Nowadays, with the widespread use of electric vehicles
and the increase in the need for energy, there are many DC-
DC converter topologies in active use. The main reason for the
increase in these structures is due to the fact that the structures
used in energy storage systems are DC. Additionally, solar
panels and electric vehicle charging stations, which are
becoming more and more common today, can be given as
examples for these. The DC-DC converter structure is used to
convert a constant DC current to an adjustable DC according
to needs. If the input voltage is lower than the output voltage,
it is called a boost converter, and if the input voltage is higher
than the output voltage, it is called a buck converter [1-5]. The
boost DC-DC converter is a popular power electronics device
with a simple low-component structure with a continuous
input current, a switch and a diode. However, this DC-DC
converter is not capable of providing a high voltage gain ratio.
The buck DC-DC converter structure is a converter structure
in which similar circuit elements are used, just like the boost
DC-DC converter structure. The main difference in this circuit
topology is the positioning of the semiconductor and passive
circuit element used in the switching. The buck DC-DC
converter is similarly incapable of providing a high voltage
gain ratio. Providing high voltage gain ratio varies depending
on the duty cycle applied to the switch. According to the ideal
voltage gain relationship of the mentioned DC-DC converter
circuit topologies, the voltage occupancy ratio should reach
infinity when the occupancy ratio reaches infinity. However,
when the duty cycle reaches infinity, it does not result in a high
value of voltage gain due to parasitic effects in the voltage
gain equation. The Cuk DC-DC converter structure is
basically similar to other topologies, but it is a topology
created by eliminating some of the disadvantages of the
amplifier topology [6]. The continuous input current in the
Amplifier and Cuk topologies helps to reduce the capacitance
value by reducing the input current stress on the capacitance.
Moreover, the Cuk topology, unlike the amplifier topology,
ensures that the output current is also continuous. Another
advantage provided by the Cuk converter structure allows it to
be used in three different operating modes; reducer, riser and
pass through. It decides in which operating mode it will work
according to the selected duty cycle. In this article, in the first
part, the DC-DC converter Cuk structure will be explained,
and the mathematical equations used in Cuk converter will be
expressed. In the second part, the modeling of the circuit
elements used in the Cuk converter structure with modified
nodal analysis (MNA) and the solution methods will be
explained. In the fourth chapter, the modeling of the circuit
structure with the package program and the comparison of the
obtained results with the modified nodal analysis (MNA)
results made in the third chapter will be made. In the final part,
conclusions and suggestions for future work will be made.
The CUK converter is a converter topology that is created
by using the above-mentioned buck and boost converter
topologies. Unlike these converter types, 2 coupled inductors
and 2 capacitors are used in this topology structure. In
addition, there are 2 semiconductor elements in the circuit
structure, one fully controlled and the other uncontrolled.
Here, it was important to take the values of the inductor acting
in conjunction with each other, which creates the
magnetomotive force that does not work like a transformer
[7]. It is known by the name of its finder, “Slobodan Cuk”.
The Cuk converter structure is actively involved in many areas
today as a field of use. These areas include various
telecommunications applications, including power supplies,
spacecraft power systems, and laptop computers. The Cuk
converter structure works differently from other PWM
converter structures and the main motivation behind the
topology is to reduce the switching losses. Figure 1 shows the
general CUK converter topology. As can be seen in the figure,
there are two modes of the circuit structure controlled by the
S1 controlled switch. These modes are called mode-1 when
the S1 switch is in the on position, and as mode-2 when the S1
switch is in the off position.
Fig. 1. CUK Converter Topology
Modeling and Analysis of DC-DC CUK Converter with Coupled
Inductors
1FATIH M. TUZTASI, 2ALI BEKIR YILDIZ, 1HASAN KELEBEK
1R&D, Inform Electronic Istanbul,TURKEY
2Electric Engineering Department Kocaeli University Kocaeli, TURKEY
Abstract: In this article, the analysis of the inductive coupled CUK topology, which is a DC-DC
converter, which is of great importance for power electronics and used in structures such as electric
vehicles and PV systems, with Modified Nodal Analysis (MNA) and the modeling of the elements in
the circuit structure will be explained. The numerical values of the semiconductors and passive circuit
elements to be modeled will be given the voltage, and current at the output will be calculated. In
addition, the graphs of the parameters analyzed and analyzed with MNA will be created with the code
system written in the MATLAB environment and will be explained in this article.
Keywords: Modified Nodal Analysis (MNA), Cuk Converter, DC-DC Converter
Received: July 24, 2021. Revised: June 28, 2022. Accepted: July 18, 2022. Published: August 5, 2022.
1. Introduction
2. The Explanation of DC- DC Cuk
Converter with Coupled
Inductors Topology
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Unlike many other DC-DC converter structures, it is the
use of capacity instead of inductor in energy storage. The
capacitor C1 in the circuit structure mediates the energy
transfer from the source to the load. [8]. The mode-1 structure
of the CUK converter is explained in figure 2.
Fig. 2. CUK Converter Mode-1
In the Mode-1 circuit structure, the Q1 switch is turned on.
The energy of inductor L1 increases in period T. Meanwhile,
the C1 capacitance both charges the C2 capacitance and
increases the energy of the L2 inductor via the Q1 switch. In
addition to these, these passive circuit elements also feed the
load.
Fig. 3. CUK Converter Mode-2
In the Mode-2 circuit structure, the Q1 switch is cut off.
The diode, which is an uncontrolled switch, turns on. Source
Vs is increasing the energy of inductor L1 while charging the
capacitance C1. The L2 inductor feeds the load and its energy
decreases. This structure is explained in figure 3.
2.1. General Equations
Due to the fact that DC-DC converters, which are
frequently used today, provide convenience in practical
calculations in general, their equations have been created
depending on certain parameters. The expression of the duty
cycle of the switches in the power electronics circuits is given
in this circuit structure. [9-11]
Also, equations such as ripple current on the input
inductor, output voltage ripple, duty cycle will be given in this
article.
Duty Cycle:
(1)
Output Voltage Ripple:
(2)
Input Inductor Ripple Current:
(3)
The state space model and modified nodal analysis (MNA)
are two often utilized methodologies for system modelling and
equations. The State space method, which is based on the
graph theory, is used in the analysis of simple circuits, it
facilitates the solution, yet requires very difficult and intensive
operations in obtaining the equations. Despite the fact that the
modified nodal analysis model has a large number of
operations and unknowns, the equations are very simple to
derive.[12] In this study, the solution of DC to DC Cuk
topology with modified nodal analysis (MNA) will be given.
Modified Nodal Analysis (MNA) can be expressed in the time
and Laplace domain as follows:
(4)
(5)
In the specified coefficient matrices, the frequency-
independent elements are represented in the G matrix. The C
matrix describe the circuit elements associated with
frequency, while the voltage and current sources connected to
the circuit are expressed in the B matrix.
In this study, MOSFET and diode semiconductors, one of
which is a fully controlled and the other an uncontrolled
switch, in a power electronics circuit will be modeled with a
bivalent resistor element.
Fig. 4. The modeling of the Mod-1
3. System Equations and Swicth Modelling
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The modeling of the switch with a resistor is shown in
Figure 4, and the , uncontrolled switch, is in cutoff.
switch is expressed as .
Fig. 5. The modeling of the Mod-2
The modeling of the , uncontrolled switch, with a
resistor is shown in Figure 5, and the switch is in
cutoff. key is denoted as .
Fig. 6. Presantation of Nodal Voltage
DC-DC Cuk converter circuit structure can basically be
examined in cases [1]. However, due to topology,
only the two modes conduct diode cut-off and
diode conduct switch cut-off status, which are two modes
in which the switches work opposite each other, will be
examined. The equation structures formed according to these
situations are given below.
When the switch is in the conduction state:
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Given equation 11 and 12 is valid for all cases. Using these
equations MNA matrix can be written as follows:
(13)
CA1=
(14)
(15)
When the diode is in the conduction state:
(16)
(17)
(18)
(19)
(20)
MNA matrix can be specified as below based on these
equations:
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(21)
CA1=
(22)
(23)
(24)
The B.Euler method is applied in order to apply the
numerical solution of the DC-DC Cuk Converter whose
equations are obtained above. The general expression of the
B.Euler method, h being the step interval;
(25)
(26)
Equation (19) is obtained by substituting the structure formed
in equation (17) in equation (18).
(19)
Numerical solution was obtained with the values given in
Table-1 below, and the code generated on MATLAB. It is also
supported by the graphics of the numerical solution.
Table 1 Design Parameter
Type
Values
Unit
L1
180
µH
L2
150
µH
M
1
µH
C1
200
µF
C2
220
µF
E
12
V
4
Ω
Ω
Ω
Ω
Ω
Fig. 7. Output Voltage
Fig. 8. Inductor Current
4. Applying the B.euler Method to
Modified Nodal Analysis
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Fig. 9. Inductor Current
In this research, DC-DC CUK converter analysis of
Modified Nodal Analysis (MNA) was performed. The stages
of obtaining the equations illustrates the superiority and ease
of the method. The switches in the converter are modeled with
the concept of the bivalent resistor element. The B. Euler
method, which is one of the numerical solution methods, was
applied to the system equations in the MATLAB and the
results of the analysis were presented with graphics.
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5. Conclusion and Future Works
References
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DOI: 10.37394/23201.2022.21.21
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Policy)
The authors equally contributed in the present
research, at all stages from the formulation of the
problem to the final findings and solution.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
No funding was received for conducting this study.
Conflict of Interest
The authors have no conflicts of interest to declare
that are relevant to the content of this article.
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