# New Multiphase Hybrid Boost Converter with Wide Conversion Ratio for PV System

Authors: Ioana-Monica Pop-Calimanu; Folker Renken
Journal: International Journal of Photoenergy
 (2014)

---

## Abstract

A new multiphase hybrid boost converter, with wide conversion ratio as a solution for photovoltaic energy system, is presented in this paper. To ensure that all the phases of the converter operate at the same switching frequency we use interleaving topology. The proposed converter can be used as an interface between the PV system and the DC load/inverter. This multiphase converter has the advantage of reduced value and physical size of the input and output capacitor as well as the effort for the inductors. To validate the operation of the converter we provide the analyses and the simulation results of the converter.


---

## Body

## 1. Introduction

Photovoltaic (PV) energy has attracted interest as an energy source capable of solving the problems of the energy crisis. Solar PV energy is becoming an increasingly important part of the renewable energy resources. It is considered one of the most promising energy resources due to its infinite power delivered directly for free, and many other advantages. These include reliability, availability, zero pollution or destruction of the land, reasonable installation and production cost, long life-span, and the capability of supporting microgrid systems and connecting to electrical grids [1–5]. One of the challenges in the case of grid connection applications or high voltage DC applications requirements is the low voltage of the PV module. For this reason, many PV modules should be either connected in series to meet these application requirements, or to use a step-up DC/DC converter. This type of converter is widely used in PV systems. Theoretically, a traditional step-up converter can achieve a high step-up voltage gain with an extremely high duty ratio near to 100% [6]. The step-up voltage gain in practice is limited due to the effect of power switches, rectifier diodes, the equivalent series resistance of inductors and capacitors, and the saturation effects of the inductors and capacitors [7]. Due to the fact that these traditional converters are not able to operate with a high duty ratio near to 100%, which also yields in a very low efficiency, scientific literature presents many topologies [8–11] that provide a high step-up voltage gain without an extremely high duty ratio. A very good review of nonisolated high step-up DC/DC converters used in renewable energy applications is presented in [12, 13], where the advantages and disadvantages of these converters and the major challenges are summarized. In [14] the architecture of a high step-up converter, which contains seven parts including a PV module input circuit, a primary-side circuit, a secondary-side circuit, a passive regenerative snubber circuit, a filter circuit, a DC output circuit, and a feedback control mechanism, is presented. The authors from [14], for raising the voltage gain, are using a coupled inductor with a low-voltage rated switch. In [15] three types of step-up converters with high-efficiency by using PV system with reduced diode stresses sharing are proposed. Through the employ of coupled inductor and switched capacitor, the proposed converters attain high step-up conversion ratio without operating at extreme duty ratio. Very often in the literature is presented high step-up DC/DC converter that utilizes at least one coupled inductor. One of these structures is presented in [16] where the operating principle and steady state analyses are discussed in detail, and a prototype of the circuit is implemented. Another configuration of step-up converter with coupled inductor is presented in [17]. This converter achieves a high step-up voltage conversion ratio, without extreme duty ratios and the numerous turn’s ratios of a coupled inductor. The leakage inductor energy of the coupled inductor is efficiently recycled to the load. Other high step-up DC/DC converters with coupled inductor are presented in [18–21].In this paper is presented and analysed the structures of the step-up hybrid boost converter [7, 22], or as named in some papers switched inductor boost type.One of the main disadvantages of this circuit is that the effort for the input and output capacitor, in the case of a single-phase DC/DC converter is very high. This is the same with the effort of the inductors. Based on the structure of the hybrid boost converter built in multiphase design, we present a method for reducing this disadvantage through a new multiphase hybrid boost converter.


## 2. Single-Phase Hybrid Boost Converter

Figure1 shows the step-up hybrid boost converter which was introduced in [22]. The hybrid boost DC/DC converter consists of a classical boost converter in which is inserted an L-switching structure. The L-switching structure consists of two inductors and three diodes. We can simply say that the input inductor from a classical boost converter was replaced by the two inductors in the new hybrid converter. This type of converter provides high gain and high efficiency and is used for many applications such as solar cell energy conversion systems [7], fuel cell energy conversion systems, battery back-up systems for uninterruptible power supplies, and high intensity discharge lamp ballast for automobile head lamps [23].Figure 1
Single-phase hybrid boost DC/DC converter.The gain of the hybrid boost converter is higher than the traditional boost converter by a factor of(
d
+
1
). Figure 2 shows a comparison between the gain of the hybrid boost converter and the traditional boost converter.Figure 2
Conversion ratio of a hybrid boost and traditional boost DC/DC converter.To ensure a better understanding, this section continues by presenting and discussing the power part of the hybrid converter, which is presented in Figure3.Figure 3
Single-phase hybrid boost DC/DC converter.The power part consists of an input network with two inductors and three diodes, a step-up circuit with the power switchS and diode DO, as well as a DC-link capacitor at the input and output side of the converter. Based only on the circuit structure, we can observe that the energy can be transferred only in one direction from input to output.For operation of the converter we use a pulse control method. Figure4 shows the current flow in the circuit in the switched-on and the switched-off state.Figure 4
Current flow in switched-on and switched-off state of the hybrid boost DC/DC converter.In the switched-on state the inductors are connected in parallel and the current of both inductors flows in the input phase and in the switch element. For this reason during the switched-on state the current in the output phasei
OP is zero (Figure 8). In the switched-off state the inductance current flows in series through the inductors and the output diode. In this moment the inductors are connected in series, while the input phase current i
IP and output phase current i
OP are the same as the inductor current. The expectation being that only the average value of the input phase current would flow in the converter input current, I
In
⁡, while the AC-current component would flow in to the capacitor C
I and the average value of the output phase current would flow in the converter output I
Out.For calculations, we assumed that all elements of the converter would work without losses, the voltage and currents at the input and output were ideally DC-values, and the converter would be controlled with pulse width modulation [24]. With these requirements in the converter switching states, the voltage at the inductors can be determined by applying the voltage-second balance on the inductor as follows:
(1)
t
on
⁡
:
u
L
=
U
In
⁡
,
t
off
⁡
:
u
L
=
-
U
Out
-
U
In
⁡
2
,
where u
L is the inductor voltage, U
In
⁡ is the input voltage, and U
Out is the output voltage.As we can see from the above formulas, the voltage at the inductors is positive in the switched-on state and negative in the switched-off state. In circuit operation the positive and negative voltage-time-area at the inductors must always be the same. With this condition the conversion ratio of the hybrid boost DC/DC converter can be calculated. Consider(2)
U
Out
=
1
+
d
1
-
d
·
U
In
⁡
with
d
=
t
on
⁡
T
P
,
1
-
d
=
t
off
⁡
T
P
.


### 2.1. DC/DC Converter Input Circuit

In Figure5 the current waveforms at the input of the hybrid boost converter is presented. The first waveform shows the currents in both inductors, and we can see that they are the same. The inductor current rises in switched-on state and fall in switched-off state, so that a triangular shape current is generated. The middle waveform presents the input phase current i
IP, and the lower waveform presents the input capacitor current i
IC.Figure 5
Current waveforms at the input of a single-phase hybrid boost DC/DC converter(
d
=
0.3
).The average currentI
L
AV depends on the duty cycle d. Consider
(3)
I
L
AV
=
I
In
⁡
1
+
d
.In order to calculate the required inductance and capacitance in the circuit we needed to fix conditions for the circuit operation. We first needed to know the rated output voltage, as well as the minimal input voltage at rated power which should be transferred. With these conditions the conversion ratio of the circuit for rated input powerP
In
⁡
⁡
R transfer is fixed.In this operation point the DC-input current and the average currentI
L
AV in the inductors can be calculated. It is assumed that this average current I
L
AV is the maximum DC-value in the inductances. Figure 6 shows the possible power transfer dependent on the duty cycle for three different converter designs. The inductivity must be calculated for the maximum inductor voltage-time-area within the pulse periods and the maximum acceptable current variation during this time. In the switched-on state t
on
⁡, the input voltage U
In
⁡ is connected at the inductors. The voltage U
In
⁡ is described in formula (5) as a function of the output voltage and the duty cycle. Consider
(4)
L
1
=
L
2
=
U
In
⁡
·
t
on
⁡
Δ
i
L
,
(5)
L
1
=
L
2
=
U
Out
·
T
P
Δ
i
L
·
d
·
(
1
-
d
)
1
+
d
.Figure 6
Maximum power transfer in case of fixed output voltage.Considering the full duty cycle range, the voltage-time-area within the pulse periods reaches its maximum for a duty cycle of approximately 41%. For this duty cycle in general the converter inductance is specified. The maximum acceptable current variationΔ
i
L
max
⁡ is chosen normally between 10% and 30% of the rated average inductance current I
L
AV
R. These inductances can be realized as individual or mutual coupled inductances.                               (6)
L
1
=
L
2
=
U
Out
·
T
P
Δ
i
L
max
⁡
·
(
3
-
2
·
2
)
with
Δ
i
L
max
⁡
=
(
0.1
–
0.3
)
·
I
L
AV
R
.We continue with the calculation of the capacity of the input side. We begin with the worst case scenario which could happen when the converter input current is an ideally average value and the overall AC-current of the input phase flows in the capacitor (see Figure4). This AC-current in the capacitor produces an AC-voltage at the input that is overlaid with the DC-input voltage. For this reason the maximum acceptable voltage variation at the capacitor must be chosen during the capacity dimension. Consider
(7)
C
I
=
i
C
·
t
on
⁡
Δ
u
C
,
C
I
=
I
L
AV
·
T
P
Δ
u
In max
·
d
·
(
1
-
d
)
.The current-time-area depends on the duty cycle having its maximum at 50% and at the rated inductance currentI
L
AV. In practice, the acceptable static voltage variation at the converter input is chosen smaller than 1% of the rated input voltage U
In
⁡
⁡
R.
(8)
C
I
=
I
L
AV
R
·
T
P
4
·
Δ
u
In
⁡
⁡
max
⁡
with
Δ
u
In
⁡
⁡
max
⁡
≤
0.01
·
U
In
⁡
⁡
R
.In the input of the DC/DC converters, electrolytic capacitors are often used [25]. The main design criteria for these capacitors are the RMS current loads. The RMS current in the input capacitor is calculated as a function of the duty cycle for an average inductance current I
L
AV and a maximum current variation Δ
i
L
max. Consider
(9)
I
IC
=
I
L
AV
·
d
·
(
1
-
d
)
+
(
Δ
i
L
max
I
L
AV
)
2
·
d
2
·
(
1
-
d
)
2
·
(
1
+
3
·
d
)
12
·
(
1
+
d
)
2
·
(
3
-
2
·
2
)
.The result can be split into two. One is dependent on the average currentI
L
AV and the other is dependent on the triangle current variation in the inductances. In Figure 7, the current in the RMS capacitor is shown. The maximum value of the capacitor current is higher than the half average inductance current I
L
AV. The current variation has, however, only a small influence on the total RMS current in the capacitor.Figure 7
RMS current in the input capacitors of a single-phase hybrid boost DC/DC converter.Figure 8
Current waveforms at the output of a single-phase hybrid boost DC/DC converter(
d
=
0.3
).


### 2.2. DC/DC Converter Output Circuit

Figure8 shows the current and voltage waveforms at the output of the hybrid boost DC/DC converter.The first waveform in Figure8 shows the current in both inductors. The middle waveform presents the output phase current i
OP. The lower waveform shows the AC-current in the output capacitor. This current can be calculated by subtraction of output phase current i
OP and output current I
Out.We continue with the calculation for the capacity of the output side. We begin with the worst case scenario which would happen when the converter output current is an ideally average value and the overall AC component of the output phase current flows in the capacitor (see Figure8). This AC-current in the capacitor produces an AC-voltage at the output that is overlaid with the DC-output voltage. For this reason the maximum acceptable voltage variation at the capacitor must be chosen during the capacity dimension. The current-time-area in the capacitor within the pulse periods can be described as a function of the output current and the duty cycle. Consider
(10)
C
O
=
I
Out
·
T
P
Δ
u
Out
max
⁡
·
d
,
C
O
=
I
L
AV
·
T
P
Δ
u
Out
max
⁡
·
d
·
(
1
-
d
)
.The current-time-area depends on the duty cycle with its maximum at 50% and at rated inductance currentI
L
AV. In practice, the acceptable static voltage variation is chosen smaller than 1% of the nominal output voltage U
Out. Consider
(11)
C
O
=
I
L
AV
R
·
T
P
4
·
Δ
u
Out
max
⁡
with
Δ
u
Out
max
⁡
≤
0.01
·
U
Out
R
.Also on the output side of the hybrid boost converters, electrolytic capacitors are often used. For design of the capacitors, the RMS current in the output must be calculated. In the next formula the RMS current is determined as a function of the duty cycle for an average inductance currentI
L
AV and a maximum inductance current variation Δ
i
L
max
⁡. Consider
(12)
I
OC
=
I
L
AV
·
d
·
(
1
-
d
)
+
(
Δ
i
L
max
I
L
AV
)
2
·
d
2
·
(
1
-
d
)
3
12
·
(
1
+
d
)
2
·
(
3
-
2
·
2
)
.The result can also be split into two: one is dependent on the average inductor currentI
L
AV, and the other is dependent on the triangle current variation in the inductances. In Figure 9, the current in the RMS capacitor is shown. The maximum value is more than the half average inductance current I
L
AV. The current variation also has only a small influence on the total RMS current in the capacitor.Figure 9
RMS current in the output capacitors of a single-phase hybrid boost DC/DC converter.The effort for the input and output capacitor in the case of a single-phase DC/DC converter is very high. In the next section a method for reducing the capacitor currents is presented. With this method, the effort for the inductors can also be reduced.


## 2.1. DC/DC Converter Input Circuit

In Figure5 the current waveforms at the input of the hybrid boost converter is presented. The first waveform shows the currents in both inductors, and we can see that they are the same. The inductor current rises in switched-on state and fall in switched-off state, so that a triangular shape current is generated. The middle waveform presents the input phase current i
IP, and the lower waveform presents the input capacitor current i
IC.Figure 5
Current waveforms at the input of a single-phase hybrid boost DC/DC converter(
d
=
0.3
).The average currentI
L
AV depends on the duty cycle d. Consider
(3)
I
L
AV
=
I
In
⁡
1
+
d
.In order to calculate the required inductance and capacitance in the circuit we needed to fix conditions for the circuit operation. We first needed to know the rated output voltage, as well as the minimal input voltage at rated power which should be transferred. With these conditions the conversion ratio of the circuit for rated input powerP
In
⁡
⁡
R transfer is fixed.In this operation point the DC-input current and the average currentI
L
AV in the inductors can be calculated. It is assumed that this average current I
L
AV is the maximum DC-value in the inductances. Figure 6 shows the possible power transfer dependent on the duty cycle for three different converter designs. The inductivity must be calculated for the maximum inductor voltage-time-area within the pulse periods and the maximum acceptable current variation during this time. In the switched-on state t
on
⁡, the input voltage U
In
⁡ is connected at the inductors. The voltage U
In
⁡ is described in formula (5) as a function of the output voltage and the duty cycle. Consider
(4)
L
1
=
L
2
=
U
In
⁡
·
t
on
⁡
Δ
i
L
,
(5)
L
1
=
L
2
=
U
Out
·
T
P
Δ
i
L
·
d
·
(
1
-
d
)
1
+
d
.Figure 6
Maximum power transfer in case of fixed output voltage.Considering the full duty cycle range, the voltage-time-area within the pulse periods reaches its maximum for a duty cycle of approximately 41%. For this duty cycle in general the converter inductance is specified. The maximum acceptable current variationΔ
i
L
max
⁡ is chosen normally between 10% and 30% of the rated average inductance current I
L
AV
R. These inductances can be realized as individual or mutual coupled inductances.                               (6)
L
1
=
L
2
=
U
Out
·
T
P
Δ
i
L
max
⁡
·
(
3
-
2
·
2
)
with
Δ
i
L
max
⁡
=
(
0.1
–
0.3
)
·
I
L
AV
R
.We continue with the calculation of the capacity of the input side. We begin with the worst case scenario which could happen when the converter input current is an ideally average value and the overall AC-current of the input phase flows in the capacitor (see Figure4). This AC-current in the capacitor produces an AC-voltage at the input that is overlaid with the DC-input voltage. For this reason the maximum acceptable voltage variation at the capacitor must be chosen during the capacity dimension. Consider
(7)
C
I
=
i
C
·
t
on
⁡
Δ
u
C
,
C
I
=
I
L
AV
·
T
P
Δ
u
In max
·
d
·
(
1
-
d
)
.The current-time-area depends on the duty cycle having its maximum at 50% and at the rated inductance currentI
L
AV. In practice, the acceptable static voltage variation at the converter input is chosen smaller than 1% of the rated input voltage U
In
⁡
⁡
R.
(8)
C
I
=
I
L
AV
R
·
T
P
4
·
Δ
u
In
⁡
⁡
max
⁡
with
Δ
u
In
⁡
⁡
max
⁡
≤
0.01
·
U
In
⁡
⁡
R
.In the input of the DC/DC converters, electrolytic capacitors are often used [25]. The main design criteria for these capacitors are the RMS current loads. The RMS current in the input capacitor is calculated as a function of the duty cycle for an average inductance current I
L
AV and a maximum current variation Δ
i
L
max. Consider
(9)
I
IC
=
I
L
AV
·
d
·
(
1
-
d
)
+
(
Δ
i
L
max
I
L
AV
)
2
·
d
2
·
(
1
-
d
)
2
·
(
1
+
3
·
d
)
12
·
(
1
+
d
)
2
·
(
3
-
2
·
2
)
.The result can be split into two. One is dependent on the average currentI
L
AV and the other is dependent on the triangle current variation in the inductances. In Figure 7, the current in the RMS capacitor is shown. The maximum value of the capacitor current is higher than the half average inductance current I
L
AV. The current variation has, however, only a small influence on the total RMS current in the capacitor.Figure 7
RMS current in the input capacitors of a single-phase hybrid boost DC/DC converter.Figure 8
Current waveforms at the output of a single-phase hybrid boost DC/DC converter(
d
=
0.3
).


## 2.2. DC/DC Converter Output Circuit

Figure8 shows the current and voltage waveforms at the output of the hybrid boost DC/DC converter.The first waveform in Figure8 shows the current in both inductors. The middle waveform presents the output phase current i
OP. The lower waveform shows the AC-current in the output capacitor. This current can be calculated by subtraction of output phase current i
OP and output current I
Out.We continue with the calculation for the capacity of the output side. We begin with the worst case scenario which would happen when the converter output current is an ideally average value and the overall AC component of the output phase current flows in the capacitor (see Figure8). This AC-current in the capacitor produces an AC-voltage at the output that is overlaid with the DC-output voltage. For this reason the maximum acceptable voltage variation at the capacitor must be chosen during the capacity dimension. The current-time-area in the capacitor within the pulse periods can be described as a function of the output current and the duty cycle. Consider
(10)
C
O
=
I
Out
·
T
P
Δ
u
Out
max
⁡
·
d
,
C
O
=
I
L
AV
·
T
P
Δ
u
Out
max
⁡
·
d
·
(
1
-
d
)
.The current-time-area depends on the duty cycle with its maximum at 50% and at rated inductance currentI
L
AV. In practice, the acceptable static voltage variation is chosen smaller than 1% of the nominal output voltage U
Out. Consider
(11)
C
O
=
I
L
AV
R
·
T
P
4
·
Δ
u
Out
max
⁡
with
Δ
u
Out
max
⁡
≤
0.01
·
U
Out
R
.Also on the output side of the hybrid boost converters, electrolytic capacitors are often used. For design of the capacitors, the RMS current in the output must be calculated. In the next formula the RMS current is determined as a function of the duty cycle for an average inductance currentI
L
AV and a maximum inductance current variation Δ
i
L
max
⁡. Consider
(12)
I
OC
=
I
L
AV
·
d
·
(
1
-
d
)
+
(
Δ
i
L
max
I
L
AV
)
2
·
d
2
·
(
1
-
d
)
3
12
·
(
1
+
d
)
2
·
(
3
-
2
·
2
)
.The result can also be split into two: one is dependent on the average inductor currentI
L
AV, and the other is dependent on the triangle current variation in the inductances. In Figure 9, the current in the RMS capacitor is shown. The maximum value is more than the half average inductance current I
L
AV. The current variation also has only a small influence on the total RMS current in the capacitor.Figure 9
RMS current in the output capacitors of a single-phase hybrid boost DC/DC converter.The effort for the input and output capacitor in the case of a single-phase DC/DC converter is very high. In the next section a method for reducing the capacitor currents is presented. With this method, the effort for the inductors can also be reduced.


## 3. Multiphase DC/DC Converter

Several solutions and their control were presented in the literature for interconnection of the converters [26–32]. Multiphase configuration is one of them [33–35]. Although the physical connection of the multiphase looks exactly the same like parallel connection, the main difference between them is the method of how they time/control their main switches. The parallel configuration is operated by having the switching signals for main switches coincide with each other (e.g., when switch from first power converter turns on, so does the switch from the second power converter and vice versa). The main advantage of parallel configuration is that the control circuit must only provide a single switching signal.In multiphase converter each switch operates at a different time with a phase shift between the switch gate drivers [36] but with common frequency. The result of the phase delay allows multiphase configurations to exhibit higher overall efficiency due to ripple cancelation, smaller output filter requirements, and smaller output voltage ripple [37–40]. The output voltage ripple is reduced because the output frequency is increased by the number of phase times of the individual switch frequency. Higher output frequency makes the output ripple easier to filter which allows smaller components and further increase in efficiency [36]. In [41] is presented another two-phase boost converter topology, which due to the fact that the multiphase configuration, at the output the circuit, will have just a single capacitor and the output voltage will have ripple component twice the operating switching frequency of each individual boost converter. The frequency multiplication effect also occurs at the input side of the converter and will reduce the input filters and will improve the quality of the input current [41].The hybrid boost DC/DC converter presented in this paper can also be built in multiphase design. Therefore the different phases are connected at a common input and output capacitor. The total current is subdivided in the different phases. By interleaving switching topology the AC-currents in the inputC
I and output capacitor C
O can be reduced clearly. In addition the frequency of the capacitor currents is increased. With suitable circuit design the effort of the inductances can be decreased. Figure 10 shows a DC/DC converter in two-phase design.Figure 10
Two-phase hybrid boost DC/DC converter.


### 3.1. DC/DC Converter Input Circuit

In Figure11 the current waveforms at the input of a two-phase hybrid boost converter are shown. First, the currents in both inductances and the input current of phase one are shown. Represented underneath in green are the same currents of phase two. The triangle shaped inductance currents of the two phases are shifted with about a half pulse period. At switched-on time the input current of each phase is twice as small as the inductance current from a single-phase converter. But in this circuit the overall input phase current I
IP consists of the sum of all the input phase currents. The overall input phase current I
IP, with the DC-component I
In
⁡ is shown in Figure 11. Also for this circuit it is assumed that only the DC-current is flowing in the circuit input. With these conditions, for multiphase converters, the function between the input current I
In
⁡ and the average inductance current of the individual phases I
L
n
AV can be calculated. Consider
(13)
I
L
n
AV
=
I
In
⁡
n
·
(
1
+
d
)
.Figure 11
Current waveforms at the input of a two-phase hybrid boost DC/DC converter(
n
=
2, d
=
0.3
).The total AC-component of the overall input phase currentI
IP flows in the input capacitor (Figure 11). This current is clearly smaller in comparison to a single-phase hybrid boost converter. In addition, the frequency of the capacitor current is doubled. For these reasons the filter effort is reduced.We continue with the calculation of the inductances and capacitors of a multiphase hybrid boost converter. The same technical conditions for a single-phase converter are applied and the calculation of inductances for ann-phase design can be accomplished in the same way as for single-phase circuits. Taking into account the input current which is subdivided into the different phases, the maximum current variation in the inductances must be based on the maximum DC-current at rated power in the individual phases. For design, the maximum current variation is selected between 10% and 30% of the phase DC-current in the inductances at rated power. Consider
(14)
L
1
n
=
L
2
n
=
U
Out
·
T
P
Δ
i
L
n
max
⁡
·
(
3
-
2
·
2
)
with
Δ
i
L
n
max
⁡
=
(
0.1
–
0.3
)
·
I
L
n
AV
R
.The amplitude of the triangle current variation in the inductors is dependent on the duty cycle of the converter. Because the duty cycle in all phases has the same value, the current variations in all inductors are equivalent. Consider(15)
Δ
i
L
n
=
(
d
)
·
(
1
-
d
)
(
1
+
d
)
·
(
3
-
2
·
2
)
·
Δ
i
L
n
max
⁡
.The necessary input capacity of the multiphase hybrid boost converter will now be calculated. Compared to a single-phase design, the capacitor current is reduced and the current frequency is increased by the number of phases. As a consequence the current in the capacitor has a voltage variation at the input. For the capacitor design, the permissible static voltage variation in general is selected smaller than 1% of the rated input voltage. Consider(16)
C
I
=
T
P
·
I
L
n
AV
4
·
n
·
Δ
u
In
⁡
⁡
max
⁡
with
Δ
u
In
⁡
⁡
max
⁡
≤
0.01
·
u
In
⁡
⁡
R
.In these DC/DC converters, electrolytic capacitors are used often. A main design criterion of these capacitors is the RMS current load. For this reason, for multiphase DC/DC converters the RMS current in the input capacitorC
I will be calculated. Therefore the switching processes in the phases are assumed as ideal. Moreover, it is accepted that the current in the input is an ideal DC-current. The worst case scenario will happen when the capacitor is loaded with the total AC-current component.The input capacitor current for two-phase converters is represented in Figure12. In the case of closer inspection the capacitor current can be split into two different components: a rectangle part and a triangle part. The RMS current of these two components has been calculated. The RMS result of the rectangle portion for multiphase converters is shown in the formula below:
(17)
I
IC
Π
=
|
I
L
n
AV
2
·
n
2
·
(
d
-
0
n
)
·
(
1
n
-
d
)
if
0
n
≤
d
≤
1
n
I
L
n
AV
2
·
n
2
·
(
d
-
1
n
)
·
(
2
n
-
d
)
if
1
n
≤
d
≤
2
n
I
L
n
AV
2
·
n
2
·
(
d
-
2
n
)
·
(
3
n
-
d
)
if
2
n
≤
d
≤
3
n
⋮
⋮
I
L
n
AV
2
·
n
2
·
(
d
-
n
-
1
n
)
·
(
n
n
-
d
)
if
n
-
1
n
≤
d
≤
n
n
.Figure 12
RMS current in the input capacitors of a one-, two-, and three-phase hybrid boost DC/DC converter.In this formula it is necessary to consider that the average inductance currentI
L
n
AV becomes smaller with an increasing number of phases. For example, the average inductance current I
L
n
AV in a two-phase converter is only half as big as in a single-phase converter. With this fact in mind the rectangle component of the input capacitor current can clearly be reduced with a multiphase design.In addition, the RMS current of the triangle has been calculated. The next formula shows the RMS results for a multiphase circuit design. Consider(18)
I
IC
Δ
=
|
Δ
i
L
n
max
⁡
2
·
n
·
[
[
2
-
(
n
+
1
)
·
d
]
2
·
(
d
-
0
/
n
)
3
+
[
0
-
(
n
+
0
)
·
d
]
2
·
(
1
/
n
-
d
)
3
]
12
·
(
3
-
2
·
2
)
2
·
(
1
+
d
)
2
if
0
n
≤
d
≤
1
n
Δ
i
L
n
max
⁡
2
·
n
·
[
[
4
-
(
n
+
2
)
·
d
]
2
·
(
d
-
1
/
n
)
3
+
[
2
-
(
n
+
1
)
·
d
]
2
·
(
2
/
n
-
d
)
3
]
12
·
(
3
-
2
·
2
)
2
·
(
1
+
d
)
2
if
1
n
≤
d
≤
2
n
Δ
i
L
n
max
⁡
2
·
n
·
[
[
6
-
(
n
+
3
)
·
d
]
2
·
(
d
-
2
/
n
)
3
+
[
4
-
(
n
+
2
)
·
d
]
2
·
(
3
/
n
-
d
)
3
]
12
·
(
3
-
2
·
2
)
2
·
(
1
+
d
)
2
if
2
n
≤
d
≤
3
n
⋮
⋮
Δ
i
L
n
max
⁡
2
·
n
·
[
[
2
·
n
-
(
n
+
n
)
·
d
]
2
·
(
d
-
(
n
-
1
)
/
n
)
3
+
[
(
2
·
n
-
2
)
-
(
n
+
n
-
1
)
·
d
]
2
·
(
n
/
n
-
d
)
3
]
12
·
(
3
-
2
·
2
)
2
·
(
1
+
d
)
2
if
n
-
1
n
≤
d
≤
n
n
.The current variationΔ
i
L
n
max in this formula is selected in relation to the rated average inductance current I
L
n
AV during the circuit dimension. This will mean that with the same circuit dimension and increasing number of phases, the current variation is reduced.The geometrical addition of rectangle and triangle RMS components results in the total capacitor current for ann-phase hybrid boost DC/DC converter. Consider
(19)
I
IC
=
I
IC
Π
2
+
I
IC
Δ
2
.Figure12 shows the RMS current in the input capacitors of multiphase DC/DC converters. The current load of the capacitor decreases with the increasing number of phases. The influence of the rectangle RMS component is clearly dominant (dotted lines, i
L
n
max
=
0). The maximum capacitor current component produced from the rectangle portion is smaller by a factor of 1
/
n for n-phase converters. The triangle capacitor current is not dependent on the converter power and has, for all loads, the same value. In case of rated power the additional load from the triangle current in the capacitors is small.


### 3.2. DC/DC Converter Output Circuit

Figure13 shows the current waveforms at the output of a two-phase hybrid boost DC/DC converter. First, the currents in both inductors and the output current of phase 1 are represented. In the middle the current of phase 2 is shown. The triangle inductance current of the two phases is shifted within about a half pulse period of each other. At switched-off times, the inductors are connected in series and the current flows to the output phase, just as in a single-phase converter. However, in this circuit, the overall output phase current I
OP consists of the sum of all the output phase currents. The overall output phase current I
OP with the DC-component I
Out is shown Figure 13. It is assumed that only the DC-current is flowing in the circuit output; the total AC-component of the overall output phase current I
OP flows in the output capacitor. In comparison to a single-phase hybrid boost converter this current is clearly smaller. In addition, the frequency of the capacitor current has been doubled.Figure 13
Current waveforms at the output of the two-phase hybrid boost DC/DC converter(
n
=
2, d
=
0.3
).The necessary output capacity of the multiphase hybrid boost converter will next be calculated. Compared to a single-phase design, the output capacitor current is reduced and the current frequency is increased by the number of phases. As a consequence the current in the capacitor has a voltage variation at the output. For the capacitor design the permissible static voltage variation in general is selected at less than 1% of the rated output voltage. Consider(20)
C
O
=
T
P
·
I
L
n
AV
4
·
n
·
Δ
u
Out
max
⁡
with
Δ
u
Out
max
⁡
≤
0.01
·
u
Out
R
.The RMS current in the output capacitorC
O will next be calculated for multiphase hybrid boost DC/DC converters. The output capacitor current for a two-phase converter is represented in Figure 13. Like the input capacitor, the output capacitor current can also be split into a rectangle and a triangle component. The RMS current of the rectangle portion for multiphase converters is shown in the formula below:
(21)
I
OC
Π
=
|
I
L
n
AV
2
·
n
2
·
(
d
-
0
n
)
·
(
1
n
-
d
)
if
0
n
≤
d
≤
1
n
I
L
n
AV
2
·
n
2
·
(
d
-
1
n
)
·
(
2
n
-
d
)
if
1
n
≤
d
≤
2
n
I
L
n
AV
2
·
n
2
·
(
d
-
2
n
)
·
(
3
n
-
d
)
if
2
n
≤
d
≤
3
n
⋮
⋮
I
L
n
AV
2
·
n
2
·
(
d
-
n
-
1
n
)
·
(
n
n
-
d
)
if
n
-
1
n
≤
d
≤
n
nThe output capacitor RMS current, that is, produced by the rectangle component is exactly the same as that in the input capacitor. It is necessary to also consider that the average inductance currentI
L
n
AV becomes smaller with the increasing number of phases. The next formula shows the output capacitor RMS component produced by the triangle part of multiphase converters. Consider
(22)
I
OC
Δ
=
|
Δ
i
L
n
max
⁡
2
·
n
·
d
2
·
[
(
n
-
1
)
2
·
(
d
-
0
/
n
)
3
+
(
n
-
0
)
2
·
(
1
/
n
-
d
)
3
]
12
·
(
3
-
2
·
2
)
2
·
(
1
+
d
)
2
if
0
n
≤
d
≤
1
n
Δ
i
L
n
max
⁡
2
·
n
·
d
2
·
[
(
n
-
2
)
2
·
(
d
-
1
/
n
)
3
+
(
n
-
1
)
2
·
(
2
/
n
-
d
)
3
]
12
·
(
3
-
2
·
2
)
2
·
(
1
+
d
)
2
if
1
n
≤
d
≤
2
n
Δ
i
L
n
max
⁡
2
·
n
·
d
2
·
[
(
n
-
3
)
2
·
(
d
-
2
/
n
)
3
+
(
n
-
2
)
2
·
(
3
/
n
-
d
)
3
]
12
·
(
3
-
2
·
2
)
2
·
(
1
+
d
)
2
if
2
n
≤
d
≤
3
n
⋮
⋮
Δ
i
L
n
max
⁡
2
·
n
·
d
2
·
[
(
n
-
n
)
2
·
(
d
-
(
n
-
1
)
/
n
)
3
+
[
n
-
(
n
-
1
)
]
2
·
(
n
/
n
-
d
)
3
]
12
·
(
3
-
2
·
2
)
2
·
(
1
+
d
)
2
if
n
-
1
n
≤
d
≤
n
n
.The geometrical addition of rectangle and triangle RMS components results in the total capacitor current forn-phase converters. Consider
(23)
I
OC
=
I
OC
Π
2
+
I
OC
Δ
2
.In Figure14 the RMS current in the output capacitors of multiphase DC/DC converters is shown. The current load of the capacitor decreases with the increasing number of phases. If neglecting the current variation (Δ
i
L
n
max
=
0, dotted lines), the maximum current in the output capacitor C
O is smaller for n-phase converters by a factor of 1
/
n compared to a single-phase design. The load in the output capacitors produced by the triangle current is fixed by the inductance converter design. This capacitor current is not dependent on the converted power. If the converter is operated with rated output power, this current has only a small influence on the overall capacitor current. In the figure, the output capacitor current is represented with a current variation of Δ
i
L
n
N max
=
0.5
I
L
n
AV. The influence of the triangle current at the output capacitors is smaller than at the input side of the converter.Figure 14
RMS current in the output capacitors of a one-, two-, and three-phase hybrid boost DC/DC converter.The calculations indicate that the triangle current load in the input and output capacitor for multiphase converters is clearly reduced. Putting this knowledge into practice, the triangle current in the inductances can be selected more largely [42, 43]. The dynamics of the hybrid boost DC/DC converter can be improved and beyond that the inductance and capacitor effort of the circuit can be reduced substantially.Besides the calculated current in the capacitors also is flowing harmonics current produced by switching processes of the phases [44]. This current has been examined in [45–47] for different converters. In consequence, these results can also be used for a hybrid boost converter. The additional current can contribute substantially to the output capacitors, heating up the capacitors during the small load of the converter. However, with higher power the calculated capacitor current dominates. A statement for all semiconductor types cannot be made. Beyond that, this additional current is dependent on the pulse frequency of the converter.


### 3.3. Simulation of the Two-Phase Hybrid Boost DC/DC Converter

We made this simulation of the two-phase hybrid boost DC/DC converter in CASPOC simulation program with a power source, not with a PV module. The following parameters are used for simulation:P
In
⁡
=
300 W, U
In
⁡
=
60 V, I
In
⁡
=
5 A, L
11
=
L
21
=
L
12
=
L
22
=
823.55 μH, C
I
=
15.625 μF, C
O
=
5.208 μF, and f
s
=
50 kHz.In previous Figures15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, and 28 are presented the results of simulation. Figure 16 presents the PWM pulses applied to switch 1, corresponding to first phase of the converter, respective the PWM pulses applied to switch 2, corresponding to the second phase of the converter. Figure 17 show the input current of phase 1, Figure 18 show the input current of phase 2, and the overall input phase current which consists of the sum of all the input phase currents, in our case phase one and phase two it is presented in Figure 19. It is obvious from Figure 20 that the currents of phase one through inductors L
11 and L
21 (i
L
11, i
L
21) are equal. The currents of phase two through inductors L
12 and L
22 (i
L
12, i
L
22) are equal, but here is represented just one of them in Figure 21. Output current of phase 1, respective 2, and the overall output phase current which consists of the sum of all the output phase currents, in our case phase one and phase two, are presented in Figures 22, 23, and 24. In the last figures are presented the output current and voltage, and the ripple of them.Figure 15
Input voltage.Figure 16
PWM pulse applied to switch one (pink signal), respective switch two (red signal).Figure 17
Input current of phase one,i
IP
1.Figure 18
Input current of phase two,i
IP
2.Figure 19
Overall input phase current,i
IP.Figure 20
Current through inductorsL
11 and L
21, i
L
11, i
L
21.Figure 21
Current through inductorL
12, i
L
12.Figure 22
Output current of phase one,i
OP
1.Figure 23
Output current of phase two,i
OP
2.Figure 24
Overall output phase current,i
OP.Figure 25
Output current,I
Out.Figure 26
Zoom on output current.Figure 27
Output voltage,V
Out.Figure 28
Zoom on output voltage,V
Out.


## 3.1. DC/DC Converter Input Circuit

In Figure11 the current waveforms at the input of a two-phase hybrid boost converter are shown. First, the currents in both inductances and the input current of phase one are shown. Represented underneath in green are the same currents of phase two. The triangle shaped inductance currents of the two phases are shifted with about a half pulse period. At switched-on time the input current of each phase is twice as small as the inductance current from a single-phase converter. But in this circuit the overall input phase current I
IP consists of the sum of all the input phase currents. The overall input phase current I
IP, with the DC-component I
In
⁡ is shown in Figure 11. Also for this circuit it is assumed that only the DC-current is flowing in the circuit input. With these conditions, for multiphase converters, the function between the input current I
In
⁡ and the average inductance current of the individual phases I
L
n
AV can be calculated. Consider
(13)
I
L
n
AV
=
I
In
⁡
n
·
(
1
+
d
)
.Figure 11
Current waveforms at the input of a two-phase hybrid boost DC/DC converter(
n
=
2, d
=
0.3
).The total AC-component of the overall input phase currentI
IP flows in the input capacitor (Figure 11). This current is clearly smaller in comparison to a single-phase hybrid boost converter. In addition, the frequency of the capacitor current is doubled. For these reasons the filter effort is reduced.We continue with the calculation of the inductances and capacitors of a multiphase hybrid boost converter. The same technical conditions for a single-phase converter are applied and the calculation of inductances for ann-phase design can be accomplished in the same way as for single-phase circuits. Taking into account the input current which is subdivided into the different phases, the maximum current variation in the inductances must be based on the maximum DC-current at rated power in the individual phases. For design, the maximum current variation is selected between 10% and 30% of the phase DC-current in the inductances at rated power. Consider
(14)
L
1
n
=
L
2
n
=
U
Out
·
T
P
Δ
i
L
n
max
⁡
·
(
3
-
2
·
2
)
with
Δ
i
L
n
max
⁡
=
(
0.1
–
0.3
)
·
I
L
n
AV
R
.The amplitude of the triangle current variation in the inductors is dependent on the duty cycle of the converter. Because the duty cycle in all phases has the same value, the current variations in all inductors are equivalent. Consider(15)
Δ
i
L
n
=
(
d
)
·
(
1
-
d
)
(
1
+
d
)
·
(
3
-
2
·
2
)
·
Δ
i
L
n
max
⁡
.The necessary input capacity of the multiphase hybrid boost converter will now be calculated. Compared to a single-phase design, the capacitor current is reduced and the current frequency is increased by the number of phases. As a consequence the current in the capacitor has a voltage variation at the input. For the capacitor design, the permissible static voltage variation in general is selected smaller than 1% of the rated input voltage. Consider(16)
C
I
=
T
P
·
I
L
n
AV
4
·
n
·
Δ
u
In
⁡
⁡
max
⁡
with
Δ
u
In
⁡
⁡
max
⁡
≤
0.01
·
u
In
⁡
⁡
R
.In these DC/DC converters, electrolytic capacitors are used often. A main design criterion of these capacitors is the RMS current load. For this reason, for multiphase DC/DC converters the RMS current in the input capacitorC
I will be calculated. Therefore the switching processes in the phases are assumed as ideal. Moreover, it is accepted that the current in the input is an ideal DC-current. The worst case scenario will happen when the capacitor is loaded with the total AC-current component.The input capacitor current for two-phase converters is represented in Figure12. In the case of closer inspection the capacitor current can be split into two different components: a rectangle part and a triangle part. The RMS current of these two components has been calculated. The RMS result of the rectangle portion for multiphase converters is shown in the formula below:
(17)
I
IC
Π
=
|
I
L
n
AV
2
·
n
2
·
(
d
-
0
n
)
·
(
1
n
-
d
)
if
0
n
≤
d
≤
1
n
I
L
n
AV
2
·
n
2
·
(
d
-
1
n
)
·
(
2
n
-
d
)
if
1
n
≤
d
≤
2
n
I
L
n
AV
2
·
n
2
·
(
d
-
2
n
)
·
(
3
n
-
d
)
if
2
n
≤
d
≤
3
n
⋮
⋮
I
L
n
AV
2
·
n
2
·
(
d
-
n
-
1
n
)
·
(
n
n
-
d
)
if
n
-
1
n
≤
d
≤
n
n
.Figure 12
RMS current in the input capacitors of a one-, two-, and three-phase hybrid boost DC/DC converter.In this formula it is necessary to consider that the average inductance currentI
L
n
AV becomes smaller with an increasing number of phases. For example, the average inductance current I
L
n
AV in a two-phase converter is only half as big as in a single-phase converter. With this fact in mind the rectangle component of the input capacitor current can clearly be reduced with a multiphase design.In addition, the RMS current of the triangle has been calculated. The next formula shows the RMS results for a multiphase circuit design. Consider(18)
I
IC
Δ
=
|
Δ
i
L
n
max
⁡
2
·
n
·
[
[
2
-
(
n
+
1
)
·
d
]
2
·
(
d
-
0
/
n
)
3
+
[
0
-
(
n
+
0
)
·
d
]
2
·
(
1
/
n
-
d
)
3
]
12
·
(
3
-
2
·
2
)
2
·
(
1
+
d
)
2
if
0
n
≤
d
≤
1
n
Δ
i
L
n
max
⁡
2
·
n
·
[
[
4
-
(
n
+
2
)
·
d
]
2
·
(
d
-
1
/
n
)
3
+
[
2
-
(
n
+
1
)
·
d
]
2
·
(
2
/
n
-
d
)
3
]
12
·
(
3
-
2
·
2
)
2
·
(
1
+
d
)
2
if
1
n
≤
d
≤
2
n
Δ
i
L
n
max
⁡
2
·
n
·
[
[
6
-
(
n
+
3
)
·
d
]
2
·
(
d
-
2
/
n
)
3
+
[
4
-
(
n
+
2
)
·
d
]
2
·
(
3
/
n
-
d
)
3
]
12
·
(
3
-
2
·
2
)
2
·
(
1
+
d
)
2
if
2
n
≤
d
≤
3
n
⋮
⋮
Δ
i
L
n
max
⁡
2
·
n
·
[
[
2
·
n
-
(
n
+
n
)
·
d
]
2
·
(
d
-
(
n
-
1
)
/
n
)
3
+
[
(
2
·
n
-
2
)
-
(
n
+
n
-
1
)
·
d
]
2
·
(
n
/
n
-
d
)
3
]
12
·
(
3
-
2
·
2
)
2
·
(
1
+
d
)
2
if
n
-
1
n
≤
d
≤
n
n
.The current variationΔ
i
L
n
max in this formula is selected in relation to the rated average inductance current I
L
n
AV during the circuit dimension. This will mean that with the same circuit dimension and increasing number of phases, the current variation is reduced.The geometrical addition of rectangle and triangle RMS components results in the total capacitor current for ann-phase hybrid boost DC/DC converter. Consider
(19)
I
IC
=
I
IC
Π
2
+
I
IC
Δ
2
.Figure12 shows the RMS current in the input capacitors of multiphase DC/DC converters. The current load of the capacitor decreases with the increasing number of phases. The influence of the rectangle RMS component is clearly dominant (dotted lines, i
L
n
max
=
0). The maximum capacitor current component produced from the rectangle portion is smaller by a factor of 1
/
n for n-phase converters. The triangle capacitor current is not dependent on the converter power and has, for all loads, the same value. In case of rated power the additional load from the triangle current in the capacitors is small.


## 3.2. DC/DC Converter Output Circuit

Figure13 shows the current waveforms at the output of a two-phase hybrid boost DC/DC converter. First, the currents in both inductors and the output current of phase 1 are represented. In the middle the current of phase 2 is shown. The triangle inductance current of the two phases is shifted within about a half pulse period of each other. At switched-off times, the inductors are connected in series and the current flows to the output phase, just as in a single-phase converter. However, in this circuit, the overall output phase current I
OP consists of the sum of all the output phase currents. The overall output phase current I
OP with the DC-component I
Out is shown Figure 13. It is assumed that only the DC-current is flowing in the circuit output; the total AC-component of the overall output phase current I
OP flows in the output capacitor. In comparison to a single-phase hybrid boost converter this current is clearly smaller. In addition, the frequency of the capacitor current has been doubled.Figure 13
Current waveforms at the output of the two-phase hybrid boost DC/DC converter(
n
=
2, d
=
0.3
).The necessary output capacity of the multiphase hybrid boost converter will next be calculated. Compared to a single-phase design, the output capacitor current is reduced and the current frequency is increased by the number of phases. As a consequence the current in the capacitor has a voltage variation at the output. For the capacitor design the permissible static voltage variation in general is selected at less than 1% of the rated output voltage. Consider(20)
C
O
=
T
P
·
I
L
n
AV
4
·
n
·
Δ
u
Out
max
⁡
with
Δ
u
Out
max
⁡
≤
0.01
·
u
Out
R
.The RMS current in the output capacitorC
O will next be calculated for multiphase hybrid boost DC/DC converters. The output capacitor current for a two-phase converter is represented in Figure 13. Like the input capacitor, the output capacitor current can also be split into a rectangle and a triangle component. The RMS current of the rectangle portion for multiphase converters is shown in the formula below:
(21)
I
OC
Π
=
|
I
L
n
AV
2
·
n
2
·
(
d
-
0
n
)
·
(
1
n
-
d
)
if
0
n
≤
d
≤
1
n
I
L
n
AV
2
·
n
2
·
(
d
-
1
n
)
·
(
2
n
-
d
)
if
1
n
≤
d
≤
2
n
I
L
n
AV
2
·
n
2
·
(
d
-
2
n
)
·
(
3
n
-
d
)
if
2
n
≤
d
≤
3
n
⋮
⋮
I
L
n
AV
2
·
n
2
·
(
d
-
n
-
1
n
)
·
(
n
n
-
d
)
if
n
-
1
n
≤
d
≤
n
nThe output capacitor RMS current, that is, produced by the rectangle component is exactly the same as that in the input capacitor. It is necessary to also consider that the average inductance currentI
L
n
AV becomes smaller with the increasing number of phases. The next formula shows the output capacitor RMS component produced by the triangle part of multiphase converters. Consider
(22)
I
OC
Δ
=
|
Δ
i
L
n
max
⁡
2
·
n
·
d
2
·
[
(
n
-
1
)
2
·
(
d
-
0
/
n
)
3
+
(
n
-
0
)
2
·
(
1
/
n
-
d
)
3
]
12
·
(
3
-
2
·
2
)
2
·
(
1
+
d
)
2
if
0
n
≤
d
≤
1
n
Δ
i
L
n
max
⁡
2
·
n
·
d
2
·
[
(
n
-
2
)
2
·
(
d
-
1
/
n
)
3
+
(
n
-
1
)
2
·
(
2
/
n
-
d
)
3
]
12
·
(
3
-
2
·
2
)
2
·
(
1
+
d
)
2
if
1
n
≤
d
≤
2
n
Δ
i
L
n
max
⁡
2
·
n
·
d
2
·
[
(
n
-
3
)
2
·
(
d
-
2
/
n
)
3
+
(
n
-
2
)
2
·
(
3
/
n
-
d
)
3
]
12
·
(
3
-
2
·
2
)
2
·
(
1
+
d
)
2
if
2
n
≤
d
≤
3
n
⋮
⋮
Δ
i
L
n
max
⁡
2
·
n
·
d
2
·
[
(
n
-
n
)
2
·
(
d
-
(
n
-
1
)
/
n
)
3
+
[
n
-
(
n
-
1
)
]
2
·
(
n
/
n
-
d
)
3
]
12
·
(
3
-
2
·
2
)
2
·
(
1
+
d
)
2
if
n
-
1
n
≤
d
≤
n
n
.The geometrical addition of rectangle and triangle RMS components results in the total capacitor current forn-phase converters. Consider
(23)
I
OC
=
I
OC
Π
2
+
I
OC
Δ
2
.In Figure14 the RMS current in the output capacitors of multiphase DC/DC converters is shown. The current load of the capacitor decreases with the increasing number of phases. If neglecting the current variation (Δ
i
L
n
max
=
0, dotted lines), the maximum current in the output capacitor C
O is smaller for n-phase converters by a factor of 1
/
n compared to a single-phase design. The load in the output capacitors produced by the triangle current is fixed by the inductance converter design. This capacitor current is not dependent on the converted power. If the converter is operated with rated output power, this current has only a small influence on the overall capacitor current. In the figure, the output capacitor current is represented with a current variation of Δ
i
L
n
N max
=
0.5
I
L
n
AV. The influence of the triangle current at the output capacitors is smaller than at the input side of the converter.Figure 14
RMS current in the output capacitors of a one-, two-, and three-phase hybrid boost DC/DC converter.The calculations indicate that the triangle current load in the input and output capacitor for multiphase converters is clearly reduced. Putting this knowledge into practice, the triangle current in the inductances can be selected more largely [42, 43]. The dynamics of the hybrid boost DC/DC converter can be improved and beyond that the inductance and capacitor effort of the circuit can be reduced substantially.Besides the calculated current in the capacitors also is flowing harmonics current produced by switching processes of the phases [44]. This current has been examined in [45–47] for different converters. In consequence, these results can also be used for a hybrid boost converter. The additional current can contribute substantially to the output capacitors, heating up the capacitors during the small load of the converter. However, with higher power the calculated capacitor current dominates. A statement for all semiconductor types cannot be made. Beyond that, this additional current is dependent on the pulse frequency of the converter.


## 3.3. Simulation of the Two-Phase Hybrid Boost DC/DC Converter

We made this simulation of the two-phase hybrid boost DC/DC converter in CASPOC simulation program with a power source, not with a PV module. The following parameters are used for simulation:P
In
⁡
=
300 W, U
In
⁡
=
60 V, I
In
⁡
=
5 A, L
11
=
L
21
=
L
12
=
L
22
=
823.55 μH, C
I
=
15.625 μF, C
O
=
5.208 μF, and f
s
=
50 kHz.In previous Figures15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, and 28 are presented the results of simulation. Figure 16 presents the PWM pulses applied to switch 1, corresponding to first phase of the converter, respective the PWM pulses applied to switch 2, corresponding to the second phase of the converter. Figure 17 show the input current of phase 1, Figure 18 show the input current of phase 2, and the overall input phase current which consists of the sum of all the input phase currents, in our case phase one and phase two it is presented in Figure 19. It is obvious from Figure 20 that the currents of phase one through inductors L
11 and L
21 (i
L
11, i
L
21) are equal. The currents of phase two through inductors L
12 and L
22 (i
L
12, i
L
22) are equal, but here is represented just one of them in Figure 21. Output current of phase 1, respective 2, and the overall output phase current which consists of the sum of all the output phase currents, in our case phase one and phase two, are presented in Figures 22, 23, and 24. In the last figures are presented the output current and voltage, and the ripple of them.Figure 15
Input voltage.Figure 16
PWM pulse applied to switch one (pink signal), respective switch two (red signal).Figure 17
Input current of phase one,i
IP
1.Figure 18
Input current of phase two,i
IP
2.Figure 19
Overall input phase current,i
IP.Figure 20
Current through inductorsL
11 and L
21, i
L
11, i
L
21.Figure 21
Current through inductorL
12, i
L
12.Figure 22
Output current of phase one,i
OP
1.Figure 23
Output current of phase two,i
OP
2.Figure 24
Overall output phase current,i
OP.Figure 25
Output current,I
Out.Figure 26
Zoom on output current.Figure 27
Output voltage,V
Out.Figure 28
Zoom on output voltage,V
Out.


## 4. Conclusion

Beginning from a step-up hybrid boost converter which was introduced in [22], after analyses this circuit and seeing if it is suitable for a PV system, we realize that one of the main disadvantages of this circuit is that the effort for the input and output capacitor, in the case of a single-phase DC/DC converter, is very high. This is the same with the effort of the inductors. A method for reducing this disadvantage was based on the same structure of the hybrid boost converter but built in a multiphase design. To ensure that all the phases of the converter operate at the same switching frequency and with phase-shift between them, we used interleaving switching strategy. After we analyze this new multiphase hybrid boost converter, made the theoretical calculation, and sketch the waveform, our presumption became true. The effort of the inductors, of the input and output capacitor, is decreased and at the same time their size is reduced. The frequency of the capacitor currents is increased with the number of phase. To validate and confirm our theoretical calculation, we simulate this circuit in CASPOC [48] simulation program.Therefore, how it is obvious from theoretical calculation and waveforms associated to it, compared with the simulation waveforms, we can see a very good accordance. Based on this, next step will be to put this circuit into practice.



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*Source: 637468-2014-04-30.xml*