International Journal of Engineering Technology, Management and Applied Sciences
www.ijetmas.com May 2016, Volume 4, Issue 5, ISSN 2349-4476
Comparison of Open Loop and Closed Loop Quadratic Buck
Converter
R.Srikanth*, K.Pavan Kumar *, T. Rajesh *
*Assistant Professsor,VNITSW, PedaPalakaluru, Andhra Pradesh,India
ABSTRACT: This paper presents a comparison of open loop and closed loop Quadratic Buck Converter. The operation
principle of the three-phase quadratic (square) buck circuit was detailed analyzed, through which we get extensive stepdown ratio of voltage. Finally, this quadratic buck converter was simulated with openloop and closed loop using
MATLAB/Simulink. The results show that the power factor and the total harmonic distortion (THD) is good for closed
loop Quadratic buck converter compared to the openloop Quadratic buck converter.
I. INTRODUCTION
Because using the non-controlled rectifier as voltage
source of the electrical equipment, the input harmonic
current of the power supply is relatively large and the
power factor is relatively low. Along with various
electrical equipments increasing, it not only affects the
normal operation of other adjacent electric equipments,
but also increases the loss of the
transmission lines. In order to effectively reduce the
harmonic pollution caused by power supply device to AC
power grid, most of the DC voltage source uses power
factor correction technology. Meanwhile, for the
conventional buck DC/DC converter topologies, the
voltage conversion ratio is a function of duty ratio D of
the buck converter . The minimum and maximum
reachable conversion ratios are both limited by the actual
converters. In recent years, the wider conversion-ratios
have required in many industrial applications, therefore,
the AC/DC or DC/DC converters must have the ability of
operating within wider-conversion ratio that can supply
the lower or higher output voltage. For achieve this
purpose, the quadratic buck converter is a good choice.
II. THE WORKING PRINCIPLE OF THE APFC
CIRCUITS BASED ON QUADRATIC BUCK
CONVERTER
Fig.1 is a three-phase circuit diagram based on quadratic
buck converter, Va, Vb and Vc are three-phase AC
voltages, are input filter inductors, Ca, Cb and Cc are
input filter capacitors. In order to achieve high power
factor and low harmonic rectifier, it must be selected
large enough input filter inductor La, Lb and Lc to ensure
that the current remains constant in one switching cycle.
Meanwhile, it must be selected sufficiently small filter
150
R.Srikanth, K.Pavan Kumar, T. Rajesh
capacitor Ca, Cb, and Cc to ensure the circuit operating at
discontinuous voltage mode.
Taking phase „a‟ as the example, suppose that
the switching frequency is much larger than the power
frequency, the current ia through the input filter inductor
remains unchanged in one switching cycle. When switch
S is „off‟, the filter capacitor Ca is in the linear charge
state by the charge current ia. When the charge process is
over, the peak voltage across the filter capacitor Ca is
proportional to the supply voltage. When switch S is
„on‟, the filter capacitor Ca releases electrical energy to
the load R through the inductor L1 and L2, and the two
inductors are in the energy storage state. When the filter
capacitor Ca discharged to zero, the energy storied in
inductor L1 and L2 will continue to transfer the energy to
load R. When switch S is „off‟, the filter capacitor Ca is
in the linear charge state again by the charge current ia,
and the inductor L2 continues to transfer
Fig.1 Three-phase APFC Circuit based on Quadratic Buck Converter
energy to load R through the freewheeling diode D3 until
the switch S is „on‟ again. While the circuit is running in
steady state, the voltage across the filter capacitor Ca is
high frequency pulsation, and its envelope line is a
sinusoidal waveform. In any half-wave cycle, the average
voltage across the filter capacitor Ca is equal to the
International Journal of Engineering Technology, Management and Applied Sciences
www.ijetmas.com May 2016, Volume 4, Issue 5, ISSN 2349-4476
average value of a phase voltage, and its peak voltage is
proportional to the current through the circuit. When the
switching frequency is far greater than the supply power
frequency and the three-phase supply voltage is a sine
wave, the current ia, ib, and ic drawn from the power
supply by the filter capacitor is also sinusoidal, and it is
proportional to the phase voltage amplitude, so input
current and supply voltage are both sinusoidal and they
are in the same phase, so that the high power factor can
be achieved.
The three-phase APFC circuit based on quadratic buck
converter has the following three working state:
(1). State 1 ( to<t ≤D1Ts):
waveform of the voltage across capacitor Ca is also
analyzed and shown in Fig.2 .
The maximum voltage across the input filter capacitor Ca
is:
Vcom =
𝐼𝐿𝑎
𝐼 − 𝐷 𝑇𝑠
𝐶𝑎
(1)
Here ILa is the average current through the inductor La in
one switching cycle. When the circuit reaches a steady
state, the average voltage through the inductor La in one
switching cycle is zero, and the input voltage is written
as:
𝑉𝑎 =
1−𝐷 +𝐷1
𝑉𝑐𝑜𝑚 =
2
1−𝐷+𝐷1 (1−𝐷)𝑇𝑠 𝐼𝐿𝐴
2𝐶𝑎
(2)
When switch S is „on‟,D2 is the forward conduction,
input capacitor is discharged, C1 is also in the discharge
state. In this state, the voltage Vca across capacitor is
reduces to 0.
(2). State 2(D1Ts <t ≤DTs):
When switch S continues to maintain the „on‟ state, the
discharge process about the input capacitor is over, there
is no current through the input capacitance,C1 continues
to discharge.
(3). State 3(DTs <t ≤Ts):
When switch S is turned off, input capacitor begins to
charge. At t=DTs, this process is over, and get into the
next cycle.
Fig.3 The Equivalent Circuit(for phase A)
Similarly, the average voltage through the inductor L2 in
one switching cycle is zero, and the output voltage can be
derived as below:
𝐷1 𝑉 𝑐𝑂𝑚
𝑉𝑐1 =
2
=
𝐷1 (1−𝐷)𝑇𝑠 𝐼𝐿𝐴
2𝐶𝑎
(3)
From the (2) and (3), the following formula can be
derived:
𝑉𝑐1
𝑉𝑎
=
𝐷1
(4)
1−𝐷−𝐷1
and
𝐷1 =
Fig.2 Waveform of the voltage across capacitor Ca
Quadratic buck converter is a cascade
connection by two buck converter which contains two
LC filters is shown in Fig.1 expected the rectifier part. In
order to simplify the analysis, only the rectifier and the
first buck converter are analyzed here. Taking phase „a‟
as an example to analyze the working principle of the
circuit, its equivalent circuit is shown in Fig.3, and the
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R.Srikanth, K.Pavan Kumar, T. Rajesh
𝑉𝑐1
𝑉 𝑎 −𝑉 𝑐1
(1 − 𝐷)
(5)
ILa can be derived from (2) and (5):
𝐼𝐿𝑎 =
𝑉𝑎 −𝑉𝑐𝑙
(1−𝐷 )2 𝑇 𝑠
2𝐶 𝑎
(6)
From equation (6), it can be seen that when the input
voltage Va is sinusoidal, the input current is also
sinusoidal, therefore the power factor correction or high
power factor can be realized.
International Journal of Engineering Technology, Management and Applied Sciences
www.ijetmas.com May 2016, Volume 4, Issue 5, ISSN 2349-4476
III. SIMULATION AND ANALYSIS OF
QUADRATIC BUCK CONVERTER
The simulation model of 3-phase quadratic buck
converter is constructed by MATLAB/ Simulink, the
opened-loop and closed-loop simulation models are
shown in Fig.4 and Fig.9 respectively. Here, the
traditional PI control method was used in closed-loop
system.
400
350
VOLTAGE
300
250
200
150
PARAMETERS OF THREE-PHASE QUADRATIC
BUCK CONVERTER:
100
50
Parameters
Values
0
0
0.005
0.01
0.015
0.02
0.025
TIME
Voltage
(𝑉𝑎 = 𝑉𝑏 = 𝑉𝑐 )
230 Volts
Frequency
50 HZ
Inductance
(𝐿1 = 𝐿2 = 𝐿3 )
𝐿4
𝐿5
2mH
0.22mH
20𝜇H
Fig.5 Output voltage of Universal Bridge Rectifier
100
90
80
70
Capacitance
(C1 = 𝐶2 = 𝐶3 )
𝐶4
𝐶5
Voltage
60
50
40
0.2μF
19.3μF
13.4μF
30
20
10
0
Resistance (Load)
1.2Ω
Switching Frequency
50KHZ
0
0.005
0.01
0.015
0.02
Time
0.025
0.03
0.035
0.04
Fig.6 Output voltage of open-loop Quadratic Buck
Converter
Fig.4 Opened-Loop Simulation Model of 3-phase Quadratic Buck Converter
152
R.Srikanth, K.Pavan Kumar, T. Rajesh
International Journal of Engineering Technology, Management and Applied Sciences
www.ijetmas.com May 2016, Volume 4, Issue 5, ISSN 2349-4476
Fig.7 Input Current amplitude frequencies of Open-loop System
Fig.8 Waveforms of open-loop input voltage and current
Fig.9 Closed-Loop Simulation Model of 3-phase Quadratic Buck Converter
153
R.Srikanth, K.Pavan Kumar, T. Rajesh
International Journal of Engineering Technology, Management and Applied Sciences
www.ijetmas.com May 2016, Volume 4, Issue 5, ISSN 2349-4476
3
2.5
VOLTAGE
2
1.5
1
0.5
0
0
0.01
0.02
0.03
0.04
0.05
TIME
0.06
0.07
0.08
0.09
0.1
Fig.10 Output voltage of closed-loop Quadratic Buck Converter
Fig.11 Input Current amplitude frequencies of Closed-loop System
Fig.12 Waveforms of Closed-loop input voltage and current
154
R.Srikanth, K.Pavan Kumar, T. Rajesh
International Journal of Engineering Technology, Management and Applied Sciences
www.ijetmas.com May 2016, Volume 4, Issue 5, ISSN 2349-4476
In MATLAB/Simulink, power system graphical user
interface (PowerGUI), an integrated environment, is an
effective graphical user interface tool used to analyze
power system model . Within PowerGUI, the FFT tool is
used to analyze harmonic orders for the input current.
The input current harmonic orders of opened-loop and
closed-loop systems are shown in Fig.7 and Fig11,
respectively.
From the simulation results Fig.8 with Fig.12, it showed
that the input current waveform follows the input voltage
waveform, the input current phase is coincident with the
input voltage phase, and the input current waveform
basically is a sine wave in closed-loop circuit, this
simulation results verify that the above analysis is
correct.
Comparision Table:
Quadratic Buck
Converter
Open-loop
Closed-loop
Power
Factor
0.9588
0.9737
THD for input
current waveform
29.84%
23.47%
IV. CONCLUSION
This paper is analyzed the basic principle of a three
phase quadratic buck converter , and then deduced the
formula to achieve unity power factor when the circuit
operating in DCVM mode. Finally, the input voltage
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R.Srikanth, K.Pavan Kumar, T. Rajesh
and input current waveforms are obtained by using
MATLAB/Simulink, and the input current harmonics
orders are analyzed through the powerGUI/FFT
toolbox. The obtained result shows that the three
phase quadratic buck converter can achieve nearly
unity power factor and obtain wider-conversion ratio.
V. REFERENCES
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the 5th IEEE Conference on Industrial Electronics
and Applications, pp. 1082 – 1087, 2010.
[2] K. Karaket, C. Bunlaksananusorn, “Modeling of a
quadratic buckconverter”, 2011 8th International
Conference on ECTI-CON, pp. 764-767, 2011.
[3] D. Maksimovic and S. Cuk, “Switching Converters
with Wide DC Conversion Range”, IEEE Trans. on
Power Electronics, vol. 6, no. 1,pp. 151-157, Jan.
1991.
[4] Zhou Zhimin, Zhou Jihai and Ji Aihua, Design and
Application of Switching Power Supply PFC Circuit,
Beijing: Telecommuni-cations press, 2004.
[5] S. Bassan and G. Moschopoulos, “A three-phase
single-switch high power factor buck-type converter
operating with soft switching”, IEEE PESC Conf.,
pp. 3053-3059, June 2007.
[6] Guo Qiong. “Using Power Graphical User Interface
Capabilities of Matlab in Teaching of Power
Engineering”, Proceedings of Electric Power System
and Automation, vol. 16 no. 02, pp. 80-84, Feb.
2004.