design of a 5.4 kj/s three-phase resonant converter based on a...

Design of a 5.4 kJ/s Three-Phase Resonant Converter based on a Lithium Polymer Battery

Chan-Gi Cho, Ziyi Jia, Jae-Beom Ahn and Hong-Je Ryoo Chung-Ang University

Department of Energy Systems Engineering Seoul, South Korea

ABSTRACT This paper describes the design and manufacture of a 5.4 kJ/s three-phase resonant converter based on a 22 and 44 V lithium polymer (LiPo) battery as a high density power supply. Using the low LiPo battery input voltage generates a relatively high current that causes problems such as a large current burden on the used components and high peak-to-peak noise when the switch is turned off. To resolve such problems, the three-phase resonant converter in this work is used to handle the high input current. In the three-phase inverter structure, the amount of current flowing in a single switch is smaller than that of a single-phase current. In addition, the delta-star structure is intentionally introduced to reduce the turns ratio which helps to decrease the current on the transformer’s primary side when the same output power is required. Furthermore, components such as series and parallel resonant capacitors are placed on the secondary side of the transformer, which have a high voltage and low current. These voltage and current conditions of the secondary side are more appropriate for commercialized film capacitors, which normally use series and parallel resonant capacitors because the film capacitors have been manufactured with high voltage and low current rated capacity. In terms of the design procedure, the used delta-star three-phase resonant circuit is redrawn on the secondary side of the transformer as a single-phase resonant equivalent circuit for the three-phase resonant converter design. Based on the simplified design, the operating mode and simulation of the 22 and 44 V LiPo battery-based chargers were analyzed, and the comparison of the resistor and capacitor load test results for the two chargers verifies both the aforementioned features and the performance of the proposed chargers using 300 and 150 A of the LiPo battery. The advantages are confirmed, and the capacitor bank is charged to 600 V for 80 ms, achieving power efficiencies of 82 and 92.5% for the 22 and 44 V based capacitor chargers, respectively.

Index Terms — DC-DC power converters, 3-phase electric power, lithium batteries

1 INTRODUCTION

COMMERCIALIZED lithium-ion batteries have been used as power sources for electric vehicles, energy storage systems, and portable devices such as mobile phones and notebook computers [1-6]. However, when a large-capacity lithium ion battery is used in a power conversion device, it is difficult to use a high current due to the battery’s low voltage. A high output current of lithium-ion battery creates a large current burden on the used components. In addition, a high di/dt generates peak noise when the switch is turned off, the driving time of the battery is very short, and controlling cell balancing is difficult [7-11].

The proposed 5.4 kW power supply is designed to use a commercialized 22 V, 16 Ah high-capacity lithium-ion battery

as an input voltage source by considering both an operation time of over 2 minutes and a capacity of over 180 Wh. However, the use of the single 22 V or series connected 44 V low voltage battery generates a high current, which causes the aforementioned difficulties, and hinders the achievement of the targeted output power.

In this work, the delta-star three-phase resonant converter is intentionally introduced to deal with the high current of the lithium batteries. In the three-phase inverter structure, the amount of current flowing in a single switch is smaller than that of a single-phase current. In addition, the delta-star structure of the three-phase transformer enables the use of the line to line voltage, and not the phase voltage, so as to reduce the turns ratio of transformers. The reduced turns ratio also decreases the conducting current under the same output power conditions.

Furthermore, the series resonant capacitors are arranged on the secondary side of the transformer because the current

Manuscript received on 31 July 2018, in final form 11 December 2018, accepted 19 December 2018. Corresponding author: H-J. Ryoo.

DOI: 10.1109/TDEI.2018.007724

IEEE Transactions on Dielectrics and Electrical Insulation Vol. 26, No. 2; April 2019 381

conducted on the secondary side of the transformer is considerably lower than that on its primary side. The conditions of the secondary side are more appropriate for the commercialized film capacitors, which normally use series resonant capacitors because the film capacitors have been manufactured with high voltage and low current rated capacity.

In terms of the three-phase resonant converter design, the three-phase circuit could be changed to the single-phase equivalent circuit to simplify the design procedure because the conducting current paths of the three-phase structure are not independent. Conventional studies have involved analysis using this method for the wye-wye three-phase connected structure [12-14]. However, the proposed 5.4 kW resonant converter uses a delta-star three-phase structure to compensate for the low voltage input of the lithium polymer battery. There is no neutral point on the primary side of the transformers, which makes it difficult to using the original wye-wye three-phase analyzing method. Therefore, in this work, the delta-star three-phase resonant converter design method is introduced by applying the existing wye-wye structure. This method draws the resonant components on the wye side of the transformer, and the three-phase circuit is changed to the equivalent single-phase circuit by connecting the neutral point to the load for the three-phase resonant converter design.

To verify the validity and performance of the offered features, we designed and implemented 5.4 kJ/s three-phase resonant converters using a 22 and 44 V commercialized lithium-ion batteries which have the maximum voltage and 16 Ah capacity. When selecting a battery, the required operating time under the physical space limitations of the power supply has been considered. The experimental results for the 22 and 44 V lithium-ion battery-based resonant converters are presented as comparisons of variables such as converter operation waveforms, full charging time, temperature increase of the used components, and the power efficiency.

This paper is structured as follows. Section II summarizes the features of the proposed three-phase delta-star structure suitable for large currents and the considerations of the large currents employed. Section III shows the design procedure and simulation results of the proposed delta-star three-phase resonant converter using an equivalent circuit, operating mode analysis, and design values. Section IV examines the advantages of the proposed three-phase resonant converter with the results of experiments using the resistor and capacitor loads of the 22 and 44 V based three-phase resonant converters. Section V concludes this paper.

2 DISTINCTIVE CHARACTERISTICS OF THE PROPOSED CONVERTER

The distinctive characteristics of the proposed three-phase resonant converter are as follows.

2.1 METHODS FOR CONDUCTING THE HIGH BATTERY CURRENT

Because the lithium battery produces a relatively high current, the primary side of the three-phase circuit is

introduced to reduce the current burden on each switch used. In addition, the transformers are connected in a delta formation so that the reduced turns ratio can be obtained as the line-to-line voltage is applied to the load and not the transformer phase voltage. The turns ratio can be reduced by the difference between the phase and line-to-line voltages. The reduced turns ratio also results in a decreased current flowing into the transformer’s primary side when the same output power is required.

In terms of the rated capacity of the used components, the commercialized film capacitors, which are used as resonant series or parallel capacitors in resonant converters, are more suitable under low current and high voltage conditions. The datasheet of most film capacitors shows that there is current limitation, which makes it difficult to directly conduct battery current. In the proposed circuit, the film capacitors, which are used in series and parallel resonant capacitors, are moved from the primary side to the secondary side of the transformers. As a result, the conducting current is sufficiently reduced, and it could be handled with the capacity of single film capacitor.

2.2 EQUIVALENT SINGLE-PHASE CIRCUIT FOR THE USED THREE-PHASE RESONANT CONVERTER

The delta-star three-phase resonant converter circuit was analyzed by using the equivalent single-phase resonant converter circuit, which was drawn on the transformer’s secondary side. The equivalent circuit makes the design procedure and analyze to be simple. If the three-phase resonant converter is analyzed without changing to the single-phase equivalent circuit, the resonant current path should be divided by the three lags of inverter; however, in practice, it is difficult because each phase current path is not independent. To make the current path independent, the single-phase equivalent circuit, which is placed on the secondary side of transformer, is introduced by connecting the neutral point of the secondary transformer to the load. Then, the single-phase resonant current is approximated as a trapezoidal waveform for the design. Analysis of the operating mode will show that the single-phase equivalent resonant converter circuit flows the divided current path as well as the trapezoidal resonant current waveform.

3 ANALYSIS AND DESIGN

Figure 1 shows a schematic of the proposed system. The system does not require an input rectifier because the LiPo battery is used as an input voltage source. The MOSFET switches operate at the fixed switching frequency and the output power is transferred to the transformer’s secondary sides, which have the resonant series and parallel capacitors. The secondary sides of the transformers are connected to the output rectifiers, which create the final DC output voltage at the load.

3.1 ANALYSIS OF THE PROPOSED THREE PHASE RESONANT CONVERTER

The operation mode of the three-phase resonant converter is more complex than that of the single-phase operation mode. The

382 C.-G. Cho et al.: Design of a 5.4 kJ/s Three-Phase Resonant Converter based on a Lithium Polymer Battery

Figure 1. Schematic of the proposed three-phase resonant converter with the resistor load.

operation waveforms and circuits are shown according to each mode in Figures 2 and 3.

Figure 2. Operating waveforms of the proposed three-phase resonant converter.

The operation mode is divided based on the single-phase resonant current (IL1p), and one cycle could be classified into six modes. The half period of one cycle is the same as the previous period, but the resonant current direction is different. Therefore, the three modes would be analyzed by the operation waveforms and circuits.

Under mode 1a (M1-a), the resonant current of the first transformer (L1p) begins to follow a positive direction. The current that travels along the transformer’s secondary side also follows the same direction. Under mode 1b (M1-b), the output

rectifier diodes are changed from D3 and D2 to D1 and D6 owing to the voltage differences between the three-phase transformers. These voltage differences also create another current path, which is the parallel resonant capacitors Cp1 and Cp3. Under the next mode, switch SW4 turns on and generates a negative current that results in a zero-voltage turn-on, reducing the switching losses. The negative current changes its direction by the resonance. After the current direction of changes from negative to positive, mode 1d commences.

Mode 2a (M2-a) begins with the change in the direction of the resonant current of the secondary transformer (L2p), and the parallel capacitors (Cp1, Cp3) remain under charging conditions. When mode 2b begins, parallel resonant capacitors Cp1, Cp2 are charged. The operation of modes 2c and 2d is the same as that of modes 1c and 1d. Switch SW5 begins with a negative current for zero-voltage switching, and its direction is changed to positive by the resonance.

Under mode 3a, the resonant current of the third transformer (L3p) changes its direction. However, the direction of other resonant currents remains the same. Like modes 1b and 2b, the voltage difference under mode 3b creates different current paths, for example, output diode D4 and parallel capacitors Cp2 and Cp3. Under mode 3c, switch SW1 is open and the current on the transformer’s primary side conducts through the anti-parallel diode of SW2. This is indicated by the negative current of Figure 2 ISW2.

Although Figures 2 and 3 show the detailed operation of the proposed three-phase delta-star connected resonant converter, it is difficult to define the current and the voltage equations in terms of the converter design the related three-phase structure. Therefore, the proposed three-phase circuit is mathematically analyzed and designed based on Figure 4, which involves the connection of the neutral point at the transformer’s secondary sides to divide the three-phase operation into single-phase operations [12-14]. The operation waveforms of the divided single phases are shown in Figure 5, and the equivalent circuits appearing on the secondary sides of the transformers are shown in Figure 6. Therefore, the input voltage (nVin) and resonant inductor (L’s) are used to calculate values that reflect the turns ratio of the transformer.

The single-phase resonant current is optimized as a trapezoidal waveform [15], and some assumptions are made. First, the value of Cp is assumed to be smaller than that of Cs.

SW1

SW2

SW3

SW4

SW5

SW6

L2s

B

D1

D2

CP1

CS1

CS3

CS2

D3

D4

D5

D6

c

Rload

+

Vout

‐

Vbattery

1:N

A

L3p

b

a

CP2 CP3

C

iL1p

iL2p

iL3piCp1

iCp2

iCp3

ISW1

+vSW1

‐ISW3

+vSW3

‐

ISW5

+vSW5

‐

ISW6ISW4ISW2


Figure 3. Operation mode circuits of the proposed three-phase resonant converter; (a) M1-a, (b) M1-b, (c) M1-c, (d) M1-d, (e) M2-a, (f) M2-b, (g) M2-c, (h) M2-d, (i) M3-a, (j) M3-b, (k) M3-c, (l) M3-d.


Figure 4. Schematic of the proposed three-phase resonant converter connecting the neutral point for single-phase analysis.

Second, the series resonant capacitor voltage is assumed to charge linearly under mode 2 owing to the trapezoidal approximation of the resonant current. Finally, the amp-second area of Q1 and Q2 in Figure 5 are considered to be higher values than those of Q1’ and Q2’, so Q1’ and Q2’ are assumed to be negligible when calculating the input and output power.

Before expressing the analysis Equations, the equivalent resonant capacitor, resonant frequency, and characteristic impedance are denominated as follows:

(1)

Based on both Equation (1) and the aforementioned assumptions, the resonant current of mode 1 could be expressed as follows, and the equivalent circuit of Figure 6a using a connected neutral point allows a more clear understanding of the mechanism.

(2)

(3)

Equation (2) is induced by the differential Equation of the inductor current, and Equation (3) can be calculated using the initial conditions of the parameters.

Mode 2 begins with a fully charged parallel capacitor, and its voltage is drawn as a voltage source in Figure 6b. Equation (5) could be induced by Equation (4), which is the differential inductor current equation. The series’ resonant frequency and characteristic impedance are used. In addition, Equation (6) presents the assumed linear charging of the voltage of the series capacitor.

)(sin)(2

)(cos)()(

11

11'2,'

ttZ

tVVnV

tttiti

osos

Csoutin

ossLMsL

(4)

)(sin2

)(cos)( 1,

1,'2,' ttZ

VttIti os

os

peakCsospeaksLMsL (5)

sMpeaksLpeakCs CtIV 2,', (6)

Figure 5. Steady state operating waveforms of the three-phase resonant converter using a neutral point for single-phase analysis.

Figure 6. Equivalent circuits for M1 – M3; (a) M1; (b) M2; (c) M3.

Under mode 3, it is notable that the input voltage is zero, because the primary sides of one transformer have the same potential by switching MOSFETs. Figure 6c shows the zero-input voltage, and its current Equation is as follows:

)(sin)(2

)(cos)()(

22

22'3,'

ttZ

tVV

tttiti

osos

Csout

ossLMsL

(7)

If linear approximation is applied to Equation (7), it can be rewritten as follows:

)('2

-)( 2,

,'3,' ttL

VVIti

s

peakCsoutpeaksLMsL

(8)

In addition, the input power of the single-phase transformer is arranged as follows:

sinin fQQnVP 2)(3

121 (9)

where

1

0

'11)(2

11 1,'1,'

t

t MsLMpeaksL QQdttitIQ (10)

eps

soeopos

epss

oeoposps

pse C

LZ

CLCC

CCC

,,,,

,,

,, ,1

,

)(sin)()(

)(cos)()(

000

00'1,'

ttZ

tVtVnV

tttiti

oeoe

CsCpin

oesLMsL

)(sin2

)( 0,

1,' ttZ

VVnVti op

op

peakCsoutinMsL


2

1

'22)(2 2,'2,'

t

t MsLMpeaksL QQdttitIQ (11)

sMMM fttt 61321 (12)

3.2 DESIGN OF THE PROPOSED THREE-PHASE RESONANT CONVERTER USING A NEUTRAL-POINT

CONNECTED EQUIVALENT CIRCUIT

The design parameters based on the analysis of the proposed 5.4 kJ/s three-phase resonant converter with trapezoidal approximation of the single-phase resonant current are presented in Table 1.

Table 1. Design parameters of the 5.4 kJ/s three-phase resonant converter.

Parameters Values Related

Equations

LiPo battery voltage (Vin) 22 V 44 V -

Switching frequency (fS) Turns ratio (n) Series resonant capacitor (CS) Resonant inductor (LS)

50 kHz 10

3 µF 0.65 µH

70 kHz 5

3 µF 1.86 µH

- (9) (10) (11)

(6) (8)

Parallel resonant capacitor (CP) 54 nF 39 nF (3)

First, the output power, input voltage, and switching frequency should be determined using the given specifications of the system. Following this, Equations (10) and (11) are submitted into Equation (9) to compare the relationship between the turns ratio (n) and peak current of the resonant inductor (IL’s,peak). The turns ratio is determined by considering the peak current value, and it is notable that the value of the turns ratio could quite small, which is used by the delta-star structure of the proposed system. If the turns ratio is simply calculated based on the input and output voltage, 27 and 13 turns ratios are required for the 22 and 44 V based capacitor chargers, respectively. Second, the series resonant capacitance should be selected considering the peak voltage of the series capacitor (VCs,peak).

Using the selected turns ratio and series resonant capacitance, the resonant inductance (IL’s) of the transformer’s secondary side could be calculated by Equation (8), which is the result of the linear approximation of the resonant current of M3. The resonant inductor (ILs) value in Table 1 is calculated using the turns ratio for reflecting to the transformer’s primary side.

Finally, the parallel characteristic impedance (Zop) is calculated from the magnitude of Equation (3), and the parallel resonant capacitance can also be obtained.

With regard to the transformer, the TDK PC40 PQ 78×89×42 is used as three-phase transformers core. The theoretical minimum turn for the primary side can be calculated using Equation (13)

Cp AB

n

2

1041

(13)

where λ1 is the applied primary volt-seconds [V·s], ΔB is the peak AC flux density [T], and Ac is the core cross-sectional area [cm2].

Based on the core datasheet and given design parameters, the minimum turn is calculated as 0.93 with a saturation magnetic flux density of 0.38 T at 100 °C and 4.8 cm2. It is possible to choose a primary turn number greater than 0.93, but as the number of primary side turns increases, the core loss decreases. As a result, the actual 5-turn for the primary side of the three-phase transformer is selected as the maximum number by considering the bobbin size and inner empty space of the power supply. The core loss graph of the datasheet shows a core loss of 8 kW/m3 when the design parameters are used.

The PSpice simulation results that used the design parameters of the 22 and 44 V input LiPo battery voltages are shown in both Figures 7 and 8. Figure 7 shows the output voltage, resonant current of the secondary side, parallel resonant capacitor voltage, and the series resonant capacitor voltage, which match the steady state operation waveforms of Figure 5. The 600 V output voltages are generated at a resistor load of 66.66 Ω for both chargers to show the maximum charging power. It should be considered that the primary resonant currents are increased by the turns ratio, so the peak current values of the primary side are 150 and 75 A, respectively. The current difference between the 22 and 44 V LiPo batteries is much higher in the single MOSFET, so the three-phase structure is useful for a high current. As shown in Figure 8, the conducting peak currents of the single MOSFET are approximately 300 and 150 A. These high currents are also exhibited in the LiPo battery current waveforms. Therefore, in terms of the drain-source voltage, the higher turn-off peak voltage occurs in the 22 V LiPo battery using the three-phase capacitor charger. We also could expect the switching loss of the MOSFET switches as heat is higher when the 22 V LiPo battery is used.

(a) (b)

Figure 7. PSpice simulation results for maximum charging power; (a) using a 22 V LiPo battery for input voltage and (b) using a 44V LiPo battery for input voltage.

4 EXPERIMENTAL RESULTS

By using the 22 and 44 V lithium polymer batteries as input voltage sources, two capacitor chargers are designed and implemented as in Figure 9. The difference between the actual leakage inductance of the used transformers and the design parameters is compensated by controlling the parallel resonant capacitance to achieve the target output voltage. Both the


resistor and capacitor loads are used to verify the performance of the chargers and demonstrate the advantages of the proposed system.

(a) (b)

Figure 8. PSpice simulation results for comparing switching conditions; (a) using a 22 V LiPo battery for input voltage, (b) using a 44 V LiPo battery for input voltage.

(a) (b)

Figure 9. Photographs of the developed three-phase resonant capacitor charger; (a) 22 V LiPo battery-based capacitor charger, (b) 44 V LiPo battery-based capacitor charger.

4.1 EXPERIMENTAL RESULTS WITH RESISTOR LOAD

Figure 10 shows the operating waveforms of the 5.4 kJ/s output power with the measured power efficiency. Both the 22 and 44 V capacitor chargers achieved the target output voltage of 600 V, and the measured waveforms are mostly matched by the simulation results. Therefore, the operation of the proposed three-phase resonant converters designed using the neutral point is verified. The results show that the current burden of the resonant components placed on the transformer secondary side is reduced. Only 20 A of the resonant peak current follows on the transformer secondary side.

From comparing the two capacitor chargers, the turns ratio of the 22 V based capacitor charger is double that of the 44 V based capacitor charger, so the transformer primary resonant current of the 22 V based charger is higher. This high current also means that the 22 V input LiPo battery is quickly discharged and vulnerable to the parasitic inductance of the PCB board or the used wires. In addition, the high current affects the power efficiency. Although the switching frequency is lower for the 22 V based capacitor charger at 50 kHz, the power efficiency is 82.0%. However, the 44 V based capacitor charger, which uses the 70 kHz switching frequency, achieved a power efficiency of 92.5%.

(a)

(b)

Figure 10. Experimental waveforms of the 5.4-kJ/s output operation with the measured power efficiency; (a) using a 22 V LiPo battery for input voltage and (b) using a 44 V LiPo battery for input voltage.

Under the maximum output charging power condition, the operating temperature presented in Figure 11 was only tested for the 44 V LiPo battery-based capacitor charger. The rate of increase for the temperature of the MOSFET exceeded 100 degrees for 30 seconds in the 22 V based capacitor charger. The MOSFET and transformer temperatures with the 44 V based charger are driven for 30 seconds to reach 55 and 40 degrees, respectively, and driven for a further two minutes to reach 130 and 80 degrees.

Figure 11. Operating temperature test results of the 44 V LiPo battery-based capacitor charger with maximum output power.

4.2 EXPERIMENTAL RESULTS WITH CAPACITOR LOAD

Depending on the input LiPo battery voltage, Figures 12 and 13 show the operating waveforms with the 1.4-mF capacitor bank load. The charger operates at a fixed switching


frequency when charging the bank from 0 to 600 V and will stop after the target voltage is reached. Thereafter, when the voltage of the capacitor bank is below the set specific voltage, the charger is operated again to maintain the target voltage of the capacitor bank.

(a)

(b)

(c)

Figure 12. 1.4-mF capacitor bank charging experimental waveforms for the 22 V LiPo battery based charger. (a) Charging voltage of the capacitor bank and battery current. (b) Waveforms when 150 V is charged at the capacitor bank. (c) Waveforms when 550 V is charged at the capacitor bank.

The 600-charging time is approximately 80 ms, which is the same for both chargers, but the output current of the LiPo battery as the input voltage source is different. The output current used for the proposed three-phase resonant capacitor charger is 300 A for the 22 V based charger and 150 A for the 44 V based charger. In addition, the voltage across the main MOSFET and the resonant current on the secondary side of the transformer were measured at the moment when the capacitor bank was charged to a specific voltage, such as 150 or 550 V. The larger the voltage charged by the capacitor bank,

the closer the resonant current waveform is to the trapezoidal shape assumed in the design.

(a)

(b)

(c)

Figure 13. 1.4 mF capacitor bank charging experimental waveforms for the 44 V LiPo battery-based charger. (a) Charging voltage of the capacitor bank and battery current. (b) Waveforms when 150 V is charged at the capacitor bank. (c) Waveforms when 550 V is charged at the capacitor bank.

5 CONCLUSIONS

Based on the mode analysis, and the design, simulation, and experimental results, the advantage of resolving the high current burden of the lithium polymer battery is verified along with the stable maximum output charging power of the proposed three-phase delta-star connected resonant converter.

One of the suggested advantages, the delta-star structure for three-phase transformers, causes the turns ratio to decrease efficiently as the output voltage is supplied by the line to line voltage of the three-phase transformers, and not the phase voltage. This also means that the resonant current of the primary sides of the three transformers is reduced when the


same output power is generated. The size of the three-phase transformers with reduced turns ratio could be reduced by using the delta-star connection. In addition, other advantages include the location of the components on the secondary side, which creates low current and high higher voltage conditions. Placing the used components on the transformer’s secondary sides reduces the current burden on the components, and it is easy to select a suitable film capacitor as a resonant element. Finally, the proposed system has merits including a suitable structure for high power generation and easier component arrangements.

To verify the aforementioned advantages, the 5.4 kJ/s 22 and 44 V LiPo battery-based capacitor chargers are tested. The resistor load experiments show both the accordance between the simulation analysis and the measured operation waveforms as well as the stable maximum output charging power. When the maximum output power is reached, its power efficiencies are 82.0 and 92.5%, respectively. The capacitor load experiments demonstrate the performance of the proposed two capacitor chargers. Both capacitor chargers of the capacitor bank achieved the same charging time required to reach 600 V.

ACKNOWLEDGMENT This research was supported in part by the National

Research Foundation of Korea (NRF) grant funded by the Korean government (MSIP) (NRF-2017R1A2B3004855) and in part by the Chung-Ang University Graduate Research Scholarship in 2018.

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