Design of High Voltage, High Power and High Frequency Transformer in LCC Resonant Converter Jun Liu, Licheng Sheng, Jianjiang Shi, Zhongchao Zhang, Xiangning He, Senior Member, IEEE College of Electrical Engineering Zhejiang University Hangzhou, 310027 China Abstract-The design of a high voltage, high power and high frequency transformer is introduced considering its operation in the LCC resonant converter. The leakage inductance and winding capacitance of the transformer are used as the resonant elements. An additional series resonant capacitor is added to form the LCC topology. The discontinuous current mode (DCM) is adopted to achieve the ZCS turn-on and ZVZCS turn-off of the power switches. Smaller value of the winding capacitance is preferred because it has the effect of decreasing the peak value of the resonant current at almost the same output voltage. The theoretic calculation of the winding capacitance and leakage inductance of the transformer is given. The error between the theoretical calculation and practical measurement is within 15%. So optimization design of the parasitic resonant elements can be achieved to meet requirement of the circuit. A prototype of LCC resonant converter with 60kW and 60kV output is built based on the designed transformer. Experiment results are given.

with a capacitive output filter has been proven a good choice for high voltage applications [6]. It can use the parasitic parameters as resonant elements and incorporate them into the operation of the circuit. This paper describes how to develop a high voltage, high power and high frequency transformer considering its operation in the LCC resonant converter. The operational principle of the LCC resonant converter considering the high voltage, high power and high frequency transformer is given in Section II. The transformer design consideration including the theoretic calculation of the winding capacitance and leakage inductance of the transformer is given in Section III. Experimental results are given in Section IV.

Keywords：transformer, high voltage, high frequency, high power, LCC, soft switching, winding capacitance, leakage inductance

The LCC resonant converter with a capacitive output filter considering the parasitic parameters of the transformer is shown in Fig.1. The leakage inductance Lr and the winding capacitance Cp of the transformer are used as the resonant inductance and the resonant capacitance, respectively. The high voltage, high power and high frequency transformer is design for the power supply used for electrostatic precipitators, which has the following electrical specifications requirement: Output voltage Vout=60kV; Output power Pout=60 kW.

I. INTRODUCTION High voltage, high frequency and high power supplies are widely used in electrostatic precipitators and wastewater treatment to achieve environment protection [1, 2]. In these applications, the high voltage, high power and high frequency transformer is the essential part because it contributes to the energy transition, voltage boost and safety isolation. Design and characteristics of such a transformer is quite different from the conventional one due to the special consideration of magnetic, electric and thermal stresses under the high voltage, high power and high frequency conditions [3]. When the secondary winding capacitance of the transformer is referred to the primary side, its value is multiplied by the square of the turns ratio, which is quite large. The referred value is considerable for the high frequency operation. There is always relatively large distance between the primary and secondary winding to ensure insulation intensity under the high output voltage. So the electromagnetic coupling is not as tight as in conventional low voltage transformer which leads to a large leakage inductance [4]. The parasitic parameters of the transformer have a great effect on the operation of the circuit, such as ringing of the input current. Therefore, a proper topology and control strategy should be adopted to avoid the bad influence of the parasitic parameters [5]. The LCC resonant converter

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1034

II. TRANSFORMER APPLICATIONS

Fig.1 LCC resonant converter considering the parasitic parameters of the transformer

Because of the high output voltage and power, reliability of the system should be considered more carefully. A simple control method called discontinuous current control mode (DCM) is adopted [7]. Fig 2 shows the typical waveforms. The control signals are very easy to be generated. ZCS turn-on and ZVZCS turn-off of the power switches can be

achieved by adopting DCM.

The amplitude of the flux density Bmax is limited to 0.2 T in order to reduce the core losses under high frequency and to prevent the transformer from saturation during the restart process of the circuit. The turns number of the primary and the secondary side winding, n1 and n2, can be calculated by (1) and (2), respectively, which yields n1=5, n2=600. B

n1 =

(1)

(2) n2 = 120 n1 Because the leakage inductance is used as resonant inductance, it will induce extra increase of the flux density which may cause the magnetic core into saturation. The bigger value of the leakage inductance is the more increase of the flux density. So the primary and secondary windings are concentric with the centre pole to get a small leakage inductance. In this design, the value of the leakage inductance is 3.5μH. Fig.4 shows the simulation waveform of the primary resonant current. The amplitude of it, ipeak, is about 300 A. Then, the maximum value of the flux density increase caused by the leakage inductance can be calculated by (3), which yield 0.03 T. Compared with Bmax, this value is quite small. So the contribution of the leakage inductance to the magnetic saturation can be ignored. Lr ii peak (3) ΔB = n1 Ae

Fig .2 Typical waveforms with DCM

III．TRANSFORMER DESIGN A.

Switching Frequency Selection High frequency switching will reduce the size and weight of the high voltage transformer. However, further reduction by higher frequency switching can’t be achieved due to the insulation requirement. The natural resonant frequency of the high voltage transformer is also a constraint. Furthermore, high frequency switching will need high driving power. Take CM600DU-24NF IGBT module for example, 40 kHz frequency switching will need a driving power of 6W. So selection of the driver for high power and high frequency uses is very difficult. As a compromise, fs=20 kHz is selected as the switching frequency.

B

B.

Turn Ratios Selection The DC link voltage is approximately 500 dc, which is obtained by the three-phase rectifier. The output voltage is 60kV. So the output-input ratio should be 120. Both the turns ratio of the transformer and LCC resonance contribute to the final voltage boost. It can be found by simulation that in the load range the step-up coefficient of the LCC resonant is about 1.2. So in practice, the step-up coefficient of the LCC resonant is used as design margin and the turns ratio of the high voltage transformer is selected as 120.

Fig.4 Simulation waveform of primary resonant current

C.

Magnetic Selection Power ferrites are employed as the magnetic material due to the high resistivity and low eddy current losses under high frequency. EE320 is selected to accommodate the large winding turns and to satisfy the insulation requirement. Its specifications are shown in Fig.3. Two pairs of EE320 are used to get a larger area of centre pole Ae, and to minimize the winding turns.

D.

A B C

Winding and Wire Design The secondary winding capacitance plays an important role in the operation of the circuit. Fig.5 shows comparison of the simulation waveforms with different values of the winding capacitance Cp. The waveforms of the output voltage and the primary resonant current are measured with the same specifications except the winding capacitance. Although the output voltage is almost the same, the peak value of the primary resonant current is quite different. Smaller value of winding capacitance gets smaller current peak value. So special winding structure should be applied to minimize the winding capacitance and at the same time the insulation requirement under high voltage should be considered. In practice, the secondary winding is wounded into eight slots, which can reduce the winding capacitance dramatically because the slot capacitance is in series rather than in parallel. Furthermore, each slot includes five layers. This structure can limit the voltage across each slot to only 1/8 of the output voltage and reduce the layer-to-layer voltage. The secondary

Fig.3 Core specifications of EE320

978-1-422-2812-0/09/$25.00 ©2009 IEEE

Vin ⋅10 4 4 Bmax Ae f s

1035

The choice of the layer-to-layer insulation material is extremely important for the following reasons: a) enough insulation strength; b) low dissipation factor to minimize the dielectric losses under high operation frequency;; c) good heat transfer coefficient to balance the temperature of the inner and outer layers; d) the dielectric constant should be considered to minimize the winding capacitance; e) insensitive to heat to have good circuit stability. The polyimide thin film is selected as the layer-to-layer insulation material due to its excellent comprehensive performance. Although the price of the polyimide thin film is very high, the amount in the design of the high frequency and high voltage transformer is little. The total cost of it is only a small part of the whole transformer’s cost.

winding structure is shown in Fig.6.

(a)

Output voltage

F.

Leakage Inductance and Capacitance Calculation The leakage inductance referred to the primary side is calculated by (4) [8]. μ ( MLT ) n12 b+d Lr = 0 (c + ) (4) 3 h

(b) Primary resonant current Fig.6 Comparison between different winding capacitance Cp

Copper foil is used as the primary wire due to the good occupation of the core window and results in a small leakage inductance. The eddy current losses caused by the fringing flux are small because no air gap exists in the magnetic core in the design. Considering the skin effect and the current value, the wire specifications and the current density are as follows: Primary winding—0.2mm copper foil, 3A/mm2; Secondary winding—AGW18 wire, 1.3A/mm2.

Where (refer to Fig.6), MLT—mean length turn; μ0—absolute permeability; h—window height; b—primary winding width; c—distance between primary and secondary winding; d—secondary winding width. Because the width of the primary and the secondary winding is small compared to the distance between them, the leakage inductance is approximately linear proportion to the distance. This distance can be changed in certain extent to satisfy the requirement of the circuit operation. However, the tradeoff between the leakage inductance and the insulation distance should be considered. The secondary winding capacitance is calculated by (5) [9, 10]. 4ε 0ε r lw(nlayer − 1) Cp = (5) 3dnslot nlayer 2 Where Cp— equivalent capacitor of the whole winding; nslot—number of slots; nlayer—number of all layers of one slot; ε0 —absolute dielectric constant; εr—effective dielectric constant of insulation material; l—mean turn length of two considered layers; w—height of one slot; d—effective distance between two layers. The theoretical calculation and the measurement results of the parasitic parameters are given in table I. The measurement results are derived from the transformer impedance by the

Fig.6 Structure of the transformer

E.

Insulation and Thermal Consideration The transformer oil is selected as the transformer encapsulation material due to its high insulation strength and good heat conductivity. Especially the transformer oil can flow through the space between the primary winding and the secondary winding and serves as the good heat conduction material.

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1036

API Model 200 Analog Network Analyzer, which is measured from primary side of the transformer with the secondary side open. The measured transformer impedance is shown in Fig.7. It can be seen that the error between the theoretical calculation and measurement of the parasitic parameters is within 15%. So the theoretical calculation can be used as a tool to design and optimize the transformer before manufacture considering its operation in the LCC resonant converter.

Fig.9 Photograph of the transformer

V. CONCLUSION Fig.7 The measured transformer impedance

A high voltage and high frequency transformer prototype has been built and tested for the LCC resonant converter. The design consideration was introduced, which is quite different from the conventional transformer design. The theoretical calculation of the parasitic parameters fit well with the results of measurement, which provides a possibility to optimize them as the resonant elements to meet the requirement of the LCC resonant converter.

Table І. Comparison of theoretical calculation and measurement

theory

measurement

error

leakage inductance

3.0 μH

3.5 μH

14.3%

winding capacitance

43 pF

50 pF

14%

IV. EXPERIMENTAL RESULTS

ACKNOWLEDGMENT

A high voltage transformer was developed for a 60kW, 60kV output LCC resonant converter used for electrostatic precipitators. Using the leakage inductance and the winding capacitance of the high voltage transformer, only an extra series capacitor is added to form the LCC resonant tank. The primary side resonant current of the transformer is shown in Fig.8 when adopting the discontinuous current control mode.

The authors would like to thank financial support of the National Science Foundation of China (50737002). They would also like to thank Zengyue Zhou, Hongxing Wang and Jianping Zhou for their technical support in the experimentation.

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REFERENCES [1] N. Grass, W. Hartmann and M. Klockner, “Application of different types of high-voltage supplies on industrial electrostatic precipitators,” IEEE Transactions on Industry Applications, 2004,40(6):1513-1520. [2] E. E. Bowles, S. Chapelle and G. X. Ferguson, et al, “A high power density, high voltage power supply for a pulsed radar system,” Costa Mesa, California, Conference, Power Modulator Symposium, 1994:170-173. [3] M. A. Perez, C. Blanco, M. Rico and F. F. Linera, “A new topology for high voltage, high frequency transformers,” APEC 1995 Conference Proceedings. 1995,2:554-559. [4] J. C. Fothergill, P. W. Devine and P. W. Lefley, “A novel prototype design for a transformer for high voltage, high frequency, high power use,” IEEE Transactions on Power Delivery.2001,16 (1): 89-98. [5] S. D. Johnson, A. F. Witulski and R. W. Erickson, “Comparison of resonant topologies in high-voltage DC applications,” IEEE Transactions on Aerospace and Electronic Systems , 1988. 24(3): 263-274. [6] A. K. S. Bhat, “Analysis and design of a series-parallel resonant converter with capacitive output filter,” IEEE Transaction on Industry Applications, 1991,21 (3): 523-530. [7] A. C. Lippincott and R. M. Nelms, “A capacitor-charging power supply using a series-resonant topology, constant on-time/variable frequency control and zero-current switching,” IEEE Transactions on Industrial Electronics, 1991,38(6):438-447.

20μs/div

Fig.8 Primary side resonant current of the high voltage transformer

The photograph of the high voltage transformer is shown in Fig.9. Its weight is about 120 kg.

978-1-422-2812-0/09/$25.00 ©2009 IEEE

1037

[8] [9]

W. T. McLyman, “Transformer and Inductor Design Handbook”, Marcel Dekker, New York and Basel, 2004. L. Dalessandro, Fabiana da Silveira Cavalcante and J.W. Kolar, “Self-Capacitance of High-Voltage Transformers,” IEEE Transactions on Power Electronics,, 2007. 22(5): 2081-2092.

978-1-422-2812-0/09/$25.00 ©2009 IEEE

[10] J. Biela and J. W. Kolar, “Using transformer parasitics for resonant converters-a review of the calculation of the stray capacitance of transformers,” Conference Record of the IAS, 2005,3:1868-1875.

1038

with a capacitive output filter has been proven a good choice for high voltage applications [6]. It can use the parasitic parameters as resonant elements and incorporate them into the operation of the circuit. This paper describes how to develop a high voltage, high power and high frequency transformer considering its operation in the LCC resonant converter. The operational principle of the LCC resonant converter considering the high voltage, high power and high frequency transformer is given in Section II. The transformer design consideration including the theoretic calculation of the winding capacitance and leakage inductance of the transformer is given in Section III. Experimental results are given in Section IV.

Keywords：transformer, high voltage, high frequency, high power, LCC, soft switching, winding capacitance, leakage inductance

The LCC resonant converter with a capacitive output filter considering the parasitic parameters of the transformer is shown in Fig.1. The leakage inductance Lr and the winding capacitance Cp of the transformer are used as the resonant inductance and the resonant capacitance, respectively. The high voltage, high power and high frequency transformer is design for the power supply used for electrostatic precipitators, which has the following electrical specifications requirement: Output voltage Vout=60kV; Output power Pout=60 kW.

I. INTRODUCTION High voltage, high frequency and high power supplies are widely used in electrostatic precipitators and wastewater treatment to achieve environment protection [1, 2]. In these applications, the high voltage, high power and high frequency transformer is the essential part because it contributes to the energy transition, voltage boost and safety isolation. Design and characteristics of such a transformer is quite different from the conventional one due to the special consideration of magnetic, electric and thermal stresses under the high voltage, high power and high frequency conditions [3]. When the secondary winding capacitance of the transformer is referred to the primary side, its value is multiplied by the square of the turns ratio, which is quite large. The referred value is considerable for the high frequency operation. There is always relatively large distance between the primary and secondary winding to ensure insulation intensity under the high output voltage. So the electromagnetic coupling is not as tight as in conventional low voltage transformer which leads to a large leakage inductance [4]. The parasitic parameters of the transformer have a great effect on the operation of the circuit, such as ringing of the input current. Therefore, a proper topology and control strategy should be adopted to avoid the bad influence of the parasitic parameters [5]. The LCC resonant converter

978-1-422-2812-0/09/$25.00 ©2009 IEEE

1034

II. TRANSFORMER APPLICATIONS

Fig.1 LCC resonant converter considering the parasitic parameters of the transformer

Because of the high output voltage and power, reliability of the system should be considered more carefully. A simple control method called discontinuous current control mode (DCM) is adopted [7]. Fig 2 shows the typical waveforms. The control signals are very easy to be generated. ZCS turn-on and ZVZCS turn-off of the power switches can be

achieved by adopting DCM.

The amplitude of the flux density Bmax is limited to 0.2 T in order to reduce the core losses under high frequency and to prevent the transformer from saturation during the restart process of the circuit. The turns number of the primary and the secondary side winding, n1 and n2, can be calculated by (1) and (2), respectively, which yields n1=5, n2=600. B

n1 =

(1)

(2) n2 = 120 n1 Because the leakage inductance is used as resonant inductance, it will induce extra increase of the flux density which may cause the magnetic core into saturation. The bigger value of the leakage inductance is the more increase of the flux density. So the primary and secondary windings are concentric with the centre pole to get a small leakage inductance. In this design, the value of the leakage inductance is 3.5μH. Fig.4 shows the simulation waveform of the primary resonant current. The amplitude of it, ipeak, is about 300 A. Then, the maximum value of the flux density increase caused by the leakage inductance can be calculated by (3), which yield 0.03 T. Compared with Bmax, this value is quite small. So the contribution of the leakage inductance to the magnetic saturation can be ignored. Lr ii peak (3) ΔB = n1 Ae

Fig .2 Typical waveforms with DCM

III．TRANSFORMER DESIGN A.

Switching Frequency Selection High frequency switching will reduce the size and weight of the high voltage transformer. However, further reduction by higher frequency switching can’t be achieved due to the insulation requirement. The natural resonant frequency of the high voltage transformer is also a constraint. Furthermore, high frequency switching will need high driving power. Take CM600DU-24NF IGBT module for example, 40 kHz frequency switching will need a driving power of 6W. So selection of the driver for high power and high frequency uses is very difficult. As a compromise, fs=20 kHz is selected as the switching frequency.

B

B.

Turn Ratios Selection The DC link voltage is approximately 500 dc, which is obtained by the three-phase rectifier. The output voltage is 60kV. So the output-input ratio should be 120. Both the turns ratio of the transformer and LCC resonance contribute to the final voltage boost. It can be found by simulation that in the load range the step-up coefficient of the LCC resonant is about 1.2. So in practice, the step-up coefficient of the LCC resonant is used as design margin and the turns ratio of the high voltage transformer is selected as 120.

Fig.4 Simulation waveform of primary resonant current

C.

Magnetic Selection Power ferrites are employed as the magnetic material due to the high resistivity and low eddy current losses under high frequency. EE320 is selected to accommodate the large winding turns and to satisfy the insulation requirement. Its specifications are shown in Fig.3. Two pairs of EE320 are used to get a larger area of centre pole Ae, and to minimize the winding turns.

D.

A B C

Winding and Wire Design The secondary winding capacitance plays an important role in the operation of the circuit. Fig.5 shows comparison of the simulation waveforms with different values of the winding capacitance Cp. The waveforms of the output voltage and the primary resonant current are measured with the same specifications except the winding capacitance. Although the output voltage is almost the same, the peak value of the primary resonant current is quite different. Smaller value of winding capacitance gets smaller current peak value. So special winding structure should be applied to minimize the winding capacitance and at the same time the insulation requirement under high voltage should be considered. In practice, the secondary winding is wounded into eight slots, which can reduce the winding capacitance dramatically because the slot capacitance is in series rather than in parallel. Furthermore, each slot includes five layers. This structure can limit the voltage across each slot to only 1/8 of the output voltage and reduce the layer-to-layer voltage. The secondary

Fig.3 Core specifications of EE320

978-1-422-2812-0/09/$25.00 ©2009 IEEE

Vin ⋅10 4 4 Bmax Ae f s

1035

The choice of the layer-to-layer insulation material is extremely important for the following reasons: a) enough insulation strength; b) low dissipation factor to minimize the dielectric losses under high operation frequency;; c) good heat transfer coefficient to balance the temperature of the inner and outer layers; d) the dielectric constant should be considered to minimize the winding capacitance; e) insensitive to heat to have good circuit stability. The polyimide thin film is selected as the layer-to-layer insulation material due to its excellent comprehensive performance. Although the price of the polyimide thin film is very high, the amount in the design of the high frequency and high voltage transformer is little. The total cost of it is only a small part of the whole transformer’s cost.

winding structure is shown in Fig.6.

(a)

Output voltage

F.

Leakage Inductance and Capacitance Calculation The leakage inductance referred to the primary side is calculated by (4) [8]. μ ( MLT ) n12 b+d Lr = 0 (c + ) (4) 3 h

(b) Primary resonant current Fig.6 Comparison between different winding capacitance Cp

Copper foil is used as the primary wire due to the good occupation of the core window and results in a small leakage inductance. The eddy current losses caused by the fringing flux are small because no air gap exists in the magnetic core in the design. Considering the skin effect and the current value, the wire specifications and the current density are as follows: Primary winding—0.2mm copper foil, 3A/mm2; Secondary winding—AGW18 wire, 1.3A/mm2.

Where (refer to Fig.6), MLT—mean length turn; μ0—absolute permeability; h—window height; b—primary winding width; c—distance between primary and secondary winding; d—secondary winding width. Because the width of the primary and the secondary winding is small compared to the distance between them, the leakage inductance is approximately linear proportion to the distance. This distance can be changed in certain extent to satisfy the requirement of the circuit operation. However, the tradeoff between the leakage inductance and the insulation distance should be considered. The secondary winding capacitance is calculated by (5) [9, 10]. 4ε 0ε r lw(nlayer − 1) Cp = (5) 3dnslot nlayer 2 Where Cp— equivalent capacitor of the whole winding; nslot—number of slots; nlayer—number of all layers of one slot; ε0 —absolute dielectric constant; εr—effective dielectric constant of insulation material; l—mean turn length of two considered layers; w—height of one slot; d—effective distance between two layers. The theoretical calculation and the measurement results of the parasitic parameters are given in table I. The measurement results are derived from the transformer impedance by the

Fig.6 Structure of the transformer

E.

Insulation and Thermal Consideration The transformer oil is selected as the transformer encapsulation material due to its high insulation strength and good heat conductivity. Especially the transformer oil can flow through the space between the primary winding and the secondary winding and serves as the good heat conduction material.

978-1-422-2812-0/09/$25.00 ©2009 IEEE

1036

API Model 200 Analog Network Analyzer, which is measured from primary side of the transformer with the secondary side open. The measured transformer impedance is shown in Fig.7. It can be seen that the error between the theoretical calculation and measurement of the parasitic parameters is within 15%. So the theoretical calculation can be used as a tool to design and optimize the transformer before manufacture considering its operation in the LCC resonant converter.

Fig.9 Photograph of the transformer

V. CONCLUSION Fig.7 The measured transformer impedance

A high voltage and high frequency transformer prototype has been built and tested for the LCC resonant converter. The design consideration was introduced, which is quite different from the conventional transformer design. The theoretical calculation of the parasitic parameters fit well with the results of measurement, which provides a possibility to optimize them as the resonant elements to meet the requirement of the LCC resonant converter.

Table І. Comparison of theoretical calculation and measurement

theory

measurement

error

leakage inductance

3.0 μH

3.5 μH

14.3%

winding capacitance

43 pF

50 pF

14%

IV. EXPERIMENTAL RESULTS

ACKNOWLEDGMENT

A high voltage transformer was developed for a 60kW, 60kV output LCC resonant converter used for electrostatic precipitators. Using the leakage inductance and the winding capacitance of the high voltage transformer, only an extra series capacitor is added to form the LCC resonant tank. The primary side resonant current of the transformer is shown in Fig.8 when adopting the discontinuous current control mode.

The authors would like to thank financial support of the National Science Foundation of China (50737002). They would also like to thank Zengyue Zhou, Hongxing Wang and Jianping Zhou for their technical support in the experimentation.

100A/div

REFERENCES [1] N. Grass, W. Hartmann and M. Klockner, “Application of different types of high-voltage supplies on industrial electrostatic precipitators,” IEEE Transactions on Industry Applications, 2004,40(6):1513-1520. [2] E. E. Bowles, S. Chapelle and G. X. Ferguson, et al, “A high power density, high voltage power supply for a pulsed radar system,” Costa Mesa, California, Conference, Power Modulator Symposium, 1994:170-173. [3] M. A. Perez, C. Blanco, M. Rico and F. F. Linera, “A new topology for high voltage, high frequency transformers,” APEC 1995 Conference Proceedings. 1995,2:554-559. [4] J. C. Fothergill, P. W. Devine and P. W. Lefley, “A novel prototype design for a transformer for high voltage, high frequency, high power use,” IEEE Transactions on Power Delivery.2001,16 (1): 89-98. [5] S. D. Johnson, A. F. Witulski and R. W. Erickson, “Comparison of resonant topologies in high-voltage DC applications,” IEEE Transactions on Aerospace and Electronic Systems , 1988. 24(3): 263-274. [6] A. K. S. Bhat, “Analysis and design of a series-parallel resonant converter with capacitive output filter,” IEEE Transaction on Industry Applications, 1991,21 (3): 523-530. [7] A. C. Lippincott and R. M. Nelms, “A capacitor-charging power supply using a series-resonant topology, constant on-time/variable frequency control and zero-current switching,” IEEE Transactions on Industrial Electronics, 1991,38(6):438-447.

20μs/div

Fig.8 Primary side resonant current of the high voltage transformer

The photograph of the high voltage transformer is shown in Fig.9. Its weight is about 120 kg.

978-1-422-2812-0/09/$25.00 ©2009 IEEE

1037

[8] [9]

W. T. McLyman, “Transformer and Inductor Design Handbook”, Marcel Dekker, New York and Basel, 2004. L. Dalessandro, Fabiana da Silveira Cavalcante and J.W. Kolar, “Self-Capacitance of High-Voltage Transformers,” IEEE Transactions on Power Electronics,, 2007. 22(5): 2081-2092.

978-1-422-2812-0/09/$25.00 ©2009 IEEE

[10] J. Biela and J. W. Kolar, “Using transformer parasitics for resonant converters-a review of the calculation of the stray capacitance of transformers,” Conference Record of the IAS, 2005,3:1868-1875.

1038