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Cuk Converter-Based PF Correction for
PMBLDCM Drive with Hysteresis Controller
Elizabeth Alphonsa Jose
Mr.Thomas K.P.
M.Tech. Scholar
Rajagiri School of Engineering and Technology, Kakkanad
Kochi, India
[email protected]
Dept. of Electrical and Electronics Engg.
Rajagiri School of Engineering and Technology, Kakkanad
Kochi, India
[email protected]
Abstract—Permanent
magnet
brushless
DC
motor
(PMBLDCM) drives are being employed in many variable speed
applications due to their high efficiency, silent operation,
compact size, high reliability, ease of control, and low
maintenance requirements. These drives have power quality
problems and poor power factor at input AC mains. Solid-state
switch-mode rectification converters have reached a matured
level for improving power quality in terms of power-factor
correction (PFC), reduced total harmonic distortion at input ac
mains etc. This paper deals with a hysteresis controller for a
permanent magnet brushless DC motor (PMBLDCM) with Cuk
dc–dc converter based power-factor-correction. A three-phase
voltage-source inverter is used as an electronic commutator to
operate the PMBLDCM. Hysteresis current control method is
used for gating of VSI so as to reduce the power consumption.
Test results of the controller is also presented to validate the
design and the advantage using the same.
Index Terms—Cuk converter, power factor correction (PFC),
permanent-magnet brushless dc motor (PMBLDCM), Hysteresis
Control, voltage-source inverter (VSI).
I. INTRODUCTION
Household appliances are the one of fastest-growing endproduct market for electronic motor drivers. The major
appliances include washing machine, room air conditioners,
refrigerators, vacuum cleaners, freezers, etc. For household
appliance, usually we prefer historical classic electric motor
technologies such as single phase AC induction motor,
including split phase, capacitor-start, capacitor–run types, and
universal motor. These classic motors typically are operated
directly from main AC power without regarding the
efficiency, at constant-speed. Consumers now demand for
lower energy costs, better performance, reduced noise, and
more convenience features. Those traditional technologies
cannot provide the solutions. In low-power appliances the use
of a permanent-magnet brushless dc motor (PMBLDCM) is
increasing because of its features of high efficiency, wide
speed range, and low maintenance[1]. Due to the use of PMs on
the rotor, it is a rugged three-phase synchronous motor. The
commutation in a PMBLDCM is accomplished by solid state
switches of a three-phase voltage-source inverter (VSI).
A typical motor drive consists of an ac/dc converter, LC dc
link, and an inverter as shown in Fig.1. The motor is fed from
a single-phase sc supply through a diode bridge rectifier
(DBR) followed by a dc capacitor and a voltage source
inverter. A large electrolytic capacitor is usually installed in dc
link to stabilize the dc voltage.[2]
Fig. 1. Typical Motor Drive System
This PMBLDC motor drive draws a pulsed current
from ac mains due to uncontrolled charging of dc link
capacitor, having peaks higher than the amplitude of the
fundamental input current. This is because, the diodes are
reverse biased during the period when the ac voltage is less
than the dc link voltage, and they does not draw any current
from the ac mains; however, it draws a large current when the
ac voltage is higher than the dc link voltage. Therefore, many
power quality (PQ) problems arise at input ac mains including
poor power factor, increased total harmonic distortion (THD),
etc. These PQ disturbances are undesirable. There are many
means explored and proposed to solve this severe problem.
Power factor correction method is a good candidate for ac to
dc power conversion in order to reduce the line current
harmonics as well as increase the efficiency and capacity of
motor drives. The use of power factor correction topologies
is, therefore, mostly recommended for such drives[3].
The dc-dc converters, which act as PFC converters,
forces the drive to draw sinusoidal ac mains current in phase
with its voltage. A DC-DC converter topologies such as buck,
boost, buck-boost, Cuk, SEPIC, zeta converters with
variations of capacitive/inductive energy transfer are mostly
preferred[4]. The net result is improved performance, such as
reduction of ac mains current harmonics, reduction of noise
and electromagnetic pollution, minimum number of
components, enhanced efficiency, utilization of the full input
voltage range etc.
In this paper a Cuk dc–dc converter is used as a PFC
converter because of its continuous input and output currents,
small output filter, and wide output voltage range as compared
to other single switch converters. A three-phase voltagesource inverter is used as an electronic commutator to operate
the PMBLDCM. Hysteresis current control method is used for
gating of VSI so as to reduce the power consumption. The
detailed modeling, design, and performance evaluation of the
proposed drive are presented.
maintain the speed of the motor close to its desired reference
value. The output of the PI controller is given to a limiter to
produce the reference torque (T*). The reference current
generator outputs the three phase reference currents (ia *, ib *,
ic *) from the reference torque and position signal. The
winding currents (ia, ib, ic), are compared with the reference
currents (ia *, ib *, ic *) and the switching signals for VSI is
generated by using a hysteresis current controller. In response
to switching signals the VSI provides voltage across the motor
terminals to produce desired currents in the winding of the
motor. These winding currents produce an electromagnetic
torque to maintain the desired speed[5].
II. CUK CONVERTER FED PMBLDCM
III. DESIGN OF CUK PFC CONVERTER FOR PMBLDCM
The Cuk PFC converter is designed for a PMBLDCM drive
having DBR at front end, on the basis of PQ constraints at ac
mains and allowable ripple in dc-link voltage. The output
voltage (Vdc) of the Cuk PFC converter is given as,
Vdc = Vin D/(1-D)
(1)
Where, Vin is the average value of the output DC voltage from
a DBR, derived from an ac input voltage (Vs) as,
Vin = Vs 2√2 / π
(2)
The values of boost inductor and capacitor used in cuk
converter for energy transfer is given by,
L1 = DVin / (fS ΔIL1)
C1=D Idc / (fS ΔVC1)
Fig.2. Hysteresis Controlled BLDCM Drive with PF Correction
Fig.2 shows the Hysteresis Controlled PMBLDC motor
drive with PF Correction. The Cuk dc–dc converter controls
the dc link voltage using capacitive energy transfer which
results in non-pulsating input and output currents. Here, the
use of current multiplier approach with average current control
scheme in continuous conduction mode (CCM) of the PFC
converter is used. In this topology, a conventional DBR is fed
from single-phase ac mains. Its output is given to a DC-DC
converter, and a VSI is used to feed the PMBLDC motor. The
DC-DC converter provides a controlled dc voltage from
uncontrolled dc output of DBR, while controlling the power
factor through high frequency switching of the PFC switch.
The control loop used for PFC action involves outer voltage
loop and inner current loop. This converter draws unity power
factor current from the ac mains; eliminates harmonic currents
and regulates the dc link voltage even under fluctuating
voltage conditions of ac mains.
A VSI is used to feed the PMBLDC motor. For the
speed control of the PMBLDCM, an outer speed & an inner
current loop with hysteresis controller is used to drive a
constant torque load. By using hall effect sensors, the rotor
position of PMBLDCM is sensed and converted to speed
signal. A proportional-integral (PI) controller is used to
(3)
(4)
where ΔIL1 is the inductor current ripple, ΔVC1 is the voltage
ripple in the intermediate capacitor (C1), and Idc is the current
drawn by the PMBLDCM from the dc link.
For ripple-free voltage at the dc link of the Cuk
converter a ripple filter is designed. For a given switching
frequency (fs), the inductance (L2) of the ripple filter restricts
the inductor peak-to-peak ripple current (ΔI L2) within a
specified value. The capacitance (C2) is calculated for the
allowed ripple in the dc link voltage (ΔVC2)[6],[7]. The values of
the ripple filter inductor and capacitor are given as,
L2 = Vdc (1-D) / (fS ΔIL2)
C2 = Idc / (2ω ΔVC2)
(5)
(6)
IV. MODELING OF PFC CONVERTER-BASED PMBLDC
MOTOR DRIVE
The modeling of PMBLDCM drive involves modeling of
the PFC converter and PMBLDCM drive. These components
are modeled in the form of mathematical equations and the
complete drive is represented as a combination of these
models.
A. PFC CONVERTER
The PFC converter consists of a DBR at front end and a
Cuk converter with an output ripple filter. The PFC converter
modeling consists of the modeling of a speed controller, a
reference current generator, and a PWM controller as given
below.
1. Speed Controller:
The Speed Controller is a PI controller which closely
monitors the speed error as an equivalent voltage error and
generates control signal (Ic) to minimize the error. If at kth
instant of time, V*dc(k) is reference DC link voltage, Vdc(k) is
sensed dc link voltage then the voltage error Ve(k) is calculated
as,
Ve(k) = V*dc(k) - Vdc(k)
(7)
The output of the controller Ic(k) at kth instant is given as,
Ic(k) = Ic(k- 1) +KpvVe(k) -Ve(k - 1) +KivVe(k)
(8)
Where, Kpv and Kiv are the proportional and integral gains of
the voltage PI controller.
2. Reference Current Generator:
The reference current at the input of the Cuk converter is,
i*d = Ic(k)ud
(9)
where ud is the unit template of the ac mains voltage,
calculated as,
ud = vd/Vsm; vd = |Vs|; Vs = Vsm sinωt
(10)
3. PWM Controller:
The reference input current of the Cuk converter (i*d) is
compared with its current (id) sensed after DBR to generate
the current error Δi. This current error is amplified by gain kd
and compared with fixed frequency (fs) sawtooth carrier
waveform md(t) to get the switching signal for the MOSFET
of the Cuk converter as,
if
kdΔid > md(t) then S = 1
if
kdΔid < md(t)
then S = 0
(11)
where S denotes the switching of the MOSFET of the Cuk
converter representing ‘on’ position with S=1 and its ‘off’
position with S=0.
reference speed, ωr(k) is the rotor speed then the speed error
ωe (k) can be calculated as,
ωe(k) = ωr*(k) - ωr(k)
(12)
This speed error is processed through the speed controller to
get desired control signal.
1. Speed controller:
The speed of the motor is compared with its reference
value and the speed error is processed in PI speed controller.
The speed controller’s output at kth instant T(k) is given as,
T(k) = T(k - 1) + Kpω [ωe(k) - ωe(k - 1)] + kiω(k)
(13)
where Kpω and kiω are the proportional and integral gains of
the PI speed controller. The output of this controller is
considered as the reference torque.
2. Reference Current Generator:
The magnitude of the three phase current iref is determined by
using reference torque Tref.
iref = Tref / Kt
(14)
where Kt is the torque constant.
Depending on the rotor position, the reference current
generator block generates three phase reference currents ( i*a,
i*b, i*c ) by taking the value of reference current magnitude as
iref . These reference currents are compared with sensed phase
currents (ia, ib, ic) to generate the current errors Δia, Δib, & Δic
for three phases of the motor.
3. Hystresis current controller:
The Hysteresis current controller contributes to the
generation of the switching signals for the inverter.
Hysteresis-band PWM is basically an instantaneous feedback
current control method of PWM where the actual current
continually tracks the command current within hysteresisband. Each comparator determines the switching state of the
corresponding inverter leg (Sa, Sb &Sc) such that the load
currents are forced to remain within the hysteresis band.
Fig. 3. PWM controller signals of PFC converter
B. PMBLDC MOTOR DRIVE
The PMBLDCM drive has a speed controller, a reference
winding current generator, a hysteresis current controller, a
voltage source inverter and a PMBLDC motor as the main
components.
The speed controller is a PI controller which closely
tracks the reference speed. If at kth instant of time, ωr*(k) is the
Fig. 4. Fixed band Hysteresis Current Controller
As the current exceed upper band limit, the upper switch
is off; and lower switch is on as the current exceed lower band
limit. ie;
If ia < (ia* − hb ) Sa1 is ON and Sa2 is OFF
If ia < (ia* + hb ) Sa1 is OFF and Sa2 is ON
(15)
Similarly for other switches also.
where, hb is the hysteresis band around the three phase’s
references currents, according to above switching condition.
4. Voltage Source Inverter:
Where x can be phase a, b, or c and fx(θ) represents a
function of rotor position with a maximum value ±1, identical
to trapezoidal induced EMF, given as,
ea = (6E/π)θ
for (0< θ < π/6)
=E
for (π/6 < θ < 5π/6)
= - (6E/π)θ + 6E
for (5π/6 < θ < 7π/6)
= -E
for (7π/6 < θ < 11π/6)
= (6E/π)θ - 12E
for (5π/6 < θ < 7π/6) (23)
The functions eb and ec are similar to ea with phase differences
of 1200 and 2400, respectively. The mechanical torque
equation of motion is given by,
Te – Tl = P/2 (J pωr + B ωr)
where ωr is the derivative of rotor position θ, P is the number
of poles, Tl is the load torque in newton meters, J is the
moment of inertia in kilogram square meters, and B is the
friction coefficient in newton meter seconds per radian. The
derivative of rotor position is given as,
Fig.5. Brushless dc motor drive system
Fig.5. shows an equivalent circuit of a VSI fed PMBLDCM.
The output of VSI to be fed to phase ‘A’ of the PMBLDC
motor is given as,
Vao = (Vdc/2) for Sa1 = 1
Vao = (-Vdc/2) for Sa2 = 1
Vao = 0
for Sa1 = Sa2 = 0
Van = Vao – Vno
(16)
where Vao, and Vno are voltages of phase A and neutral
terminal with respect to virtual mid-point of the dc link. Using
similar logic Vbo, Vco, Vbn, Vcn are generated for other two
phases of the VSI feeding PMBLDC motor. The voltages Van,
Vbn, and Vcn are voltages of three-phases with respect to the
motor neutral terminal (n).
5.
(24)
PMBLDC Motor:
The PMBLDCM is represented in the form of a set of
differential equations given as,
Va = iaRa + L (d/dt) ia + ea
(17)
Vb = ibRb + L (d/dt) ib + eb
(18)
Vc = ibRb + L (d/dt) ic + ec
(19)
In these equations, ia, ib, and ic are currents, and ea, eb, and ec
are the back EMFs of PMBLDCM, in respective phases; R is
the resistance of motor windings/phase and L is the
inductance.
The developed torque Te in the PMBLDCM is given
as,
Te = (ea ia + ebib + ecic)/ωr
(20)
where ω is the motor speed in radians per second. Since
PMBLDCM has no neutral connection,
ia + ib + ic = 0
(21)
The back EMF is a function of rotor position (θ) as,
ex = Kb fx(θ)ωr
(22)
pθ = ωr
(25)
These equations represent the dynamic model of the
PMBLDC motor.
V. RESULTS AND DISCUSSION
A. Performance During Starting:
Fig. 6 shows the variation of single-phase ac supply
voltage (Vs), current (Is), dc link voltage (Vdc), motor speed,
and motor winding currents ia, ib, and ic with time. It can be
seen from this figure that the input current remains sinusoidal
and is found to be in time phase with the input voltage. The
supply current during starting is distortion free and therefore
the operating power factor is close to unity. During starting of
the motor the supply current is found to increase with the
speed because the power demand of the system is proportional
to the speed (the load torque being constant). Once the motor
attains the steady speed, the supply current also decreases due
to absence of accelerating torque.
B. Comparison between open loop & closed loop:
Fig.6 shows the simulated performance of power factor
corrected PMBLDC motor drive under open loop, and Fig.7
shows that of hysteresis current controlled method. It can be
seen that in case of open loop method, the speed is settled at
2000rpm at 0.45secs. Once the machine reaches its steady
value, the supply current also decreases.
In case of hysteresis current controlled method, the drive
reaches its reference value ie. 1500rpm. Once the machine
reaches its steady value, the supply current decreases. In this
method, the active power consumed from the source is less
compared to open loop method, and therefore there is an
energy saving. The tables I & II shows a comparison between
the two.
REFERENCES
[1] T. Kenjo and S. Nagamori, Permanent Magnet Brushless DC
Motors. Oxford, U.K.: Clarendon, 1985.
[2] Tze-Yee Ho, Mu-Song Chen, Lung-Hsian Yang, Wei-Lun, Lin,
“The Design of a High Power Factor Brushless DC Motor Drive”,
International Symposium on Computer, Consumer and Control,2012
[3] Sanjeev Singh, Member, IEEE, and Bhim Singh, “A VoltageControlled PFC Cuk Converter-Based PMBLDCM Drive for AirConditioners”, IEEE Trans.on Ind. Appl., vol. 48, no. 2, March/April
2012
[4] B. Singh, B. N. Singh, A. Chandra, K. Al-Haddad, A. Pandey, and
D. P. Kothari, “A review of single-phase improved power quality ac–
dc converters,” IEEE Trans. Ind. Electron., vol. 50, no. 5, pp. 962–
981, Oct. 2003.
Fig 6. Performance of Hysteresis controlled PMBLDC motor Drive
[5] Alamelu Nachiappan, Sundararajan K, and Malarselvam V
“Current Controlled Voltage Source Inverter Using Hysteresis
Controller And PI Controller” IEEE Trans 2012
[6] N. Mohan, M. Undeland, and W. P. Robbins, Power Electronics:
Converters, Applications and Design. Hoboken, NJ: Wiley, 1995.
[7] Daniel W Hart, Power Electronics
Fig.7. Performance of open loop PMBLDC motor Drive
Table I. Variation of Active power, power factor and speed with load for
open loop BLDC motor Drive
Table II. Variation of Active power, power factor and speed with load for
Hysteresis controlled BLDC motor Drive