 Open Access
 Total Downloads : 1004
 Authors : Sinsha V, E Thangam
 Paper ID : IJERTV3IS20110
 Volume & Issue : Volume 03, Issue 02 (February 2014)
 Published (First Online): 12022014
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Bridgeless Cuk Converter Fed BLDC Motor with Power Factor Correction for Air Conditioning System
Sinsha V1 , E Thangam2
1.PG Student (Power Electronics &Drives), Dept of EEE, Ranganathan Engineering College, Coimbatore,
2. Assistant Professor, Dept of EEE, Ranganathan Engineering College, Coimbatore, Tamilnadu. India.
AbstractThis paper deals with bridgeless cuk converter operating in discontinuous inductor current mode (DICM) for singlestage power factor correction converter for a permanent magnet brushless dc motor (PMBLDCM).A threephase voltagesource inverter is used as an electronic commutator to operate the PMBLDCM driving an airconditioning system. The speed control of PMBLDC motor achieved by controlling the voltage at DC bus using single voltage sensor. The bridgeless cuk converter topology is used for obtaining low switching losses and low size heat sink is used for switches.
KeywordsBridgeless cuk converter Permanent magnet brushless DC motor (PMBLDCM),Discontinous inductor current mode(DICM),Power factor correction(PFC),Voltage source inverter(VSI).

INTRODUCTION
The use of a permanentmagnet brushless dc motor (PMBLDCM) is used in low and medium power applications because of their high efficiency, wide speed range, high energy density ,high torque/inertia ratio, low maintenance and wide range of speed control. The BLDC motor has three phase distributed winding on stator and permanent magnet on the rotor. There is no brushes used for commutation. It is an electronically commutated motor. The hall sensors are used for rotor position sensing and it is used for commutation state of voltage source inverter switches. The problems associated with mechanical commutator such as sparking, electromagnetic interference, wear and tear and noise problems in brush and commutator assembly are eliminated.BLDC motors are used household equipments like air conditioners, washing machines,refrigerators,fans etc and it is also used in medical equipments, industrial tools, heating ,ventilation and motion control systems.
A BLDC motor has the developed torque proportional to its phase current and its back electromotive force (EMF), which is proportional to the speed [1][4]. A constant current in its stator windings with variable voltage across its terminals maintains constant torque in a PMBLDCM under variable speed operation. A speed control scheme uses a reference voltage at dc link proportional to the desired speed of the permanentmagnet brushless direct current (PMBLDC) motor.
The BLDC motor fed by a diode bridge rectifier (DBR) with a high value of DClink capacitor results in highly distorted supply current and a poor factor [9]. Hence,
a power factor corrected (PFC) converter is required for obtaining the improved PQ at the AC mains for a VSIfed BLDC motor drive. Two stage PFC converters have been in normal practice in which one converter is used for the PFC operation which is typically a boost converter and other converter is used for the voltage control, selection of which depends upon the type of application [10]. This has more losses because of higher number of components and two switches. A single stage PFC converter has gained popularity because of single stage operation which has reduced number of components. A PFC and DClink voltage control can be achieved in a single stage operation[11, 12].
Two basic modes of operation of a PFC converter, continuous conduction mode (CCM) and discontinuous conduction mode (DCM) [11,12]. In CCM or DCM, the inductors current or the voltage across intermediate capacitor in a PFC converter remains continuous or discontinuous in a switching period. The PFC converter operate in CCM, requires three sensors (two voltage, one current) while in DCM operation can be achieved by using a single voltage sensor [12]. The stresses on PFC converter switch operating in DCM are comparatively higher as compared with its operation in CCM.
A PFC boost halfbridgefed BLDC motor drive using a four switch VSI has been proposed by Madani et al.
[13] which uses a constant DClink voltage with PWM switching of VSI and have high switching losses. Ozturk et al. [14] have proposed a PFC boost converter feeding a direct torque controlled (DTC)based BLDC motor drive which requires higher number of sensors for DTC operation, have higher switching losses in PWMVSI and increased complexity of the control unit. A similar configuration using a frontend cascaded buckboost converterfed BLDC motor drive has been proposed by Wu and Tzou [15], which also confronts same difficulties. Gopalarathnam and Toliyat [16] have proposed an active PFC using a single ended primary inductance converter (SEPIC) for feeding a BLDC motor drive which again utilized a PWMbased VSI for speed control of BLDC motor which have switching losses corresponding to the switching frequency of PWM pulses.A PFC Cuk converter operating in CCM for feeding a BLDC motor drive has been proposed by Singh and Singh [17], but it requires three sensors for DClink voltage control and PFC operation and hence this topology
is suited for highpower applications. This main objective of this paper is the development of cost effective motor drive which requires minimum sensors and has reduced switching losses in the VSI. Moreover, the proposed drive operates for improved PQ operation at AC mains over a wide range of speed control.

PROPOSED BRIDGELESS CUK CONVERTERFED BLCD MOTOR DRIVE
Fig. 1 shows the bridgeless Cuk converterfed BLDC motor driving an air conditioning compressor. The bridgeless Cuk converter is used to control the DClink voltage (Vdc) of the VSI and to achieve a unity power factor at AC mains. To eliminate a DBR in the front end, a bridgeless converter topology is used which has an advantage of low conduction losses and thermal stress on the devices. A new approach of speed control by controlling the voltage at the DC link is used which utilizes a fundamental frequency switching of VSI (i.e. electronic commutation of BLDC motor) hence offers reduced switching losses. A voltage follower approach is used for the control of bridgeless Cuk converter operating in discontinuous inductor current mode (DICM) in which a single voltage sensor is required for the sensing of DClink voltage (Vdc). The proposed drive is designed to operate
over a wide range of speed control with improved PQ at AC mains.

OPERATION OF BRIDGELESS CUK CONVERTER To eliminate the requirement of a DBR such that
its conduction losses are reduced, a bridgeless converter topology is used [1820]. The converter is designed to operate in DICM, in which the current in output inductor Lo1 and Lo2 remains discontinuous while the current in input inductors (Li1 and Li2) and voltage across the intermediate capacitors (VC1 and VC2) remain continuous to achieve a PFC at the AC mains. Figs. 2a and b show the operation of the converter for a positive and negative half cycles of the AC supply, respectively. As shown in Fig. 2a, for the positive half cycle of the supply voltage, switch Sw1 is in conduction through Li1 and Dp. The energy is transferred through the energy transferring capacitor C1 through Lo1 and D1. Similarly, for negative half cycle of supply voltage, switch Sw2 is conducting through Li2 and Dn as shown in Fig. 2b. A common DClink capacitor Cd is used for both the positive and negative half cycle of operation. The voltage across this DClink capacitor Cd is controlled to achieve the speed control of the BLDC motor.
Figs. 2ce show the operation of bridgeless Cuk converter for a complete sitching cycle during the positive half cycle of supply voltages. Different modes of operation are described below.
Fig. 1 Bridgeless Cuk converterfed BLDC motor drive
Mode I: When switch Sw1 is turned on, an energy is stored in the input inductor Li1 via diode Dp, hence the inductor current iLi1 increases as shown in Fig. 2c. Moreover the energy stored in intermediate capacitor C1 is discharged to the DClink capacitor Cd and the output inductor Lo1. Therefore the current iL01 and DClink voltage Vdc are increased and the voltage across the intermediate capacitor Vc1 reduces in this mode of operation.
Mode II: When switch Sw1 is turned off, the inductor Li1 discharges through intermediate capacitor C1 via diode D1 and Dp. Moreover, inductor Lo1 also transfers its stored energy to DClink capacitor Cd as shown in Fig. 2d. Hence, in this mode of operation, the current in inductors iLi1 and iLo1 continues to decrease while the voltage across DClink capacitor Cd and intermediate capacitor C1 increases.
Mode III: Fig. 2e shows the DCM of operation. In this mode, none of the energy is left in the output inductor Lo1,
that is, iLo1= 0. The voltage across intermediate capacitor C1 and current in input inductor iLi1 increases, while the DC link capacitor Cd supplies the required energy to the load,
hence Vdc reduces in this mode of operation . This operation continues till the switch Sw1 is again turned on.
Fig 2.Operation of bridgeless cuk converter for positive (fig. 2a) and negative (fig. 2b) half cycle of supply voltage
Different modes of operation of bridgeless Cuk converter in a complete switching cycle (Figs. 2ce ) for a positive half cycle of supply voltage
a Operation for positive half cycle of supply voltage b Operation for negative half cycle of supply voltage c Mode I
d Mode II
e Mode III
Vin =
22Vs

DESIGN OF BRIDGELESS CUK CONVERTER
A bridgeless Cuk converter is designed for its operation in discontinuous inductor current mode (DICM) to act as a power factor (PF) preregulator with a wide voltage conversion ratio. In this mode, the input inductors (Li1 and Li2) and intermediate capacitors (C1 andC2) are designed to operate in continuous conduction whereas; the current in output inductors (Lo1 and Lo2) becomes discontinuous in a complete switching period. A PFC converter of 500W is
= 22 Ã— 220
198V (1)
The PFC bridgeless Cuk converter is designed for the DClink voltage control from 70 V (Vdcmin) to 310V(Vdcmax) with a nominal value DClink voltage as 190 V (Vdcdes) .The duty ratio D, for a Cuk converter which is a buckboost converter topology is given as
designed for a 0.5 hp BLDC motor . For the supply voltage (Vs) of 220 V, the input average voltage Vinav is given as
D = Vdc
Vdc +Vin
(2)
Hence the duty ratio for designed (ddes) maximum (dmax) and minimum (dmin,) corresponding to Vdcdes, Vdcmax and Vdcmin are calculated using (2) as 0.4897, 0.6103 and
where Ro is the equivalent load resistance. Now the value of output side inductor (Lo1 and Lo2) is given as
0.2612, respectively.
Now the nominal duty ratio (dnom) is taken less than ddes (designed duty ratio) for an efficient control in DICM, hence dnom is taken as 0.2. If the amount of permitted ripple current is iLi (30% of Iin, where Iin= 2P/Vin =3.215A) in both inductors Li1 and Li2, then the value of Li1 and Li2 is given as
Lo1
= Lo2
= Li Leq
Li Leq
= 3000 Ã—234.65
3000 234.65
= 254.56H (7)
Li1
= Li2
= Vm dnom Ts
iLi
= 311Ã—0.2Ã—(1/20000 )
0.3Ã—3.215
Hence a value of 100 H is selected to ensure a deep DICM condition (i.e. discontinuous conduction at very low duty ratio) to maintain a high PF even at very low value of DC link voltage. The capacitance of the energy transferring capacitors C1 and C2 is given as
= 3.22 (3)
C = C = 1
1 2 2(Li + Lo )
r
Where Vm is the peak of supply voltage (i.e.
2202 V), Ts is the switching period (i.e 1/fs, where fs is the switching frequency = 20 kHz). Hence, a value of 3 mH is selected for inductor Li1 and Li2. The critical conduction parameter Kacrit is given as
Kacrit =
1
2(M +n)2
1
=
2 Ã—5000 2 3000 +100 Ã—106
=0.327 (8)
where r = 2fr , fr is resonant frequency of intermediate capacitor (C and C ) and f > f > f where
1 2 s r L
= 1
2[ V dcdes + n]2 V m
2[ 190 2 +1]
= 1
311
fL is the line frequency. Hence for the line frequency and switching frequency of 50 and 20000 Hz, a resonant frequency of 5000 Hz is selected. Hence the value of capacitors C1 and C2 is selected as0.33 H. The value of DClink capacitor is given as
= 0.1927 (4)
Where M = Vdc/Vm and n is the turns ratio for
C = Id
d 2LVdc
(500 )
isolated converter, (here n = 1 for nonisolated converter). Now, the conduction parameter Ka for operation in DICM is to be taken a
Ka < Ka (critical) (5)
The value of Ka is taken around twothirds of Ka(critical) for an efficient control in [DICM]. Hence Ka is taken as 00.13.Now, the equivalent inductance Leq is calculated as
= 190
2 Ã—314 Ã—0.01 Ã—190
2205 F (9)
where Id is the DClink current, is the line frequency in rad/s and Vdc is the permitted ripple voltage of DClink capacitor which is taken as 1% of DClink voltage.
To avoid the reflection of highorder harmonics in s
L eq
= Ro Ts Ka
2
V 2
P
dcdes (1/fs )Ka
= 2
190 2 1 Ã—0.13
supply system, a lowpass LC filter is designed. For a line frequency of 50 Hz, the cutoff frequency of filter is selected as 200 Hz. The maximum value of filter capacitance, Cfmax is g given and calculated as
= 500
20000
2
= 234.65H (6)
=
tan()
C. PWM generator
A fixed frequency, varying duty ratio PWM is generated by a PWM generator by comparing the controlled output of the speed controller with a high frequency saw
= (5002/220)
314 Ã—2202
tan(10)
tooth generator
If md(t) < Vc(k) then Sw1=Sw2=1
574 nF (10)
else Sw1=Sw2=0
(14)
Hence a value of filter capacitor of 330 nF is selected. Finally, the value of filter inductor Lf is calculated using the expression given as
L =
1
f 42 f 2C
where Sw1 and Sw2 denote the switching signals as 1 and 0 for MOSFET Sw1 and Sw2 to switch on and off, respectively.

MODELING OF PROPOSED DRIVE SYSTEM The modeling of a BLDC motor drive consists of a
c f modeling of a BLDC motor, a VSI and an electronic
= 1
42 Ã— 2002 Ã— 330 Ã— 109
=1.918mH (11)
Hence a LC filter with inductance Lf and capacitance Cf is selected as 2 mH and 330 nF, respectively.
commutation.
A. BLDC motor
The dynamic modeling of the BLDC motor is governed by following equations [7, 17]. Per phase voltage (Vxn, where x represents a, b or c and n represents neutral) are given as [7]
V. CONTROL OF PROPOSED DRIVE SYSTEM
The control algorithm of the proposed drive is divided into
Vxn = Rsis + px + exn
Vxn = Vxo Vno
(15)
(16)
following different sections.

Reference voltage generator
A reference DC voltage Vdc* is generated by a reference voltage generator which is equivalent to the particular reference speed of the BLDC motor. This voltage is compared with the sensed DClink voltage to produce a voltage error signal to be fed in the speed controller. The reference voltage is generated by multiplying the voltage constant (Kv) of the BLDC motor with the reference speed.

Speed controller
A voltage error signal is given to the speed controller which is a proportional integral ontroller for generating a controlled output for the PWM generation stage. At any time instant k, the voltage error signal Ve(k) and controller output Vc(k) is given as
where p is the time differential operator, Rs represents resistance per phase, ix is the phase current, exn represents back emf, x represents flux linkages, Vxo and Vno is potential difference of a particular phase x and neutral n with the zero reference potential o which at the mid point of DClink respectively as shown in Fig. 3.
The flux linkages are represented as [7]
x = Lsis M(iy + iz ) (17)
where Ls is the selfinductance per phase and M is the mutual inductance of the windings. If x represents phase a, then y and z represent the phases b and c, respectively, and vice versa.
Moreover for star connected three phase windings of the stator of BLDC motor
= 0 (18)
Hence by substituting (18) in (17) the flux linkages are
(k) = Vdc*(k) Vdc(k)
(12)
obtained as
x = (Ls + M)ix (19)
Vc(k) = Vc(k1) + Kp{Ve(k) Ve(k1)} + KiVe(k)
(13)
Hence, the phase current derivative by using (15) and (19) are obtained as
where Kp and Ki represent the proportional and integral gain constants, respectively.
=
( +)
(20)
The developed electromagnetic torque of the BLDC motor is given as [7]
Te =
(21)
Thus
=
3
(32)
where r is the rotor speed electrical rad/s.
This expression for the torque confronts computational difficulty at zero speed as induced emfs are zero. Hence, it is reformulated by expressing backemf as a function of rotor position angle , which can be written as [17]
= () (22)
where kb is the back emf constant and fx() are functions of rotor position having the trapezoidal shape as that of back emf obtained in BLDC motor with a maximum magnitude of + or 1.The function fa() corresponding to phase a is represented as [17]
= 1 ; for 00 < < 1200 (23)
() = 6 ( ) 1; for 1200 < < 1800
Moreover, the rotor position derivative of the BLDC motor is given as [7]
= (33)
Hence, (20), (29) and (33) represent the time derivative of current, speed and rotor position and hence govern the dynamic model of a BLDC motor.
B. Voltage Source Inverter
The output of the VSI for phase a is given as [17]
= ( 2 ) , for S1 = 1 (34)
= ( 2 ) , for S2 = 1 (35)
= 0 , for S1 = 0, S2 = 0 (36)
(24)
= 1 ; for 1800 < < 3000 (25)
= 6 2 + 1; for 3000 < < 3600
where Vdc represents the DClink voltage and the on and off conditions for the IGBTs S1 and S2 are represented as 1 and 0, respectively.
6.3 Electronic Commutation
(26)
The switching sequence of the VSI is the state of switches for a particular rotor position of the BLDC motor as sensed by the Hall effect sensor. The turn on and turn off
Similarly the function fb() and fc() for phase b and c
can be obtained by using a phase difference of 120Â° and 240Â°, respectively. Now, substituting (22) into (21), the torque expression becomes
= (27)
The torque balance equation is given as [7]
= + + 2 (28)
where Te is developed electromagnetic torque, TL is the load torque, B is the friction coefficient in N ms/rad, J is moment of inertia in kg m2 and P is the number of poles. Now (28) is used with (27) to obtain the time derivative of torque as
condition of the IGBTs is represented as 1 or 0, respectively. The switching sequence of VSI for different positions of the rotor are shown in Table 1.
Hall signals
Switching signals
Ha
Hb
Hc
S1
S2
S3
S4
S5
S6
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
Table 1 Switching states based on Hall effect position sensor signal
pr =
Te TL Br J(2 P)
(29)
The potential of neutral terminal with respect to zero potential (Vno) is required to be considered in order to avoid unbalance in applied voltage. Substituting (16) in (15) and taking the sum for three phases, it results in
= + ( + ) + (30)
Substituting (18) in (30) one obtains


SIMULATED PERFORMANCE OF THE PROPOSED BRIDGELESS CUK CONVERTERFED BLDC MOTOR DRIVE
The performance of the proposed bridgeless Cuk converterfed BLDC motor drive is evaluated on the basis of performance indices such as supply voltage (Vs), supply current (is), DClink voltage (Vdc), speed (),electromagnetic torque (Te), input inductor current(iLi1, iLi2), output inductor current (iLo1, ilo2) and intermediate
3
=
(31)
capacitors voltage (Vc1, Vc2).
a
b
c
d
Fig 3 Steady state performance of the bridgeless cuk converter fed BLDC motor drive.

CONCLUSION
The bridgeless PFC cuk converter fed PMBLDC motor drive system has been proposed for an air conditioning system. The attention devoted to the quality of the currents absorbed from the utility line by electronic equipment is increasing due to several reasons. In fact a low power factor reduces the power available from the utility grid while a high harmonic distortion of the line current causes EMI problems and crossinterferences. From this point of view the standard rectifier employing a diode bridge followed by a filter capacitor gives unacceptable performances. Thus the development of bridgeless cuk converters as interface systems improved the power factor of standard electronic loads. The front end PFC bridgeless cuk converters operating in DICM has been used for dual operation of PFC and DC link voltage control. The proposed drive system has maintained high power factor and improved power quality for a wide range of speed control for varying supply voltages. An efficient topology modification of the combined system with DBR to bridgeless cuk converter is presented in this project provide more convenient operation and improve the system efficiency.
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SINSHA V presently pursuing his M.E in Power Electronics & Drives, in Ranganathan Engineering College, Coimbatore. Her area of interest includes power electronics, electric drives, electric machines.
E THANGAM presently working as assistant professor in Ranganathan Engineering College, Coimbatore. His area of interest is power electronics & drives, electric machines, power system, power quality.