 1.5 2 2.5 3 3.5 4-20246

(a)

0 0.5 1 1.5 2 2.5 3 3.5 4-20246

Time (sec)

(d)

0 0.5 1 1.5 2 2.5 3 3.5 4-20246

(c)

0 0.5 1 1.5 2 2.5 3 3.5 4-20246

(b)

Figure9: Comparison between the proposed algorithm and some other techniques

5. EXPERIMENTAL RESULTS

A DSP control card (d-Space 1104) and its interface unit are used to implements the Classical and the Proposed DTC schemes for IPM drive system. Additional hardware cards are used for measurements of currents and the DC-bus voltage, which is required for the calculation of the two-phase voltage vectors. An incremental encoder is used in order to carry out the optimal voltage vector calculation and generating the optimal reference voltage vector. The used sampling time is 100 μ sec (sampling frequency 10 kHz) and the switching frequency is 5 kHz. A step change of 1000 rpm is applied to the motor then a load torque is added, after speed response reach its steady state value, with a value of about 2 Nm for a certain time interval. The corresponding flux linkage and torque response at steady state condition for both Classical and Proposed DTC schemes are given in Fig. 10. From Figure 10, the torque response of the proposed DTC scheme introduces a great torque ripple reduction in comparison to the torque response for the classical DTC scheme. It also indicated in Figure 10 that a good ripple reduction in the flux linkage magnitude response. The estimated torque and the corresponding phase current response dynamics at loading condition is indicated in Figure 11. The peak value for the phase current is approximately 0.6 A as indicated in Figure 11, which is corresponding to a root mean square value of about 0.8 A at a load torque of 2 Nm. Also the speed dynamics is considered by applying step increments and decrements at the reference speed. The speed dynamic responses for both classical and proposed DTC schemes are introduced in Fig. 12. A step increment in speed reference from 250 rpm to 1000 rpm at time equals to 1 sec. and two step decrements from 1000 rpm to 900 rpm, then from 900 rpm to 700 rpm at times 2 and 3 sec. are applied. It's indicated that the speed response for the proposed DTC is approximately rippled free. The phase current waveforms at instance of the speed transition from 250 rpm to 1000 rpm under no-load for the classical DTC and the proposed DTC is declared in Fig. 13. As shown in this Fig., the phase current of the proposed DTC is approximately sinusoidal which reduce the current harmonics and ripple.

Time ( 200 ms / dev.)

Torq

ue(1

Nm

/dev

.)

Time ( 200 ms / dev.)

Torq

ue(1

Nm

/dev

.)

Time ( 200 ms / dev.)

Torq

ue (

1Nm

/ de

v.)

Cur

rent

( 1

A /

dev.

)

(a) Classical (b) Proposed DTC

Figure10: Speed and torque responses for both schemes.

Figure11: Torque and phase current response at 2 Nm loading.

Flux

(1w

b/d

ev.)

Time ( 200 ms / dev.)

Flux

(1w

b/d

ev.)

Time ( 200 ms / dev.)

(a) Classical DTC (b) Proposed DTC Figure12: Speed dynamic responses for classical and proposed schemes.

(a) the classical DTC (b) the proposed DTC

Figure13: Phase current response with speed transition from 250 rpm to 1000 rpm under no-load.

6.CONCLUSION

In this paper a new DTC algorithm for the IPM synchronous machine has been developed. The effectiveness of the proposed DTC algorithm in reducing the torque ripples was verified by computer simulations and experimentally on a 3-phase IPMSM rated at 1 kW. The presented results have demonstrated that the problems which were associated with conventional DTC schemes such as, high torque ripples and variable switching frequency have been completely avoided. It is also interesting that the proposed torque controller has been shown to be robust to control the machine flux, allowing satisfactory overall performance of the machine under study. The developed algorithm also offers the prospect

Cur

rent

(0.1

A/d

ev.)

Time ( 100 ms / dev.)

Cur

rent

(0.1

A/d

ev.)

Time ( 100 ms / dev.)

Time ( 500 ms / dev.)

Spee

d(3

00rp

m/d

ev.)

Time ( 500 ms / dev.)

Spee

d(3

00rp

m/d

ev.)

for optimizing the machine performance in a manner similar to conventional vector controllers.

APPENDIX

Parameters of the used IPM synchronous machine are given in table 1; Table 1:

Number of pole pairs, P 2 Armature resistance, R 10 ohm Magnet flux linkage, λpm 0.765 V.S/rad d-axis inductance, Ld 159 mH q-axis inductance, Lq 245 mH Phase voltage, V 240 V Phase current, I 1.6 A

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