Download Fig. 4(a) Waveforms for positive and negative half cycles of supply

Power Quality Improved Bridgeless Buck-Boost
Converter-Fed Vector Controlled PMSM Motor Drive
Rintu Mathunni (1)
Sreelekha V(2)
Dept. of Electrical Engineering
Rajiv Gandhi Institute of Technology
Kottayam, India
[email protected]
Dept. of Electrical Engineering
Rajiv Gandhi Institute of Technology
Kottayam, India
[email protected]
Rajesh K(3)
Dept. of Electrical Engineering
Rajiv Gandhi Institute of Technology
Kottayam, India
[email protected]
Abstract— This paper deals with the analysis, design and
implementation of a power factor corrected (PFC) bridgeless
(BL) Buck-Boost Converter in discontinuous current mode
(DCM) of operation used for power quality improvement at AC
mains in vector controlled permanent magnet synchronous motor
(PMSM) drives. The designed converter feeds a vector controlled
PMSM drive system. Modeling and simulation is carried out in
MATLAB/Simulink environment. The results obtained
demonstrate the effectiveness of the converter in improving
power quality at AC mains in the PMSM drive system.
Keywords—Bridgeless (BL) buck-boost Converter; permanent
magnet synchronous motor (PMSM); vector controlled; power
quality.
I.
INTRODUCTION
Brushless Permanent magnet synchronous motors (PMSM)
are used nowadays, in a large scale owing to its simple
structure, reliability, high power density, supreme efficiency,
and high dynamic response. PMSM motors are used mostly in
applications requiring fast torque response and high
performance.
A PMSM motor has a wound stator, a permanent magnet
rotor assembly and internal or external devices to sense rotor
position. The sensing devices provide position feedback for
adjusting frequency and amplitude of stator voltage reference
properly to maintain rotation of the magnet assembly. The
combination of an inner permanent magnet rotor and outer
windings offers the advantages of low rotor inertia, efficient
heat dissipation, and reduction of the motor size. Moreover,
the elimination of brushes reduces noise, EMI generation and
suppresses the need of brushes maintenance.
Ann Mary Joshua(4)
Dept. of Electrical Engineering
Rajiv Gandhi Institute of Technology
Kottayam, India
[email protected]
Power quality have become one of the key issue to be
considered due to recommended limits for harmonics for
supply current set by various international power quality
standards such as International Electrotechnical Commission
(IEC) 61000-3-2. For class A equipment (< 600 W, 16 A per
phase), IEC 61000-3-2 restricts the harmonic current of
different order such that the total harmonic distortion (THD)
of the supply current should be below 19%. A PMSM motor
when fed by a diode bridge rectifier (DBR) with a high value
of dc link capacitor draws peaky current which can lead to a
THD of supply current of the order of 65% and power factor
as low as 0.8. In this paper a DBR followed by a power factor
corrected (PFC) converter is utilized for improving the power
quality at ac mains for a PMSM drive incorporating vector
control. [1]
The choice of mode of operation of a PFC converter is an
important issue because it directly affects the cost and rating
of the components used in the PFC converter. The continuous
conduction mode (CCM) and discontinuous conduction mode
(DCM) are the two modes of operation in which a PFC
converter is designed to operate. In CCM, the current in the
inductor or the voltage across the intermediate capacitor
remains continuous, but it requires the sensing of two voltages
(dc link voltage and supply voltage) and input side current for
PFC operation, which is expensive. On the other hand, DCM
requires a single voltage sensor for dc link voltage control, and
inherent PFC is achieved at the ac mains, but at the cost of
higher stresses on the PFC converter switch; hence, DCM is
utilized for converter operation. [2]
Fig. 1. Discussed PMSM motor drive with front end BL buck-boost converter.
II.
PROPOSED PFC BL BUCK-BOOST CONVERTER-FED PMSM
MOTOR DRIVE
Fig. 1 shows the discussed BL buck–boost converter-based
VSI-fed PMSM motor drive. The parameters of the BL buck–
boost converter are designed such that it operates in
discontinuous current mode (DCM) to achieve an inherent
power factor correction at ac mains. Vector Control is applied
for the speed control of PMSM motor drive.
Fig. 1. Discussed PMSM motor drive with front end BL buck-boost converter.
Fig. 2.(a) Positive half cycle of supply voltage. Switch Sw1 conducts to charge
the inductor Li1;hence an inductor current iLi1 increases. Dc link capacitor Cd
is discharged. (Mode I)
The discussed configuration of the BL buck–boost converter
has the minimum number of components and least number of
conduction devices during each half cycle of supply voltage
which governs the choice of the BL buck–boost converter for
this application.
III.
OPERATING PRINCIPLE OF PFC BL BUCK-BOOST
CONVERTER
The operation of the PFC BL buck–boost converter is
classified into two parts which include the operation during
the positive and negative half cycles of supply voltage and
during the complete switching cycle.
A. Operation during positive and negative halfcycles of
supply voltage
In the discussed scheme of the BL buck–boost converter,
switches Sw1 and Sw2 operate for the positive and negative half
cycles of the supply voltage, respectively. During the positive
half cycle of the supply voltage, switch Sw1, inductor Li1, and
diodes D1 and Dp are operated to transfer energy to dc link
capacitor Cd as shown in Fig. 2(a)–(c).
Fig.2. (b) Positive half cycle of supply voltage. Switch Sw1 is turned off, and
the stored energy in inductor Li1 is transferred to dc link capacitor Cd until the
inductor is completely discharged. The current in inductor Li1 reduces and
reaches zero.(Mode II)
Fig.2.(c) Positive half cycle of supply voltage. Inductor Li1 enters
discontinuous conduction, i.e., no energy is left in the inductor; hence, current
iLi1 becomes zero for the rest of the switching period. None of the switch or
diode is conducting, and dc link capacitor Cd supplies energy to the load.
(Mode III)
Similarly, for the negative half cycle of the supply voltage,
switch Sw2, inductor Li2, and diodes D2 and Dn conduct as
shown in Fig. 3(a)–(c). In the DCM operation of the BL buck–
boost converter, the current in inductor Li becomes
discontinuous for certain duration of switching period.
Fig. 4(a) Waveforms for positive and negative half cycles of supply
voltage
Fig. 4(b) shows the waveforms during complete switching
cycle.
Fig.3. (a) Negative half cycle of supply voltage. Switch Sw2 conducts to charge
the inductor Li2; hence, an inductor current iLi2 increases. Dc link capacitor Cd
is discharged. (Mode I)
Fig. 4(b) Waveforms during complete switching cycle
IV.
Fig.3. (b) Negative half cycle of supply voltage. Switch Sw2 is turned off, and
the stored energy in inductor Li2 is transferred to dc link capacitor Cd until the
inductor is completely discharged. The current in inductor Li2 reduces and
reaches zero.(Mode II)
A PFC BL buck–boost converter is designed to operate in
DCM such that the current in inductors Li1 and Li2 becomes
discontinuous in a switching period. For a PMSM of power
rating 400 W (complete specifications of the PMSM motor are
given in the Appendix), a power converter of 550 W (Po) is
designed. For a supply voltage with an rms value of 220 V, the
average voltage appearing at the input side is given as
𝑉𝑖𝑛 =
Fig.3. (c) Negative half cycle of supply voltage. Inductor Li2 enters
discontinuous conduction, i.e., no energy is left in the inductor; hence, current
iLi2 becomes zero for the rest of the switching period. None of the switch or
diode is conducting, and dc link capacitor Cd supplies energy to the load.
(Mode III)
Fig. 4(a) shows the waveforms of different parameters
during the positive and negative half cycles of supply voltage.
DESIGN OF PFC BL BUCK-BOOST CONVERTER
2√2𝑉𝑠
2√2 × 220
=
= 198 𝑉
𝜋
𝜋
(1)
The relation governing the voltage conversion ratio for a
buck–boost converter is given as
𝑑=
𝑉𝑑𝑐
𝑉𝑑𝑐 + 𝑉𝑖𝑛
(2)
The discussed converter is designed for dc link voltage
control from 50 V (Vdc min) to 200 V (Vdcmax) with a nominal
value (Vdc des) of 100 V; hence, the minimum and the
maximum duty ratio (dmin and dmax) corresponding to Vdc min
and Vdcmax are calculated as 0.2016 and 0.5025, respectively.
A. Design of input inductors (Li1 and Li2)
. The value of inductance Lic1, to operate in critical
conduction mode in the buck–boost converter, is given as
𝐿𝑖𝑐1 =
𝑅(1 − 𝑑)2
2𝑓𝑠
(3)
where R is the equivalent load resistance, d is the duty
ratio, and fs is the switching frequency.
Now, the value of Lic1 is calculated at the worst duty ratio
of dmin such that the converter operates in DCM even at very
low duty ratio. At minimum duty ratio, i.e., the PMSM motor
operating at 50 V (Vdc min), the power (Pmin) is given as 110 W
(i.e., for constant torque, the load power is proportional to
speed). Hence, from (4), the value of inductance Lic min
corresponding to Vdcmin is calculated as
𝐿𝑖𝑐𝑚𝑖𝑛 =
2
(1
𝑉𝑑𝑐𝑚𝑖𝑛
− 𝑑𝑚𝑖𝑛
𝑃𝑚𝑖𝑛 2𝑓𝑠
)2
=
2 (1
2
50
− 0.2016)
110 × 2 × 20000
= 362.18 µ𝐻
(4)
The values of inductances Li1 and Li2 are taken less
than1/10th of the minimum critical value of inductance to
ensure a deep DCM condition. Hence, the values of inductors
Li1 and Li2 are selected around 1/10th of the critical inductance
and are taken as 35 μH. It reduces the size, cost, and weight of
the PFC converter.
B. Design of input capacitor (Cd)
The design of the dc link capacitor is governed by the
amount of the second-order harmonic (lowest) current flowing
in the capacitor and is derived as follows.
For the PFC operation, the supply current (is) is in phase
with the supply voltage (vs). Hence, the input power Pin is
given as
𝑃𝑖𝑛 = √2𝑉𝑆 sin ω𝑡 ∗ √2𝐼𝑆 sin ω𝑡
= 𝑉𝑆 𝐼𝑆 (1 − cos 2ω𝑡)
(5)
where the latter term corresponds to the second-order
harmonic, which is reflected in the dc link capacitor as
𝑉𝑆 𝐼𝑆
𝑖𝐶 (𝑡) = −
cos 2ω𝑡.
𝑉𝑑𝑐
(6)
The dc link voltage ripple corresponding to this capacitor
current is given as
𝛥𝑉𝑑𝑐 =
1
∫ 𝑖𝐶 (𝑡)𝑑𝑡
𝐶𝑑
𝐼𝑑
=−
sin 2ω𝑡.
2𝜔𝐶𝑑
(7)
For a maximum value of voltage ripple at the dc link
capacitor, Sin(ωt) is taken as 1. Hence, (7) is rewritten as
𝐶𝑑 =
𝐼𝑑
2ω𝛥𝑉𝑑𝑐
(8)
Now, the value of the dc link capacitor is calculated for the
designed value Vdc des with permitted ripple in the dc link
voltage (ΔVdc) taken as 4% as
𝐶𝑑 =
𝐼𝑑
𝑃𝑜 ⁄𝑉𝑑𝑐 𝑑𝑒𝑠
550⁄100
=
=
2ω𝛥𝑉𝑑𝑐
2ω𝛥𝑉𝑑𝑐
2 × 314 × 0.04 × 100
= 2189.4 µ𝐹
(9)
Hence, the nearest possible value of dc link capacitor Cd is
selected as 2200 μF.
C. Design of input filter (Lf and Cf)
A second-order low-pass LC filter is used at the input side
to absorb the higher order harmonics such that it is not
reflected in the supply current. The maximum value of filter
capacitance is given as
𝐶𝑚𝑎𝑥 =
𝐼𝑝𝑒𝑎𝑘
550
1
tan θ =
tan(1°)
𝜔𝐿 𝑉𝑝𝑒𝑎𝑘
220 314 × 220√2
= 446.67 𝑛𝐹
(10)
where Ipeak, Vpeak, ωL, and θ represent the peak value of supply
current, peak value of supply voltage, line frequency in
radians per second, and displacement angle between the
supply voltage and supply current, respectively.
Hence, a value of Cf is taken as 330 nF. Now, the value of
inductor Lf is calculated as follows.
The value of the filter inductor is designed by considering
the source impedance (Ls) of 4%–5% of the base impedance.
Hence, the additional value of inductance required is given as
𝐿𝑓 = 𝐿𝑟𝑒𝑞 + 𝐿𝑠 ⇒
𝐿𝑟𝑒𝑞 =
1
1
Vs2
=
𝐿
+
0.04
(
)
(
)
𝑟𝑒𝑞
4π2 fc2 Cf
ωL Po
1
1
2202
−
0.04
(
)
(
)
4π2 × 20002 × 330 × 10−9
314 550
= 7.97 mH
(11)
where fc is the cutoff frequency of the designed filter
which is selected as
fL < fc < fsw.
Hence, a value of fc is taken as fsw/10.
Finally, a low-pass filter with inductor and capacitor of 8
mH and 330 nF is selected for this particular application.
V.
CONTROL OF PFC BL BUCK-BOOST CONVERTER FED
PMSM MOTOR DRIVE
The control of the PFC BL buck–boost converter-fed
PMSM motor drive is classified into two parts as follows.
A. Control of Front-End PFC Converter: Voltage follower
approach
The control of the front-end PFC converter generates the
PWM pulses for the PFC converter switches (Sw1 and Sw2) for
dc link voltage control with PFC operation at ac mains. A
single voltage control loop (voltage follower approach) is
utilized for the PFC BL buck–boost converter operating in
∗
DCM. A reference dc link voltage ( 𝑉𝑑𝑐
) is generated as[3]
∗
𝑉𝑑𝑐
= 𝑘𝑣 ω∗
(12)
Where 𝑘𝑣 and ω∗ are the motor’s voltage constant and the
reference speed, respectively.
The voltage error signal (𝑉𝑒 ) is generated by comparing the
∗
reference dc link voltage (𝑉𝑑𝑐
) with the sensed dc link voltage
(𝑉𝑑𝑐 ) as
∗ (𝑘)
𝑉𝑒 (𝑘) = 𝑉𝑑𝑐
− 𝑉𝑑𝑐 (𝑘)
(13)
where 𝑘 represents the 𝑘th sampling instant.
This error voltage signal (𝑉𝑒 ) is given to the voltage
proportional–integral (PI) controller to generate a controlled
output voltage (𝑉𝑐𝑐 ) as
𝑉𝑐𝑐 (𝑘) = 𝑉𝑐𝑐 (𝑘 − 1) + 𝑘𝑝 {𝑉𝑒 (𝑘) − 𝑉𝑒 (𝑘 − 1)}
+ 𝑘𝑖 𝑉𝑒 (𝑘)
(14)
where 𝑘𝑝 and 𝑘𝑖 are the proportional and integral gains of
the voltage PI controller.
Finally, the output of the voltage controller is compared with a
high frequency saw tooth signal (md ) to generate the PWM
pulses as
For 𝑉𝑠 > 0; {
For 𝑉𝑠 < 0;{
Fig. 5. Basic Scheme of Vector Control
if md < 𝑉𝑐𝑐 then Sw1 = ‘ON’
}
if md ≥ 𝑉𝑐𝑐 then Sw1 = ‘OFF′
𝑖𝑓 𝑚𝑑 < 𝑉𝑐𝑐 𝑡ℎ𝑒𝑛 𝑆𝑤2 = ‘𝑂𝑁’
}
𝑖𝑓 𝑚𝑑 ≥ 𝑉𝑐𝑐 𝑡ℎ𝑒𝑛 𝑆𝑤2 = ‘𝑂𝐹𝐹′
(15)
where Sw1 and Sw2 represent the switching signals to the
switches of the PFC converter.
B. Vector Control of PMSM motor
Vector control use mathematical transformations in order
to decouple the torque generation and the magnetization
functions in PM motors to separately control the torque
producing and magnetizing flux components.[4]
Fig. 5 summarizes the basic scheme of torque control with
Vector Control:
Two motor phase currents are measured. These
measurements feed the Clarke transformation module. The
outputs of this projection are designated isα and isβ. These two
components of the current are the inputs of the Park
transformation that gives the current in the d,q rotating
reference frame. The isd and isq components are compared to
the references isdref (the flux reference) and isqref (the torque
reference). As in synchronous permanent magnet motor, the
rotor flux is fixed determined by the magnets; there is no need
to create one. Hence, when controlling a PMSM, i sdref should
be set to zero. The torque command isqref is the output of the
speed regulator. The outputs of the current regulators are Vsdref
and Vsqref; they are applied to the inverse Park transformation.
The outputs of this projection are Vsαref and Vsβref which are the
components of the stator vector voltage in the (α, β) stationary
orthogonal reference frame. These are the inputs of the Space
Vector PWM. The outputs of this block are the signals that
drive the inverter. Both Park and inverse Park transformations
need the rotor flux position.
Knowledge of the rotor flux position is the core of the
vector control. In the synchronous machine the rotor speed is
equal to the rotor flux speed. Therefore θ (rotor flux position)
is directly measured by position sensor.
VI.
SIMULATED PERFORMANCE OF PROPOSED
PMSM MOTOR DRIVE
The performance of the discussed PMSM motor drive is
simulated in MATLAB/Simulink environment using the Sim
Power-System toolbox. The performance evaluation of the
discussed drive is categorized in terms of the performance of
the PMSM motor and BL buck–boost converter and the
achieved power quality indices obtained at ac mains. The
parameters associated with the PMSM motor such as speed
(N), electromagnetic torque (Te), and stator current (Is) are
analyzed for the proper functioning of the PMSM motor.
Parameters such as supply voltage (Vs), dc link voltage (Vdc),
of the PFC BL buck–boost converter are evaluated to
demonstrate its proper functioning.
The different parameters of the drive are given in Table I
TABLE I
Parameters of the Proposed PMSM Drive
Sl. No.
Parameter
Value
1
Back emf constant
31.63 V/Kr/min
2
Phase Resistance
4.7 Ω
3
Phase Inductance
25.71 mH
4
Moment of Inertia
3.1x10^-5
kg/m2
5
Proportional gain
0.4
6
Integral gain
0.001
The steady-state behavior of the proposed PMSM motor
drive for three cycles of supply voltage at rated condition (rated
dc link voltage of 200 V) is shown in Fig. 6
Fig. 8. Speed waveform of the PMSM drive during vector control
VIII.
Fig. 6. Steady state performance of the proposed PMSM drive at rated
conditions
The harmonic spectra of the supply current at rated and light
load conditions, i.e., dc link voltage of 200 V, is also shown in
Fig. 7, which shows that the THD of supply current obtained is
under the acceptable limits of IEC 61000-3-2.
CONCLUSION
A PFC BL buck–boost converter-based Vector controlled
PMSM motor drive has been proposed targeting low-power
applications. The front-end BL buck–boost converter has been
operated in DCM for achieving an inherent power factor
correction at ac mains. A satisfactory performance has been
achieved for speed control with power quality indices within
the acceptable limits of IEC 61000-3-2.
ACKNOWLEDGMENT
I extend my sincere gratitude towards Prof. Vijayakumari
C. K. Head of the Department of Electrical Engineering, for
giving us her invaluable knowledge and excellent technical
guidance.
I express my thanks to P.G Coordinator Mrs. Shanifa
Beevi S. and Mrs. Sreelekha V. for their kind co-operation
and guidance during the work.
I also thank all other faculty members of Electrical
Department and my friends for their help and support.
Fig. 7. Harmonic spectra of the supply current with rated dc voltage of 200 V
and supply voltage of 230 V
Last but not the least I thank the God Almighty for having
made my endeavor successful.
VII. HARDWARE VALIDATION OF PROPOSED PMSM MOTOR
DRIVE
Vector control of the PMSM was done using DSP 320F
28035. Obtained Speed waveform of the drive is shown in
Fig.8
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[2]
[3]
[4]
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