Full-Bridge Dc-Dc Converter with Planar Transformer

16th European Conference on Power Electronics and Applications (EPE'14-ECCE Europe), August 2014, Lappeenranta, Finland

Full-Bridge Dc-Dc Converter with Planar Transformer and Center-Tap Rectifier for Fuel Cell Powered Uninterruptible Power Supply

Martin Rosekeit∗ , Johannes Burkard∗ , Markus Lelie∗† , Dirk Uwe Sauer∗† , and Rik W. De Doncker∗ ∗ Institute for Power Electronics and Electrical Drives † Jülich Aachen Research Alliance RWTH Aachen University Forschungszentrum Jülich GmbH Jägerstr. 17-19, 52066 Aachen, Germany 52425 Jülich, Germany Email: [email protected]

Acknowledgement The project underlying this publication was funded by the Federal Ministry of Education and Research as part of the CLIENT program, project number 01RD1104C. The responsibility for the content of this publication lies within the author.

Keywords «Dc power supply», «Fuel cell system», «Uninterruptible power supply (UPS)», «Transformer», «Converter control»

Abstract This paper shows the design of a galvanically isolated phase-shifted dc-dc converter. The converter, rated at a power of 1 kW and an input current of 50 A, is designed to connect a fuel cell to a 48 V dc bus of a UPS system. Special attention is given to the design of the planar transformer, which consists of several stacked PCBs. The copper losses, including skin and proximity effects, as well as the core losses are analyzed for the design process of the transformer. A construction method to reach high interleaving of the primary and secondary windings is developed and efficiency measurements of the system are performed and analyzed. A snubber circuit is used to limit the overvoltage on the rectifier. The effects of the snubber circuit on the current waveforms and the switching behavior of the input H bridge are analyzed. Furthermore, a control strategy is shown that reduces the effect of a fluctuating dc-bus voltage on the transfered power.

Introduction Uninterruptible power supplies (UPS) are used to increase the reliability of the electric grid [1]. Small UPS systems with a power of a few kilowatts often use a battery as energy source. As a result, the active operation time of the system is determined by the battery capacity and usually limited to a few hours. However, the hurricanes Sandy and Isaac have shown that this is insufficient for infrastructure installations [2, 3]. Possible solutions are fuel-cell systems with a reformer powered by natural gas or propane gas. The gas needed to supply the loads for days can be stored in gas bottles. In case of a longer-lasting blackout, gas bottles can be exchanged easily. The structure of the UPS system described in this paper is shown in Fig. 1(a). It has a nominal power of 1 kW at a dc-link voltage of 48 V and consists of a primary energy supply (e. g. natural gas), a reformer, a fuel cell (FC), and the power electronics. A battery is connected via an additional dc-dc converter to provide energy during the start up of the fuel-cell system and to buffer fluctuation of the power demand during operation. Under normal operation the loads are supplied by the utility grid


natural gas

230 V~ grid

FC

fc dc-dc converter rectifier H-bridge transformer output inductor

UPS DC

DC

DC

48 V=

AC

DC DC

battery dc-dc converter

(a) Schematic

(b) Photo of the two dc-dc converters

Fig. 1: UPS system using a power electronic converter. The converter between the fuel cell and the dc bus is based on a phase-shifted full-bridge converter (see Fig. 2(a)). The fuel cell has a voltage range from 20 V to 40 V with the maximum power output at 20 V. The dc-dc converter needs to control the fuel-cell current continuously from zero to full power because the fuel cell is sensitive to abrupt load changes. Planar transformers and inductors gained attention for low power application in the last years. The production is simple and has a high repeat accuracy, especially when the windings are integrated into printed circuit boards (PCB). Furthermore, a low stray inductance and a simple interleaved design are interesting attributes for the design of phase-shifted full-bridge converters [4]. In this paper, a planar transformer is constructed that uses stacked double layer PCBs as windings (see Fig. 3).

Topology

i in A

uAB in V

gate

The phase-shifted full-bridge converter as shown in Fig. 2(a) is an attractive topology for medium to high power applications. Its desirable features are low current and voltage stress as well as zero-voltageswitching (ZVS) operation of all switches [5] and a high utilization of the transformer. Drawbacks of the topology are the discontinuation of ZVS operation for low input power, the high voltage stress of the rectifier diodes, and the hard turn-off switching of the rectifier diodes [6].

on

ϕ

off 40 0 −40

ϕ S4

50

Lσ

0

Lout

S2

−50 0 T/2 T 2/3T 2T 0 T/2 T 2/3T 2T t in s t in s (a) Schematic

(b) Ideal voltage and current waveforms (left: DCM, right: CCM)

Fig. 2: Phase-shifted full-bridge converter


For the use together with a fuel cell, the topology has the advantage of providing its highest efficiency at low input voltage, where the fuel cell has its highest output power. Assuming a constant output voltage, no power is transfered if the input voltage falls below a certain threshold. This behavior protects the fuel cell of a to low voltage that could damage the fuel cell. The basic operating method of the topology is to switch the two half bridges with a fixed duty cycle of 50 % and use a phase shift ϕ = [0..1] = b [0◦ ..180◦ ] between the two half bridges to apply positive, negative, and zero voltage on the primary side of the transformer. The behavior of the topology is similar to the behavior of a buck converter. The converter has two operation modes as depicted in Fig. 2(b). In the discontinuous conduction mode (DCM) the current in the output inductance iL,out drops back to zero each cycle. During DCM one half bridge works in ZVS mode and the other half bridge in zero-current-switching (ZCS) mode. In the continuous conduction mode (CCM) iL,out is always positive and all switches operate under ZVS conditions. The voltage transfer function for DCM operation (1) and CCM operation (2) were derived in [7] with the output voltage at the dc link in DCM operation udc,DCM and CCM operation udc,CCM , the input voltage from the fuel cell ufc , the output current idc , the output inductor Lout , the transformer ratio n = Np/Ns , the number of turns on the primary winding Np and secondary winding Ns , and the switching frequency f = 1/T . udc,DCM = udc,CCM =

1 · n 4·f ·

idc n

u2fc · ϕ2 · (Lσ + n2 Lout ) + ϕ2 · ufc

(1)

n · ufc · Lout · ϕ · ufc − 4 · f · Lσ ·

idc n

· Lσ + n2 Lout

4f indc L3σ + L2σ (4f n idc Lout + ufc (ϕ2 − ϕ)) + Lσ ufc ϕ n2 Lout + ufc n4 L2out

(2)

Assuming that the stray inductance Lσ of a planar transformer is very low, as has been shown in [4], equation (2) can be reduced to udc,CCM ≈ ϕ/n · ufc .

(3)

Design of the Transformer In Fig. 3(b) the basic design of the planar transformer is shown. It consists of a stack of PCBs. Each PCB is one turn of the windings. The different turns are connected with copper straps on the outside of the PCBs. Each winding has its own PCB design as shown in Fig. 4(a). The copper straps are soldered at the outside of the transformer on the top and bottom layer of the PCB (see Fig. 4(b)). The entry and exit connections are placed above each other, one on the bottom layer and the other in the top layer. Outside the connection area both layers are interconnected via vias and both layers conduct current.

wCu,in wCu,out

lCu (a) Inductor with folded copper foil (top) and planar transformer with stacked PCBs (below)

hCu

(b) Layout of the planar core [8] with winding

Fig. 3: Planar transformer


(a) Three different PCB layouts for the windings

(b) Model of interconnections between PCBs

Fig. 4: Planar transformer PCBs

Winding Ratio It has been shown in [9] that the highest possible transformer winding ratio n should be used to minimize the converter losses. The maximum n can be calculated by (3). However an extra margin should be provided to compensate for losses and the stray inductance which is neglected in the equations.

Core Losses The peak value of the magnetic flux density in the core is given by ˆµ = B

Φµ Np · AFE

(4)

with the magnetic flux Z T/2 1 ϕ Φµ = uAB (t) dt = · ufc , 2 0 4·f

(5)

the effective core area AFE , and the primary transformer voltage uAB (t). By inserting (3) and (5) into (4) the peak value of magnetic flux density is given by n · udc ˆµ = B 4 · f · Np · AFE

(6)

which is independent of the actual operating point. In [10] it was shown that the specific losses created by a magnetic flux with a triangular waveform and a pause between each cycle, as shown in Fig. 5, can be expressed as ∆B/T β 1 2 4 (α−1) pv,core = Cm · Tu +Tv · · (7) π 2 Tu/s 2 s

mag. flux

ˆµ and the Steinmetz parameters Cm , α, and β [11]. with ∆B = 2 · B approach by Brockmeyer phase shifted converter ∆B

0 Tv

Tu time

Fig. 5: Waveform of magnetic flux over time as used by Brockmeyer [10]


The primary transformer voltage uAB (t) of the phase-shifted converter has a rectangular shape with zero-voltage intervals. Therefore, the magnetic flux has a trapezoidal shape as shown in Fig. 5. Hence, the specific core losses are obtained by inserting (6) and (3) into (7):

pv,core

f = Cm · · Hz

8 f/Hz ·n π 2 uudc fc

!(α−1) ·

n·udc 4·f ·Np ·AFE

!β

T

(8)

As evident from this equation, the losses increase with higher input voltage ufc and they decrease with higher number of winding turns Np . The effects of the turn ratio n and the switching frequency f depend on the material parameters α and β .

Copper Losses To calculate the copper losses in the transformer, first, the current waveform has been derived, then assumptions of the copper and current distribution in the core window were done. The complete derivation of the tranformer current is given in [7]. By neglecting the stray inductance Lσ the equations are simplified. The mean output current ¯iL,out depending on the output power Pout , the ripple of the output current ∆iL,out , and the rms value of the ac component of the output current IL,out,ac are calculated as follows: ¯iL,out = Pout udc u2dc 1 1 ∆iL,out = · udc − u fc/n Lout 2·f ∆iL,out √ IL,out,ac = 2· 3

(9) (10) (11)

2 2 With IL,out = ¯i2L,out + IL,out,ac , the rms value of the current in the output inductor IL,out is given by s 2 u2dc 1 1 Pout 2 √ + udc − IL,out = . (12) ufc/n udc Lout 3·4·f

In Fig. 3(b) the shape of a planar core is shown. The mean length of one turn is ¯lCu,turn = 2 · lCu + 2 · π · wCu,out + wCu,in 4 where lCu , wCu,out , and wCu,in are the dimensions of the core as depicted in Fig. 3b.

(13)

In a planar winding setup each layer consists of one PCB. The core of the PCB takes a significant area of the available cross section. This reduces the fill factor FCu on a two-layer PCB with the copper thickness dPCB,Cu and the core thickness dPCB,core to FCU