A High Voltage Gain Modular Multilevel DC-DC Converter Yanchao Li, Xiaofeng Lyu, Dong Cao Electrical and Computer Engineering Department North Dakota State University Fargo, ND 58105, USA Email:
[email protected];
[email protected];
[email protected] Abstract— This Paper presents a new modular multilevel converter (MMC) concept to achieve high ratio DC-DC power conversion purpose. This converter can be deployed in Highvoltage direct current (HVDC) system, or it can be used as a Solid-state Transformer (SST). The proposed converter is flexible, reliable and it possesses scalability and simplicity. The conversion ratio can be regulated by the phase-shifted control, without any hardware modification. Using the MMC concept, this converter can be implemented with lower voltage rating switching devices instead of much higher voltage rating switches, which is usually unavailable. Two kinds of submodules are outlined for building the MMC. By utilizing inductance distributed on wire/trace and equivalent series inductance (ESL) of the capacitors, no inductors are needed to build the converter. Resonant operation between wire/trace inductance, ESL of capacitors and submodule capacitors assists the converter work under ZCS mode for higher efficiency. The operation principle as well as simulation results of a 20kW converter are presented in this paper. Keywords—DC-DC, Step-up, modular multilevel converter (MMC), resonant, soft switching, transformerless, solid-state transformer (SST)
I. INTRODUCTION Modular Multilevel Converter is becoming more and more popular in recent years. Researches have been done regarding different MMC applications [17]-[20]. And Wide bandgap devices are widely used in a variety of power converter applications [9]-[11]. High power density operated dc-dc converter become a trend of development. The utilizing of silicon carbide(SiC) switching devices and smaller components can effectively reduce the converter size. Some topologies for DC-DC conversion have been developed during the past years [1]-[3], [12]-[16]. To be specific, for step down purpose, a transformerless step-down dc-dc MMC is proposed [4]. In another case, two branches are used to generate two inversed ac voltage, respectively. Then a lower dc voltage can be get by adding this two ac voltage together [5]. In some of the converters, transformers are used to attain dc-dc conversion [6]. For stepup purpose, some MMCs connect their output in series in order to get high voltage output [7]. However, they may need to change their hardware in order to change their conversion ratio or have large size passive components.
978-1-4673-7151-3/15/$31.00 ©2015 IEEE
This paper presents a new method to generate high DC voltage by using low DC voltage source with the proposed MMC topology. The proposed converter has the following advantages: 1) Flexible. Theoretically, the number of the submodule can be changed from 2 to very large value. And the number of the submodule can be either odd or even. 2) Highly modular. This feature makes the converter can be easily modified by just adding or removing a submodule. The cost and difficulty of replacing a submodule can become lower. And no additional part (except the output DC capacitor) is needed to build the converter. 3) Simple. The structure of each submodule is quite simple, it is designed based on half-bridge or full-bridge structure. 4) High conversion ratio. By using multiple submodule, a very high conversion ratio can be achieved. The more submodule one converter have, the higher conversion ratio can be achieved. 5) Variable conversion ratio. With the same hardware configuration, not only high conversion ratio but also lower one can be achieved by changing the control method. 6) Phase-shift control. The converter uses Phase-shifted Pulse-Width Modulation (PWM) control, which is easy to be implemented. 7) Zero current switching (ZCS). Resonant makes it possible to let the converter working under ZCS mode [8]. 8) Less and smaller passive components. Because only small inductance is needed under high resonant frequency, so wire inductance can be utilized instead of using larger sized inductor. Unlike [21], an additional large inductor is required in the converter. II. THE PROPOSED MULTILEVEL DC-DC CONVERTER TOPOLOGY AND ITS OPERATION PRINCIPLE In this section, system structures of the proposed converter are given in the first part. In the second part, the circuit structure of different submodules will be shown. Then the operation principle and control method will be demonstrated. At last a set of in-depth analysis will be executed to show how to make this converter work under ZCS mode. A. System Level Topology The system configuration of proposed converter is shown in Fig.1. As shown in the figure, the number of submodule could be even. If there are odd submodules, the extra one can be put in either the upper branch or lower branch. All the submodules have been divided into two groups, and submodules in each group are put in series in order to boost up
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Module 1
Module 2
Module 3
ĂĂĂ
Module N/2
-
-
-
ĂĂĂ
-
idc Vsb_1
+
Vsb_2
+
Vsb_3
+
Vsb_n/2
+
+
ic
DC Vout
VDC -
+
-
+
-
Module N-1
Vsb_n-2
Module N-2
Vsb_n/2+1
+
+
Module N
Vsb_n-1
ĂĂĂ
-
Vsb_n
-
Module N/2+1
ĂĂĂ
Fig.1. System level configuration of the proposed converter with even submodules
+ Lwire Sp Vsb_i Ci Sn
-
Fig.2. Circuit Structure of Full-Bridge Submodule
Sp
Vsb_i
Ci
Sn
-
Fig.3. Circuit Structure of HalfBridge Submodule
the voltage. Fig.1 shows series resonant version converter in which the resonance is between the wire/trace inductance and the capacitor distributed in each submodule shown in the following part. B. Structure of Each Submodule Fig.2 shows the circuit configuration of full-bridge submodule used to build the converter. Similarly, fig.3 shows the configuration of half-bridge submodule. In fig.3, when one or more modules are deactivated, corresponding wire/trace inductance still stays in the resonant loop, thus another resonant frequency needs to be calculated in order to maintain ZCS operation. By using either of the configurations, inductance of the solid wires and ESL of capacitors will be
V - C6+
D. Resonant and ZCS Operation In this part, in order to demonstrate general operation principle, the converter in fig.1 with 6 full-bridge submodules is used as an example. Fig.4 shows the example converter to be analyzed. The analysis of the modular multilevel DC-DC boost converter is based on the following assumptions: 1) The power MOSFETs and the diode are ideal. 2) The parameters of all components in each submodule are identical, which include Ci, LCi, Lwire and parameters of switches. 3) No dead time is considered in the analysis.
V - C5+
LC6
LC5
V - C4+
LC4
idc +
ibus Sb
Sa
iQ23
Q21
ic
Q24 iQ22 Q22
Q23
iout Vinv
Vin
Lwire
Lwire
Lwire
Lwire
Lwire Q9
Q11
Q12
Q10
DC Vout
Sb
-
+
LC1
VC1
LC2
+
Sa
Lwire
-
Sp
LCi + VCi -
C. Phase-shifted PWM Control for Full Bridge Submodules As shown in fig.4, the proposed converter with 6 fullbridge submodules is analyzed in this part. In order to achieve high conversion ratio, Fig.5 shows the phase-shifted PWM signal used for the open loop control of the proposed converter. The PWM signals from submodule 1 to submodule 6 has been shifted by 0ƕ, 60ƕ, 120ƕ, 180ƕ, 240ƕ and 300ƕ respectively. The switching frequencies of each switch are the same, and duty cycles of switch pairs Sp and Sn shown in fig.2 are identical for all submodules.
VC2
LC3
Fig.4. The proposed converter with six full-bridge submodules
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+
Sn
Lwire
-
LCi + VCi -
utilized, thus no inductors are needed in the converter.
+
VC3
-
4) Voltage variation across the capacitors is neglected, which means VCi = VC. When the converter is working under steady state, switching frequencies of all the switches are fs, average voltage stress of the ith capacitor is VCi and voltage across submodules are Vsb_i. Also, iQn, ibus and iout are used to denote the current flow through the nth switch, DC bus and wires respectively. Thus the voltage across the resonant tank is V= σ6i=1 V̴i , and output voltage can be derived as Vout=Vinv σ6i=1 Vsb̴i. With all the assumptions above, all average voltages across the capacitors are assumed to be the same. Then the average voltage across each submodule should be ǦVC or VC. According
ൌǦൌሺ െ ͳሻ െ ൌሺ െ ʹሻ כ. From previous analysis, the average output voltage can be derived as
ܸ௨௧ ൌ ሺܰ െ ͳሻ ܸ כ
(1)
From (1) the average voltage generated on the output side is ͷ when ܰ ൌ , which means the dc offset generated by the resonant tank is ͷ. Fig.5 shows the voltage relationship betweenܸ௨௧ ,ܸ௩ andܸ . By repeating equivalent mode 1 and equivalent mode 2 for six submodules, the converter always works under resonant status, which makes it possible that the converter work under ZCS mode. III. FEATURES OF THE PROPOSED TOPOLOGY A. Analysis of The Full Bridge Version 1) Tansfer Function
1
2
3
4
5
6
7
8
9
10
11
12
Q21,22
t
Q17,18
t
Q13,14
t
Q9,10
t
Q5,6
t
Q1,2
t
Referring to voltage relationship between Vin and Vout in equivalent mode 1 and equivalent mode 2, voltage stress on the capacitor is VCൌVin . And the transfer function of the full bridge version converter can be derived as (2).
ܸ௨௧ ൌܰെͳ ܸ 2) Resonant Frequency
Since N submodules are used to build the MMC, and every one of them has the same parameters, then the resonant frequency for positive part of iout and negative part of iout can be written as (3).
Ts ͷܸܥ
vout
vinv -vin
ͳ
݂ ൌ ݂ ൌ
Tr
+vin
(2)
ʹߨ כට൫ܮ௪ ܮ̴ாௌ ൯ כ ܰ כே
t
(3)
Once (3) has been derived, the resonant frequency and switching frequency can be easily derived as (4).
Fig.5. Phase-shifted PWM and Voltage Waveform for Proposed Converter with 6 Full-Bridge Submodules
to fig.4 and fig.5, there are 12 operating status in total during each cycle Ts. However, every submodule has the same operation patterns, thus analysis for only equivalent mode 1 and equivalent mode 2 is enough to show how the converter works. From fig.6, when the converter works in mode 1, all the 6 capacitors are connected in positive way, which means for all ith submodules, have ܸ௦̴ ൌ ܸ ൌ VC . Then the voltage across the resonant tank = כVC. In general case with N submodules, the voltage relationship between Vdc and Vout can be written as Vrt = ܸௗ + ܸ௨௧ = ܰ כVC. When the converter works in mode 2, switch Q21, Q22 kick out and Q23, Q24 kick in, then the connection of capacitor C6 changes from positive to negative. This means in mode 2, ܸ௦̴ ൌ ܸ ൌ VCሺ݅ ൌ ͳ ǥ ͷሻ, while ܸ௦̴ ൌ Ǧܸ ൌ Ǧ. Then ൌ ͷVC െ VC ൌ ͶVC. In general case with N submodules, the voltage relationship between Vin and Vout can be written as
݂ ൌ ܰ ݂ כ௦ ൌ ʹ כ
݂ ݂ כ ݂ ݂
(4)
3) Duty Cycle With the phase-shift angle of 360ƕ/N, the duty cycle of all the switches in submodule can be found.
ܦ௦ ൌ
ʹܰ െ ͳ ʹܰ
(5)
At the same time, it is worth mention that the duty cycle of the full-bridge used to generate Vinv is 0.5. 4) Variable conversion ratio Also, the conversion ratio could be adjusted by changing the duty cycle of phase-shifted PWM signal used to control all those switches. The transfer function of the converter under this operation mode is
3537
V - C6+
V - C5+
LC6
LC5
V - C4+
LC4
idc +
ibus Sa
iQ23
Q21
ic
Q24 iQ22
Q23
Q22
iout
+
Vinv Lwire -
Vin
Lwire
Lwire
Lwire
Lwire Q9
Q11
Q12
Q10
DC Vout
Sb
-
VC1
+
LC2
-
+
LC1
VC2
+
Sa
Lwire
LC3
-
-
Sb
VC3
(a) Equivalent mode 1
V - C6+
V - C5+
LC6
LC5
V - C4+
LC4
idc +
ibus Sa
iQ23
Q21
ic
Q24 iQ22
Q23
Q22
iout
+
Vinv Lwire -
Vin
Lwire
Lwire
Lwire
Lwire Q9
Q11
Q12
Q10
DC Vout
Sb
-
VC1
+
LC2
-
+
LC1
VC2
LC3
+
Sa
Lwire
-
Sb
-
VC3
(b) Equivalent mode 2 Fig.6. Operation modes of first operating cycle that is equivalent to operating modes of each submodule.
ܸ௨௧ ൌ ʹܲ ͳ െ ܰ ܸ
(6)
Here parameter P means during equivalent mode 1, there are ܲ ͳ submodules have been connected in positive way. And after that, 1 of the ܲ ͳ submodule will be changes from positive connection to negative connection during equivalent mode 2. Which means in equivalent mode 2, P submodules are connected in positive and ܰ െ ܲ are connected in negative. Thus the duty ratio of switching device Sp in submodules can be derived
ܦ௦
ʹܲ ͳ ൌ ʹܰ
(7)
Although duty cycle of the submodules needs to be changed in order to change the conversion ratio. However, the change of duty ratio will not affect resonant frequency of the converter. So, the duty cycle of Vinv is still 0.5.
1) Tansfer Function By using the same method used to get the transfer function of the full-bridge version converter. The voltage stress on the capacitors is VC = 2 כVin. And the transfer function can also be derived as
ܸ௨௧ ൌ ʹܰ െ ͳ ܸ
(8)
2) Resonant Frequency If half-bridge submodules are to be adopted to build the converter, then the resonant frequencies of the positive part of iout and negative part of iout can be derived. According to fig.3, the inductance of the loop is always the same, while capacitance keeps changing. And the resonant frequency for both parts are derived as
B. Analysis of The Half Bridge Version
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ͳ
݂ ൌ
function are derived as
ͳ
݂ ൌ ʹߨ כට
(10)
ሺಶೄಽ כሺேିଵሻାேכೢೝ ሻכ ேିଵ
According to (9) and (10), two resonant frequencies are existed if half-bridge submodules are employed. This is obviously different from full-bridge version converter. 3) Duty Cycle ƕ
With the phase-shift angle of 360 /N, the duty cycle of each
ܦൌ
ʹܰ െ ͳ ʹܰ
(11)
And the duty cycle of the full-bridge used to generate Vinv LVQRWDQ\PRUH,WFDQEHGHULYHGDV
ܦ ൌ ͳ െ
݂ ݂ ݂
ͲǤͷ െ ܦ ܰ
(13)
Plug (11) and (12) into (13), ܦ௦ can be found derived
ܦ௦ ൌ
൫݂ ݂ ൯ ܰ כെ ݂ ൫݂ ݂ ൯ ܰ כ
ܦൌ
ʹܲ ͳ ʹܰ
ܶ௦ ൌ ʹܲ ͳ ܶ௦
Q21,22
IV. SIMULATION RESULT Simulation has been performed to verify the theory of the proposed full-bridge version dc-dc boost MMC. Table I shows
Unbalanced Mode
t Tsn
Q21,22
Tr
(17)
When ܲ ൌ Ͷ is applied to (17), ܦ௦ will change correspondingly, as shown in fig.7. Thus a relatively more balanced conducting time among switches in each pair has been achieved. Which means the RMS values of the current flow through Sp and Sn become balancer. However, this need to trade off the conversion ratio of this converter. According to previous analysis, half-bridge cell is more suitable to work under balanced switching mode. Because changing of duty cycle has less effect on the conversion ratio of the converter.
Same with the full-bridge version converter, the conversion ratio could be changed by adjusting the duty ratio of each pair of switches in every submodules. The transfer
Ts
(16)
C. Balanced Switching Pattern According to (5) and (14), with a high duty ratio, it is obvious that the conducting time between two pairs of switches is quite different, unbalanced. Which means Sp in each submodule has longer conduction time than Sn. Thus the RMS values of the current flow through Sp and Sn are very different. However, much more balanced conducting time among the switches is desired under some situation. For converter using full-bridge submodules, conduction time regarding Sp and Sn is shown as
(14)
4) Variable conversion ratio
Tsn
(15)
In (16), P means P+1 submodules are activated in equivalent mode 1. Then, in equivalent mode 2, one of the P+1 submodule has been kicked out, which means P submodules are working in equivalent mode 2.
(12)
Due to different resonant frequency between ݂ and݂. The duty cycle of switching device Sp in submodules needs toEHUHFDOFXODWHG
ܦ௦ ൌ ܦെ
ܸ௨௧ ൌ ʹܲ ͳ ܸ
(9)
ʹߨ כට൫ܮ௪ ܮ̴ாௌ ൯ כ ܰ כே
Balanced Mode
t
Fig.7. Comparison of Sp conduction time between unbalanced and balanced mode.
Fig.8. ZCS operation with open loop control
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a comparison between converters built by this two types of submodules. And all key data used to simulate the full-bridge version converter are given in Table II. Table III describes the configuration of the simulated converter.
TABLE I. COMPARISON OF THE PROPOSED CONVERTER USING TWO TYPES OF SUBMODULES Description
Value
Submodule Type
Full- Bridge
Half-Bridge
Submodule Number
N
N
Device Number
4N+4
2N+4
Max Conversion Ratio
N-1
2N-1
Voltage Stress of Devices
Vin
2Vin
Voltage stress of Capacitors
Vin
2Vin
Fig.8 shows the simulation result of the proposed converter with 6 full-bridge submodules at 20kW. In the simulation, a resistive load of 454ohm is used. This result indicate that the converter is working under ZCS mode with open loop phase-shift PWM control. Fig.9 shows the resonant current flow through the loop and the voltage used to maintain the resonance, which are ݅௨௧ and ܸ௩ ǡrespectively. Also fig.9 shows that amplitude of DC bus current, which is݅௨௦ , during the first half resonant cycle and the second half cycle are different.
TABLE II. KEY DATA USED TO SIMULATE THE PROPOSED CONVERTER WITH FULL-BRIDGE CELLS Description Input voltage Power rating of the converter
Items
Values
Vin
600 V
P
20 kW
Resonant frequency
fr
200 kHz
Switching frequency
fs
33.42 kHz
Capacitor used in each submodule
C
4.7 uF
Inductance distributed on wires
Lwire
159.8 nH
Duty cycle of Sp (submodule)
Dsb
0.917
Resistive Load
Rload
454 ohm
Output Capacitor
Cout
10 uF
According to fig.10, the proposed converter has boosted the voltage from 600V to 3kV as expected, with little voltage drop. And the average voltage of the capacitors in submodules is around 600V, matches the theoretical analysis. In fig.11, when duty cycle of the power device Sp in
TABLE III. CONFIGURATION OF THE SIMULATED CONVERTERS Description Submodule type
Value Full- Bridge
Submodule number
6
Max Conversion Raito
5 Fig.10. Key voltage waveform when converter has max conversion ratio
Fig.9. Resonant current waveform and DC bus current waveform
a comparison between converters built by this two types of
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Fig.11. Key voltage and current waveform when converter working under lower conversion ratio status
submodules is decreased, the RMS values of current flow through two pairs of switching devices become more balanced. And the output voltage drops from 3kV to 1.8kV, which means the conversion ratio drops from 5 to 3. However, the average voltage across submodule capacitors is still 600V. This indicate that the change of submodule duty cycle will not have an effect on the capacitor average voltage. V. CONCLUSION Since more and more people are becoming interested in high conversion ratio dc-dc modular multilevel converters, this means a new topology for dc-dc MMC would be meaningful. This paper presents a new transformerless dc-dc MMC. The proposed converter makes use of the parameters in the physical layout, which makes each submodule in the converter inductorless, thus all the submodules can become very small. Also, the easy structure of each submodule made this converter very easy to build. Only one resonant frequency is existed in the converter with full-bridge submodule, and this feature makes the converter can easily work under ZCS mode. Compare to some other dc-dc MMC converters, the proposed one can change its conversion ratio by modifying the duty cycle of the switches instead of modifying the hardware. Hence, the proposed converter is very flexible, reliable and a potential winner of scalability and simplicity.
[7]
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[14]
ACKNOWLEDGEMENT
[15]
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