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Abstract-- This paper presents and investigates planar

and coaxial high frequency power transformers used for

DC/DC converters in a three phase photo voltaic (PV)

power systems. The winding structure including a Faraday

shield between the primary and secondary windings is

designed to minimize eddy current losses, skin and

proximity effects, and to reduce the leakage inductance, and

the inter winding coupling capacitance. Finite Element

Method is employed to analyze the magnetic flux and eddy

current distributions. The two different kinds of prototype

high frequency transformers are designed and tested. The

simulation and experiment results are demonstrated and

compared with non-shielded transformers. The shielded

transformers have achieved the expected results with a

relatively small coupling capacitance, compared with the

conventional high frequency transformer. This shield

decreases the inter-winding coupling capacitance Cps.

Index Terms -- DC/DC converter, High frequency

transformer, Solar PV system, Shielding.

I. INTRODUCTION

Photovoltaic arrays are coupled to the power grid

using a DC-DC converter, a DC-AC inverter and an

isolation transformer. The isolation transformer is

typically large and bulky as the operating frequency is the

utility frequency. A way of avoiding the use of a large

transformer is to employ a DC-AC-DC (DC/DC)

converter with a high frequency (HF) link isolation

transformer, as shown in Fig. 1. Higher output power

from multiple solar PV modules is achieved by

connecting each PV array to its own full bridge DC/DC

converter and single phase transformer. The topology

chosen is for a 3-phase open delta to wye converter. The

DC-AC converter output voltages are phase shifted with

respect to each other by 120°. Overshoot and ringing on

the primary side is almost completely avoided and there

is a factor of 6 reduction in ripple current magnitude.

This means a reduction of 6 in the size of both the output

inductor and the input capacitor over the single phase

alternative. The secondaries of the HF link transformers

are connected in a three-phase wye configuration and the

output is connected to a three phase rectifier. This

configuration concept can be extended to n phases. The

DC/AC inverter is used to transfer power to the utility

and is synchronized to the utility frequency. The three

full bridge converters are phase controlled to provide a

minimal switching loss waveform. Voltage stresses are

minimised and there is excellent current sharing among

the active devices.

With a 1:1 transformer ratio there is a 1:2 voltage

step up, this is advantageous PV array matching for

maximum power transfer. The power converter

architecture connected to the primary terminals of the

transformers and the output rectifier can be either current

source fed or voltage source. Inverters with isolation

transformers are essential in many countries considering

the safety and reliability of solar PV installations.

In this paper, high frequency planar and coaxial

transformers [1-3], with and without Faraday shield, with

an operating frequency up to 300 kHz, using a FEM

based numerical modelling technique and high frequency

measurement techniques are investigated. A number of

issues related to magnetic flux, current distributions,

power losses in windings and the Faraday shield

implementation are discussed. Finally, the parasitic

capacitances of the model are evaluated using a FEM

based commercial available simulator (such as Ansys)

and measurements for the intra- and inter- winding

capacitances.

Fig.1. The three phase DC/DC converter for solar PV power conversion

systems and the block diagram of PV system.

II. STRUCTURE CONFIGURATIONS OF HF TRANSFORMERS

The basic structure of the shielded HF coaxial

transformer (HFCT) [4] is shown in Fig. 2. Surrounded

by four round ferro-magnetic cores, the primary and the

secondary winding are connected through the planar

layers on the top and bottom (a). Inside the cores,

between the primary and secondary side, the faraday

shield is implemented with a copper cylinder (b). It can

be seen, that there is a 30 degree offset between the turns.

High Frequency and High Power Density

Transformers for DC/DC Converter used in

Solar PV System

J. Lu*, S. Stegen*, and D. Butler**

* School of Engineering, Griffith University, Nathan, Brisbane, Qld 4111, Australia

** Surtek Pty Ltd, Acacia Ridge, Brisbane, Qld 4110, Australia

2010 2nd IEEE International Symposium on Power Electronics for Distributed Generation Systems

978-1-4244-5670-3/10/$26.00 ©2010 IEEE481

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The planar transformer (step up) version as shown in

Fig. 3 has a faraday shield copper coated layer between

the primary and secondary side. With a 1:1 or 1:n turns

ratio the delta wye transformer yields a 2 times voltage

increase that is useful for PV converters as it allows

operation over a wide voltage range with minimal stress

on the active devices. As only uni-directional power is

required there is no need for active devices on the

secondary side and the complexity of a dual active bridge

is avoided.

(a) HFCT over view

(b) HFCT winding structure of half cross-section

Fig.2 Configuration of 1kW HFCT with shield at operating frequency

above 100kHz

(a) Planar transformer over view

(b) Planar transformer winding structure

Fig.3 Configuration of 1.5kW Planar transformer with shield at

operating frequency above 100kHz.

III. MAGNETIC FIELD SIMULATION AND ANALYSIS

A. Magnetic field analysis using FEM

A Finite Element Method (FEM) frequency domain

based numerical modelling technique was employed to

analyze the magnetic field and eddy current distributions

for different winding configurations. The nonlinear

magnetic field can be presented by the following

equation,

(/AAt

νσ∇× ∇×+∂∂ +∇

where A is magnetic vector potential, B represents flux

density, v and σ are reluctivity and conductivity

respectively, J is exciting current.

The detailed magnetic field properties for the high

frequency magnetics were then used to facilitate the

design of a low loss winding and high efficiency

structure. The mathematical problem can be formulated

as a sinusoidal quasi-static eddy current problem and is

derived from Maxwell’s equations. Figures 4 and 5

visualize that the eddy current, induced from the one

winding to the other, is smaller with the inserted Faraday

shield. As it can be seen in Fig. 4(b) and 5(b), the current

distribution with shielding is slightly higher than without

shielding, for the simulation results focusing to the

primary winding and the secondary windings are under

open circuit conditions.

)0(1)J

ϕ−=

(a) Primary inside without shield

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(b) Primary inside with shield

Fig.4 Current distribution in different winding configurations under

open circuit conditions.

(a) Without shielding

(b) With shielding

Fig.5 Eddy current distribution without shielding and with shielding.

B. Capacitance network model

The high frequency (HF) noise voltage vs can be easily

propagated to the secondary winding through the

coupling capacitance in the no shield case, as shown in

Fig. 6(a), is given by:

(a) without shield

(b) with shield

Fig.6 The HF transformer equivalent circuit.

/(v v CC

=+

sppspss

)C

(3)

In the perfectly grounded shield case, HF noise voltage

vs is then given by (as shown in Fig. 6(b),)

/() v CCCC

′′

=++

p ps ps pgssv

(4)

and for the shield in the floating case, HF noise voltage

is given by:

CC

v

CCCC

+++

()()

pggs

gs spg0gss

sp

s

v

C C

⋅

=

(5)

The single capacitances in Fig. 7(a) create coupling

and therefore HF impacts between the primary and the

secondary winding. After insertion of the faraday shield,

the HF noise between the windings are strongly dropped,

as it can be seen in Fig. 7(b).

(a) Without Faraday shield, (b) With Faraday shield.

Fig.7 The parasitic capacitance network model of HF coaxial

transformer for HF noise voltage analysis.

For HF noise analysis of the HFCT, the shield or each

turn of the winding can be taken as an independent

conductor. Based on the theory of capacitances in multi-

conductor systems, we can obtain the following set of N

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equations relating the potentials V1, V2, …, VN of the N

conductors to the charges Q1, Q2, …, QN:

Q C VC VC V

Q C VC V C V

=+++

L

M

L

where the Cii coefficients are called the coefficients of

capacitance, and the capacitances Cij (i≠j ) are referred to

as the coefficients of induction. The condition of

reciprocity, assuming isotropy and linearity, guarantees

that Cij= Cji. The relation between potential and charge in

a multi-conductor system can be described by the electric

scalar potential V, which satisfies Poisson’s equation,

ρε=∇⋅∇−

)(V

(7)

where ε is the permittivity, and ρ ρ is the space charge

density.

To obtain the capacitance from Eq. (6), the charge

density must be calculated using a FEM analysis. The 2D

FEM system matrix equation can be expressed as (8) for

the relationship between charge and potential,

}{}]{[QVS

=

(8)

where [S] is the global coefficient matrix and {Q} is the

charge matrix. By setting up the boundary condition,

V1=1, V2=V3= … =VN=0, we can obtain Q1=C11, Q2=C21,

…, QN=CN1, and in the same manner, the coefficients

Cii’s and Cij’s can be calculated.

From the Cii and Cij coefficients, the capacitance of the

ith conductor to ground, ci0, and the capacitance between

the ith conductor and the jth conductor, cij (i≠j), can be

calculated. Thus, all of the parasitic capacitances in the

network model shown in Fig.7 can be obtained.

The calculated results show that the inter- winding

capacitance is reduced significantly from 19.96pF to

0.08pF due to the insertion of a Faraday shield in the

HFCT. While, the intra- winding capacitance Cp increases

from 7.67pF to 24.67pF and Cs increases from 3.55pF to

22.50pF, because Cpg and Cgs are added to the primary

and secondary sides respectively through the ground, as

shown in Fig. 7(b). The capacitance Cs0 does not exist if

the shield is perfectly grounded. It is obvious that by

integrating a Faraday shield into the HFCT, the value of

Cps is decreased, and at the same time the value of Cs is

increased. Both the decreased value for Cps and the

increased value for Cs will improve the noise suppression

and reduce the impact of transients on semiconductor

devices [6]. The measured value for the prototype HFCT

is 21.7pF, which is in good agreement with the calculated

value of 19.96pF.

From (3), (4), and (5), the EMI noise reduction can be

calculated for the aforementioned

respectively. TABLE I confirms that a perfectly grounded

shield can provide the best EMI suppression. The EMI

111 1122 1NN

221 12222NN

N N1 1

C V

N22NNN

QC V C V

=+++

=+++

L

(6)

three cases,

reduction is down to -49.90db [7].

TABLE I

TIMES NEW ROMAN TYPE SIZES AND STYLES

No shield

Shield

grounded

Shield

floating

Voltage

ratio

0.849 0.0032 0.473

EMI

reduction

(db)

-1.42

-49.90

-6.50

IV. CONCLUSIONS

A detailed discussion of a high frequency coaxial and

planar isolation transformers used for a solar PV DC/DC

converter is presented. A FEM eddy current simulation is

used to investigate the winding configurations and

Faraday shield arrangements under different load

conditions. The results show that the extra peak current

density and the extra power loss caused by the insertion

of Faraday shield can be neglected and the magnetic flux

distribution is not influenced by the insertion. A parasitic

capacitance network model is proposed to calculate these

capacitances by FEM for a HFCT with or without a

Faraday shield. The calculated inter-capacitance value for

the HFCT without shield is in good agreement with the

experimental result. The presented approach for

calculating intra- and inter- capacitances of HFCT can be

extended to the calculation of the intra- and inter-

capacitance for other high frequency transformers.

ACKNOWLEDGMENT

The authors would like to thank Dr. X. Yang for his

helpful discussion and the assist on magnetic field

simulation.

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