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2010-2011

UNIVERSITATEA TRANSILVANIA DIN BRAOV

FACULTATEA DE INGINERIE ELECTRIC

I TIINA CALCULATOARELOR

BUCK-BOOST CONVERTER FOR

WIND TURBINE BATTERY SYSTEM

Students:

ORZAN IULIAN-ALEXANDRU

POPESCU RADU-ANDREI

SEAGR.4797


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TABLE OF CONTENTS

1. Project description...32. Buck-boost converters.....43. Sizing active and passive components ............. 114. Modeling and simulation of buck-boost converter for WT battery system...125. Sizing semiconductorprotections. 146. Heat radiatorsizing157. Annex 1 - IRFB4310GPBF Data sheet.168. Annex 2 - Manual calculations..259. Bibliography..31


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1. Project descriptionFor the Buck-boost converter for WT battery system we established that we have to:

-

Established the structure (Fig.AWT Battery System)- Modelling the converter with ideal components- Simulation in Matlab- Calculation of the passive components- Calculation of the active components- Sizing of semiconductor elements and the heat sink

Fig.AWT Battery System


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2. Buckboost converterThis page describes the switched-mode power supply. For the autotransformer, see buck

boost transformer.

The basic schematic of a buckboost converter

Two different topologies are called buckboost converter. Both of them can produce an

output voltage much larger (in absolute magnitude) than the input voltage. Both of them can

produce a wide range of output voltage from that maximum output voltage to almost zero.

The inverting topologyThe output voltage is of the opposite polarity as the input A buck (step-down) converter followed by a boost (step-up) converter The outputvoltage is of the same polarity as the input, and can be lower or higher than the input. Such a

non-inverting buck-boost converter may use a single inductor that is used as both the buck

inductor and the boost inductor.

The buckboost converter is a type of DC-DC converter that has an output voltage

magnitude that is either greater than or less than the input voltage magnitude. It is a switch mode

power supply with a similar circuit topology to the boost converterand the buck converter. The

output voltage is adjustable based on the duty cycle of the switching transistor. One possible

drawback of this converter is that the switch does not have a terminal at ground; this complicates

the driving circuitry. Also, the polarity of the output voltage is opposite the input voltage.

Neither drawback is of any consequence if the power supply is isolated from the load circuit (if,

for example, the supply is a battery) as the supply and diode polarity can simply be reversed.The switch can be on either the ground side or the supply side.

Principle of operation

Fig. 1: Schematic of a buckboost converter.

Fig. 2: The two operating states of a buckboost converter
http://en.wikipedia.org/wiki/Switched-mode_power_supplyhttp://en.wikipedia.org/wiki/Autotransformerhttp://en.wikipedia.org/wiki/Buck%E2%80%93boost_transformerhttp://en.wikipedia.org/wiki/Buck%E2%80%93boost_transformerhttp://en.wikipedia.org/wiki/Buck%E2%80%93boost_transformerhttp://en.wikipedia.org/wiki/Buck_converterhttp://en.wikipedia.org/wiki/Boost_converterhttp://en.wikipedia.org/wiki/DC_to_DC_converterhttp://en.wikipedia.org/wiki/SMPShttp://en.wikipedia.org/wiki/SMPShttp://en.wikipedia.org/wiki/Boost_converterhttp://en.wikipedia.org/wiki/Buck_converterhttp://en.wikipedia.org/wiki/Duty_cyclehttp://en.wikipedia.org/wiki/File:Buckboost_operating.svghttp://en.wikipedia.org/wiki/File:Buckboost_conventions.svghttp://en.wikipedia.org/wiki/File:Buck_boost.pnghttp://en.wikipedia.org/wiki/File:Buckboost_operating.svghttp://en.wikipedia.org/wiki/File:Buckboost_conventions.svghttp://en.wikipedia.org/wiki/File:Buck_boost.pnghttp://en.wikipedia.org/wiki/File:Buckboost_operating.svghttp://en.wikipedia.org/wiki/File:Buckboost_conventions.svghttp://en.wikipedia.org/wiki/File:Buck_boost.pnghttp://en.wikipedia.org/wiki/Duty_cyclehttp://en.wikipedia.org/wiki/Buck_converterhttp://en.wikipedia.org/wiki/Boost_converterhttp://en.wikipedia.org/wiki/SMPShttp://en.wikipedia.org/wiki/SMPShttp://en.wikipedia.org/wiki/DC_to_DC_converterhttp://en.wikipedia.org/wiki/Boost_converterhttp://en.wikipedia.org/wiki/Buck_converterhttp://en.wikipedia.org/wiki/Buck%E2%80%93boost_transformerhttp://en.wikipedia.org/wiki/Buck%E2%80%93boost_transformerhttp://en.wikipedia.org/wiki/Autotransformerhttp://en.wikipedia.org/wiki/Switched-mode_power_supply


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When the switch is turned-on, the input voltage source supplies current to the inductor and

the capacitor supplies current to the resistor (output load). When the switch is opened (providing

energy is stored into the inductor), the inductor supplies current to the load via the diode D.

The basic principle of the buckboost converter is fairly simple (see figure 2):

while in the On-state, the input voltage source is directly connected to the inductor (L).This results in accumulating energy in L. In this stage, the capacitor supplies energy to the

output load.

while in the Off-state, the inductor is connected to the output load and capacitor, soenergy is transferred from L to C and R.

Compared to the buckand boost converters, the characteristics of the buckboost converter

are mainly:

polarity of the output voltage is opposite to that of the input; the output voltage can vary continuously from 0 to (for an ideal converter). The

output voltage ranges for a buck and a boost converter are respectively 0 to and to .

Continuous Mode

Fig 3: Waveforms of current and voltage in a buckboost converter operating in continuous

mode

If the current through the inductorL never falls to zero during a commutation cycle, the

converter is said to operate in continuous mode. The current and voltage waveforms in an ideal

converter can be seen in Figure 3.

From to , the converter is in On-State, so the switch S is closed. The rate of

change in the inductor current (IL) is therefore given by

At the end of the On-state, the increase ofIL is therefore:

D is the duty cycle. It represents the fraction of the commutation period Tduring which the

switch is On. ThereforeD ranges between 0 (Sis never on) and 1 (Sis always on).

During the Off-state, the switch Sis open, so the inductor current flows through the load. If

we assume zero voltage drop in the diode, and a capacitor large enough for its voltage to remain

constant, the evolution ofIL is:
http://en.wikipedia.org/wiki/Buck_converterhttp://en.wikipedia.org/wiki/Boost_converterhttp://en.wikipedia.org/wiki/File:Buckboost_chronogram.svghttp://en.wikipedia.org/wiki/File:Buckboost_chronogram.svghttp://en.wikipedia.org/wiki/File:Buckboost_chronogram.svghttp://en.wikipedia.org/wiki/File:Buckboost_chronogram.svghttp://en.wikipedia.org/wiki/File:Buckboost_chronogram.svghttp://en.wikipedia.org/wiki/File:Buckboost_chronogram.svghttp://en.wikipedia.org/wiki/File:Buckboost_chronogram.svghttp://en.wikipedia.org/wiki/File:Buckboost_chronogram.svghttp://en.wikipedia.org/wiki/File:Buckboost_chronogram.svghttp://en.wikipedia.org/wiki/File:Buckboost_chronogram.svghttp://en.wikipedia.org/wiki/File:Buckboost_chronogram.svghttp://en.wikipedia.org/wiki/File:Buckboost_chronogram.svghttp://en.wikipedia.org/wiki/File:Buckboost_chronogram.svghttp://en.wikipedia.org/wiki/File:Buckboost_chronogram.svghttp://en.wikipedia.org/wiki/File:Buckboost_chronogram.svghttp://en.wikipedia.org/wiki/File:Buckboost_chronogram.svghttp://en.wikipedia.org/wiki/File:Buckboost_chronogram.svghttp://en.wikipedia.org/wiki/File:Buckboost_chronogram.svghttp://en.wikipedia.org/wiki/File:Buckboost_chronogram.svghttp://en.wikipedia.org/wiki/File:Buckboost_chronogram.svghttp://en.wikipedia.org/wiki/Boost_converterhttp://en.wikipedia.org/wiki/Buck_converter


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Therefore, the variation ofIL during the Off-period is:

As we consider that the converter operates in steady-state conditions, the amount of energy

stored in each of its components has to be the same at the beginning and at the end of a

commutation cycle. As the energy in an inductor is given by:

it is obvious that the value ofIL at the end of the Off state must be the same as the value ofIL

at the beginning of the On-state, i.e. the sum of the variations ofIL during the on and the off

states must be zero:

Substituting and by their expressions yields:

This can be written as:

This in return yields that:

From the above expression it can be seen that the polarity of the output voltage is alwaysnegative (as the duty cycle goes from 0 to 1), and that its absolute value increases with D,

theoretically up to minus infinity as D approaches 1. Apart from the polarity, this converter is

either step-up (as a boost converter) or step-down (as a buck converter). This is why it is referred

to as a buckboost converter.

Discontinuous Mode

Fig 4: Waveforms of current and voltage in a buckboost converter operating in

discontinuous mode
http://en.wikipedia.org/wiki/File:Buckboost_chronogram_discontinuous.pnghttp://en.wikipedia.org/wiki/File:Buckboost_chronogram_discontinuous.pnghttp://en.wikipedia.org/wiki/File:Buckboost_chronogram_discontinuous.pnghttp://en.wikipedia.org/wiki/File:Buckboost_chronogram_discontinuous.pnghttp://en.wikipedia.org/wiki/File:Buckboost_chronogram_discontinuous.pnghttp://en.wikipedia.org/wiki/File:Buckboost_chronogram_discontinuous.pnghttp://en.wikipedia.org/wiki/File:Buckboost_chronogram_discontinuous.pnghttp://en.wikipedia.org/wiki/File:Buckboost_chronogram_discontinuous.pnghttp://en.wikipedia.org/wiki/File:Buckboost_chronogram_discontinuous.pnghttp://en.wikipedia.org/wiki/File:Buckboost_chronogram_discontinuous.png


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In some cases, the amount of energy required by the load is small enough to be transferred in

a time smaller than the whole commutation period. In this case, the current through the inductor

falls to zero during part of the period. The only difference in the principle described above is that

the inductor is completely discharged at the end of the commutation cycle (see waveforms infigure 4). Although slight, the difference has a strong effect on the output voltage equation. It

can be calculated as follows:

As the inductor current at the beginning of the cycle is zero, its maximum value (at

) is

During the off-period,ILfalls to zero after .T:

Using the two previous equations, is:

The load currentIo is equal to the average diode current (ID). As can be seen on figure 4, the

diode current is equal to the inductor current during the off-state. Therefore, the output currentcan be written as:

Replacing and by their respective expressions yields:

Therefore, the output voltage gain can be written as:

Compared to the expression of the output voltage gain for the continuous mode, this

expression is much more complicated. Furthermore, in discontinuous operation, the outputvoltage not only depends on the duty cycle, but also on the inductor value, the input voltage and

the output current.


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Limit between continuous and discontinuous modes

Fig 5: Evolution of the normalized output voltage with the normalized output current in a

buckboost converter

As told at the beginning of this section, the converter operates in discontinuous mode when

low current is drawn by the load, and in continuous mode at higher load current levels. The limit

between discontinuous and continuous modes is reached when the inductor current falls to zero

exactly at the end of the commutation cycle. with the notations of figure 4, this corresponds to :

In this case, the output current (output current at the limit between continuous and

discontinuous modes) is given by:

Replacing by the expression given in the discontinuous mode section yields:

As is the current at the limit between continuous and discontinuous modes of

operations, it satisfies the expressions of both modes. Therefore, using the expression of the

output voltage in continuous mode, the previous expression can be written as:

Let's now introduce two more notations:

the normalized voltage, defined by . It corresponds to the gain in voltage of theconverter;

the normalized current, defined by . The term is equal to the maximumincrease of the inductor current during a cycle; i.e., the increase of the inductor current with a

duty cycle D=1. So, in steady state operation of the converter, this means that equals 0 for no

output current, and 1 for the maximum current the converter can deliver.
http://en.wikipedia.org/wiki/File:Buck-boost_continuous_discontinuous.pnghttp://en.wikipedia.org/wiki/File:Buck-boost_continuous_discontinuous.pnghttp://en.wikipedia.org/wiki/File:Buck-boost_continuous_discontinuous.pnghttp://en.wikipedia.org/wiki/File:Buck-boost_continuous_discontinuous.pnghttp://en.wikipedia.org/wiki/File:Buck-boost_continuous_discontinuous.pnghttp://en.wikipedia.org/wiki/File:Buck-boost_continuous_discontinuous.pnghttp://en.wikipedia.org/wiki/File:Buck-boost_continuous_discontinuous.pnghttp://en.wikipedia.org/wiki/File:Buck-boost_continuous_discontinuous.pnghttp://en.wikipedia.org/wiki/File:Buck-boost_continuous_discontinuous.pnghttp://en.wikipedia.org/wiki/File:Buck-boost_continuous_discontinuous.pnghttp://en.wikipedia.org/wiki/File:Buck-boost_continuous_discontinuous.pnghttp://en.wikipedia.org/wiki/File:Buck-boost_continuous_discontinuous.pnghttp://en.wikipedia.org/wiki/File:Buck-boost_continuous_discontinuous.png


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Using these notations, we have:

in continuous mode, ; in discontinuous mode, ;

the current at the limit between continuous and discontinuous mode is. Therefore the locus of the limit between continuous and

discontinuous modes is given by .

These expressions have been plotted in figure 5. The difference in behaviour between the

continuous and discontinuous modes can be seen clearly.

Non-ideal circuit

Effect of parasitic resistances

Fig 6: Evolution of the output voltage of a buckboost converter with the duty cycle whenthe parasitic resistance of the inductor increases

In the analysis above, no dissipative elements (resistors) have been considered. That means

that the power is transmitted without losses from the input voltage source to the load. However,

parasitic resistances exist in all circuits, due to the resistivity of the materials they are made

from. Therefore, a fraction of the power managed by the converter is dissipated by these

parasitic resistances.

For the sake of simplicity, we consider here that the inductor is the only non-ideal

component, and that it is equivalent to an inductor and a resistor in series. This assumption is

acceptable because an inductor is made of one long wound piece of wire, so it is likely to exhibit

a non-negligible parasitic resistance (RL). Furthermore, current flows through the inductor both

in the on and the off states.

Using the state-space averaging method, we can write:

where and are respectively the average voltage across the inductor and the switch over

the commutation cycle. If we consider that the converter operates in steady-state, the average

current through the inductor is constant. The average voltage across the inductor is:

When the switch is in the on-state, . When it is off, the diode is forward biased (we

consider the continuous mode operation), therefore . Therefore, the average voltageacross the switch is:
http://en.wikipedia.org/wiki/Resistorhttp://en.wikipedia.org/wiki/Resistivityhttp://en.wikipedia.org/wiki/File:Buckboost_resistance.svghttp://en.wikipedia.org/wiki/File:Buckboost_resistance.svghttp://en.wikipedia.org/wiki/File:Buckboost_resistance.svghttp://en.wikipedia.org/wiki/File:Buckboost_resistance.svghttp://en.wikipedia.org/wiki/File:Buckboost_resistance.svghttp://en.wikipedia.org/wiki/File:Buckboost_resistance.svghttp://en.wikipedia.org/wiki/File:Buckboost_resistance.svghttp://en.wikipedia.org/wiki/File:Buckboost_resistance.svghttp://en.wikipedia.org/wiki/File:Buckboost_resistance.svghttp://en.wikipedia.org/wiki/File:Buckboost_resistance.svghttp://en.wikipedia.org/wiki/File:Buckboost_resistance.svghttp://en.wikipedia.org/wiki/Resistivityhttp://en.wikipedia.org/wiki/Resistor


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The output current is the opposite of the inductor current during the off-state. the average

inductor current is therefore:

Assuming the output current and voltage have negligible ripple, the load of the converter can

be considered as purely resistive. If R is the resistance of the load, the above expression

becomes:

Using the previous equations, the input voltage becomes:

This can be written as:

If the inductor resistance is zero, the equation above becomes equal to the one of the ideal

case. But asRL increases, the voltage gain of the converter decreases compared to the ideal case.

Furthermore, the influence ofRL increases with the duty cycle. This is summarized in figure 6.


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3. Sizing active and passive componentsStarting from the WT battery system scheme (Fig.A) and the buck-boost equations:

Voltage transfer function (CCM)

soV

D

DV

1

Current transfer function (CCM)

soI

D

DI

1

Boundary between CCM and DCM (L design 1)

Maximum current ripple through L (L design 2)

fL

DVI sL

Voltage output ripple (C design)

, we made the active and passive components sizing.

Input data:

Us=[2060] V

Ubat=[38,457,6] V

P=500 W

Pmin = 10%*P=50 W

The worst case scenario: Us=60V and Ubat=38,4V

Rezults:

D=0,39

Rmin=29,5

Lb=270H

L1=1440 H

L=max(Lb,L1)=1440 H

Cmin=66 F

For detailed calculations see Annex 2.


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4. Modeling and simulation of buck-boost converter for WT battery system

Fig.7 WT Battery System Mathlab Simulation

Fig.8 Current graph from Scope


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Fig.9 Voltage graph from Scope1


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5. Sizing semiconductor protectionsUsing the calculated data from chapter 3 we determined the current and the voltage used in

transistor sizing.

IT,calc=91,63A

I T=128,2A

U T,calc=57,6V

U T=86,4V

According to this calculation we choose MOSFET IRFB4310GPbF fromwww.irf.com.

The transistor data sheet can be found in Annex 1.

Fig.10 Basic specifications
http://www.irf.com/http://www.irf.com/http://www.irf.com/http://www.irf.com/


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6. Heat radiator sizingWe calculated the dissipated power (Pd) using the data sheet MOSFET information from

Annex 1.

Pd=18,56W

From the MOSFET data sheet we identified the maximum operating temperature and the

usual ambient temperature and calculated the thermal resistance from sink to ambient.

Rsa=4,38C/W

According to this we selected the heat sink no.2 from CAD Course 5 with the parameters:

Rsa=2,3C/W and a volume of 99 cm3.


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7. Annex 1 - IRFB4310GPBF Data sheet


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8. Annex 2 - Manual calculations


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9. Bibliography[1]www.wikipedia.org

[2]

https://ec.irf.com/v6/en/US/adirect/ir?cmd=catProductDetailFrame&productID=IR

FB4310GPBF
http://www.wikipedia.org/http://www.wikipedia.org/http://www.wikipedia.org/https://ec.irf.com/v6/en/US/adirect/ir?cmd=catProductDetailFrame&productID=IRFB4310GPBFhttps://ec.irf.com/v6/en/US/adirect/ir?cmd=catProductDetailFrame&productID=IRFB4310GPBFhttps://ec.irf.com/v6/en/US/adirect/ir?cmd=catProductDetailFrame&productID=IRFB4310GPBFhttps://ec.irf.com/v6/en/US/adirect/ir?cmd=catProductDetailFrame&productID=IRFB4310GPBFhttps://ec.irf.com/v6/en/US/adirect/ir?cmd=catProductDetailFrame&productID=IRFB4310GPBFhttp://www.wikipedia.org/

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