elec 6411 - project final report final

8/18/2019 ELEC 6411 - Project Final Report Final

1/29

ELEC-6411 Final Project Report

Bi-directional Cascaded Buck

-Boost Converter

Design and simulation

Submitted to:

Dr Luiz A. C. Lopes

Submitted by:

Andrew Jensson, 40009961

Rajendra Thike, 27679319

Date of Submission: December 21, 2015

Term: Fall 2015


2/29

i

ABSTRACT Power electronic converters are efficient in supplying power at a regulated voltage or regulated

current. Buck converters can supply power at a voltage level lower than the source while boost

converters can supply power at higher voltage level than the supply. Besides these converters,

there are converters which can source or sink the power depending on the requirement. In

general, these are bi-directional converters either with current reversal capability or voltage

reversal capability.

In this project, a cascade type bi-directional buck - boost converter has been analyzed and

designed for supplying power to charge an ultracapacitor or use the power stored in the

ultracapacitor. The converter is capable of changing the direction of the current and

incrementing the voltage level either lower or higher compared to the source voltage. Analytical

design of each component’s parameters including inductor, MOSFET rating, and harmonic filter

for safe operation of the selected 165 F ultracapacitor from Maxwell. The converter was

simulated in PSIM for four of its operating conditions, viz. buck charging of ultracapacitor, boost

charging of the ultracapacitor, buck discharge of ultracapacitor and boost discharge of

ultracapacitor. The harmonics from the simulation for each case was analyzed and a second

order LC filter was designed for the supply and load accordingly. The resulting current ripple

waveforms were found to have less harmonic magnitude as calculated.


3/29

ii

TABLE OF CONTENTS

Abstract i

Table of contents ii

List of Figures iii

List of Tables iv

Chapter 1 1

1. Introduction 1

2. Scope 2

Chapter 2 3

1. Converter components 3

2. Converter Analysis 5

3. Converter Operation 5

Chapter 3 8

1. Specification of the ultracapacitor 8

2. Selection of the switch 8

3. Switching frequency 8

4. Inductor design 9

5. Battery 9

Chapter 4 10

1. PSIM simulation 10

2. Buck - Charge mode 11

3. Boost - Charge Mode 12

4. Buck – Discharge Mode 13

5. Boost - Discharge Mode 14

Chapter 5 15

1. Harmonic analysis 15

2. Numerical Fourier analysis 15

3. Filter design 16

4. Filter implementation 17

5. Simulation 17

Chapter 6 20

1. Results 20

2. Conclusions 21

Appendix

Datasheets

References


4/29

iii

LIST OF FIGURES

Figure 1. 1 Conceptual Bi -directional Cascaded Buck -Boost Converter topology _____________________________ 1

Figure 2. 1 MOSFET schematic diagram _____________________________________________________________ 3

Figure 2. 2 Inductor schematic diagram _____________________________________________________________ 4 Figure 2. 3 Schematic diagram of a battery __________________________________________________________ 4

Figure 2. 4 Basic structure of a capacitor ____________________________________________________________ 5

Figure 2. 5 Schematic diagram of the converter ______________________________________________________ 6

Figure 4. 1 Converter schematic in PSIM ___________________________________________________________ 10

Figure 4. 2 Buck - Charge waveforms ______________________________________________________________ 11

Figure 4. 3 Boost - Charge waveforms _____________________________________________________________ 12

Figure 4. 4 Buck - Discharge waveforms ____________________________________________________________ 13

Figure 4. 5 Boost - Discharge waveforms ___________________________________________________________ 14

Figure 5. 1 Ideal rectangular current waveform ______________________________________________________ 15

Figure 5. 2 Current harmonic content without filter __________________________________________________ 16

Figure 5. 3 Harmonic filter implementation in simulation ______________________________________________ 17

Figure 5. 4 Current waveforms for Buck - Charge mode with filter _______________________________________ 18

Figure 5. 5 Current waveforms for Boost - Charge mode with filter ______________________________________ 18

Figure 5. 6 Current waveforms for Buck - Discharge mode with filter _____________________________________ 19

Figure 5. 7 Current waveforms for Boost - Discharge mode with filter ____________________________________ 19


5/29

iv

LIST OF TABLES Table 2. 1 Converter modes of operation ____________________________________________________________ 6

Table 2. 2 Relation of drive-mode and switching state _________________________________________________ 6

Table 3. 1 Ultracapacitor parameters _______________________________________________________________ 8

Table 3. 2 MOSFET parameters ____________________________________________________________________ 8

Table 3. 3 Inductor parameters ____________________________________________________________________ 9

Table 6. 1 Design and simulated converter results ____________________________________________________ 20

Table 6. 2 Design and simulated filter results ________________________________________________________ 20


6/29

1

CHAPTER 1

1. Introduction

Power electronics converters have a wide range of applications. One of particular interestis the regulated dc supply. In many applications, the output voltage may be required to be

higher or lower compare to the source. Buck -Boost converters can be used to achieve this

requirement. However, in some applications, the direction of power flow should also be

reversible. For such conditions, bi-directional converters are used. There are many

different topologies for the bi-directional converters with each topology having certain

advantages over others.

The Bi-directional Cascaded Buck -Boost Converter, which for simplicity will be referred

to as “converter” from herein, is one topology of dc-dc converters that has unique

features and functions that make it an attractive option for certain applications. Whenvariable power must be sent and returned to a dc source (hence bi-directional), a dc-dc

converter may be selected; even providing a more stable operating dc source for critical

loads, a Bi-directional Cascaded Buck -Boost Converter may be utilized. The “cascaded”

component stems from the series connection of both types of converters. The converter

presented in this project has application in many systems.

Electric Vehicle Drive and Regenerative Brakingi

Back -up Power Supplyii

Photo-voltaic Systems

Energy Recovery Systems

Back -to- back Wind Power Systems

For the purpose of this project, the converter will be modeled in an electric vehicle

inspired application, with the load of the converter being an ultracapacitor. Depending on

the status of the ultracapacitor, it will be charged or discharged using a Buck or Boost

configuration. The topology for this converter is shown in figure 1.1 iii.

Figure 1. 1 Conceptual Bi -directional Cascaded Buck -Boost Converter topology


7/29

2. Scope

This project is limited to the design of the inductor between the two legs, selection of the

switching devices and the rating of the switches based on the load. Additionally, a second

order LC filter is designed and component are selected for the battery side and theultracapacitor side. Design of the controller is out of the scope of this course project, so it

is not discussed in this report. The designed converter is simulated in PSIM software for

validation.


8/29

CHAPTER 2

1. Converter components

Before designing a functional converter, one must understand the fundamentals of

operation of the circuit, as well as fundamental components and concepts individually.

i. MOSFET

Based on the characteristics of different available power electronic switches, the

MOSFET was selected; the criteria which will be discussed in a later chapter of this

report. For the purpose of design and analysis of the converter, the MOSFET operates

as an idealized switch. This means that the MOSFET will not have a voltage drop

across it when closed and no current will leak through it when opened. The idealized

MOSFET will also have an instantaneous turn-on and turn-off time and is capable of

operating under all voltage and current conditions present in the converter. To operate

the MOSFET, a gate signal will be applied to the “G” node when a closed switch isdesired; under all other conditions, the gate signal will be grounded with 0 v.

Figure 2. 1 MOSFET schematic diagramiv

ii. Inductor

The inductor plays a vital role in the converter circuit; namely to act as the energy

storage medium while the MOSFETs are switching to provide the desired output

voltage. The basic inductor is a simple component in that it has a magnetic or air core

with a wire coiled around. There are many other types of inductors, but the scope of

this project will not explore these configurations, rather the inductance is the only

parameter considered. When current passes through the coil of wire, the inductor presents “inertia”, or resists the change of current, depending upon the current applied

and the inductance, measured in henries.


9/29

Figure 2. 2 Inductor schematic diagramv

iii. Battery

Batteries are the portable source of power which can store and generate electrical

power as a result of a chemical reaction. For electrical vehicle and other applications

where power is bi-directional, rechargeable batteries are used. These batteries can go

through many charge and discharge cycles, however there is some limit on the

continuous current and the current should have low ripple to maintain expected life of

the battery.

Figure 2. 3 Schematic diagram of a battery

iv. Capacitor

The capacitor is another energy storing element in the converter to aid in reducing the

voltage ripple and is often applied on the supply and output of a converter. For the

design of the converter within the scope of this project, the capacitor will be

considered ideal, meaning that it contains no parasitic resistance. A capacitor acts as

an energy storage device and will oppose the change in voltage by drawing in the

ripple currents, so the current that is supplied to the capacitor is dependent on the rate

of change of the voltage applied, and the capacitance, measured in farads.


10/29

Figure 2. 4 Basic structure of a capacitor vi

v. Ultracapacitor

An ultracapacitor is an energy storage device that is utilized in applications wherefrequent bursts of power is required for short duration. The energy storage density

for ultracapacitor is very high compared to normal capacitors. Ultracapacitors

typically store 10 to 100 times more energy per unit volume or mass than

electrolytic capacitors, can accept and deliver charge much faster than batteries,

and tolerate many more charge and discharge cycles than rechargeable batteries.

2. Converter Analysis

i. Steady-state Analysis

Steady-state analysis is an important tool used by designers and engineers to allow for

certain assumptions that simplify the design process. The assumptions presume that

all analyses of the circuit will be done after any transient or sub-transient responses of

the components have been cleared. This is done to allow designers to calculate

parameters and components while utilizing simplified equations and processes.

ii. Continuous Conduction Mode

Also known as CCM, this describes the operation principle of the converter when the

inductor is not allowed to fully discharge its stored energy. Forcing the converter to

operate in CCM will simplify the design procedure and analysis of the circuit. This is

done by sizing the inductor so that the current flowing through the inductor never

reaches a zero-value and this allows for a designer to use common analysis and

design equations to create a converter that operates as expected.

iii. Discontinuous Conduction Mode

Known as DCM, this mode of operation is more difficult to analyze than CCM. DCM

occurs when the current flowing through the inductor is allowed to reach a zero-value

and therefore becomes discontinuous with respect to time. The converter used for this

project never operates in this condition.

3. Converter Operation

The converter in figure 2.5 operates in four modes as listed in table 2.1 where specific

nomenclature and the convention of current direction is outlined. Here, the terms

“charging” and “discharging” are used with respect to the ultracapacitor.

https://en.wikipedia.org/wiki/Energy_densityhttps://en.wikipedia.org/wiki/Power_densityhttps://en.wikipedia.org/wiki/Rechargeable_batteryhttps://en.wikipedia.org/wiki/Rechargeable_batteryhttps://en.wikipedia.org/wiki/Power_densityhttps://en.wikipedia.org/wiki/Energy_density


11/29


12/29

i. Buck - Charge

In this mode the ultracapacitor voltage is less than the battery voltage. Switch Q1 is

switched in pwm mode to charge the ultracapacitor in current controlled mode. The

switching is based on the maximum current through the ultracapacitor.

ii. Boost - Charge

When the ultracapacitor voltage is greater than the battery voltage, switch Q1 is kept

on and switch Q4 will be switched on pwm mode to get higher output voltage than

the battery voltage. Here again the control is done based on the current through the

inductor.

iii. Buck - Discharge

To discharge the ultracapacitor when its voltage is greater than the battery voltage, the

converter is operated in current controlled mode operating the switch Q3 in pwmmode.

iv. Boost - Discharge

When the ultracapacitor voltage is lower than the battery voltage, the converter is

operated in this mode to supply power to the battery. This is done by keeping Q3 on

all the time and switching Q2 in pwm mode with current through inductor being

controlled.


13/29

CHAPTER 3

1. Specification of the ultracapacitor

To specify the individual components that make the converter, a circuit consisting of a

battery and an ultracapacitor was selected. This type of load and source is an analogy to

an electric vehicle application. In this application, the current flowing is bi-directional

and the magnitude must be limited to a value within the tolerable levels of the

components. The Maxwell BMOD0165 P048 BXX ultracapacitor with the parametersvii

given in table 3.1 was selected as an appropriate load for this study.

Table 3. 1 Ultracapacitor parameters

Capacitance Rated Voltage Max Continuous Current Leakage Current ESR

165 F 48 V 77 A 5.2 mA 6.3 mΩ

From the leakage current, the leakage resistance is calculated to be 9,231 Ω.

2. Selection of the switch

From the rating of the ultracapacitor and the level of the operating voltage, the switching

device should be selected. The maximum voltage across each switch is 48 V and the

average current through each of the switch is maximum continuous current through the

ultracapacitor. Because of the low voltage, high current, high switching frequency

capability, a MOSFET is selected as the switching device. The MOSFET must be

capable of handling the application demands without damage; therefore the

STMicroelectronics STH185N10F3-2 MOSFETviii with 100% safety margin was

selected. The parameters of the MOSFET are listed in table 3.2.

Table 3. 2 MOSFET parameters

Voltage, 100 V Continuous current, 180 A Thermal resistance junction-case, − 0.48 °C/W Turn on delay time, , 25.6 ns Rise time, 97.1 ns Turn-off delay, , 99.9 ns Fall time, 6.9 ns Resistance of drain-source, R DS(on) max 4.5 mΩ

3. Switching frequency

The MOSFET must be able to dissipate the heat generated due to conduction and

switching losses. The switching frequency, of the converter, is calculate by balancingthe rate of heat generation and the rate of heat loss.

The conduction loss is given by Pcond= R ds(on)*ID2*duty_cycle …(2.1)

For the worst case, duty_cycle is considered unity.


14/29

The switching loss is given by Psw= ½*VDS*IDS*(td(on)+ tr +td(off)+tf )*f sw …(2.2)

The maximum allowable power loss can be calculated using equation (2.3)

Pallowable=∆

…(2.3)

To limit the junction temperature to 100oC, the maximum allowable power loss is

calculated to be 156.25 watts. As per the datasheet, the drain to source resistance varies

with temperature, at 100oC, it is given by equation (2.4).

R DS(on)=1.5*R DS(normal) …(2.4)

Considering the non- perfect junction between the MOSFET and the heat sink the

switching frequency is selected to be 1/5th of the switching frequency given by the

calculations using equations (2.1) to (2.4) which is 50 kHz.

4.

Inductor design

Once the switching frequency is fixed, the size of the coupling inductor, L, can be

properly designed. In order to maintain the continuous current mode operation of the

converter, the inductor can be sized according to the following equationix:

=

8,

Using a fair assumption of maintaining continuous conduction mode at 5% of the safe

continuous current value, which is set at 80% of the maximum continuous allowable

current, the following values are obtained and are listed in table 3.3.

Table 3. 3 Inductor parameters

Switching Time,

Battery

Voltage, 80% Max Continuous

Current, Safe Operating Point

Minimum Inductor

Current, , Induct

ance,

L

= µ 24 80% ∗ 77 = 61.6 5% ∗ 61.6 = 3.08 20 µH

5. Battery

For this project, an ideal battery in the PSIM software component library is selected. A

small resistance of 5 mΩ is added in series with the battery to represent the internal

resistance of the battery. Other parasitic and intrinsic factors of the battery are not

considered in this project.


15/29

CHAPTER 4

1. PSIM simulation

A circuit shown in figure 4.1 is made in PSIM for simulation realization.

Figure 4. 1 Converter schematic in PSIM


16/29

2. Buck - Charge mode

Figure 4. 2 Buck - Charge waveforms

In this mode Q1 is operated in pwm mode with Q2, Q3 and Q4 turned off. For simulation

purpose, the battery voltage is fixed at 24 V and ultracapacitor voltage is set to 20 V. The

inductor current is forced to maintain 80% of rated ultracapacitor current i.e. 62 A. The

modulating triangular waveform, gate signal to transistor Q1, battery voltage,

ultracapacitor voltage, capacitor current, inductor current and the battery current are

plotted


17/29

3. Boost - Charge Mode

Figure 4. 3 Boost - Charge waveforms

In this mode Q1 is on all the time with Q4 operated in pwm mode while Q2 and Q3 are

turned off. For simulation purpose, the battery voltage is fixed at 24 V and the

ultracapacitor voltage is set to 40 V. The inductor current is forced to maintain an average

value of 62 A. The waveforms as in buck charge mode are plotted in figure 4.4 and figure

4.5. It shows that ultracapacitor current has a pulsed waveform while inductor current and battery current has an average value of current close to 65 A.


18/29

4. Buck – Discharge Mode

Figure 4. 4 Buck - Discharge waveforms

The ultracapacitor is discharging into the battery with current being maintained within a

ripple of approximately 3 A near an average value of 62 A. The voltage of the

ultracapacitor in this simulation is 40 V, and the battery voltage is 24 V; this gives a duty

cycle for the switching MOSFET (Q3) of 0.6, which can be seen in the gate voltage

waveform. The current in the ultracapacitor is pulsed waveform with a peak to peak

ripple of around 65 A.


19/29

5. Boost - Discharge Mode

Figure 4. 5 Boost - Discharge waveforms

The voltage of the ultracapacitor is measured to be 20 V and is slowly decreasing as it discharges

into the battery; this explains the negative values for current in figure 4.5. The duty cycle of the

switching MOSFET, Q2 is calculated as 0.2, which can be seen in the gate voltage waveform.

The inductor current is held within the 3 A ripple around 72 A, while the battery current is a

pulsed waveform with a peak to peak ripple of nearly 75 A.


20/29

CHAPTER 5

1. Harmonic analysis

From the waveforms shown in figure 4.2 to 4.5, the battery current is pulsed in buck

charge mode and boost discharge mode while the ultracapacitor current is pulsed in boost

charge mode and buck discharge mode. This is due to the nature of the circuit and the

switching operation required to obtain the buck and boost modes. To determine the

harmonic content present in the pulsed waveforms, the pulsed waveform is assumed to

have an ideal rectangular shape as shown in figure 5.1.

Figure 5. 1 Ideal rectangular current waveform

With the idealized rectangular waveform shown in figure 5.1, the Fourier series analysis

is simplified and using equation 5.1, the amplitude of the harmonic currents is calculated.

=

(sinℎ)… (5.1)

When d is 0.5, the amplitude of harmonics is largest. The fundamental component, ,with a frequency of 50 kHz, which is the same as the switching frequency, , has a peak

to peak amplitude of

.

This large amplitude is undesirable for the life of the battery and ultracapacitor, and afilter is needed to limit this value.

2. Numerical Fourier analysis

The fast Fourier transform (FFT) tool of the PSIM software used for buck charge mode

without filter results the graph in figure 5.2 showing the dominant harmonic to be 50

kHz.


21/29

Figure 5. 2 Current harmonic content without filter

3. Filter design

It is chosen to limit the peak to peak amplitude of the currents in the devices to 5% of the peak amplitude. For that following equations are used to design the second order LC

filter.

=__

… (5.2)

() = 20log() … (5.3)

log( ) log( ) =()

−

… (5.4)

=

()/

… (5.5)

Using equations 5.2 to 5.5, the resonant frequency of the filter, , is calculated to be9.9 kHz. The angular frequency becomes = 2 = 62.25 /.

The resonant angular frequency of the second order harmonic filter can be written as

equation 5.6.


22/29


23/29

Figure 5. 4 Current waveforms for Buck - Charge mode with filter

Figure 5. 5 Current waveforms for Boost - Charge mode with filter


24/29

Figure 5. 6 Current waveforms for Buck - Discharge mode with filter

Figure 5. 7 Current waveforms for Boost - Discharge mode with filter

Comparing the results in figure 4.2 to figure 4.5 with figure 5.4 to figure 5.7 respectively, the

current waveforms have lost their pulsed rectangular shape and are now much closer to an ideal

dc voltage. There is still a ripple due to the sizing of the filter, which was necessary to maintain

designed operation characteristics after implementation, while removing as much of the

harmonic current content as possible. There is a possible resonance effect shown in the

waveform shape, but this impact on the components is much less than the large pulsed current

waveform that was present prior to filter implementation.


25/29

CHAPTER 6

1. Results

The average inductor current was designed to sustain 80% of the maximum continuous

current rating of the ultracapacitor with a maximum ripple of 5% at a switching

frequency of 50 kHz. The second order LC filters were designed to limit the current

ripple in the battery and ultracapacitor to 5% of the battery voltage and 5% peak -to- peak

of the current amplitude. A summary of the results are listed in table 6.1 and table 6.2.

Table 6. 1 Design and simulated converter results

Mode of

Operation

Inductor Average

Current, Inductor Ripple

Current, Comments

Designed Simulated Designed Simulated

Buck - Charge 61.6 A 62 A 3.08 A 2.2 A Simulation as designed

Boost - Charge 61.6 A 64 A 3.08 A 7.0 A higher than designed

Buck- Discharge

61.6 A

60 A

3.08 A

9.0 A

higher than designed

Boost - Discharge 61.6 A 72 A 3.08 A 4.0 A IL,design< < IL,max

Inspiration for the controller came from a similar projectx that utilized separate

controllers for each mode. However, a single controller was implemented for every mode

of operation which may have influenced the switching control. This controller does not

have precise control over the controlled variable.

Table 6. 2 Design and simulated filter results

Mode of

Operation

Battery Ripple

Current, ∆ Ultracapacitor Ripple

Current, ∆ Comments

Designed Simulated Designed Simulated

Buck - Charge 3.5 A 3.0 A 3.5 A 0.5 A Simulation as designed

Boost - Charge 3.5 A 1.2 A 3.5 A 4.5 A higher than designed Buck - Discharge 3.5 A 0.4 A 3.5 A 2.5 A Simulation as designed

Boost - Discharge 3.5 A 4.5 A 3.5 A 0.5 A higher than designed

As table 6.2 indicates, the peak -to- peak amplitude of the currents are limited near 5% of

the peak amplitudes of the battery and ultracapacitor currents, as designed using the

simulated results in figures 4.2 to 4.5. The rectangular wave assumption used to size the

filter may have introduced the deviation from 5% limit in the Boost modes listed above.

The effects seen in the resulting waveforms in figures 5.5 and 5.7 seem to identify aresonance scenario within the filter design.


26/29

2. Conclusions

The Bi-directional Cascaded Buck -Boost Converter topology was analyzed and designed

for a specific application supplying power to charge the ultracapacitor or use the power in

the ultracapacitor. The size of the switches, inductor and filter were determined using

analytical equations. The converter was simulated in PSIM to verify its operation. The

harmonics in current was analyzed using both Fourier series method and numerical

Fourier transform in software. Designing a second order LC filter, the dominant harmonic

current was limited to with 5% of the peak amplitude which was verified in simulation.


27/29

a

APPENDIX


28/29

b

DATASHEETS


29/29

elec 6411 - project final report final

Documents