high gain dc-dc boost converter with a coupling inductor

7/16/2019 High Gain Dc-dc Boost Converter With a Coupling Inductor

1/7

HIGH GAIN DC-DC BOOST CONVERTER WITH A COUPLING INDUCTOR

Felinto S. F. Silva1,Antnio A. A Freitas2, Srgio Daher2, Saulo C. Ximenes2, Sarah K. A. Sousa2,

Edilson M. S. Jr.3 , Fernando L. M. Antunes2, Ccero M. T. Cruz2.1IFPI Instituto Federal de Educao, Cincia e Tecnologia do Piau CAMPUS/Picos

2

Universidade Federal do Cear3IFCE Instituto Federal de Educao, Cincia e Tecnologia do Cear CAMPUS/Sobral

Av. da Universidade, 2853 Benfica

[email protected]

Abstract This paper presents a design, mathematical

modeling, simulation results and laboratory

implementation of a 300W high gain dc-dc boost

converter with a coupled inductor, to step up the 24V of a

battery bank to 311Vdc, aiming to supply residential

loads with dc voltage in an off-grid PV system. The

converter can supply most of the residential ac loads

which input stage is a single-phase rectifier. Laboratorytests with the 300W converter supplying electronic lights,

mobile charger and audio-video system ac showed the

viability of the proposed idea.

Keywords DC-DC converter, PV system, Battery

charger.

I. INTRODUCTION

The necessity of off-grid electric systems to supply remote

areas rural loads led the Brazilian Electricity RegulatoryAgency ANEEL to establish guidelines for intermittentelectric energy systems such as wind and PV systems. In that

sense, in September of 2004 it was issued by ANEEL the

guideline 83 which states that the electric energy supplied byElectric Energy Production Units should have a sinusoidal

output voltage waveform with magnitude and frequency

compatible with the utility grid. However, aiming to boost

the production of electric energy from renewable sources, in

Brazilian remote areas with difficult access, ANEEL has

authorized, throughout the Resolution 927 of May 2007, thedevelopment of a pilot project with the option to supply

remote low consumption areas not in ac, but in dc voltage.

In the context of the Resolution 927, this paper presents the

design, the mathematical modeling, the simulation and the

laboratory implementation of high gain coupled inductor dc-

dc boost converter, to step up the 24V of a battery bank to311Vdc, as part of an off-grid PV system suitable for isolated

areas, where the cost to extend the electric utility is

prohibitive. The converter can supply most of the residential

ac loads which input stage is a single-phase rectifier.

Laboratory tests with the 300W converter supplyingelectronic lights, mobile charger and audio-video system ac

showed the viability of the proposed idea.

Figure 1 shows the proposed PV system, highlighting in a

dashed circle the high gain dc-dc boost converter discussed

in this paper.

II. BOOST CONVERTER TOPOLOGY SELECTION

Considering the cost of the electricity produced from PV

conversion, it is mandatory the search for efficient

converters. In relation to the efficiency of dc-dc converters,

the non-isolated can be more efficient than the isolated ones.

The literature about non-isolated dc-dc converters presents

some topologies as: classical boost, modified boost, highgain boost, cascade, interleaved boost, high gain interleaved

boost and classic boost converter.

PV

BATTERY

BATTERY BANK

BOOST CONVERTER

CHARGER

DC

ELECTRONIC

AC LOADS

LIGHTS

MOBILECHRAGER

HI FIRADIO

24 Vdc

PROPOSED SYSTEM

CONTROLLER

311 Vdc

Fig. 1. Block diagram of the whole PV system(boost converter

highlighted).

It can be seen in Figure 1 that the discussed boost

converter (in the dashed circle) requires a static gain of 13.

For this level of gain, the classical converters are not

appropriate, due to the fact that the power switches operatewith high input current and high output voltage [1]. This is

unfavorable, regarding the practical implementation andefficiency.

On the other hand, non-isolated high gain topologies are

adequate for this kind of application, using associated

switches and inductors. Figure 2 presents some high gain,non-isolated topologies.

Comparing the topologies presented in figure 2 it can be

observed that topologies C) and D) employ two switches,

while A) and B) only one switch. So, as far as efficiency is

concerned, topologies A) or B) are more suitable for the

application. Looking to the polarity of both topologies it can

be concluded that the topology B) is an inverting polarity

topology which makes difficult the practical implementation

of the control circuit. Therefore, the high gain boost withcoupled inductor topology has been chosen.

978-1-4244-3370-4/09/$25.00 2009 IEEE 486


2/7

A) High gian boost converter-

CARGA

L1 L2

Vin S1 C1D1

loadVin

S1

C1L1

L2 D1

B)High gain buck-boost- -

C) Cascade boost

CARGA

L1 L2

Vin S1 S2C1 C2

D1

C1

LbD1

S2S1

T2

T1

Vin

D2T3 C2

C3D3

LoadD4

D) High gain interleaved boost converter- Fig. 2. High gain, non-isolated and modified topologies.

A. Basic circuit of the dc-dc high gain boost topology with acoupling inductor

Figure 3 presents the basic topology from which the

topology presented in Figure. 2.A) is based on.

Fig. 3. High gain boost converter with clamped circuit.

The difference between the topologies of Figure 2.A) and

the one of Figure 3 is the snubber circuit to minimize

possible overvoltages, due to the non-ideal coupling between

inductors L1 and L2 [2].

III. OPERATION STAGES OF THE DC-DC HIGH GAIN

BOOST TOPOLOGY WITH COUPLING INDUCTORS

Figure 4 presents the complete and simplified circuits for

the converter. The simplified version presented in figure 4.b),is used to make the converter analysis.

a) Complete circuit

L1 L2

LOADC1Vin

D1

Cg

Dg

S1

b) Simplified circuit

Vin

I1 IDI L

VoICI SVS

L1 L2

LOADC1

Fig. 4. a) Proposed converter complete circuit; b) Proposed

converter simplified circuit.

The operation principle of the high gain boost converter is

illustrated in stages in Figure 5.

It is important to note that the presented analysis wasdone considering the continuous conduction mode of

operation. In this case, due to the coupled inductors, abrupt

current variation may occur in each inductor, while the stored

energy is still continuous. This fact explains the abrupt

current variations in IL1 and IL2 waveforms.

a) Stage I( 0 < t < t1)

L1

I

I

1

SLOAD

C1

IL

VoVS

ICVin

b) Stage II( t1 < t < T)

LOAD

L1

L2

C1

II

I1

DL

IC

ISVS

VL1

Vin Vo

Fig. 5. Operating stages.

In Figure 5, from the first operation stage (switch isclosed), it can be observed that the input energy source

delivers energy to the inductor L1, while the load is suppliedby the energy stored in the output capacitor C1 [4], [5].

In the second operation stage, the energy stored in the

coupled inductor is then transferred to the output (added to a

component directly supplied by the input source, which is inseries). In this stage, the current that flows through the output

diode, charges the output capacitor and also supplies the

load.

The main voltage and current waveforms are

presented in Figure 6. It is possible to observe that the

maximum voltage across the power switch is equal to theinput voltage added by the voltage across L1. Since the

voltage across L1 is just a fraction of the output voltage, the

voltage stress in the power switch is strongly limited (in this

case, around twice the input voltage). In fact, compared to

978-1-4244-3370-4/09/$25.00 2009 IEEE 487


3/7

the classical boost topology, this is the most important

advantage presented by the proposed topology.

Drive

(t1)

t

(t2)

T

SI I

SV

Vi + V

I

Stage - I Stage - II

t10 Tsignals to S

t

L1Vi

L1 I

L2I

CI

oI

Fig. 6. Converter of main voltage and current waveforms.

During the interval where the power switch is closed, it is

possible to see the linear variation of the current through L1,

since the voltage across it is approximately constant. It is

also important to notice that the current through the powerswitch does not starts at zero, but presents an offset value,

revealing that the converter is operating on the continuous

mode (for the continuous operation mode, the stored energy

never reaches zero).

The continuous current operation mode can also be

observed over the continuity of the inductor L1 current, IL1.However, in opposition to the operation principle of the

classical boost where the current variations I in the

inductor are equal in amplitude for both the charge and

the discharge stages in the coupled inductor topology the

amplitude of these variations are not equal. This occurs

because the charge interval is performed through L1, while

the discharge interval is performed through the totalinductance, composed by L1 plus L2. In addition, it can be

also observed that the current through L2 is zero during the

charge interval (switch is on).

Finally, the output capacitor current Ic presents a zero dc

component, as expected, and this capacitor supplies all the

load current during the charge interval.

IV. HIGH-GAIN BOOST CONVERTER MATHEMATICMODEL

The equation of the proposed converter can be easily

obtained through the equivalent model shown in Figure 7. In

this model it is assumed that an inductive load Lm (Lm = L1)is charged during the initial stage of operation and it is

discharged through an ideal transformer whose

transformation ratio is a function of L1 and L2.

Fig. 7. Obtaining the model for equating: a) simplified circuit; b)

equivalent model in the range of loading; c) equivalent modelduring unloading.

For the equation, it is preferable use the transformation

relation of the equivalent model k, given by (1).

1 2 2

1 1

1N N

kN

+= = + (1)

Where:

k: Relation of transformation of the ideal transformer;N

1: Number of turns of the inductor L

1;

N2: Number of turns of the inductor L

2;

Indeed, although equation 1 is dependent on number of

turns N1 and N2, it is not necessary to know their absolute

values, since k contains only information about the

relationship N2 / N1. The values of L1 and L2 can be

obtained from the parameters k and Lm , used in (2) and

(3b).mLL =1 (2)

( )( ) == )(k

NNe

NN

LL 1

2

12

2

2

1

2

1 (3a)

22

12 11 )(kL)(kLL m == (3b)Returning now the attention to the equivalent model

stages of operation shown in Figure 7, it can be noted that the

inductor Lm is influenced by input voltage Vin (considered

constant) during the charging interval. Thus, it is the

differential equation which rules the behavior of an idealinductor. Through this, it can determined the behavior of ILM

in this range, as shown in (4a).

Lm

tv

dt

tdi

dt

tdiLmtv LmLmLmLm

)()()()( == (4a)

978-1-4244-3370-4/09/$25.00 2009 IEEE 488


4/7

Lm

tVI iLm

cteVitvLm

= == .)(

(4b)

Equation 4 states that the current ILM varies in a linear

form over time. Taking into account the linearity of the

current ILM variation, equation (5) can determine, which then

provides a range of ILM for the discharge range.( )

.o i

Lm

V Vt

kILm

=(5)

Similarly to the range of load, the equation 5 states that the

current ILM also varies in a linear form on time for the range

of discharge. However, this range variation of current is

negative.

From equations (4) and (5), considering the appropriate

intervals of time and current variation, the instantaneous

coupled inductance current is shown in Figure 8.

LmI

t

2I

t = D.T1 t = (1-D).T2t T1

1I

Fig. 8. The current wave form from the ILM model equivalent.

From Figure 8, the duty-cycle is given by (6).

1 1

1 2

t tD

t t T= =

+(6)

Where:

t1: Time which the switch is closed;

t2: Time which the switch is opened;

T: Switching period;D: Duty-cycle;

In figure 8, the current variation through Lm during the

charging interval should be equal to the current variation

through Lm during the discharging interval. Using (4) and

(5) together with the definitions set in Figure 8, the current

ripple is given by (7).

1 2

( )(1 ).. . o i

i

m m

V VD TV D T kI I

L L

= = (7)

The simplification of (7) is illustrated from (8) to (11),

thus resulting in (12), which provides the static gain of theproposed converter.

)1()(

. Dk

VVDV ioi

= (8)

k

DV

k

DVDV ioi

)1()1(.

= (9)

k

DV

k

D

DV

o

i

)1()1( =

+

(10)

)1(

1.

)1(

)1(.

D

DDK

D

k

DDk

V

V

i

o

+=

+

=(11)

)1(

1)1(

D

kD

V

V

i

o

+= (12)

Rearranging (12), equation (13) is obtained.

i

io

VD

VVDk

.

)).(1( = (13)

From (7) and(14), it is determined the value of Lm.

1

..

I

VTDL im

= (14)

V. BOOST CONVERTER DESIGN

The proposed system is designed to supply the loads listed

on Table 1.

TABLE 1

Loads estimated in a rural school.

Quantity Load Type Power

(W)

Demand

(h/ day)

06 EletronicLamps 23W

(23x6) 138 5

01 TV Set 55 3

01 Parabolic

aerial

25 3

01 Radio set 10 3

According to Table 1, in the worst case, when all loads are

connected at the same time, the system should be able tosupply 228W of power. Considering a safety margin, therated power of boost converter has been defined as 300W.

VI. SIMULATION RESULTS

The proposed converter was simulated using the PSPICE-based simulation tool. The diagram of the circuit simulationis shown in Figure 9. The simulations were made for aconstant duty-cycle, and presented the results for load outputof 300 W and steady state operation.

C2

9.7u

D2

mur2100e/ON

R1

322.4

1 2

L1

136.8uH

V1

24Vdc

V2

TD = 0

TF = 10n

PW = 15.22u

PER = 33.33u

V1 = 0

TR = 10n

V2 = 10

0

1 2

L2

26mH

1

1

2

2

3

3

U3

IRFP3710

C3

100u

D4

DMBRF20100CT

Fig. 9. Schematic diagram of the simulation circuit.

Figure 10 shows the current waveform through inductor

L1, where it can be observed the continuous conductionmode in this inductor.

978-1-4244-3370-4/09/$25.00 2009 IEEE 489


5/7

Fig. 10. Current in inductor L1.

Figure 11 shows the current in inductor L2, where there iscurrent only in the second stage of operation (when theswitch is open). The value of current that passes through theinductor will depend on the relation of the number of turns ofthe two inductors in series.

Fig. 11. Current in inductor L2.

Figure 12 shows the current and voltage waveforms in the

power switch. It is observed that the overvoltages across the

switch is much smaller than the output voltage.

Fig. 12. Current and voltage in the power switch.

Figure 13 shows the current and voltage waveforms in thediode. The diode operates in a discontinuous conductioncurrent mode, and the conduction interval occurs when theswitch is turned off. It can also be observed that themaximum reverse voltage across the diode is larger thantwice the output voltage.

Fig. 13. Current and voltage in the diode.

Figure 14 shows the ripple voltage and average output voltage, clearly showing that the output voltage has a small

"ripple", which depends on the added capacitance value atthe converter output.

Fig. 14. Ripple voltage and average output voltage.

Finally, the switching on and the switching off processes

are shown in Figures 15 and 16, respectively. It can be seen

an excellent switching characteristic, and the relatively low

level of voltage surge in the switch.

Fig. 15. Switch S1 turn on process.

978-1-4244-3370-4/09/$25.00 2009 IEEE 490


6/7

Fig. 16. Switch S1 turn off process.

VII. EXPERIMENTAL RESULTS

A photograph of the implemented laboratory prototype is

shown in Figure 17. The results of the preliminary test of theprototype (no-load and with a 150W load) are presented in

this topic.

Fig. 17. Top view of the implemented prototype.

The voltage waveform across the power switch for the

converter operating at no-load is shown in Figure 18. It can

be observed that there are no voltage overshoots across the

power switch.

On the other hand, when the converter operates with load,

the voltage across the power switch presents some overshoot

when it is switched off, as shown in Figure 19. This voltage

overshoot is due to the sudden charge of the snubber

capacitor, which occurs due to the dispersion inductance ofthe coupled inductor.

.

Fig. 18. Voltage across the switch of power (no load) (10V/div).

Fig. 19. Voltage across the power switch (with load) (10V/div).

Figure 20 shows the current through L1 and the voltageacross the power switch. It can be noticed that

the variation of the inductor current is almost linear, as

demonstrated in the theoretical analysis previously discussed.

Also some oscillations occur in the current IL1 just after the

power switch is turned on. Such behavior can be attributed to

the parasite inductance and capacitance presented in theprinted circuit board layout of the implemented prototype. It

can also be seen some oscillations on the current IL1 that

occur as soon as the power switch goes into conduction. Here

there is also some relation to the parasite inductance and

capacitance presented in layout of this prototype.

Fig. 20. Current through L1 and voltage across the power switch.

(10V/div), (5A/div).

The current across inductor L2 is showed in Figure 21. As

expected, it is possible to notice that IL2 is discontinuous. It

can also be seen the linear variation of IL2 during the second

operation cycle (discharge of the coupled inductor).

Fig. 21. Current through inductor L2 (500mA/div).

978-1-4244-3370-4/09/$25.00 2009 IEEE 491


7/7

Figure 22 shows the input current in the other words, the

current on batteries. You can see that the current ispractically constant, because the prototype has a large input

capacitance, as seen in Figure 17 (on the left of the inductor).

Fig. 22. Input current (into the battery) (5A/div).

Finally, Figure 23 shows the output voltage, where it can

be seen it is around 311V and its ripple is low.

Fig. 23. High gain boost converter output voltage (100V/div).

Finally, Figure 24 shows the converter efficiency, where

the value average of this efficiency is 95%.

Fig. 24. High gain boost converter efficiency.

VIII. CONCLUSION

The simulation and the experimental results of a 300Wlaboratory prototype have been presented to demonstrate the

proposed converter performance. With the proposed

topology, it has been possible to achieve efficiency of 95%.The proposed system presents high efficiency and low cost

when compared with other solar home systems, and it is an

eco-friendly electric energy production unit. It is applicable

in small power consumption rural loads, which is the case of

most houses in remote areas of the northeast of Brazil.

IX. REFERENCES

[1] M. T. Peraa, Conversores CC-CC Elevadores para

Aplicao em Equipamentos de Refrigerao. MSc

Dissertation - UFSC, Florianpolis, Brazil, February

2002.

[2] Q. Zhao, Performance Improvement of PowerConversion by Utilizing Coupled Inductors. MSc

Dissertation - Faculty of the Virginia Polytechnic

Institute and State University, Blacksburg, Virginia,

February 2003.

[3] T. L. Skvarenina, The Power Electronics Handbook,

CRC Press LLC, Boca, ISBN 0-8493-7336-0, Raton -Florida, 2002.

[4] P. Lee, Y. Lee, D. K. W. Cheng, Steady-State Analysis

of an Interleaved Boost Converter with Coupled

Inductors, in Proc. IEEE Transactions on Industrial

Electronics, vol. 47, no. 4, pp. 787-795, August 2000.

[5] Q. Zhao, F. Tao, F. C. Lee, A Front-end DC/DC

Converter for Network Server Applications, in

Proceedings of IEEE, pp. 15351539, 2001,.

[6] F. L. M. Antunes, E. M. S. Junior, S. Daher, C. M. T.

Cruz, K. M. Silva, A. R. Filgueira Photovoltaic System

For Supplying Public Lighting as Peak Demand

Shaving, in Eletrnica de Potncia - SOBRAEP. v. 12,no 2. pp. 113-120, July 2007.

978-1-4244-3370-4/09/$25.00 2009 IEEE 492

high gain dc-dc boost converter with a coupling inductor

Documents