Arab J Sci Eng (2014) 39:4765–4773DOI 10.1007/s13369-014-1087-6

RESEARCH ARTICLE - ELECTRICAL ENGINEERING

PMSM Drive Fed by Sliding Mode Controlled PFC BoostConverter

Omur Aydogmus · Erkan Deniz · Korhan Kayisli

Received: 20 January 2013 / Accepted: 15 May 2013 / Published online: 5 April 2014© King Fahd University of Petroleum and Minerals 2014

Abstract In this study, a vector controlled permanent mag-net synchronous motor (PMSM) drive fed by a two-levelinverter which is connected to a boost converter with slid-ing mode control (SMC) for power factor correction (PFC)is presented. The performance of the drive system is ana-lyzed with all the system details such as speed control ofPMSM, SMC, and PFC. The simulation results are obtainedusing MATLAB/SimPowerSystem blocks. The waveformsof source and motor currents are analyzed with their har-monic spectrum. The unity power factor is performed byobtaining a low input current with total harmonic distortion(THD). The experimental results of PFC are analyzed withinput current waveforms and THD values for with/withoutPFC.

Keywords Inverters · Permanent magnet motor · Powerquality · Sliding mode · Vector control · Space vector PWM

O. AydogmusDepartment of Mechatronics Engineering, Faculty of Technology,Firat University, Elazig, Turkey

E. Deniz (B)Department Electrical and Electronic Engineering, Facultyof Technology, Firat University, Elazig, Turkeye-mail: erkan.edeniz@gmail.com

K. KayisliDepartment of Computer Engineering, Faculty of Engineering,Istanbul Gelisim University, Istanbul, Turkey

1 Introduction

The efficiency of electric motors and their drives has anessential role on the electrical energy consumption in indus-try because most mechanical movements are performed usingelectrical motors in almost every industrial process. In addi-tion, various requirements such as speed, torque and positioncan be requested from the motors used in these processes.The speed controlled ac motors are widely used in indus-trial applications for these requirements. These applicationsare provided by motor drives which are generally built bytwo-level inverters which are fed by uncontrolled rectifiers.Furthermore, switched-mode and uninterrupted power sup-plies obtain the required dc voltages using uncontrolled rec-tifiers. Thus, these systems inject currents with high THDto the ac mains and reduce the power quality. All electri-cal and electronic equipments connected to the public mainsup to and including maximum 16A nominal input currentmust comply with EN 61000-3-2. Passive and active har-

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monic line current reduction solutions can be used to ful-fill the limits of the standard which greatly influences thedesign of all power supplies [1]. The power quality problemsshould be solved for increasing the efficiency of the drivesystem.

The PFC can be built with active and passive techniques.An input filter as passive technique can be used for a practi-cal solution of these problems; however, this solution is notenough to increase the power factor and reduce the harmoniccontent. In addition, not only the system’s size, weight andvolume increase but also the efficiency of system decreases.A boost PFC converter as active technique is an effectivesolution to increase the power quality, power factor andreduce the input current THD, size, weight and volume ofthe drive. The DC-DC converters are operated using con-tinuous conduction mode (CCM), discontinuous conductionmode (DCM) and CCM-DCM boundary. The CCM is widelyused in PFC circuits [2]. A well-known control approachfor CCM-PFC is averaged current mode control in com-bination with a slow voltage control loop and a multiplier[3,4]. The control of average current mode can be achievedusing Hysteresis controller, PI controller, Fuzzy controlleror SMC [5–8]. In this paper, the PFC is controlled usingSMC since robustness of algorithm for load and parameterchanges.

In this study, a PMSM is used since it has higher powerdensity, efficiency and dynamic response. Today, the popu-larity of PMSMs rapidly increases but their drive systems areusually built by two-level inverters which are fed by uncon-trolled rectifiers. This work proposes an effective solution forPMSM drive system with unity power factor and low sourcecurrent THD. The simulation results are obtained using MAT-LAB/SimPowerSystem blocks. The vector control of PMSM,space vector PWM (SVPWM) and SM Controlled PFC aregiven in detail. In addition, an implementation of PFC is per-formed for analyzing the input current by dSPACE-1103. Asa second work, the waveforms and THD of input currentsare compared using with/without PFC. The circuit of PFCconverter is given in Fig. 1.

2 Vector Control of PMSM

Nowadays, PMSM is popular in variable-speed applicationssince PMSM has low inertia, high efficiency, high power den-sity and reliability. Besides, the permanent magnet rotor hasmany advantages including the elimination of brushes slip-rings and rotor chopper losses in the field winding whichleads to higher efficiency. The higher efficiency allows areduction in the machine frame size [9]. The voltage equa-tions of PMSM are given as:

ud(t) = Rsid(t)+ dψd(t)

dt− ωeψq(t) (1)

uq(t) = Rsiq(t)+ dψq(t)

dt+ ωeψd(t) (2)

where ωe is the electrical rotor frequency, Rs is the statorwinding resistances and ψd and ψq are linkage fluxes ofd-axis and q-axis, respectively. The linkage fluxes are givenin Eqs. 3 and 4:

ψd = Ldid + ψm (3)

ψq = Lqiq (4)

where ψm is the flux linkage due to the rotor magnets. Theelectromagnetic torque for synchronous machines in the d,q-axis is given by:

Te = 3

2p[ψd id − ψq iq ] (5)

where p is pole pairs number. If Eqs. 3 and 4 are substitutedinto Eq. 5, the torque can also be expressed in the followingway [10].

Te = 3

2p[ψmiq + (Ld − Lq)iq id ] (6)

If the surface mounted PMSM is used, the reluctance torqueis not produced due to Ld = Lq . In this situation electro-magnetic torque is proportional to iq as a dc motor armaturecurrent, so the torque expression for surface mounted PMSMbecomes:

Fig. 1 Boost PFC convertercircuit

Q

Lf

D

CdcCfVs

Load

Lb

Sliding ModePFC Controller

+

-

IL

Vo

Boost Converter

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Fig. 2 The vector controldiagram of a PMSM

n*

n

PI PI

PIid*

Space VectorPWM

Algorithm

PMSM

+

-

iq*

+

-

-

iaib

icid

iq

ud*

uq*

6

3/2Transform

uv

w

2-L

evel

Inv

erte

r

Q

Lf D

CdcCfVs

Lb +

-

IL

Boost ConverterAC/DC Rectifier

S1

S4

S3

S6

S5

S2

Cdc

u

v

w

Vdc

N P

Te = 3

2pψmiq (7)

The mechanical equation is given by:

Te = TL + Jdωm

dt+ Bωm (8)

where J is inertia, B is the friction coefficient, TL is loadtorque and ωm is mechanical angular velocity of the rotordefined as ωe = pωm . In Eq. 7, iq is controlled by a vectorcontrol algorithm; thus a simple control is achieved as in adc motor. The controllers are designed using internal modelcontrol method. Details of the speed and current controllers’design can be found in [11,12]. Vector control diagram of aPMSM drive is shown in Fig. 2.

3 Space Vector PWM Technique

SVPWM is based on the representation of three-phase volt-ages as a reference vector rotating in α − β reference frameusing Clarke Transformation. The amplitude and phase angleof the reference vector can be determined by instantaneousvalues of these voltages. Figure 3a shows the circuit modelof a three-phase two-level PWM inverter. It has eight differ-ent switching states. Among the eight switching states, 111and 000 are zero states and the others active states. Each ofswitching states can be represented in vector form using thefollowing expression:

�V = 2

3(Va e j0 + Vb e j2π/3 + Vc e− j2π/3) (9)

where Va , Vb and Vc are three-phase reference voltages. Thespace vector diagram for the two-level inverter is shown in

Fig. 3a, where the six active vectors ( �V1 − �V6) constitute aregular hexagon with six sectors. The zero vector �V0 lies onthe center of the hexagon [13].

In SVPWM, calculation of the dwell times (Ta , Tb, T0) isbased on “volt-second balancing” principle. If the switchingperiod Ts is assumed sufficiently small, reference vector �Vref

can be considered constant during Ts . In this case, �Vsref can besynthesized by three nearest voltage vectors [14]. For exam-ple, when �Vref lies in the sector-1, it can be composed by �V1,�V2 and �V0. For sector-1, the volt-second balancing equationcan be given as in Eq. 10.

�V1 Ta + �V2 Tb + �V0 T0 = �Vref Ts

Ta + Tb + T0 = Ts(10)

Similarly, the volt-second balancing equations are written forother sectors. If values of the voltage vectors are substitutedin these equations, the dwell-times of all voltage vectors areobtained as follows:

Ta =√

3Vref

VdcTs sin

(kπ

3− θ

)

Tb =√

3Vref

VdcTs sin

(θ − (k − 1)π

3

)(11)

T0 = Ts − Ta − Tb

where k is number of sector. After the dwell-times are calcu-lated for all sectors, the switching sequence has to be deter-mined. The switching sequences can be arranged accordingto minimum switching loss or minimum THD [15]. In thiswork, they are arranged for minimum THD. For example,the switching sequences for sector-1 are arranged in Fig. 4.

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4768 Arab J Sci Eng (2014) 39:4765–4773

S1

S4

S3

S6

S5

S2

Cdc

uv

w

+

-

Vdc

N

PMSM

P

1V

3V

4V

5V

6V

refV

000

110010

011

001 101

2

3

4

1

5

6

ω

θ α

jβ

111 100Ta

T0

Tb

0V

2V

(a) (b)

Fig. 3 a The circuit connection of a two-level inverter. b Space vector diagram for two-level inverter

0V 1V2

V

000 100 110 111 110 1000V

2V 1V 0V

000

2

Ta

2

Tb

2

T0

2

Tb

2

Ta

sT

4

T0

4

T0

0

0

0

Va

Vb

Vc

1

1

1

Fig. 4 Switching sequence for sector-1

u

S

maxu

max-u

-

Fig. 5 Graphically sat(S) function

4 Sliding Mode Controlled PFC

The control of systems, being non-linear, having parameterschanging in time and having complex dynamics is hard with

VS+-ks*|.|

IL*|sinwt|

X

PIVO*

+-|IL

*|

λ +-

Δ(.)

e

S

umax

-umax

us+-

ueq

uTs

Δd+-

umax

-umax

Z-1

d

Fig. 6 Sliding mode controller diagram for PFC

traditional controllers. SMC is an effective control methodin controlling such systems. The purpose of the applicationof SMC to closed-loop control systems is to push the error tosliding surface (switching surface) and hold it on this surface.Since sliding surface is defined as a function of linear com-bination of state variable, they have a linear connection withthis surface. With this, the degree of the system is reduced asmuch as independent input variable and the system is con-trolled with reduced control rule [16]. State variables of anonlinear system are given below:

•x = A(x, t)+ B(x, t).u(t) (12)

where x ∈ Rn , A ∈ Fn , u ∈ Rm , rank(B(x, t)) = m,u ∈ [umin, umax] and u(t) states the system input. A robustcontroller as shown in Eq. 13 consists of parameter varia-tions, term against external disturbances and ueq defined asequivalent control rule. In other words, statement makingthe change of switching function zero is named as equivalentcontrol.

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Fig. 7 The model of drive system by using MATLAB

u(t) = ueq(t)− N .sat(S(x, t)) (13)

In this, N , a constant, determines the maximum control out-put. sat function is defined in Eq. 14. and the function is givenin Fig. 5.

sat(S) ={

s/ϕ |S| ≤ ϕ

sgn(S) |S| > ϕ(14)

Since control operation is performed with around S = 0depending on satfunction, it is named as S sliding function.The main purpose in systems controlled with SMC is to holdthe system on the surface defined in Eq. 15.

S =(

d

dt+ g

)e (15)

Tracking error e in S sliding function is as defined below:

e = xr − x (16)

When S sliding function goes zero, then e goes zero. In otherwords, the requirement defined in Eq. 17 should be providedto approach in finite time to the S = 0 line.

S•S < −β |S| (17)

Here, β is a positive constant number and grants the systemmove in finite time to the S = 0 line. In other words, in PFCoperations, it is required that current and resistance be inthe same phase and include less harmonic component. In thecontrol operation, first a value for line current is calculatedas a reference. To this end, output of voltage controller iscompared with an example of main voltage. Since the powerloss is low in amplifier type converter and inductance filtershigh level harmonics, input and output powers will be equal(Pi = P0) and then the relation below is formed.

1

2Vm Im = V 2

o

R(18)

After Im result in Eq. 18 is obtained and input in Eq. 19,reference current is obtained as below:

I ∗L = |Im sinωt | (19)

The S sliding surface’s determined in SMC for current controland reference current value as follows:

I ∗L =

∣∣∣∣2V 2

o

Vm Rsinωt

∣∣∣∣ (20)

S sliding surface used for current control in SMC is shownin Eq. 21 [17]:

S = I ∗L − IL (21)

If control entry is u then Eq. 13 is selected [17],

u = 1

2(1 − sat(S)) (22)

The next stage is after access is provided to the sliding sur-face, to determine the equivalent control entry ueq that canhold the system in this surface. The diagram of SMC for PFCalgorithm is given in Fig. 6. As for that,

ueq = u|dS/dt = 0 (23)

When Eq. 23 is applied to the system,

dS

dt= d(I ∗

L − IL)

dt= dI ∗

L

dt+ Vo

L(1 − ueq)− VS

L= 0 (24)

ueq =(

L .dI ∗L

dt+ Vo − VS

)1

Vo(25)

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4770 Arab J Sci Eng (2014) 39:4765–4773

Fig. 8 a Motor speed (rpm), bmotor torque (Nm), c statorcurrents (A), d dc-link voltage,source voltage and current(×100), e detail of dc-linkvoltage

0 0.05 0.1 0.15 0.2 0.25 0.3-750

-500

-250

0

250

500750

(a)

n [r

pm]

0 0.05 0.1 0.15 0.2 0.25 0.3-20

-10

0

10

20

(b)T e [N

m]

0 0.05 0.1 0.15 0.2 0.25 0.3-50

-25

0

25

50

(c)

i stat

or [A

]

0 0.05 0.1 0.15 0.2 0.25 0.3-500

-250

0

250

500700

(d)

Vs ,

i s , V

dc

0 0.05 0.1 0.15 0.2 0.25 0.3540

550

560

570

(e)

Vdc

[V]

is obtained. In order to realize SMC depending on the Ssliding function and u control entry, the condition 0 ≤ ueq ≤1 should be provided.

5 Simulation and Experimental Results

The simulation of drive system is performed using MAT-LAB/SimPowerSystem blocks as shown in Fig. 7. The con-trol blocks and the power blocks are used in different sampletimes to obtain realistic results. The sample times of the con-trol blocks model and power blocks model are taken as 50and 1 µs, respectively. Thus the power blocks sample time

is obtained higher than the controller sample time. The rate-transition blocks are used between the control blocks andthe power blocks for connecting two different sample timeenvironments at the same simulation.

The PMSM drive is carried out at ±500 and +250 rpmunder the load conditions about 85 % to demonstrate the per-formance of the drive at speed transitions. The speed tran-sition of the motor has an important role when the motor isoperated in generator mode. The dc-link voltage of inverteris increased due to the operation of the generator mode. Thedc-link voltage should be kept constant in rated value. In thisstudy the dc-link voltage is not affected from the speed transi-tions since the PFC has been adjusted to hold nominal value.

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Fig. 9 At steady-state(500 rpm). a Source-line voltageand current, b harmonicspectrum of source current, cmotor current, d harmonicspectrum of motor current

0.12 0.16-400

-200

0

200

400

Time (s)

(a)

Vs a

nd 1

00 x

is [

A]

0.035 0.0938-30

-20

-10

0

10

20

30

Time (s)

(c)

i a [A

]

0 5 10 15 200

20

40

60

80

100

Fundamental (50Hz) = 1.41 ATHD= 5.52%

Frequency (kHz)

(b)

Mag

(%

of

Fund

amen

tal)

0 5 10 15 200

20

40

60

80

100

Fundamental (34Hz) = 15.02 ATHD= 21.90%

Frequency (kHz)

(d)

Mag

(%

of

Fund

amen

tal)

is

Vs

The simulation results of this operation are given in Fig. 8.The effective source line voltage is 220 V ac. However, themotor require 560 V dc-link voltage. For this reason the PFCincreases the input voltage from 311 to 560 V. The changeof the motor speed is shown in Fig. 8a. The torque of themotor is given in Fig. 8b. The stator currents of the motor areobtained as shown in Fig. 8c. The source current is obtainedwith unity power factor as given in Fig. 8d. In addition the dc-link voltage is given in the same figure. It should be noted thatthe dc-link voltage is not affected by the generator operationwhen the speed of motor reduces to the lower references. Ifthe dc-link voltage is not controlled with a breaking resistoror a circuit as boost converter it will increase over the ratedvoltage. In this case the drive system can be damaged byover voltage. A robust control of PFC has been achieved forPMSM drive system by eliminating this problem.

In this study the dc-link voltage is controlled by a boostconverter and nominal voltage of dc-link is fixed at 560 Vwhich is determined by motor nominal value. The motorparameter can be found in MATLAB program as a presetmodel no 09 of PMSM model. In addition, the source currentis performed with low THD using PFC. The details of sourcevoltage and current are given in Fig. 9a for two periods. Theharmonic spectrum of source current is shown in Fig. 9b and

THD value of source current is achieved about 5.52 %. Themotor current ia is given in Fig. 9c and its harmonic spectrumis shown in Fig. 9d.

As a second work, the experimental results are obtainedusing uncontrolled rectifier circuit and boost converter toobtain a stabile the dc-link voltage. The experimental resultswithout using PFC are given in Fig. 10a–c. The resultswith PFC are given in Fig. 10d–f. These implementationsare compared for the same input line voltage as effectively50 V. The output of uncontrolled rectifier with capacitorsmoothing is given in Fig. 10a. In the figure the voltage isobtained as 69 Vdc since the drop of diode voltage about 1V. In theory, the voltage can be obtained as 70.7 V dc. Thewaveforms of the source voltage and current are shown inFig. 10b and THD value of current is measured as 75.8 %shown in Fig. 10c with its harmonic spectrum. The cur-rent distortion is not acceptable for power quality. The PFCis operated in the same conditions as input voltage, inputfrequency and load. The output voltage is increased usingboost converter from 69 to 200 V as shown in Fig. 10d.The source current is achieved with low THD as shownin Fig. 10f. The experimental results are obtained usingdSPACE-1103 platform and the switching frequency is takenas 20 kHz.

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Fig. 10 Experimental results without PFC; a output voltage of recti-fier with capacitor smoothing; b source voltage and current; c harmonicspectrum of source current, experimental results with PFC; d output

voltage of boost converter; e source voltage and current, f harmonicspectrum of source current

6 Conclusions

A two-level voltage source inverter with PFC fed vector con-trolled PMSM drive is performed to show the performance ofPFC. The boost converter is controlled robustly using SMCalgorithm for PFC. The results show that this controller is anefficient method for improving the power factor. Thus, theboost PFC converter not only increases the dc-link voltage,

but also reduces the THD of the source current. In additionthe unity power factor is obtained for source.

The source current THD is an very important issue forthe power quality of grid. For this reason, the motor drivesystems require a low THD for input current. The simulationand experimental results show that THD of the input currentcan be reduced from about 75 to 5 %. A boost converterwith PFC can be used instead of an uncontrolled rectifier for

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PMSM drive system because a boost converter with PFC hassome advantages as follow:

• The dc-link voltage can be controlled,• No need for a braking resistor circuit,• Unity power factor can be achieved,• The THD of source current can be reduced to low levels.

The PFC has no contribution for motor side signals such ascurrent and torque ripples indicated in results. In addition thesignals of motor are not distributed with the usage of PFC.These advantages are improving the power quality of motordrive system. Especially, the proposed drive system shouldbe used for low power 2 kW.

Appendix

Motor Parameters;Vdc = 560 V; Rs = 0.24 ; Ld = 1.015 mH; Lq =

1.015 mH; p = 8; Tn = 7.14 Nm; J = 480.10−6 kg m2;B = 160.10−6 Nm s/rad.

Vector Control PI Parameters;Speed controller: kps = 0.1619; kis = 88.9556.Current controller: kpd = 2.2302; kid = 4,900; kpq =

2.2302; kiq = 4,900.

Sliding Mode Control Parameters;Voltage controller: kpv = 1.45; kiv = 24.2.Current controller: λ = 9.4.

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