The authors express their gratitude to the Brazilian Coordination for the Improvement of Higher Level
Personnel (CAPES) for the financial support given in this research.
«Boost converter», «Dc-dc converter», «High Voltage», «Multilevel», «Capacitor voltage balancing control».
This paper presents a nonisolated multilevel step-up dc-dc converter suitable for high power and high output voltage application. The main features of proposed converter are: reduced voltage across the semiconductors; low switching losses; and reduced volume of input inductor. This paper focuses on the five-level structure of the proposed converter, in which the theoretical analysis is carried out and discussed. The five-level proposed dc-dc converter has four capacitors and their voltages should be balanced for its correct operation. Therefore, a capacitor voltage balancing active control is presented and analyzed in detail herein. In order to demonstrate the performance of this converter, experimental results were obtained for an output power of 5kW. The results attest the advantages of the proposed dc-dc topology and it is reported herein.
High voltage DC transmission (HVDC) has become more attractive in large offshore wind farm, since the cable losses are reduced and the reactive power requirements are decreased [1]. The advantage of this kind of transmission is discussed in detail in [1]-[5]. In this kind of system, high voltage dc-dc converters are required to suit the voltage level necessary to transmission. A basic configuration of offshore wind farm is shown in Fig. 1, according to [1]-[4]. In this figure, it is observed the presence of medium-voltage (MV) dc-dc converters, which is used to step-up the voltage generated by the wind turbine, and also a high-voltage (HV) dc-dc converter, which is used to step-up the voltage for HVDC transmission level. Nevertheless, this kind of converter is still a challenge to power electronics, due to the technological limitation of the semiconductors available in the market, mainly about its blocking voltage. To overcome this limitation, some solutions of high voltage dc-dc converter have been proposed in literature and they will be discussed herein.
A common solution for MV and HV dc-dc converter is to employ thyristor based converter, such presented in [1]. This kind of converter can support the high voltage levels, due the high breakdown voltage of the used semiconductors. On the other hand, due to the low frequency operation characteristic of those converters (limited by the high switching losses of the semiconductors devices), its volume, mainly magnetic volume, is very high.

Fig. 1: Example of a large offshore wind farm employing medium and high voltage dc-dc converter.
In [6], the author proposes series connection of semiconductor, in order to operate with high voltage and high switching frequency. This solution is very attractive, since their modularity. However the complexity of gate driver is very high, since it should take into consideration the static and dynamic characteristics of semiconductor.
Another common solution is to employ low voltage converters with parallel input and series output connections, as described in [7]. This converter has the feature of low voltage across switches, modularity and it can be extended regardless of the input voltage. On the other hand, the input voltage is always very low, thus it is limited to application which requires low input and high output voltage.
Within this context, this paper presents a nonisolated multilevel Boost dc-dc converter for high voltage application. The proposed topology is an extension of the basic three-level double-boost dc-dc converter [8], shown in Fig. 2 (a). The three-level boost converter reduces the blocking voltage of the semiconductors to half of the output voltage, thus it is still inappropriate to medium or high voltage application. In order to reduce even more the blocking voltage of the semiconductors, the multilevel
Boost converter is proposed in this paper. The generalized multilevel Boost topology is shown in Fig.
2 (b). The main features of this converter are: reduced blocking voltage of the switches and diodes; low switching losses, reduced volume of input inductor and low voltage across capacitors (when compared with flying-capacitor converter [9]). The most critical components of the proposed converter are the extern capacitors, since they are submitted to high voltage (a half of output voltage).
For safety operation of proposed converter, the voltage across the capacitors must be balancing.
Unbalanced voltage will imply in higher blocking voltage of semiconductors, which may lead to the destruction of the device. Therefore, a capacitor voltage balancing active control is required in this converter. This topic is addressed in this work.
The Five-Level (5L) structure of proposed Boost converter, as shown in Fig. 3 (a), will be analyzed and discussed in this paper. The theoretical analysis, including the modulation strategy description, operation principle, main waveforms, components design, as well as capacitor voltage balancing control and, finally, experimental results are shown in this paper.
(a) (b)
Fig. 2: Double-Boost converter and proposed generalized multilevel Boost converter.

The theoretical analysis is performed considering the steady-state operation in continuous-conductionmode of the 5L-Boost converter. Therefore, the voltage over the semiconductors and the capacitors C3 and C4 is Vo/4, while the voltage across the capacitors C1 and C2 is Vo/2, where Vo is the output voltage. The modulation strategy and the four operation regions of the proposed 5L-Boost converter are described following. The main waveforms for each operation region are shown and explained, as well as the topological states are described in detail. The mathematical expression of output-input voltage relationship (static gain) is derived. The inductor and capacitor design is also presented in section.
The adopted modulation strategy is based on phase-shift PWM, with four triangular carriers shifted off
90º. Each carrier is used to generate the gating signal of one switch. This modulation technique allows the charge and discharge of each capacitor, making possible the implementation of the active control of capacitor voltage balancing. Using this modulation strategy, the 5L-Boost converter presents four operation regions, according to the duty-cycle value D, as described in Table I. The operation region defines the voltage v a
limits, as shown in Table I. This table also shows the time intervals t
1
and t
2
for each operation region, which are the time of charge and discharge of the inductor, and they are exposed in Fig. 4.
(a) (b)
Fig. 3: Five level proposed Boost topology and waveform of modulation strategy illustrating the carries signal, modulator signal and voltage v a
.
Fig. 3 (b) illustrates the waveforms of the carrier signals, modulator signal and voltage v a
during the transition of operation regions, in order to show the behavior of voltage v a
. As can be seen in this figure, the voltage v a
levels changes according to the operation region of the converter, and the voltage v a
levels is described in Table I.
Table I: Operation region of 5L-Boost converter
Operation
Regions
R1
R2
R3
R4
Duty-Cycle
0 < D < 1/4
1/4 < D < 1/2
1/2 < D < 3/4
3/4 < D < 1 t
1
D·T s
(4·D - 1) ·T s
/4
(2·D - 1) ·T s
/2
(4·D - 3) ·T s
/4 t
2
Voltage v a
(1 - 4·D) ·T s
/4 3V o
/4 to V o
(1 - 2·D) ·T s
/2 V o
/2 to 3V o
/4
(3 - 4·D) ·T s
/4 V o
/4 to V o
/2
(1 - D) ·T s
0 to V o
/4

The proposed 5L-Boost converter presents four controlled switches, which implies in 16 topological states. The states are described in Table II, including the switches states, capacitors currents and voltage v a
for each state. From this table, it can be concluded that the 5L-Boost converter presents four redundant states able to generate the voltage v a
equal to 3V o
/4, six redundant states able to generate the voltage v a
equal to V o
/2, four redundant states able to generate the voltage v a
equal to V v o
/4, one state able to generate the voltage v v possible to generate the same value of voltage v a in second state the voltage a a
equal to V is 3V o o
, and, finally one state null, i.e.
, charging or discharging each capacitor. For example,
/4, and the capacitor C
1 a
= 0. Thus, it is
is charging, while capacitor C
2
is discharging. However, in the third state the voltage v a is also 3V o
/4, but now the capacitor C
1
is discharging, while capacitor C
2
is charging. It proofs that the converter has enough redundant switching states to perform the control of the capacitors voltages.
Although the converter presents 16 available topological states, each operation region presents only eight operations stage, using up to eight topological states. Fig. 4 shows the main waveforms for a switching period of the proposed 5L-Boost converter for each operation region. From this figure, it is observed that the operation frequency of voltage current i
L v a
, and consequently the operation frequency of
is four times higher than the switching frequency, regardless of the operation region.
Moreover, the voltage across the inductor is minimized, since the voltage v a
operates with two reduced levels voltage and these levels are nearby of the input voltage. Therefore, a reduced required inductance is expected for this topology.
v a
State s
1 s
2 s
3 s
4 i
C1 i
C2 i
C3 i
C4
1º on off off off 0 0 - 0 v a
3V o
/4
4º off off off on 0 0 0 -
6º on off on off + - - +
V o
/2
9º off on off on - + + -
11º on on on off 0 0 0 +
V o
/4
14º off on on on 0 0 + 0
º off off off off 0 0 0 0 V o
In order to obtain the output-input voltage relationship of the 5L-Boost converter, the volt-second balance of the inductor L for one fourth of the switching period is analyzed, using (1). Solving equation (1), it is obtained the mathematical expression of the static-gain as function of duty-cycle D, as shown in (2).
1
T
S t o
+ T
S t o
∫
/ 4
( ) = 0
(1)

(a) (b)
(c) (d)
Fig. 4: Main waveforms of the 5L-Boost converter: (a) first operation region; (b) second operation region; (c) third operation region; (d) fourth operation region;
Equation (2) shows that static-gain of 5L-Boost converter is the same of the conventional two level
Boost converter.
V o
V i
=
1
1 − D
(2)
The current ripple in the inductor can be calculated during the storage energy stage or transfer energy stage and using the equation (3).

Δ i
L
=
1
L
∫
0 t
1
( )
(3)
In this equation, t
1
is the time interval of current charging in the inductor and it has different values according to the operation region, as can be seen in Table I. Thus, the inductor ripple analysis must be realized for each operation region. By doing this, it is obtained the current ripple equation for each operation region, as shown in (4).
Δ i
L
⎪
⎪
⎪
⎪
⎪⎩
= ⎨
⎪
⎪
⎪
⎪
⎪⎪
⎪
⎪
⎪
⎪
⎧
⎪
4
4
V o
V o
4
V o
4
(
(
V o
(
−
1
−
−
(
D
D
D
−
)(
)(
2
)(
2
4
2
4
D
D
D
)
−
−
−
3
)
)
)
,
,
,
4
2
3
4
D <
1
4
≤ <
1
1
2
3
4
(4)
Fig. 5: Normalized inductor current ripple of the proposed and conventional Boost converter.
Fig. 5 shows the normalized current ripple of the inductor for the 5L-Boost converter and the conventional Boost converter. The normalization is given by Δ iL = 4( Δ i L f
S
L)/Vo. As expected, the inductor current presents reduced ripple. Comparing with conventional Boost converter, the current ripple is 16 times reduced for the 5L-Boost converter. Furthermore, the inductor current has no ripple in some specific points of the duty-cycle. These points are exactly the transitions between the operation regions. For each operation region there is a duty-cycle which implies in maximum current ripple of the inductor. Thus, the inductance expression, presented in (5), is derived considering the maximum current ripple.
L =
64
V o
⋅ ⋅ Δ i
L
(5)
In this subsection, the voltage ripple on the capacitors C1, C2, C3 and C4 is analyzed and the mathematical expression for calculation of this capacitance is derived.
The voltage ripple on the capacitor can be calculated during the storage energy stage or transfer energy stage and using (6). Some parameters are required in (6), as the charge or discharge time interval Δ tc and instantaneous capacitor current i
C text.
(t). They are not shown in Fig. 4, but they will be exposed in the
Δ v
C
=
1
C
Δ t c
∫
0 i
C
( ) (6)
For capacitor C1 and C2, the charge time interval is given by Δ t
(1 − D)·T s
C
= D·T
for D > 1/2. The charge current of these capacitors are i
C
(t) = I
L s
, for D < 1/2, and Δ t
C
=
/2, independently of the dutycycle. Substituting these values in (6), the voltage ripple of the capacitors C1 and C2 is obtained, as shown in (7). i
Likewise, for capacitor C3 and C4, the charge time interval is given by Δ t
C
T
C s
/4 for 1/4 < D < 3/4; and Δ t
(t) = I
L
C
= (1 − D) ·T s
, independently of the duty-cycle. Substituting these values in (6), the voltage ripple of the capacitors C1 and C2 is obtained, as shown in (8).
= D·T s
for D < 1/4; Δ t
C
=
for D > 3/4. The charge current of these capacitors are

Fig. 6 shows the normalized voltage ripple of the capacitors, as function of duty-cycle. It is observed that the maximum voltage ripple occurs for D = 0.5, for all capacitors.
Δ v =
⎪⎪
⎧
⎪
⎪
⎪
⎪⎩
2
2 f
S
I
L
C
I
L (
D,
1 − D
)
D <
1
2
, D >
1
4
(7)
Δ v =
⎪
⎪
⎨
⎪
⎪⎩
⎪
⎪⎪
⎧
⎪
4 f f
S
C f
I
I
S
I
L
L
S
C
L
C
(
D, D <
1
,
−
1
)
4
1
4
3
4
3
4
1
(8)
Fig. 6: Normalized capacitor voltage ripple proposed Boost converter.
Thus, the capacitance expression, presented in (9), is derived considering the maximum voltage ripple.
Δ v
C
=
1
C
Δ t c
∫
0 i
C
( )
(9)
As cited before, the capacitors voltage must be balanced for the correct operation of the proposed converter. For some reasons, the capacitors voltage can change (e.g., during the start of the converter, input-voltage variations or slight difference between the drive signals of the switches). As a result, the voltage on switches can increase to an unsafe value, thus, a balancing strategy is necessary. In addition, in the dynamic states, the balancing process is very important [10].
In this paper, an active control technique to balance the capacitor voltage is used, because of its effectiveness. This technique was previously used in [11] for a three level flying capacitor converter and in [12] for a multilevel Buck converter. Thus, a briefly explanation of this technique applied to the proposed 5L-Boost converter is presented in this section.
The behavior of capacitors current must be analyzed. Thus, the simplified circuit, shown in Fig. 7 (a) is used.
(a) (b)
Fig. 7: (a) Simplified circuit of 5L-Boost converter for capacitor currents analysis and (b) PWM modulator circuit of the proposed converter, including the action of the capacitor voltage control.
From this circuit, it is observed that the current through capacitor C3 é given by (10). On the other hand, the diode D1 current is i
D1
(t) = [1 - d
1
(t)]·I
L
, where d
1
(t) is the duty-cycle of switch S1. Likewise,

the diode D1 current is i
D2
(t) = [1 – d
2
(t)] ·I
L
. Applying these equations ( i
D1
(t) and i
D2
(t)) in (10), it is obtained (11). Thus, it is observed that the current of capacitor C3 do not depends only of the dutycycle, but it depends of the difference of duty-cycles of switches S1 and S2. Performing the same procedure to the others capacitors, it is obtained (12). i
C
3
( ) = i
D
1
( ) − i
D
2
( ) (10) i
C
3
( ) = ( ) − ( )
L
(11)
⎪
⎩
⎧
⎪ i i
C
3
C
4
( )
( )
( ) =
=
=
⎡
⎣
⎡
⎣
⎡
⎣
( )
( )
( ) −
−
−
( )
( )
( ) ⎤
⎦
⎤
⎦
⎤
⎦
⋅
⋅
⋅
I
I
I
L
L
L
(12)
According to [12], it should be applied perturbation to the duty-cycle of the switches, in order to control the voltage across the capacitors, as shown in Fig. 7 (b). By doing this, the control variables
Δ d
1 duty-cycle by (13). Therefore, Δ d
1
( v
C1
, Δ d
2
(t));
, and Δ d
Δ d
2
4
are incorporated to the system, and they are mathematically related with the switches
is the variable responsible to control the voltage in capacitor C1
is the variable responsible to control the voltage in capacitor C3 ( v variable responsible to control the voltage in capacitor C4 ( v
C3
(t)); and Δ d
4
is the
C4
(t)).
By substituting (13) and (12), and applying the small-signal analysis, the transfer function necessary to perform the capacitors voltage control is obtained, as shown in (14).
⎧
⎪
⎨
⎪
D
D
1
3
= +
= −
Δ
Δ
Δ
Δ d
1
D
2
= + d
2 d
1
D
4
= + d
4
(13)
⎧
⎪
⎪ v
C
1
( )
=
⎪
⎪
⎨
⎪
⎪⎩ v v
C
C
3
4
( )
( )
=
=
− I
L sC
1
I
L sC
3
− I
L sC
4
Δ
Δ
Δ
( )
( )
−
( ) −
I
L sC
3
I
L sC
4
Δ
Δ
( )
( )
(14)
Fig. 8 (a) illustrates the block diagram of the converter model, represented by equation (14). It is observed in this figure and in equation (14) that the system model presents coupled voltage loops, since Δ d
1
has influence in v
C3
(t) and v
C4
(t). In order to avoid the action of Δ d
1
in v
C3
(t) and v
C4
(t), a simple decoupling scheme is incorporated to the control system. Fig. 8 (b) shows the block diagram of the capacitor voltage control system, including the decoupling scheme, which is very simple to be implemented through a microcontroller.
The transfer functions shown in Fig. 8 (a) are first-order functions, wherein the gain depends on the steady-state value of I
L
. To avoid the use of a complex adaptive controller, a P-type controller with constant gain is used. It is important to note, that a P-type controller ensure a low error in steady-state, due to the integrator characteristic of the system transfer function. Besides that, the implementation is simplified.
The controller is design for nominal output current, so for light load, the closed loop system will present slowly dynamic response. On the other hand, regardless the output current, the system is stable.

(a) (b)
Fig. 8: Block diagram: (a) system model; (b) control system, including the decoupling action.
In order to verify the operation and evaluate the performance of the proposed 5L-Boost converter, a 10 kW prototype with 20 kHz of switching frequency was design and the proposed topology was experimentally verified. Fig. 9 (a) shows the designed prototype, as well its dimensions. A 600V
IGBT with reference of IRGP50B60PD1 was used as the main (S1, S2, S3 and S4) switch of implemented prototype. The diodes used were the intrinsic diodes of the IGBT. Film capacitors with low series resistance, capacitance of 40µH and maximum voltage of 1.3 kV are used as C1, C2, C3 and C4. An inductor with inductance value of 468µH is employed. The capacitor voltage balancing control was implemented digitally through a Texas Instruments TMS320F28335 floating point DSP
(32-bit CPU, 150 MHz), as well as the main control system of the converter.
The experimental results consist of relevant voltage and current waveforms in steady-state for converter operating with only 5 kW of output power, 320 V input voltage and 550 V output voltage.
Due the relation of the input-output voltage, the converter operates in the region R2.
Fig. 9 (b) shows the inductor current, voltage v a
and switch voltage. This result is according to the theoretical waveform shown in Fig. 4. Fig. 9 (c) shows the capacitors voltage, in which it is observed a balance condition. In this figure, it is observed a slight variation of the voltage vC3, due the use of a
P-type controller. Nevertheless, the voltage variation is very low, and it can be disregarded. i
L v a v
C2 v
C1 v
S1 v
C4 v
C3
(a) (b) (c)
Fig. 9: Photo of implemented prototype and experimental results: (b) inductor current (5A/div.), voltage v a
(250V/div.) and switch S1 voltage (100V/div.); (c) Capacitors voltages (50V/div.).
A nonisolated multilevel Boost converter with high output voltage was proposed and a five-level structure was analyzed in detail in this paper. This converter presents as advantage the absence of a transformer, a reduced number of components, a reduced volume of output filter and low voltage across the semiconductors. A capacitor voltage balancing active control was presented and analyzed

briefly. From this brief analysis, it is concluded the there is an interaction between the voltage loops.
To avoid this interaction, a decoupling circuit was incorporated to the closed loop control system.
Besides that, it is possible to use a simple P-type controller to control the capacitors voltage, due to the integrator characteristics of the system transfer functions.
Finally, experimental results were exposed and they have demonstrated the performance and feasibility of proposed converter.
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