567Acemp - Electromotion 2011, 8 - 10 September 2011 İstanbul - Turkey

matrix converter is observed as an inverter which switches

only one combination over the entire switching cycle (vector

selected by the DTC algorithm from the Voltage Vector

Selection Table – Table I), whereas the input of the matrix

converter is regarded as a rectifier, whose role is to generate

the virtual DC link voltage, and to control the input

displacement angle. The block diagram of the implemented

control scheme is illustrated in Fig. 8. The selection of the

output voltage vector from Table I is done in the same way as

in the conventional DTC for VSI-fed induction motor.

The numerical simulations and the experiments have been

performed under the same conditions as in the case of the

FOC. The simulation results are presented in Fig. 9 and

in Fig. 10, and the experimental results in Fig. 11 and

in Fig. 12. Fig. 12 demonstrates the ability of the drive system

to control the speed under load disturbances. Fig. 9 and

Fig. 12 show a fast torque response.

IV. CONCLUSIONS

The main goal of this paper was to address the most

important difference between the implementation of the FOC

and DTC in the drives supplied by the matrix converter from

the implementation in the drives supplied by the VSI. As seen

from section II, there is no significant difference if the motor is

supplied by the VSI or by the matrix converter from the FOC

implementation aspect. The output of the FOC controller is the

motor reference voltage. That reference voltage is then

generated by the matrix converter in the same way it would be

generated by the VSI. The only circumstance that should be

kept in mind is the voltage transfer ratio limitation of 86.6 %

which has to be taken into account when selecting the motor

and converter rated voltages.

The DTC, on the other hand, requires either the introduction

of the input displacement angle controller [15], or

a modification of the modulation algorithm [16], in order

to control the torque and to maintain the required input power

factor. The disadvantage of the first approach is the

nondeterministic power factor control, especially at low motor

speed, and the disadvantage of the second approach is that it

requires the use of the SVM to switch the vectors selected

by the DTC algorithm, which leads to higher switching losses

and increases the torque ripple.

In case of both, FOC and DTC, the simulation and

experimental results show a fast torque response and a good

input power factor control, which proves that the modern

control methods can be successfully implemented in the matrix

converter supplied drives.

REFERENCES

[1] P. W. Wheeler, J. Rodriguez, J. C. Clare and L. Empringham, “Matrix

converter: a technology review,” IEEE Trans Ind. Appl., vol. 49, pp. 276-

288, April 2002.

[2] T. F. Podlesak, D. Katsis, P. Wheeler, J. C. Clare, L. Empringham and

M. Bland, “A 150 kVA vector controlled matrix converter induction

motor drive,” IEEE Trans Ind. Appl., vol. 41, pp. 841-847, May-June

2005.

[3] S. Kwak, T. Kim and G. Park, “Phase-redundant-based reliable direct

AC/AC converter drive for series hybrid off-highway heavy electric

vehicles,” IEEE Trans. Veh. Technol., vol. 59, pp. 2674 – 2688, Jul.

2010.

[4] S. Khwan-on, L. de Lillo, P. Wheeler and L. Empringham, “Fault

tolerant four-leg matrix converter drive topologies for aerospace

applications,” in Proc. IEEE ISIE ’10, Bari, Italy, pp. 2166 – 2171,

July 2010.

[5] L. Empringham, L. de Lillo, P. W. Wheeler and J. C. Clare, “Matrix

converter protection for more electric aircraft applications,” in Proc.

IEEE IECON ‘06, Paris, France, pp. 2564 – 2568, November 2006.

[6] P. Zanchetta, P. W. Wheeler, J. C. Clare, M. Bland, L. Empringham and

D. Katsis, “Control design of a three-phase matrix-converter-based AC–

AC mobile utility power supply,” IEEE Trans. Ind. Electron., vol. 55, pp.

209 – 217, January 2008.

[7] P. W. Wheeler, P. Zanchetta, J. C. Clare, L. Empringham, M. Bland and

D. Katsis, “A utility power supply based on a four-output leg matrix

converter,” IEEE Trans. Ind. Appl., vol. 44, pp. 174 – 186,

January-February 2008.

[8] M. Hornkamp, M. Loddenkotter, M. Munzer, O. Simon and

M. Bruckman, “EconoMAC the First All-in-one IGBT Module

for Matrix Converters,” in Proc. of PCIM ‘01, 2001.

[9] E. R. Motto, J. F. Donlon, M. Tabata, H. Takahashi, Y. Yu and

G. Majumdar, “Application Characteristics of an Experimental

RB- IGBT (Reverse Blocking IGBT) Module,” in Conf. Rec. IEEE IAS

’07, vol. 3, pp. 1540-1544, 2007.

[10] O. Zoubek and J. Zdenek, “Induction motor field oriented control using

soft processor implemented in field programmable gate array”, in Proc.

EDS 2011, Brno, Czech Republic, pp. 153-158, June 2011.

[11] F. Blaschke, “The Principle of Field Orientation as Applied to the New

“Transvektor” Closed-loop Control System for Rotating-field Machines,”

in Siemens Review, vol.1972, pp. 217 – 219, February 1972.

[12] M. Depenbrock, “Direkte selbstregelung (DSR) für hochdynamische

srehfeldantriebe mit stromrichterspeisung,” in ETZ Archive, no. 7,

pp. 211–218, 1985.

[13] I. Takahashi and T. Noguchi, “A new quick-response and high-efficiency

control strategy of an induction motor,” IEEE Trans Ind. Appl., vol. IA-

22, pp. 1820-1827, September/October 1986.

[14] M. P. Kazmierkowski, R. Krishnan and F. Blaabjerg, “Control in Power

electronics – Selected Problems”, Academic Press, 2002,

ISBN 0-12-402772-5.

[15] D. Casadei, G. Serra and A. Tani, “The use of matrix converters in direct

torque control of induction machines”, IEEE Trans. Ind. Electron.,

vol. 48, pp. 1057-1064, December 2001.

[16] J. Lettl and D. Kuzmanovic, “Matrix converter induction motor drive

employing direct torque control method, “ in Proc. PIERS 2010,

Cambridge, USA, vol. 6, pp. 711 – 715, 2010

[17] L. Huber and D. Borojevic, “Space vector modulator for forced

commutated cycloconverters,” in Conf. Rec. IEEE IAS ’89, San Diego,

USA, pp. 871-876, October 1989.

[18] L. Huber and D. Borojevic, “Space vector modulation with unity input

power factor for forced commutated cycloconverters,” in Conf. Rec.

IEEE IAS ’91, Dearborn, USA, pp. 1032-1041, September 1991.

Modeling and Simulation of a Boost DC/AC Inverter fed Induction Motor Drive

Tolga Sürgevil

Dokuz Eylül University, Faculty of Engineering, Department of Electrical & Electronics Engineering, Kaynaklar Campus 35160, Buca, Izmir, Turkey

e-mail: tolga.surgevil@deu.edu.tr Abstract- Single-stage three-phase boost dc/ac inverters can provide sinusoidal ac output voltages which are greater than input dc voltage without needing an intermediate dc voltage boost stage. Such a topology is cost-effective due to reduced switch count and it is suitable for compact design These unique features of this type of inverter makes it a suitable choice in many applications such as uninterruptible power supplies, variable speed ac drives, and some distributed power generation schemes. This paper aims to investigate the performance of the inverter in variable-speed control of an induction motor through the simulation models. The simulation results obtained from a three-phase boost dc/ac inverter controlled induction motor drive system are obtained from mathematical models and presented in this paper.

I. INTRODUCTION

The three-phase voltage source inverter (VSI) is the most common power circuit topology that is used in dc/ac power conversion applications. The main feature of this topology is that it provides ac output voltages which are lower than its input dc voltage and non-sinusoidal in shape, so output filters are required in order obtain sinusoidal output voltages. When it is required to have ac output voltage levels larger than the input dc voltage, it is boosted by means of a boost dc/dc converter at an intermediate stage as shown in Fig.1. Also, the topology shown in Fig.1 provides a bidirectional power flow between the input dc voltage and ac output load. With these features, it can be used in uninterruptible power supplies, variable speed ac drives, and distributed power generation such as fuel-cells and photovoltaic systems [1-3].

Another power circuit topology that has the aforementioned features above is the single-stage boost dc/ac inverter as shown in Fig.2. This three-phase inverter circuit consists of three bidirectional boost converters each of which is modulated by sinusoidal voltages over a dc component. This topology can provide output voltages greater than dc input voltage, so it does not require an intermediate stage for dc voltage boosting unlike the topology shown in Fig.1. In addition, it is cheaper due to reduced switch count and suitable for compact design [1-5].

In this paper, it is aimed to investigate the performance of the inverter when used for the speed control of an induction motor through the simulation models. The simulation models were constructed from mathematical equations of 3-phase boost dc/dc inverter and induction motor. A sliding mode controller was employed for the inverter output voltage and frequency control. In the speed control of the induction motor

slip regulation method was used. The system structure and mathematical models are given in Section II and the simulation results are given in Section III.

Fig. 1. The conventional circuit scheme of 3-phase VSI with an intermediate bidirectional boost dc/dc converter stage.

Fig. 2. The circuit scheme of a 3-phase boost dc/ac inverter feeding a balanced 3-phase load.

II. SYSTEM OVERVIEW

The system here consists of a 2-kW, 220-V, 50-Hz, 4-pole induction motor fed by a 3-phase boost dc/ac inverter. The

978-1-4673-5003-7/11$26.00©2011 IEEE

568 Acemp - Electromotion 2011, 8 - 10 September 2011 İstanbul - Turkey

block scheme of the complete system is shown in Fig.3. The output voltages of the boost inverter are controlled by a sliding mode controller [3] such that the output voltages and inductor currents track the generated references within a defined hysteresis band (εh). The voltage references are applied through a sine wave generator and current references are obtained by passing the actual inductor current through a low-pass filter. In the speed control of the induction motor, slip regulation method [7] was employed. The required inverter frequency is determined from the speed feedback error through a PI controller and the slip command is limited such that the machine is not loaded beyond its maximum torque. The inverter output voltage magnitude is determined by the V/f profile of the machine. Both voltage and frequency commands are processed in a sine wave generator and reference waveforms are generated for the inverter. The system model was built in MATLAB/Simulink using the mathematical models given in the following sections.

A. Mathematical Model of Boost Inverter The mathematical model for the 3-phase boost DC/AC

inverter was derived in [2]-[3]. The input and output equations in the convenient state-space form are as follow:

kokLkdcLk vSRiV

dtdi

L (1)

kLkkko iiS

dtdv

C (2)

where k=a,b,c, iLabc are the boost inductor currents, vabco are the capacitor voltages, Sabc are the switching functions, Vdc is the dc input voltage, and iabc are the load currents. The output voltages across the capacitors are in the form of

cbakvvv dckoackoko ,,,, (3)

The voltage relationship for each boost converter for the

continuous conduction mode is given by [5]

k

dcko d

Vv

1 (4)

where dk is the duty cycle, which is varied around an average value D to obtain ac voltages varying around a dc bias voltage at the output. Hence, the dc output voltage can be expressed as

DV

v dcdcko

1, (5)

The superimposed 3-phase voltages on the Y-connected

stator windings of the induction motor can be obtained as

Fig. 3. The block scheme of 3-phase boost dc/ac inverter fed induction motor speed control

cbakvvvCBAn

nokokn ,,31

,,

(6)

The ac components of the capacitor voltages have the

equal magnitudes and displaced by 120o in phase, while the dc components are equal. Hence, for a balanced set of three-phase voltages, the second term in (6), which is the zero sequence component is equal to the vko,dc and the applied phase voltages become

cbakvv ackokn ,,, (7)

For proper operation of the inverter, the required dc bias

voltage is expressed as [5]

dcdcko VA

v 2, (8)

where A is the peak amplitude of each phase voltage.

B. Mathematical Model of Induction Motor The voltage equations for a single-cage induction machine

at stationary qd reference frame with zero-sequence equations omitted are as follow [6]:

'

'

'''

'''

00

00

dr

qr

ds

qs

rrrrrrr

rrrrrrr

rssssr

sss

ds

qs

iiii

dtd

LrLdtd

MM

Ldtd

LrMdtd

M

dtd

MMdtd

LrL

dtd

Mdtd

Lr

vv

(9) The torque equation for mechanical motion is

569Acemp - Electromotion 2011, 8 - 10 September 2011 İstanbul - Turkey

dtd

JP

TT reL

2 (10)

where TL is the load torque, r is the electrical rotor speed, J is the motor moment of inertia, and Te is the electromagnetic torque and expressed as

''

223

qrdsdrqse iiiiMP

T (11)

III. SIMULATION RESULTS

The performance of the system was investigated through MATLAB/Simulink simulation models. The model of the complete system given in Fig.3 was constructed using the equations (1)-(7) and (9)-(11) for inverter and induction motor, respectively. The system parameters including the controllers are shown in Table I. The induction machine stator phase voltages are applied by transforming the abc voltages to qdo stationary reference frame as

abcnqdos vv sK (11)

where

21

21

21

23

230

21

211

32

sK (12)

In simulations, the rotor speed reference was set to 1pu and the response of the system was shown in Fig.4, Fig.5, and Fig.6. In Fig.4, the variations of the induction motor torque and rotor speed are shown. The machine is accelerated at no-load from standstill to its rated speed and the load on its shaft is changed to TL=10Nm at t=0.5s for motoring, to TL=-10Nm at t=1.0s for regenerative operation, and to zero at t=1.5s, respectively. The speed controller establishes the rotor speed at the given reference value with a steady-state error of about 2% when the motor is fully loaded. In Fig.5, the capacitor voltage and inductor current of the boost inverter are shown. During startup, the capacitor voltage is boosted up to 300V and then the ac voltage magnitude is gradually increased due to increasing rotor speed. In Fig.6, the applied phase voltage and stator current are shown. It must be noted that the slip regulation method inherently limits the starting current. Inverter output voltage has a tracking error of about 6% in magnitude when the motor is fully loaded during t=0.5-1.0s.

In Fig.7, the variations of the stator phase voltage and current are shown during load transitions. The boost inverter successfully performs its operation and provides a sufficient transient response during these extreme changes. In Fig.8, the

stator phase voltage and current are shown during steady-state for both motoring and regenerative modes. The boost inverter provides sinusoidal output voltages with low total harmonic distortion values of approximately 5.7% and 2.8% in motoring and regenerative modes, respectively. The frequency spectrum of the inverter inductor current is shown in Fig.8. The average switching frequency changes depending on the load conditions. In motoring mode, the sliding mode hysteresis controller achieves a switching frequency of 8 kHz, while it is about 3 kHz in regenerative operation. The switching frequency of the inverter can be fixed replacing the hysteresis block given in Fig.3 by the pulse-width modulation scheme. Setting the controller parameters same, the switching frequency of the inverter was set to 5kHz and almost the same responses were obtained. The frequency spectrum of the PWM switched inverter currents is shown in Fig.10.

TABLE I

SYSTEM PARAMETERS 3-phase boost dc/ac inverter circuit parameters:

FCRmHL

VVVV dckodc

50,01.0,1300,100 *

,

sliding mode controller parameters of the boost inverter:

Askk h 5.0,001.0,04.0,2.0 21

Induction motor parameters:

2

'

'

.0131.0,4

2583.0,2641.0

3950.1,4050.1

mkgJP

HMHLL

rr

rrss

rs

Slip regulation controller parameters:

1.0,01.0,2 max, slipIp KK

Fig. 4. The response of induction motor during start-up and against load variations (a) load and electromagnetic torque (b) rotor speed

570 Acemp - Electromotion 2011, 8 - 10 September 2011 İstanbul - Turkey

Fig. 5. The response of boost dc/ac inverter during induction motor start-up and load variations (a) capacitor phase voltage (b) inductor phase current

Fig. 6. The variations of the electrical quantities on the stator of the induction motor during start-up and load variations (a) stator phase voltage (b) stator phase current

IV. CONCLUSION

The speed control of induction motor by a 3-phase boost dc/ac inverter was investigated in this study. The operation of the inverter was tested under different loading conditions. The performance of the boost inverter is quite satisfactory under these conditions. It is providing almost sinusoidal output voltages, fast transient response with the employed controller, and regenerative capability. From these points of view, boost inverters are good candidates for variable speed ac drives intended for the use in applications such as electric cars when compared to the conventional voltage source inverters. The pulse-width modulated switching can be employed in control of the inverter. These aspects were investigated through simulation models developed in MATLAB/Simulink and their validity was verified by simulation results.

Fig. 7. The variations of the electrical quantities on the stator of the induction motor during load transitions (a) stator phase voltage and current from no-load to full-load motoring (b) stator phase voltage current from full-load motoring to full-load generating

Fig. 8. The electrical quantities on the stator of the induction motor during steady-state (a) stator phase voltage and current at full-load motoring mode (b) stator phase voltage current at full-load regenerative mode

571Acemp - Electromotion 2011, 8 - 10 September 2011 İstanbul - Turkey

Fig. 9. Frequency spectrum of the inverter inductor current during steady-state (a) full-load motoring mode (b) at full-load regenerative mode

REFERENCES [1] R.O. Caceres, and I. Barbi, ‘A Boost DC-AC Converter: Operation,

Analysis, Control, and Experimentation’, Industrial Electronics Control and Instrumentation Cofenerence, 1995, pp. 546-551.

[2] R.O. Caceres, and I. Barbi, ‘A Boost DC-AC Converter: Analysis, Design, and Experimentation’, IEEE Trans. on Power Electronics, vol.14, no.1, 1999, pp. 134-141.

[3] C. Cecati, A. Dell’Aquila, and M. Liserre, ‘A Novel Three-Phase Single-Stage Distributed Power Inverter’, IEEE Trans. on Power Electronics, vol.19, no.5, 2004, pp. 1226-1233.

[4] B.Koushki, H. Khalilinia, J. Ghaisari, and M.S. Nejad, ‘A New Three-Phase Boost Inverter: Topology and Controller’, IEEE 2008, pp.757-760.

[5] M. Jang and V.G. Agelidis, ‘A Minimum Power Processing Stage Fuel Cell Energy System Based on a Boost-Inverter with a Bi-directional Back-up Battery Storage’, IEEE 2010, pp.295-302.

[6] P.C. Krause, O. Wasynczuk, and S. D. Sudhoff, Analysis of Electric Machinery, IEEE Press, 1994.

[7] G.K. Dubey, Power Semiconductor Controlled Drives, Prentice-Hall, 1989.

Fig. 10. Frequency spectrum of the inverter inductor current during steady-state with PWM switching (a) full-load motoring mode (b) at full-load regenerative mode