lightweight dc-dc converter with partial power processing ... · pdf filelightweight dc-dc...

Lightweight DC-DC Converter with Partial PowerProcessing and MPPT for a Solar Powered Aircraft

by

Ahmad Diab-Marzouk

A thesis submitted in conformity with the requirementsfor the degree of Master of Applied Science

Graduate Department of Electrical and Computer EngineeringUniversity of Toronto

© Copyright 2015 by Ahmad Diab-Marzouk

Abstract

Lightweight DC-DC Converter with Partial Power Processing and MPPT for a Solar

Powered Aircraft

Ahmad Diab-Marzouk

Master of Applied Science

Graduate Department of Electrical and Computer Engineering

University of Toronto

2015

A lightweight dc-dc partial power processing converter is demonstrated for solar

aerospace applications. A system-level model is conceived to determine conformity to

payload and target distance objectives, with the Solarship aircraft used as an application

example. The concept of partial power processing is utilized to realize a high efficiency

lightweight converter that performs Max Peak Power Tracking (MPPT) to transfer power

from the aircraft solar array to the high-voltage battery bus. The isolated Cuk is deter-

mined to be a suitable converter topology for the application. A small-signal model is

derived for control design. The operation of a 400V, 2.7 kW prototype is verified at high

frequency (200 kHz), high efficiency (> 98%), small mass (0.604 kg), and uses no elec-

trolytic capacitors. MPPT operation is verified on a 376 V commercial solar installation

at The University of Toronto. The prototype serves as an enabling technology for solar

aerospace applications.

ii

Acknowledgements

I begin by praising God for the great blessings he has given me. To him I owe my health,

well-being, and any good that has befallen me. I thank him for allowing me to complete

this work and I pray that it is of benefit to the reader.

I would like to thank Professor Olivier Trescases for his constant encouragement and

support. I have known Prof. Trescases since my undergraduate studies, and I feel very

privileged to have had him as a supervisor. He has constantly aimed for a high standard of

work, and encouraged his students to meet it. He was also available to address questions

and/or concerns and listen to feedback. I want to thank him for his patience and all that

he has done throughout my years of working with him.

I would like to also thank Shahab Poshtkouhi and Mike Ranjram, both whom I’ve

also known since undergraduate. Shahab has always provided a much-needed optimistic

outlook on matters, and would always try to help anyone in whatever they are facing.

Mike has been the best partner I have worked with on various projects. I very feel

privileged to have them both as colleagues.

I also cannot forget Leonard Shao, Ryan Fernandes, Shuze Zhao, Victor (Yue) Wen,

and Miad Fard for all their help and companionship. It’s humbling to have worked with

a team of brilliant individuals. I would also like to thank Romina Abachi and Kevin

Rupasinghe for their help during the summer; they have done great efforts and I am very

grateful for their work.

I would like to thank Jessica Yablecki, Kenneth McLean, Sebastien Fournier, and all

the team from Solarship for their hard work and contributions. I am grateful to have

had the chance to work on such an exciting project.

Lastly, I would like to thank my parents and brother for their patience and constant

encouragement and support. I owe them very much for their sacrifices.

iii

Contents

1 Introduction 1

1.1 Solar Powered Electric Vehicles . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 The Solarship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Partial Power Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2.1 Modes of Operation . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.3 Thesis Motivation and Objectives . . . . . . . . . . . . . . . . . . . . . . 11

2 Modeling of Photovoltaic Electric Aircraft 15

2.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.1.1 Environmental Model . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.1.2 Electrical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.1.3 Mechanical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.2.1 Exploring the Design Space . . . . . . . . . . . . . . . . . . . . . 29

2.3 Chapter Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . 32

3 Partial Power Processing Converter Topology 35

3.1 Converter Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.1.1 Partial Power Processing Converter Requirements . . . . . . . . . 36

3.2 Rating the Partial Power Processing Converter . . . . . . . . . . . . . . . 40

3.3 Comparison to Prior Work . . . . . . . . . . . . . . . . . . . . . . . . . . 42


4 Converter Design and Analysis 47

4.1 Steady-State Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.2 Closed Loop Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.2.1 Small-Signal Model . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.2.2 Control Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

iv


5 System Implementation 71

5.1 Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

5.2 Thermal Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

5.3 Operation Waveforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79


6 Conclusions 87

6.1 Thesis Summary and Contributions . . . . . . . . . . . . . . . . . . . . . 87

6.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

v

List of Tables

2.1 Value of n for days of the year . . . . . . . . . . . . . . . . . . . . . . . . 18

2.2 Simulation Parameters for Solarship Application . . . . . . . . . . . . . . 28

3.1 Converter Specifications for Solarship Application . . . . . . . . . . . . . 35

4.1 Component specifications for Isolated Cuk converter. . . . . . . . . . . . 48

4.2 Comparison between full and partial power schemes for Isolated Cuk con-

verter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.3 Component DC steady-state values for converter analysis. . . . . . . . . 58

4.4 Parameters used for Isolated Cuk analysis . . . . . . . . . . . . . . . . . 59

4.5 Control parameters for lead-lag controller used in boost mode compensa-

tion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

5.1 Converter Prototype Specifications . . . . . . . . . . . . . . . . . . . . . 74

5.2 Operating modes for thermal performance. . . . . . . . . . . . . . . . . . 77

5.3 Commercial PV string specifications for 10 series panels. . . . . . . . . . 79

vi

List of Figures

1.1 (a) 11 Meter prototype during test flight. (b) Solarship for future design. 3

1.2 Solarship electrical system overview. . . . . . . . . . . . . . . . . . . . . 3

1.3 (a) Full power processing (b) Partial power processing. . . . . . . . . . . 4

1.4 Partial power processing converter in buck mode. . . . . . . . . . . . . . 6

1.5 System efficiency for PPP converter in buck mode as a function of PPP

efficiency, ηP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.6 Partial power processing converter in boost mode. . . . . . . . . . . . . . 8

1.7 System efficiency for PPP converter in boost mode as a function of PPP

efficiency, ηP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.8 Relative magnitudes of VBATT and VPV (a) buck-boost (b) buck mode only

(c) boost mode only. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.1 System block diagram of the simulation model. . . . . . . . . . . . . . . 15

2.2 Resulting irradiance profile based on average irradiation method for Thun-

der Bay, Canada in June for clear-sky conditions. . . . . . . . . . . . . . 19

2.3 Cumulative mean number of days above specified clear day % Irradiation.

1985 - 2004. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.4 Schematic of battery cell model. . . . . . . . . . . . . . . . . . . . . . . . 24

2.5 System level diagram of solar vehicle. . . . . . . . . . . . . . . . . . . . . 25

2.6 Top level Simulink model. . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.7 System parameters during flight of W = 26 m Solarship, Vf = 35 mph. . 28

2.8 System parameters during flight of W = 47 m Solarship, Vf = 15 mph. . 29

2.9 Design space for Cd = 0.05. . . . . . . . . . . . . . . . . . . . . . . . . . 30



3.1 Partial Power Processing converter in (a) buck mode (b) boost mode. . . 36

3.2 Isolated Cuk converter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

vii

3.3 (a) Relative magnitudes of VBATT and VPV (b) Required ∆V at converter

output. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.4 Boost mode achieved using bidirectional converter. The unfolder changes

the connection point so that ∆V is positive at the dc-dc converter output. 39

3.5 Four quadrant partial power processing isolated Cuk converter. . . . . . . 40

3.6 Relative magnitudes of VBATT and VPV (a) buck-boost (b) buck mode only

(c) boost mode only. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.7 Series connected buck-boost regulator from [15]. . . . . . . . . . . . . . . 43

4.1 Partial power processing isolated Cuk converter. . . . . . . . . . . . . . . 48

4.2 Non-isolated Cuk converter. . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.3 High-level control diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.4 VPV tracking VPV,ref using an inner loop. . . . . . . . . . . . . . . . . . . 51

4.5 Isolated Cuk Converter under study. . . . . . . . . . . . . . . . . . . . . 52

4.6 IV curve points under consideration. . . . . . . . . . . . . . . . . . . . . 59

4.7 PLECS simulation model to verify transfer function. . . . . . . . . . . . . 60

4.8 Validation of GV pv,d(s) model for buck mode using PLECS simulation (a)

frequency response (b) phase response. . . . . . . . . . . . . . . . . . . . 61

4.9 Validation of GV pv,d(s) model for boost mode using PLECS simulation (a)

frequency response (b) phase response. . . . . . . . . . . . . . . . . . . . 62

4.10 Plant response of buck mode at remarkable points of IV curve (a) frequency

response (b) phase response. . . . . . . . . . . . . . . . . . . . . . . . . . 64

4.11 Pole-Zero plot for buck mode. . . . . . . . . . . . . . . . . . . . . . . . . 65

4.12 Compensated system for buck mode, Kp = 0, KI = 0.5. . . . . . . . . . . 65

4.13 Plant response of boost mode at remarkable points of IV curve (a) fre-

quency response (b) phase response. . . . . . . . . . . . . . . . . . . . . . 67

4.14 Pole-Zero plot for boost mode. . . . . . . . . . . . . . . . . . . . . . . . . 68

4.15 Compensated system for boost mode using higher order controller. . . . . 68

5.1 Converter connected as part of a larger 10 kW system. . . . . . . . . . . 72

5.2 Converter prototype. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

5.3 Mass distribution of the converter. . . . . . . . . . . . . . . . . . . . . . 73

5.4 Converter connected setup. . . . . . . . . . . . . . . . . . . . . . . . . . . 75

5.5 Converter efficiency in (a) buck mode at the maximum battery voltage,

VBATT,max = 400 V (b) boost mode at the minimum battery voltage,

VBATT,min = 288 V. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

viii

5.6 Thermal performance in buck mode (a) ∆V = 30 V (b) ∆V = 100 V and

in boost mode (c) ∆V = 30 V (d) ∆V = 100 V. No active cooling is used. 78

5.7 Roof panel setup at The University of Toronto. . . . . . . . . . . . . . . 79

5.8 Steady-state operating waveforms at PPV 1.2 kW for (a) buck ∆V = 120

V and (b) boost mode ∆V = 30 V. . . . . . . . . . . . . . . . . . . . . . 81

5.9 Steady-state operating waveforms at PPV 300 W for (a) buck ∆V = 100

V and (b) boost mode ∆V = 40 V. . . . . . . . . . . . . . . . . . . . . . 82

5.10 MPPT Startup waveforms for PPV (a) 1.65 kW (b) 1.1 kW. . . . . . . . 83

5.11 Dynamic step during MPPT operation. . . . . . . . . . . . . . . . . . . . 84

ix

Chapter 1

Introduction

1.1 Solar Powered Electric Vehicles

The trend towards reducing fuel emissions and greenhouse gas emissions has lead to the

growth and development of Electric Vehicles (EVs). EVs can reduce emissions by up to

92% [1] compared to conventional Internal Combustion Engine (ICE) vehicles. The In-

ternational Energy Agency has set a goal of 20 million Electric Vehicles (EVs) by the year

2020 [2], and projections indicate that Norway may surpass 200,000 chargeable vehicles

(hybrid and EV) by 2020 [3]. One advantage EVs have is the flexibility of obtaining their

energy from clean renewable energy sources such as wind and Photovoltaics (PVs) [2]. An

example of this is the body of literature dedicated to the development of solar-powered

cars [4–7].

This interest in vehicle electrification is not restricted to ground-based automobiles.

There is a growing body of literature regarding the development and optimization of

solar-powered electric Unmanned Aerial Vehicles (UAVs) [8–11]. The objective of these

applications is to sustain operation solely using solar power. The consideration in these

applications is multidisciplinary, where one variable, such as the weight of the power

electronic converter (PEC), plays a significant role in the optimization process [11]. An-

other field is the category of manned solar aircraft. One prominent example is the solar

impulse aircraft which aims to circumnavigate the globe using solar power only [12].

1

Chapter 1. Introduction 2

In general, applications that solely rely on PV for their sustained operation have

the objective of satisfying the load demand given an amount of energy storage and PV

available. The availability of PV energy however, is dependent on several considerations

at the system level:

• The limited power of the PV dictates that the mechanical design be carefully con-

sidered. For example, the mechanical design needs to minimize the aerodynamic

drag, to reduce the electrical power required [5].

• The integration of PV is dependent on the mechanical structure of the system,

where different configurations have different surface areas and orientation, each

impacting the amount of energy harvested from the PV.

• The operating environment of the application, where geographically dependent el-

ements such as cloud cover and/or irradiance influence the harvested energy; many

of these variables are time varying and inter-dependent.

A time-domain model is required to capture all these systems simultaneously. This is used

to predict adherences to objectives such as a targeted distance given a specific design.

1.1.1 The Solarship

Canada, Africa, Australasia, Brazil, and Northern Eurasia represent the world’s largest

commodity regions and have combined remote areas of over 50 million square km, with

over 90% unpaved roads and very limited fuel infrastructure. The world’s largest com-

modity economies have gaps in their ability to move cargo. To move goods from Cal-

ifornia to Toronto by truck costs less than 10 cents per ton/km, while moving goods

from Bujumbura to the eastern Congo costs more than $10 per ton/km. Solarship is a

buoyantly-assisted airplane made possible through a confluence of modern developments,

as shown in Fig. 1.1. Advanced aerodynamics, synthetic textile laminates, smart power

electronics, lightweight batteries, and high-efficiency photovoltaics are the enabling tech-

nologies for a practical solar aircraft.

The Solarship aims to address the economic and logistical barriers that prevent ad-

equate supply delivery to remote regions around the globe by (1) reducing the cost of

transport, (2) enabling movement in-and-out of areas where other transport methods

are ineffective due to lack of fuel and runways, and (3) ensuring cold chain storage and

distribution. The Solarship is a hybrid between a bush plane and an airship. The added

buoyancy from the Helium filled wing increases the payload compared to a bush plane,

while the heavier-than-air design eliminates expensive anchors needed for airships.


(a) (b)

Figure 1.1: (a) 11 Meter prototype during test flight. (b) Solarship for future design.

One of the greatest advantages of the Solarship design compared to standard aircraft

is the ability to land in a small area the size of a soccer field. This eliminates the need

for runways and airstrips, making the Solarship versatile for use in remote areas where

such infrastructure does not exist. The Solarship also has a PV array mounted on its

wing, making it independent of fossil fuels achieving self-sufficient operation.

The simplified Solarship electrical architecture is shown in Fig. 1.2. The architecture,

which is similar to ground based Electric Vehicles (EVs) [14], consists of a central battery

pack, two electric motors driven by inverters, and a set of dc-dc converters for performing

Distributed Maximum Power Point Tracking (DMPPT) on the wing-mounted PV array.

String Converter

PV

Module

VBATT

DC-DC/MPPT

VPV

String Converter

VBATT

DC-DC/MPPT

VPV

Motor

Controller(s)

Electric

Motor(s)

Battery

Figure 1.2: Solarship electrical system overview.


1.2 Partial Power Processing

The nature of aerospace applications such as the Solarship imposes constraints on the

power electronics used. In general, components in an aerospace system must be as

lightweight as possible, since an aircraft with excess mass may not achieve continuous

flight [8]. For a power converter, this means minimizing the power rating and increasing

efficiency in order to minimize the component size.

A Partial Power Processing converter only processes a portion of the input power

to transfer power to the output, and is a means of reducing the converter power rating

[15–17]. This is unlike a full power processing scheme, where the entire power is processed

inside the converter. An illustration of a power converter connected in both full power

and partial power processing schemes is shown Fig. 1.3, where the dc-dc converter is used

to charge the battery using power from the PV array.

ηP VBATT

+

IBATT

VPV

-

+

-

IPV

PP

(a)

ΔV ηPVBATT

+

-

IPV

IPV

IPIBATT

VPV

+

-

+

-

IPV

IP

PP

(b)

Figure 1.3: (a) Full power processing (b) Partial power processing.

In a full power processing scheme, the PV power, PPV , is fed directly to the converter

and processed at an efficiency of ηP . Thus for this system

PBATT = ηPPP , (1.1)

PP = VPV IPV , (1.2)

where PP is the processed power, and PBATT is the power delivered to the battery. The


thermal losses are then found to be

Ploss = (1− ηP )PP = (1− ηP )VPV IPV . (1.3)

The expression in (1.3) shows that the losses are directly proportional to the full power

of the converter.

In the partial power processing scheme, the converter is series-connected between the

PV and battery, where only the difference in voltage between the buses, ∆V , is processed.

As a result, the battery and PV share the same ground, and the dc-dc converter is isolated.

The expression for PP becomes:

PP =∆V IPV

ηP, (1.4)

where PP is a function of the difference in voltage instead of the full battery voltage,

where ∆V is defined as

∆V = VBATT − VPV . (1.5)

The loss expression then becomes

Ploss =1− ηPηP

∆V IPV . (1.6)

If the system design is such that the voltage buses are close to each other in value (∆V

small), then the converter processes little power and the losses are minimized. In addition,

it is also possible to have a low ηP and still achieve low losses with sufficiently low ∆V .

This is in contrast to the full power processing converter, where Ploss is a function of the

entire battery bus voltage. With sufficiently low ∆V , Ploss decreases and the efficiency

increases as a result. In addition, the power rating of the dc-dc converter, Pr, decreases,

where

Pr =∆VmaxIPV

ηP. (1.7)

If ∆Vmax is sufficiently small, the converter power rating becomes small. The total power

transfer from input to output however, is not affected. Using the convention in Fig. 1.3

(b)

PBATT = VBATT IPV −∆VmaxIPV

ηP, (1.8)


where as ∆Vmax → 0, the converter is almost behaving in passthrough mode, and hence

the converter processes little to no power. As ∆V increases, the processed power in-

creases.

1.2.1 Modes of Operation

It is possible to operate the converter in one of two modes: buck or boost mode. In

this work, the battery bus voltage, VBATT , is the input to the converter. Buck mode

and boost mode result in lower and higher VPV compared to VBATT , respectively. An

illustration of the converter in buck mode is shown in Fig. 1.4. Since the PV and Battery

share the same ground connection

VPV = VBATT −∆V, (1.9)

where VBATT has decreased by ∆V . The direction of PP is determined by the polarity of

voltage and current at the terminals of the converter. The system efficiency, ηsys, is then

ΔV ηPVBATT

+

-

IPV

IPV

IPIBATT

VPV

+

-

+

-

IPV

IP

PP

Figure 1.4: Partial power processing converter in buck mode.

defined as

ηsys =Pout

Pin

=PBATT

PPV

=

VBATT IPV −∆V IPV

ηpVPV IPV

, (1.10)


using the relation in (1.5), the expression becomes

ηsys =

1− ∆V

ηpVBATT

1− ∆V

VBATT

. (1.11)

A plot of (1.11) is shown in Fig. 1.5, where ηsys is plotted at different∆V

VBATT

for (∆V > 0)

as a function of the Partial Power Processing (PPP) converter efficiency ηP .

60%

65%

70%

75%

80%

85%

90%

95%

100%

50% 60% 70% 80% 90% 100%

Sys

tem

Effi

cien

cy

PPP Converter Efficiency

0.01 0.05 0.1 0.2 0.3 0.5

ΔV/VBATT =

Figure 1.5: System efficiency for PPP converter in buck mode as a function of PPPefficiency, ηP .

A diagram of the boost mode operation is shown in Fig. 1.6. The expression for the

PV voltage is:

VPV = VBATT + ∆V, (1.12)

where VBATT has increased by ∆V . The direction of PP within the converter is in the

opposite direction, and ∆V is the opposite polarity. Using Fig. 1.6 and (1.12), the system


ΔV ηPVBATT

-

+

IPV

IPV

IPIBATT

VPV

+

-

+

-

IPV

IP

PP

Figure 1.6: Partial power processing converter in boost mode.

efficiency expression for boost mode becomes

ηsys =Pout

Pin

=PBATT

PPV

=VBATT IPV + ∆V IPV ηp

VPV IPV

=1 +

∆V ηpVBATT

1 +∆V

VBATT

. (1.13)

A plot of boost mode system efficiency is given in Fig. 1.7.

The system efficiency in partial power processing converter is dependent on two vari-

ables:∆V

VBATT

and ηp. This is unlike the full power processing scheme, where the system

efficiency is ηp. The following remarks can be made:

• The efficiency of the dc-dc converter ηp can be low, but ηsys can still be high despite

this fact, since with sufficiently low∆V

VBATT

, ηsys → 1.

• The partial power scheme allows for more conventional PWM control methods,

since a hard-switching converter with lower efficiency, ηP can be used.


80%

82%

84%

86%

88%

90%

92%

94%

96%

98%

100%

50% 60% 70% 80% 90% 100%

Sys

tem

Effi

cien

cy

PPP Converter Efficiency

0.01 0.05 0.1 0.2 0.3 0.5

ΔV/VBATT =

Figure 1.7: System efficiency for PPP converter in boost mode as a function of PPPefficiency, ηP .


Benefits of Buck-Boost Operation

A dc-dc converter with a lower processed power increases the power density of the con-

verter, making it lighter and more efficient. The use of Buck-Boost operation for the

partial power converter allows to minimize the processed power and decrease the power

rating Pr. This is achieved by designing VPV to be similar in magnitude to VBATT in

order to minimize ∆Vmax.

A plot of VBATT and VPV versus time is shown in Fig. 1.8 for the three modes of

operation: (a) Buck-Boost, (b) Buck, and (c) Boost. The maximum voltage difference,

∆Vmax, is minimized in Fig. 1.8 (a), compared to a larger ∆Vmax in Fig. 1.8 (b) and (c).

time

VBATT, VPV

ΔVmax

(a)

time

VBATT, VPV

ΔVmax

(b)

time

VBATT, VPV

ΔVmax

(c)

Figure 1.8: Relative magnitudes of VBATT and VPV (a) buck-boost (b) buck mode only(c) boost mode only.


1.3 Thesis Motivation and Objectives

This work is divided into two main components: 1) System-level modeling, 2) Partial

Power Processing converter design and implementation.

The system level modeling provides a means to converge on a solution given mechan-

ical, electrical, and environmental constraints. The goal is to develop a time-domain

simulation model to determine a Solarship design that meets target objectives of 200 km

distance with 200 kg payload for a demonstration in Thunder Bay, Canada. In addi-

tion, it serves to model the behavior of the battery and PV voltage buses needed for the

converter design. The model should address the following points:

• Environmental modeling of cloud cover effects, temperature, and time varying ir-

radiance.

• Mechanical modeling of the Solarship through parameters such as surface area, lift,

and coefficient of drag.

• Electrical subsystem modeling of the battery module and PV array, used in the

design of the dc-dc converter.

The concept of partial power processing is a solution to achieving a lightweight dc-dc

power converter. The goal is to design and implement a modular Partial Power Processing

converter used to transfer power from the PV to the battery. The following specifications

are targeted for the converter:

• Interface between high-voltage (400 V) battery and PV buses

• Buck-Boost operation,

• Digital control,

• High frequency (> 100 kHz) high power (> 2 kW) operation,

• Small mass (< 1 kg),

• No electrolytic capacitors,

• High efficiency (> 95%) over wide operating range,

• Closed-loop MPPT operation on PV array.


The thesis is organized as follows: the system-level modeling is covered in Chapter 2.

The partial power processing converter topology is introduced in Chapter 3. The design

of the partial power processing converter is covered in Chapter 4. The experimental

results are presented in Chapter 5. The work is concluded in Chapter 6, with comments

on future work.

References

[1] P. Guo and P. Liu, “Research on development of electric vehicles in china,” in Future

Information Technology and Management Engineering (FITME), 2010 International

Conference on, vol. 1, Oct 2010, pp. 94–96.

[2] E. Rigas, S. Ramchurn, and N. Bassiliades, “Managing electric vehicles in the smart

grid using artificial intelligence: A survey,” Intelligent Transportation Systems, IEEE

Transactions on, vol. PP, no. 99, pp. 1–17, 2015.

[3] O. Sagosen and M. Molinas, “Large scale regional adoption of electric vehicles in

norway and the potential for using wind power as source,” in Clean Electrical Power

(ICCEP), 2013 International Conference on, June 2013, pp. 189–196.

[4] M. Daniels and P. Kumar, “The optimal use of the solar powered automobile,”

Control Systems, IEEE, vol. 19, no. 3, pp. 12–22, Jun 1999.

[5] J. Connors, “On the subject of solar vehicles and the benefits of the technology,” in

Clean Electrical Power, 2007. ICCEP ’07. International Conference on, May 2007,

pp. 700–705.

[6] S. Ahmed, A. Zenan, and M. Rahman, “A two-seater light-weight solar powered

clean car: Preliminary design and economic analysis,” in Developments in Renewable

Energy Technology (ICDRET), 2014 3rd International Conference on the, May 2014,

pp. 1–7.

[7] J. Qian and S. Jie, “Aerodynamics analysis on solar car body based on fluent,” in

World Automation Congress (WAC), 2012, June 2012, pp. 1–4.

[8] S. Morton, L. Scharber, and N. Papanikolopoulos, “Solar powered unmanned aerial

vehicle for continuous flight: Conceptual overview and optimization,” in Robotics

and Automation (ICRA), 2013 IEEE International Conference on, May 2013, pp.

766–771.

13

REFERENCES 14

[9] H. Torabi, M. Sadi, and A. Varjani, “Solar power system for experimental unmanned

aerial vehicle (uav); design and fabrication,” in Power Electronics, Drive Systems

and Technologies Conference (PEDSTC), 2011 2nd, Feb 2011, pp. 129–134.

[10] S. Hosseini, R. Dai, and M. Mesbahi, “Optimal path planning and power allocation

for a long endurance solar-powered uav,” in American Control Conference (ACC),

2013, June 2013, pp. 2588–2593.

[11] Y. Perriard, P. Ragot, and M. Markovic, “Round the world flight with a solar air-

craft: complex system optimization process yves perriard, senior member, patrick

ragot, student member, miroslav markovic, member ecole polytechnique f6d6rale de

lausanne (epfl),” in Electric Machines and Drives, 2005 IEEE International Con-

ference on, May 2005, pp. 1459–1465.

[12] N. Smith, “Solar flying grows wings - [electronics aviation],” Engineering Technology,

vol. 4, no. 13, pp. 32–35, July 2009.

[13] “Solar impulse, the dawn of solar airplanes,” Berkeley Energy & Re-

sources Collaborative (BERC), accessed in February 2015 available at

http://berc.berkeley.edu/solar-impulse-the-dawn-of-solar-airplanes/.

[14] M. Lukasiewycz, S. Steinhorst, S. Andalam, F. Sagstetter, P. Waszecki, W. Chang,

M. Kauer, P. Mundhenk, S. Shanker, S. Fahmy, and S. Chakraborty, “System archi-

tecture and software design for electric vehicles,” in Design Automation Conference

(DAC), 2013 50th ACM / EDAC / IEEE, 2013, pp. 1–6.

[15] R. Button, “An advanced photovoltaic array regulator module,” in Energy Conver-

sion Engineering Conference, 1996. IECEC 96., Proceedings of the 31st Intersociety,

vol. 1, 1996, pp. 519–524 vol.1.

[16] J. Zhao, K. Yeates, and Y. Han, “Analysis of high efficiency dc/dc converter pro-

cessing partial input/output power,” in Control and Modeling for Power Electronics

(COMPEL), 2013 IEEE 14th Workshop on, June 2013, pp. 1–8.

[17] A. Marzouk, S. Fournier-Bidoz, J. Yablecki, K. McLean, and O. Trescases, “Analysis

of partial power processing distributed mppt for a pv powered electric aircraft,” in

Power Electronics Conference (IPEC-Hiroshima 2014 - ECCE-ASIA), 2014 Inter-

national, May 2014, pp. 3496–3502.

Chapter 2

Modeling of Photovoltaic Electric

Aircraft

2.1 Motivation

A solar vehicle system is subject to mechanical, electrical, and environmental constraints.

It is necessary to model these constraints to capture the accurate operation of the vehicle.

The results of the model can then be used to determine a design that meets the target

objective. A generic representation of a conceived model is shown in Fig. 2.1.

Environment

Model

Photovoltaic Model

DC-DC MPPT

Battery

Model

Mechanical

Model

Time/Date/Location

Cloud Cover Model

Time-varying

Irradiance

Temperature

Cell Specifications

Efficiency Profile

Battery

Power

Peak PV

Power

Specifications

(e.g. Speed,

Wingspan)

Load

Power

Cell Characteristics

(e.g. Capacity,

Specific energy)

Figure 2.1: System block diagram of the simulation model.

15

Chapter 2. Modeling of Photovoltaic Electric Aircraft 16

The representation in in Fig. 2.1 captures the main components required to simulate

the characteristic of a solar vehicle:

• The environment model details the external factors impacting the vehicle, such as

the irradiance level at specific date, time, and location conditions.

• The electrical model details the electrical subsystems. This includes modeling the

behavior of the PV, energy storage (battery, fuel cell, etc..), and power electronics.

• The mechanical model is necessary to model the load power required by the motors

to set the vehicle in motion and/or maintain altitude. Variables such as the mass,

surface area, and speed are considered.

All three components are necessary to determine the behavior of the solar vehicle. For

example, if the irradiance level changes, this impacts the PV power output by the electri-

cal system, and subsequently the ability to meet the target objective given a load power

demand. The purpose of this section is to describe how each of the system components

is modeled in order to capture the overall behavior of the system.

2.1.1 Environmental Model

The environmental model aims to represent the working environment of the solar vehicle.

The level of irradiance changes during the day as a result of the earth’s position with

respect to the sun, and a constant irradiance model is not applicable as a result. The

purpose is to determine an accurate representation of the power produced by the PV. The

aim is to model: 1) The irradiance profile with respect to time, date, and geographical

location and 2) the impact of cloud cover. The approach is based on using historical data

obtained as opposed to using derived equations. This is because historical data captures

effects such as cloud cover, which may be challenging to obtain by calculation. The

historical data used was obtained from the NASA Langley Research Center Atmospheric

Science Data Center Surface meteorological and Solar Energy (SSE) web portal supported

by the NASA LaRC POWER Project [1].

Irradiance Profile

The clear-sky irradiance profile for a day in a particular month is derived based on

averaged historical clear-sky daily data for that month. The method in [2] is used,

whereby hourly irradiation data, I, is derived from daily clear-sky irradiation data, H

I = rtH, (2.1)


where rt is the ratio defined by

rt =π

24(a+ b cosω)

cosω − cosωs

sinωs −πωs

180cosωs

, (2.2)

where ω is the hour angle in degrees for the hour in question (morning negative, afternoon

positive), ωs the sunset hour angle in degrees, and a and b are given by

a = 0.409 + 0.5016 sin(ωs − 60), (2.3)

b = 0.6609− 0.4767 sin(ωs − 60), (2.4)

the hour angle for each hour of the day is given by

w = 15(h− 12) (2.5)

where h is the time of day in hours in 24 hour format. The sunset hour angle is given by

cosωs = − tanφ tan δ, (2.6)

where φ is the latitude at the location, and δ is the declination (in degrees) given by

δ = 23.45 sin

(360

284 + n

365

), (2.7)

where n is the day of the year whose value is obtained from Table 2.1. Note that the

values shown are not valid for |φ| > 65◦, and the monthly average day is the day whose

declination is closest to the average declination for that month [3]. After obtaining the

value of the hourly irradiation, this is converted into irradiance, G (W/m2), by dividing

by the number of seconds in an hour

G =I

3600. (2.8)

Choosing as an example Thunder Bay, Canada, during the month of June, the clear-sky

irradiance profile versus time which results is found in Fig. 2.2.


Table 2.1: Value of n for days of the year

Month n for ith Day of Month n for Average Day of Month

January i 17

February 31 + i 47

March 59 + i 75

April 90+ i 105

May 120+ i 135

June 151 +i 162

July 181 + i 198

August 212 + i 228

September 243+ i 258

October 273 + i 288

November 304+ i 318

December 334 + i 344


0 5 10 15 20 250

100

200

300

400

500

600

700

800

900

1000

Hour in Solar Time

Irra

dian

ce [W

/m2]

Figure 2.2: Resulting irradiance profile based on average irradiation method for ThunderBay, Canada in June for clear-sky conditions.


Cloud Cover

It is necessary to model the effect of cloud cover since clouds impact the irradiance level.

If the solar vehicle is designed around the clear-sky assumption, the objectives may not

be met in the event that a cloudy day arises. The other extreme however, is designing

for a completely cloudy day assumption.

The effect of cloud cover is modeled by analyzing the distribution of daily irradiation

at a given location. For a given month, the number of days with a clear sky is different

than the number of completely cloudy days. Using the clear-sky monthly daily average

as a reference, it is possible to capture the effect of cloud cover by considering percentage

values of that reference, and establish a metric for cloud cover with respect to that. The

end goal is to determine an irradiation level that is suited for the application. If the

cloud factor, C, represents the percentage with respect to clear-sky due to cloud cover,

then

Href,C =CHclear

100, (2.9)

this reference can then be used to determine how many days exceed this amount of irra-

diation per month, thus establishing an irradiation that is representative of the operating

environment of the vehicle. The cumulative number of days is determined by applying

the condition

Href,C > In (2.10)

for each day of the month, where In represents the irradiation on a particular day of the

month (i.e. June 21) from historical data. With this method, it is possible to determine

the irradiation level which is most frequently occurring in a month, and use that as the

reference for the model.

The outcome of this method is shown in Fig. 2.3 for the months of June, July, and

August, with the number of days above a specific percentage averaged over a period of

20 years. The number of clear-sky days is less than 5: if the aircraft is designed under

the clear-sky assumption, it would not be able to fly for most days of the month. If

the application requires that the vehicle operate for more days in a month, then lower

percentages of clear-sky need to be taken (e.g. 70%, 80%). If the application demands

that the vehicle operate on very low levels of irradiation, then an even lower percentage

may need to be used as the level for the design.


50 60 70 80 90 1000

5

10

15

20

25

Mea

n N

umbe

r of

Day

s A

bove

%

% of Clear Day Irradiation

JuneJulyAugust

Figure 2.3: Cumulative mean number of days above specified clear day % Irradiation.1985 - 2004.

2.1.2 Electrical Model

The electrical model captures the behavior of the components that influence the electrical

system of the solar vehicle. This includes the PV array, battery, and power electronics.

The model may however be augmented to capture more details such as losses in the

cables. The scope of this work is mainly concerned with modeling the major subsystems.

PV Model

The PV array is modeled according to [4]. The goal is to predict the behavior of the PV

under different irradiance and temperature conditions. The governing I-V characteristic

equation is:

I = Np

(Ipv − I0

[exp

(V +RsI

Vta

)− 1

])−V +

Ns

Np

RsI

Ns

Np

Rp

, (2.11)

where I is the output current, V the PV voltage at the terminals, Ipv the PV current,

I0 the saturation current, Rs the PV series resistance, Rp the PV parallel resistance,

and Vt = NskT/q is the thermal voltage of Ns cells connected in series, Np the number

of parallel strings, k the Boltzmann constant, T the temperature of the p-n junction in

Kelvin, and a the diode ideality constant. I0 is determined by

I0 =Isc,n +KI∆T

exp((Voc,n +KV ∆T )/aVt)− 1, (2.12)


where KV is the open-circuit voltage/temperature coefficient, KI the short-circuit cur-

rent/temperature coefficient, Isc,n the nominal short circuit current, Voc,n the nominal

open circuit voltage, and ∆T = T - Tn (where T and Tn are the actual and nominal

temperature, respectively). The expression for Ipv is

Ipv = (Ipv,n +KI∆T )G

Gn

, (2.13)

where G is the irradiance on the surface, and Gn the nominal irradiance on the surface.

G is an input to the model, and is determined based on the method in Section 2.1.1.

Ipv,n the nominal PV current found as

Ipv,n =Rp +Rs

Rp

Isc,n. (2.14)

The equation in (2.11) is solved to determine the IV characteristics of the PV array

within the system. The series and parallel resistances, Rs and Rp, are determined using

the iterative method described in [4]. The parameters required to perform this estimation

is found in the panel manufacturer’s datasheet [4]. Note that this modeling scheme is

idealized, where the effect of bypass diodes is not considered at a module level. The size

of the panel (Ns x Np) is determined based on two constraints: 1) The available area

for PV on the vehicle, Asolar 2) The desired bus voltage of the string at the maximum

power point, VPV,mpp. The total number of cells based on the area of one cell, Acell is first

determined

Ncells =Asolar

Acell

(2.15)

The number of series cells is then determined

Ns =VPV,mpp

Vcell,mpp

, (2.16)

where Vcell,mpp is the solar cell voltage at the maximum power point point at nominal

conditions. The number of parallel strings is then determined based on the available

number of cells that can fit

Np =Ncells

Ns

. (2.17)


The resulting Np is rounded down in order to ensure sufficient area to fit the cells. The

total power of the panel array at nominal conditions, PPV,mpp is then determined

PPV,mpp = NsNpPcell,mpp, (2.18)

where Pcell,mpp is the peak power of one PV cell at nominal conditions. Determining

the panel voltage using nominal conditions is deemed appropriate since the voltage is

a strong voltage of temperature [5] which does not vary widely in many applications.

The PV cell heating due to solar radiation is taken into account using the linear model

in [6, 7]

Tc = Ta +RthG, (2.19)

where Rth is the overall heat transfer coefficient, Tc the cell temperature, Ta the ambient

temperature.

Battery Model

The vehicle battery module is modeled based on discharge curve data, where the method

in [8] is used. This model captures the behavior of Lithium-Ion batteries, suitable for

the scope of this work. One of the mode assumptions is that temperature does not affect

the model’s behavior. The reference circuit for one battery cell is shown in Fig. 2.4. The

voltage at the terminals is estimated as

Vcell = Vcell,i −RcellIcell, (2.20)

Vcell,i = E0 −KQ

Q−∫ t

0Icell dτ

+ A exp

(−B

∫ t

0

Icell dτ

), (2.21)

where Vcell,i is the no-load voltage, Rcell the battery ESR, E0 the battery constant voltage

(V), Q the battery capacity (Ah), K the polarization voltage (V), A the exponential zone

amplitude (V), and B the exponential zone time constant inverse (Ah−1). A solar vehicle

has a battery module comprised of several cells in series and/or in parallel. The design

of the module may depend on the available mass within the vehicle. For example, based

on the mechanical model, only a limited mass is available for the entire battery module.

In the proposed model, a battery module is designed around three constraints: 1) The

desired battery bus voltage, VBATT (V) 2) The battery specific energy, SE (kWh/kg),

and 3) the mass of the battery mbatt (kg). The goal is to determine the number of series


Vcell,i Vcell

+

-

Rcell

Icell

Figure 2.4: Schematic of battery cell model.

cells Ns,cell, and battery capacity Q (Ah):

Ns,cell =VBATT

Vcell,nom, (2.22)

Q =SEmbatt

VBATT

, (2.23)

where it is assumed that each series module has a capacity of Q. This approximation is

considered to be valid, since the end goal is to model the system level behavior of the

battery, as opposed to the exact internal composition. Practically however, there needs

to be several strings of Ns,cell in parallel depending on the available cell capacities. The

bus voltage is designed around the nominal cell voltage, since the battery is expected to

operate for the longest duration at that voltage.

Power Electronic Converter

The role of the Power Electronic Converter (PEC) is to perform Max Peak Power Track-

ing (MPPT) on the PV Panel, and subsequently transfer the power at high efficiency.

The level of detail can vary from having the full switching model running within the

simulation, to a block level representation. A block level representation has been chosen,

since the goal is to model the input-output behavior of the PEC. The system-level con-

nection diagram is found in Fig. 2.5. The PEC performs MPPT, and transfers power to

the battery according to

Pout = ηPPPV , (2.24)

Iout = ηPVPV

IPV

VBATT , (2.25)


where ηP is the efficiency of the PEC. The system can be studied under partial or full

power processing by modifying ηP , where in partial power processing ηP becomes a

function of ∆V as highlighted in Section 1.2. The Perturb and Observe (P&O) method [9]

is used to track the MPP.

The PEC also performs charge control on the battery. If the State of Charge (SOC)

reaches an upper limit, power transfer from the PV to the battery is ceased until the

SOC drops below the threshold value.

PV Array Battery Pack Motor ControllerElectric

Motor(s)DC-DC/MPPT

PBATT

POUT PLOADPPV

ηP

Figure 2.5: System level diagram of solar vehicle.

Electric Motor(s)

The electric motors represent the load demand by the solar vehicle. The amount of

load power depends on the mechanical modeling, outlined in Section 2.1.3. The motors

themselves can be modeled to include parasitics. For the purposes of this model, the

motors and inverter have been modeled as a lumped efficiency term

Pload,e =Pload,m

ηm, (2.26)

where ηm is the lumped efficiency term, Pload,m the mechanical power, and Pload,e the

electrical power.

Interconnection

Referring to Fig. 2.5, the systems are connected together by applying KCL at the battery

node

Pbatt = Pload,e − Pout, (2.27)

where Pbatt represents the power going into or out of the battery.


2.1.3 Mechanical Model

The mechanical model captures the behavior of the physical system. The load power

and mass allowance for the electrical system are determined by the drag force, and

lift capability, respectively. The mechanical structure also determines the surface area

available for PV, Asolar. The drag force is found by the expression [10]

FD =1

2CDρSV

2, (2.28)

where FD is the drag force, CD the coefficient of drag, ρ the density of air, S the surface

area, and V the vehicle speed. The load power is that which overcomes the drag force,

and is expressed by [11]

Pload = FDV =1

2CDρSV

3. (2.29)

The expression in (2.29) is a general one, and different systems may be modeled using

other methods [10]. The end goal is to determine a load power that is a result of the

mechanical structure of the system.

The lift capability dictates the mass of the battery and PV system. Given a specific

payload, PL (kg), and lift, L (kg), the mass allowance for the electrical system (battery,

PV, etc..), melec, is found as

melec = L−mmech − PL, (2.30)

where mmech represents the mass of the mechanical structure of the system (chassis,

fuselage, etc..). Given a specific melec, the suitable mass of battery and PV that achieve

the mission objectives need to be obtained. If entire allowance is catered for the battery,

then the system reduces to a pure EV with no PV, and conversely, if the allowance is

catered for the PV system, then the system reduces to a static grid-tied PV installation.

For the Solarship application, we have the following relations,

L ∝ W 3, (2.31)

Asolar ∝ W 2, (2.32)

where W is the wingspan of the Solarship in meters. The cubic relation in (2.31) is due

to the increase in envelope volume as a function of increasing the wingspan, where the lift

is directly proportional to the volume due to the increase in helium. The square relation


in (2.32) is due to the increase in surface area when W increases.

2.2 Simulation Results

A Simulink model is developed to simulate the entire solar vehicle system. The model

is shown in Fig. 2.6. The model runs until one of two conditions is met: The battery

reaches under-voltage, or the flight objective is achieved. The Solarship is used as the

example system with mission objectives of 200 kg payload and 200 km range.

Figure 2.6: Top level Simulink model.

Fulfillment of Mission Objectives

The goal of the model is to determine, for a given design, whether the mission objectives

are met. The input parameters to the model are found in Table 2.2. The simulation runs

until either the distance objective, d, is met, or until the battery charge is depleted when

it reaches VBATT,L.

The simulation results for the parameters in Table 2.2 are found in Fig. 2.7. The

flight duration is 1.2 hours and the distance traveled is 68.16 km. The figures show the

real-time behaviour of the system level parameters.

The results for an increased W = 47 m and decreased Vf = 15 mph is found in Fig 2.8.

The results show that the objective of 200 km is achieved at a flight duration of 8.2 hours,

with remaining SOC = 31 %. The remaining SOC indicates that it is possible to run

this system at lower irradiance conditions and/or lower wingspan and/or greater speed.

The exact values of which would need to be determined after a series of simulation runs

to determine the suitable system design.


Table 2.2: Simulation Parameters for Solarship Application

Parameter Value

Ambient Temperature, Ta 25◦C

Wingspan, W 26 m

Target Distance, d 200 km

Target Payload , PL 200 kg

Flight Speed, Vf 35 mph

String Voltage (STC Conditions), VPV 352 V

PV Power (STC Conditions), PPV 75.29 kW

Maximum Battery Voltage, VBATT,H 400 V

Minimum Battery Voltage, VBATT,L 288 V

Specific Energy, SE 0.126 kWh/kg

Coefficient of Drag, Cd 0.12

Motor Efficiency, ηm 0.9

Converter Efficiency at Rated PV Power, ηP 0.95

Cloud Factor, C 70%

0 0.2 0.4 0.6 0.8 1 1.2200

300

400

500Battery (Bus) Voltage (V vs Time)

0 0.2 0.4 0.6 0.8 1 1.20

50

100Battery State of Charge (%SOC)

0 0.2 0.4 0.6 0.8 1 1.20.5

1

1.5Current Leaving Battery (C Normalized)

0 0.2 0.4 0.6 0.8 1 1.20

20

40

60Cumulative PV Energy (kW.h)

0 0.2 0.4 0.6 0.8 1 1.20

20

40

60Averaged PV Power (kW)

0 0.2 0.4 0.6 0.8 1 1.20

100

200Current Leaving PV Converter (A)

0 0.2 0.4 0.6 0.8 1 1.2500

1000

1500Load Current (A)

Time (h)0 0.2 0.4 0.6 0.8 1 1.2

0

200

400

600Panel Voltage (V)

Time (h)

Figure 2.7: System parameters during flight of W = 26 m Solarship, Vf = 35 mph.


0 1 2 3 4 5 6 7 8350

400

450Battery (Bus) Voltage (V vs Time)

0 1 2 3 4 5 6 7 80

50

100Battery State of Charge (%SOC)

0 1 2 3 4 5 6 7 80

0.5

1Current Leaving Battery (C Normalized)

0 1 2 3 4 5 6 7 80

500

1000

1500Cumulative PV Energy (kW.h)

0 1 2 3 4 5 6 7 80

50

100

150Averaged PV Power (kW)

0 1 2 3 4 5 6 7 80

200

400Current Leaving PV Converter (A)

0 1 2 3 4 5 6 7 8300

350

400

450Load Current (A)

Time (h)0 1 2 3 4 5 6 7 8

0

200

400

600Panel Voltage (V)

Time (h)

Figure 2.8: System parameters during flight of W = 47 m Solarship, Vf = 15 mph.

2.2.1 Exploring the Design Space

The objective of the model is to determine adherence to target objectives of distance

and payload for a specific design. The results of the model are dependent on the design

parameters employed. For example, the coefficient drag, Cd, plays an important role in

the drag equation [11], and subsequently in the amount of load power that is required to

make the system reach the required speed as indicated earlier in (2.29). The value of Cd

however, is known to require wind tunnel testing or simulation techniques to determine

[12]. Wind tunnel testing may be difficult for an aircraft the size of Solarship, and

simulation techniques may not present the most accurate results. To converge on a

design that meets the requirements with an uncertain Cd, it is possible to explore the

design space for a range of Cd. This is achieved by iterating the model for several Cd and

observing the patterns that arise.


Figures 2.9 to 2.11 show the possible designs given particular Cd for a target objective

of 200 km and 200 kg payload. Several observations are noted:

• Designs of (W , Vf ) that meet the objectives decrease with increasing Cd.

• Designs common to all Cd are narrowed in the range of high wingspan W and low

flight speed Vf . This is attributed to the lift increasing as a cubic function of W ,

resulting in greater allowance for battery mass. The increase in W also increases

the surface area available for solar panels. Lower values of Vf result in a decrease

of load power.

The results show that a higher Cd results in larger (higher W ) and slower (lower Vf )

designs to achieve the target objectives. In contrast, a lower Cd makes smaller and faster

aircraft designs more feasible.

2025

3035

4045

50

1015

2025

3035

400

50

100

150

200

250

Wingspan (m)Flight Speed (mph)

Dis

tanc

e C

onve

red

(km

)

0

20

40

60

80

100

120

140

160

180

200

Figure 2.9: Design space for Cd = 0.05.


2025

3035

4045

50

1015

2025

3035

400

50

100

150

200

250


Dis

tanc

e C

onve

red

(km

)

0

20

40

60

80

100

120

140

160

180

200


2025

3035

4045

50

1015

2025

3035

400

50

100

150

200

250


Dis

tanc

e C

onve

red

(km

)

0

20

40

60

80

100

120

140

160

180

200



2.3 Chapter Summary and Conclusions

This chapter targets the system level simulation of a solar vehicle. The electrical, mechan-

ical, and environmental components of the simulation model are outlined. Simulation

results are presented for the Solarship application, where the model is used to show sys-

tem parameters such as battery and PV voltages and currents, which can be used to aid

in the power converter design. In addition, the model is used to predict the size and speed

of aircraft that adhere to mission objectives of a 200 kg payload over a traveling distance

of 200 km. The results show that for a range of Cd, it is advantageous to have lower

values of Cd to achieve designs that minimize aircraft size and maximize flight speed.

The number of days in a month which the Solarship can make a successful journey

depends on the cloud factor with respect to clear-sky. The results have shown that it is

only possible to achieve flight in a limited number of days in a month depending on the

chosen cloud factor for the Solarship design.

References

[1] “Surface meteorology and solar energy,” available at https://eosweb.larc.nasa.gov/

sse/.

[2] J. A. Duffie and W. A. Beckman, Solar Engineering of Thermal Processes. Hoboken,

New Jersey: John Wiley and Sons, Inc., 2013.

[3] S. Klein, “Calculation of monthly average insolation on tilted surfaces,”

Solar Energy, vol. 19, no. 4, pp. 325 – 329, 1977. [Online]. Available:

http://www.sciencedirect.com/science/article/pii/0038092X77900019

[4] M. Villalva, J. Gazoli, and E. Filho, “Comprehensive approach to modeling and sim-

ulation of photovoltaic arrays,” Power Electronics, IEEE Transactions on, vol. 24,

no. 5, pp. 1198–1208, 2009.

[5] M. Zaman, S. Poshtkouhi, V. Palaniappan, K. Li, H. Bergveld, S. Myskorg,

and O. Trescases, “Distributed power-management architecture for a low-profile

concentrating-pv system,” in Power Electronics and Motion Control Conference

(EPE/PEMC), 2012 15th International, 2012, pp. LS2d.4–1–LS2d.4–8.

[6] A. Malik and S. J. B. H. Damit, “Outdoor testing of single crystal silicon solar

cells,” Renewable Energy, vol. 28, no. 9, pp. 1433 – 1445, 2003. [Online]. Available:

http://www.sciencedirect.com/science/article/pii/S0960148102002550

[7] W. Maranda and M. Piotrowicz, “Extraction of thermal model parameters for field-

installed photovoltaic module,” in Microelectronics Proceedings (MIEL), 2010 27th

International Conference on, 2010, pp. 153–156.

[8] O. Tremblay, L.-A. Dessaint, and A.-I. Dekkiche, “A generic battery model for the

dynamic simulation of hybrid electric vehicles,” in Vehicle Power and Propulsion

Conference, 2007. VPPC 2007. IEEE, 2007, pp. 284–289.

33

REFERENCES 34

[9] T. Esram and P. Chapman, “Comparison of photovoltaic array maximum power

point tracking techniques,” Energy Conversion, IEEE Transactions on, vol. 22, no. 2,

pp. 439–449, June 2007.

[10] S. Morton, L. Scharber, and N. Papanikolopoulos, “Solar powered unmanned aerial

vehicle for continuous flight: Conceptual overview and optimization,” in Robotics

and Automation (ICRA), 2013 IEEE International Conference on, May 2013, pp.

766–771.

[11] M. Daniels and P. Kumar, “The optimal use of the solar powered automobile,”

Control Systems, IEEE, vol. 19, no. 3, pp. 12–22, Jun 1999.

[12] J. Qian and S. Jie, “Aerodynamics analysis on solar car body based on fluent,” in

World Automation Congress (WAC), 2012, June 2012, pp. 1–4.

Chapter 3

Partial Power Processing Converter

Topology

3.1 Converter Topology

The Partial Power Processing concept has been introduced in Section 1.2, where the dc-

dc converter is only assumed to have an efficiency ηP , with no details on implementation.

The Solarship is the intended application for the dc-dc converter discussed in this work.

A modular scheme is adopted, where each converter interfaces between the battery and a

string of PV panels as shown in Fig. 1.2. The system is easily augmented by connecting

a converter for each string of panels. The converter design specifications for one string

are found in Table 3.1, where the voltage bus parameters previously listed in Table 2.2

remain the same.

Table 3.1: Converter Specifications for Solarship Application

Parameter Value Description

VPV 352 V String Voltage (STC Conditions)

PPV 2 kW PV Power (STC Conditoins)

VBATT,H 400 V Maximum Battery Voltage

VBATT,L 288 V Minimum Battery Voltage

The following sections aim to detail the requirements of a partial power processing

converter, range of topologies for implementation, and the choice of a specific topology

for the converter design.

35

Chapter 3. Partial Power Processing Converter Topology 36

3.1.1 Partial Power Processing Converter Requirements

The goal is to determine the characteristics of a converter topology to meet the specifi-

cations in Table 3.1. The Partial Power Processing scheme is shown in Fig. 3.1 for buck

and boost mode operation.

ΔV ηPVBATT

+

-

IPV

IPV

IPIBATT

VPV

+

-

+

-

IPV

IP

PP

(a)

ΔV ηPVBATT

-

+

IPV

IPV

IPIBATT

VPV

+

-

+

-

IPV

IP

PP

(b)

Figure 3.1: Partial Power Processing converter in (a) buck mode (b) boost mode.

Examining Fig. 3.1 and Table 3.1, several characteristics are deduced regarding the

dc-dc converter.

1. Step-down capability, this is because ∆V < VBATT .

2. Bilateral power flow and Bipolar voltage output. Buck-Boost capability is desired

to reduce the processed power.

3. Isolation. The PV and battery share a common ground, and isolation is necessary

to avoid a short-circuit between input and output.

Isolated Bidirectional Topologies

The class of Isolated bidirectional topologies can be categorized into two groups: 1)

hard switching, 2) soft-switching. Examples of hard switching converters include the

bidirectional flyback [1], bidirectional full bridge [2], and Isolated Cuk [3]. Examples

for the soft switching category include the Dual Active Bridge (DAB) [4], bidirectional

LLC [5], and Series Resonant Converter (SRC) [6].

Hard switching converters have the advantage of being more immune to line and

load variation, with simple PWM control, at the drawback of incurring lower efficiency


and potentially higher switch stresses at higher switching frequencies. Soft switching

converter on the other hand can achieve high efficiency under specific operating conditions

with more unconventional control schemes required, such as Phase Shift control for the

DAB, and frequency control for LLC.

Looking closely at the specifications in Table 3.1, the hard switching class of converters

is more suitable for the following reasons:

• The battery voltage varies between 400V and 288V and is not fixed. A soft-

switching converter such as the DAB loses soft switching depending on the line

variation [4], while a hard-switching does not suffer from this drawback.

• Simpler control. The penalty of hard switching is reduced by the use of wide-

bandgap devices such as SiC devices, which have higher FOM in high voltage

applications compared to Silicon devices [7]. This makes converters more resilient,

making implementation more feasible under high switch stress conditions.

Examining all the hard-switching topologies, the topology of choice is the Isolated

Cuk converter [3, 8] shown in Fig. 3.2. Referring to Fig. 3.2, this topology is suitable for

the following reasons:

1. The converter features continuous input and output current. This is to eliminate

the use of electrolytic capacitors.

2. The magnetics design is standard compared to LLC: the inductors follow stan-

dard design procedures, with the transformer being a conventional high frequency

transformer.

3. There are only two high frequency MOSFETs, unlike a DAB which has 8. While

higher stresses are present, this is circumvented by using wide band-gap devices

such as Silicon Carbide

4. The MOSFETs are controlled in complimentary fashion, using simple PWM con-

trol. They are also low-side MOSFETs resulting in a simpler driving mechanism.

5. The topology offers passive protection against transformer saturation through the

series capacitors, compared to DAB which does not have passive protection.


Lpri Lsec

Cpri Csec

COUT

Q1

+

-

VBATT CIN

Q2

+

-

n1 : n2

VOUT

Figure 3.2: Isolated Cuk converter.

Bipolar Operation

Buck-Boost mode is required for the intended application. The battery voltage decreases

as a function of time, and ∆V will change polarity as a result, as shown in Fig. 3.3. The

Isolated Cuk converter while bidirectional, is not capable of inherently providing bipolar

output; VOUT is always positive. To achieve a bipolar output, a concept is borrowed from

time

VBATT, VPV

(a)

time

ΔV = VBATT - VPV

(b)

Figure 3.3: (a) Relative magnitudes of VBATT and VPV (b) Required ∆V at converteroutput.

micro-inverters [9], where a low-frequency unfolder is used to change the polarity of the

output voltage. The unfolder connects the bus with the higher voltage (VPV in boost

mode, VBATT in buck mode) to the dc-dc converter with the objective of maintaining a

positive dc-dc converter output voltage. For boost mode, the result is adopting a system-

level connection scheme similar to the one shown in Fig. 3.4. Note that in this scenario,

∆V at the dc-dc converter output is positive similar to buck mode in Fig. 3.1.


ΔV ηPVBATT

+

-

IPV

IPV

IPIBATT

VPV

+

-

+

-

IPV

PP

IP

Figure 3.4: Boost mode achieved using bidirectional converter. The unfolder changes theconnection point so that ∆V is positive at the dc-dc converter output.

Partial Power Processing Buck-Boost Isolated Cuk converter

The topology of choice consists of an Isolated Cuk converter augmented with an unfolder

bridge, and is found in Fig. 3.5. This scheme is capable of meeting the requirements in

Fig. 3.1, and achieve buck-boost operation. The Isolated Cuk converter always outputs

a positive voltage at its terminals.

The unfolder realization is also shown in Fig. 3.5. It consists of four bi-directional

blocking switches which enable depending on the mode of operation. The polarity of

VBATT − VPV is changed through the control of switches S1 to S4, in order to meet the

profile in Fig. 3.3. For example, when VBATT − VPV > 0, S1 and S4 are on for buck

mode. When VBATT − VPV < 0, S2 and S3 are on for boost mode. Note that when in

boost mode, the power flow reverses within the converter. Note that while the unfolder

introduces additional switches, the switches are not operated at high frequency: only one

set of switches (S1,S4) or (S2,S3) is always on, and only conduction losses are incurred.

Transition between modes occurs when ∆V is close to zero, when VBATT approaches

VPV . To switch modes, the converter is first turned off by driving Q1, Q2 low, in addition

to turning off S1 to S4. Then, the appropriate set of switches, (S1,S4) for buck or (S2,S3)

for boost, is enabled to enter the desired mode of operation.


Lpri Lsec

Cpri Csec

COUT

Q1

+

-

VBATT CIN

Q2

n1 : n2

-ΔV

+

+

-

VPV

S1 S2

S3 S4

Unfolder

Figure 3.5: Four quadrant partial power processing isolated Cuk converter.

3.2 Rating the Partial Power Processing Converter

The rating of the partial power processing converter, Pr, can be defined as the maximum

processed power inside the converter. It is an indicator of the power density of the

converter. It is desired to minimize Pr to have a lightweight converter. PP has been

defined as

PP = IPV ∆V, (3.1)

where ∆V = VBATT − VPV or ∆V = VPV − VBATT , depending on the mode of operation.

Determining the power rating is equivalent to determining the maximum values 1) ∆V

2) IPV . This can be deduced by looking at the maximum and minimum values of the

system voltages and currents. VBATT is a strong function of the SOC (State of Charge)

[10], and VPV a strong function of temperature [11]. The parameters of, VBATT,max, the

maximum battery voltage, VBATT,min the minimum battery voltage are determined from

the discharge curve characteristics. The PV peak power voltages are determined based on

the ambient temperature variation: VPV,max at Tmin and VPV,min at Tmax. Two maximum


values of PP can be defined assuming MPPT operation:

PP,1 = (VBATTmax − VMPPmin)IPVmin (3.2)

PP,2 = (VMPPmax − VBATTmin)IPVmax, (3.3)

where (3.2) occurs at Tmax and (3.3) occurs at Tmin. Pr is then defined as:

Pr = MAX {PP,1, PP,2} , (3.4)

where (3.2) and (3.3) apply for buck and boost modes, respectively, assuming that the

VPV range intersects with the battery discharge curve, and ∆V is as shown in Fig. 3.6

(a).

If the application is such that VPV is outside the range of VBATT as shown in Fig. 3.6

(b) and (c), then only one mode of operation is valid. While this results in a higher

∆V leading to a higher Pr, the unfolding bridge would not be necessary, simplifying the

overall design. This is because the sole purpose of the unfolding bridge is to achieve the

bipolar operation resulting in buck-boost operation. If unipolar operation is required,

the bidirectional isolated Cuk, without the unfolder, can be connected to achieve either

only buck or only boost depending on the relative magnitudes of the voltages.


time

VBATT, VPV

ΔVmax

(a)

time

VBATT, VPV

ΔVmax

(b)

time

VBATT, VPV

ΔVmax

(c)

Figure 3.6: Relative magnitudes of VBATT and VPV (a) buck-boost (b) buck mode only(c) boost mode only.

3.3 Comparison to Prior Work

The partial power processing scheme has been discussed in the literature [12–14]. The

closest implementation to this work is the Series Connected Buck Boost Regulator

(SCBBR) in [13, 15], which uses a modified full-bridge topology to achieve buck-boost op-

eration. The topology is shown in Fig. 3.7 [15]. For boost mode (VOUT > VIN), switches

Q1 to Q4 actively switch, in addition to Q7 and Q8; switches Q5 and Q6 remain in the

ON state. In buck mode (VOUT < VIN), switches Q5 and Q6 actively switch, and switches

Q1 to Q4 act as a full-wave bridge rectifier; switches Q7 and Q8 remain in the ON state.


Q8

Q7

Q6

Q5

Lout

VIN

Q1 Q2

Q3Q4

VOUT

Figure 3.7: Series connected buck-boost regulator from [15].

There are several notable differences between the topology in this work and [15]:

• The SCBBR uses a center-tap transformer to achieve partial power operation, while

this work uses a conventional transformer.

• The SCBRR uses 6 high-frequency active switching elements compared to two high-

frequency active switching elements in this work. The unfolder switches in this work

only contribute to conduction losses, and only switches during mode transitions.

• The SCBRR requires the use of high-side driving for the high-frequency active

switching elements, while this work only requires low-side driving, simplifying the

driver requirements.

• The full-bridge implementation needs to protect against transformer saturation

through appropriate control; the Isolated Cuk in this work has inherent protection.

• The SCBBR prototype has been demonstrated in closed-loop at high efficiency (>

98%) at 25 kHz, with no mention of the converter mass. The goal of this work is

to demonstrate at high efficiency (> 98%) , a higher switching switching frequency

(> 100 kHz), a lightweight (< 1 kg) converter, and closed-loop MPPT operation

on a solar array.



The requirements of the Partial Power Processing converter are discussed. The power

rating of the partial power converter is determined to be a function of the voltage variation

of the battery and PV voltage buses. It is required to determine the voltage ranges for

each in order to determine ∆V , a parameter which determines the power rating of the

converter along with the current.

Isolation, bilateral power transfer and bipolar operation are needed for buck-boost

capability to reduce the converter power rating, at the cost of having an unfolding bridge.

The unfolding bridge is necessary due to the change of voltage and power polarity between

buck and boost modes. If the system voltages are such that the PV voltage does not

overlap with the battery discharge curve, it is possible to use only one mode of operation

(buck or boost) and simplify the design by removing the unfolding bridge, at the expense

of a higher power rating due to a larger ∆V .

The bidirectional isolated Cuk converter is chosen as the dc-dc converter topology to

implement the partial power scheme for the Solarship application. It features advantages

such as inherent transformer saturation protection, standard transformer design, and

only two low-side high-frequency active switches compared to other topologies such as

the LLC or DAB.

References

[1] H.-H. Chung, W.-L. Cheung, and K. Tang, “A zcs bidirectional flyback dc/dc con-

verter,” Power Electronics, IEEE Transactions on, vol. 19, no. 6, pp. 1426–1434,

Nov 2004.

[2] A. Mehdipour and S. Farhangi, “Comparison of three isolated bi-directional dc/dc

converter topologies for a backup photovoltaic application,” in Electric Power and

Energy Conversion Systems (EPECS), 2011 2nd International Conference on, Nov

2011, pp. 1–5.

[3] A. Aboulnaga and A. Emadi, “High performance bidirectional cuk converter for

telecommunication systems,” in Telecommunications Energy Conference, 2004. IN-

TELEC 2004. 26th Annual International, Sept 2004, pp. 182–189.

[4] M. Kheraluwala, R. Gascoigne, D. Divan, and E. Baumann, “Performance character-

ization of a high-power dual active bridge dc-to-dc converter,” Industry Applications,

IEEE Transactions on, vol. 28, no. 6, pp. 1294–1301, 1992.

[5] A. Hillers, D. Christen, and J. Biela, “Design of a highly efficient bidirectional

isolated llc resonant converter,” in Power Electronics and Motion Control Conference

(EPE/PEMC), 2012 15th International, Sept 2012, pp. DS2b.13–1–DS2b.13–8.

[6] F. Krismer, J. Biela, and J. Kolar, “A comparative evaluation of isolated bi-

directional dc/dc converters with wide input and output voltage range,” in Industry

Applications Conference, 2005. Fourtieth IAS Annual Meeting. Conference Record

of the 2005, vol. 1, Oct 2005, pp. 599–606 Vol. 1.

[7] J. Hefner, A.R., R. Singh, J.-S. Lai, D. Berning, S. Bouche, and C. Chapuy, “Sic

power diodes provide breakthrough performance for a wide range of applications,”

Power Electronics, IEEE Transactions on, vol. 16, no. 2, pp. 273–280, Mar 2001.

45

REFERENCES 46

[8] A. Aboulnaga and A. Emadi, “Performance evaluation of the isolated bidirectional

cuk converter with integrated magnetics,” in Power Electronics Specialists Confer-

ence, 2004. PESC 04. 2004 IEEE 35th Annual, vol. 2, June 2004, pp. 1557–1562

Vol.2.

[9] M. Joshi, E. Shoubaki, R. Amarin, B. Modick, and J. Enslin, “A high-efficiency

resonant solar micro-inverter,” in Power Electronics and Applications (EPE 2011),

Proceedings of the 2011-14th European Conference on, Aug 2011, pp. 1–10.

[10] O. Tremblay, L.-A. Dessaint, and A.-I. Dekkiche, “A generic battery model for the

dynamic simulation of hybrid electric vehicles,” in Vehicle Power and Propulsion

Conference, 2007. VPPC 2007. IEEE, 2007, pp. 284–289.

[11] M. Zaman, S. Poshtkouhi, V. Palaniappan, K. Li, H. Bergveld, S. Myskorg,

and O. Trescases, “Distributed power-management architecture for a low-profile

concentrating-pv system,” in Power Electronics and Motion Control Conference

(EPE/PEMC), 2012 15th International, 2012, pp. LS2d.4–1–LS2d.4–8.

[12] R. Button, “An advanced photovoltaic array regulator module,” in Energy Conver-

sion Engineering Conference, 1996. IECEC 96., Proceedings of the 31st Intersociety,

vol. 1, 1996, pp. 519–524 vol.1.

[13] A. G. Birchenough, “A High Efficiency DC Bus Regulator / RPC for Spacecraft Ap-

plications,” in Space Technology and Applications, ser. American Institute of Physics

Conference Series, M. S. El-Genk, Ed., vol. 699, Feb. 2004, pp. 606–613.

[14] J. Zhao, K. Yeates, and Y. Han, “Analysis of high efficiency dc/dc converter pro-

cessing partial input/output power,” in Control and Modeling for Power Electronics

(COMPEL), 2013 IEEE 14th Workshop on, June 2013, pp. 1–8.

[15] A. Birchenough, “Series connected buck-boost regulator,” May 9 2006, uS Patent

7,042,199. [Online]. Available: http://www.google.com/patents/US7042199

Chapter 4

Converter Design and Analysis

The design of the isolated Cuk converter is focused on component selection and small-

signal modeling. The analysis assumes a converter of ideal efficiency to simplify the

expressions. Given that the unfolder bridge in Fig. 3.5 is not actively switching, the

design of the unfolder is treated separately from the design of the converter itself.

4.1 Steady-State Analysis

The DC analysis of the isolated Cuk converter is based on the topology shown in Fig. 4.1.

Note that ∆V shown in Fig. 4.1 is the output voltage of the converter, and is always

a positive value. Following inductor volt-second balance, and capacitor charge balance

using [1], the steady state conversion ratio can be found as:

∆V =n2

n1

D

D′VBATT , (4.1)

with component ratings as in Table 4.1 The transformer can be designed following design

procedures in [1]. One important factor to keep in mind is interleaving the windings to

minimize the leakage inductance [2]. A large leakage inductance results in significant

spikes on the switching MOSFETs. It is possible to integrate an RCD snubber as shown

in [3] to protect the switching MOSFETs and increase reliability.

The unfolder bridge is designed considering the operation conditions of the converter.

When either (S1,S4) or (S2,S3) are on for buck and boost modes respectively, the voltage

stress on the off switches will be ∆V . The same applies when all switches are off. It is

important to consider however, that in dark conditions VPV can drop to very low values,

and hence the full battery voltage, VBATT , could be imposed on the unfolder bridge,

where the bridge would be required to be rated at that voltage.

47

Chapter 4. Converter Design and Analysis 48

Lpri Lsec

Cpri Csec

COUT

Q1

+

-

VBATT CIN

Q2

n1 : n2

-

ΔV

+

+

-

VPV

S1 S2

S3 S4

+

VQ1

+

-

VQ2

iLpri iLseciCpri

iCout

IPV

-

iCsec

Figure 4.1: Partial power processing isolated Cuk converter.

Table 4.1: Component specifications for Isolated Cuk converter.

Component Steady State Ripple

Lpri ILpri =∆V IPV

VBATT

∆iLpri =DVBATT

2Lprifs

Lsec ILsec = IPV ∆iLsec =D′∆V

2Lsecfs

Cpri VCpri = VBATT ∆VCpri =D′ILpri2Cprifs

Csec VCsec = −∆V ∆VCsec =DIPV

2Csecfs

Cout VCout = ∆V ∆VCout =∆iLsec8Coutfs

Q1 VQ1,blocking = VBATT +n1

n2

∆V -

Q2 VQ2,blocking = ∆V +n2

n1

VBATT -


Comparison to Full Power Processing

A comparison is made between the full and partial power processing versions of the

isolated Cuk converter in Table 4.2. In the full processing scheme, it is assumed that the

output voltage is VPV .

Table 4.2: Comparison between full and partial power schemes for Isolated Cuk converter.

Design Parameter Full Power Processing Partial Power Processing

Q1 Stress VBATT +n1

n2

VPV VBATT +n1

n2

∆V

Q2 Stress VPV +n2

n1

VBATT ∆V +n2

n1

VBATT

Lpri Current Rating ILpri,rated =VPV IPV

VBATT

ILpri,rated =∆V IPV

VBATT

Lsec Ripple Rating ∆ILsec,pk−pk =D′VPV

Lsecfs∆ILsec,pk−pk =

D′∆V

Lsecfs

Csec, Cout Voltage Ratings VPV ∆V

As Table 4.2 shows, with sufficiently low ∆V the component ratings can be signif-

icantly reduced. The switching MOSFETs may be rated at lower voltages, and the

primary and secondary inductors can be rated at lower steady state and ripple currents,

respectively, allowing for an overall reduction in the inductance. The capacitor voltage

ratings can also be reduced, allowing for lower cost components.

Note that the non-isolated Cuk converter is also a suitable candidate for comparison

since it is transformer-less whilst maintaining many characteristics of the isolated Cuk

such as continuous input and output current, in addition to low-side switches. The

scheme is shown in Fig. 4.2, where the polarity of the PV is reversed due to the negative

polarity at the output.


L1 L2

C

COUT

Q1

+

-

VBATT CIN

Q2

-

VPV

iL1 iL2 IPV

+

Figure 4.2: Non-isolated Cuk converter.

While the non-isolated Cuk has the advantage of having weight savings due to being

transformer-less, it has the following drawbacks:

• The capacitor C in the Cuk is rated at a high voltage (i.e. 1 kV) since it interfaces

between two high-voltage buses. This means that electrolytic capacitors are likely

required, reducing lifetime and reliability.

• The inductors are rated for high-voltage swings and high currents, requiring greater

energy storage capacity. This increases the mass of the inductors, reducing the

power density of the converter as a result.

• The active switches are exposed to higher switching losses due to larger stresses,

requiring heavier heatsinks.

• The output capacitor is rated at the full bus-voltage in the non-isolated Cuk, com-

pared to ∆V in the partial power isolated Cuk.

Loss Analysis

Calculating the losses in the system follows a typical procedure as mentioned in [1]. The

switching losses, core losses, and conduction losses are the predominent losses that feature

in the converter. The main difference compared to a conventional scheme is that stresses

and ratings will be as in Table 4.1. In addition, this work uses an active unfolder to

switch between modes. The losses are estimated as

Ploss,unf = 2(RonI2pv + VfIpv). (4.2)

Note that if the unfolder implementation consisted entirely of MOSFETs, there would

only be losses associated with the Ron of four switches in the conduction path.


4.2 Closed Loop Design

The partial power processing converter is used to perform maximum peak power point

tracking (MPPT) on the solar array. This requires developing a controller that performs

this function whilst adhering to requirements such as high bandwidth and adequate phase

margin. A high level control scheme is shown in Fig. 4.3. The MPPT block generates a

reference for an inner loop to track the MPP point as shown in Fig. 4.4. High bandwidth

is desired since this allows the inner-loop to track the reference voltage faster, resulting

in a system more robust to disturbances and faster MPPT convergence. Adequate phase

margin is required to ensure closed-loop stability.

IPV

VPV

MPPTVPV,ref

+-

Gc(s) PWMc1

c2

VPV

Figure 4.3: High-level control diagram.

VPV,ref

VPV

Figure 4.4: VPV tracking VPV,ref using an inner loop.


To develop the control Gc(s), it is required to obtain the small-signal model of the

converter. After the small-signal model is derived, the control-to-output transfer function

GV pv,d can be obtained . The plant is then analyzed to evaluate a suitable control scheme

for regulation. Note that the converter is considered ideal to simplify the derivation.

4.2.1 Small-Signal Model

The topology under study can be found in Fig. 4.5, which represents the buck mode of

operation (S1, S4 on). The DC operation of the Cuk in steady-state has been discussed in

the literature [1] and is not repeated in this work. The aim is to perform ac small-signal

modeling of the converter, where the method in [4] is used to model the PV.

Lpri Lsec

Cpri Csec

COUT

Q1

+

-

VBATT

Q2

n1 : n2

-

ΔV

+

+

-

VPV

S1 S2

S3 S4

+

VQ1

+

-

VQ2

iLpri iLseciCpri

iCout

IPV

-

iCsec

Veq

Req

Figure 4.5: Isolated Cuk Converter under study.

The first step is to obtain the control-to-output transfer function, GV pv,d(s). The

method of averaging [1] is used, where the nonlinear averaged equations are linearized

about an operating point to obtain the small-signal ac model of the system. In other

words, the non-linear high frequency terms are neglected since they are low amplitude,

and only the low-frequency terms are preserved. The following assumptions are made:


• The converter is considered ideal; losses are not modeled. The assumption is that

losses introduce damping, and hence make the system easier to control.

• The transformer is considered ideal, where the magnetizing inductance is not in-

corporated in the analysis.

The analysis uses the sign conventions mentioned in Fig. 3.2 for the passive components.

Note that all lower-case variables presented in the following sections are with respect to

time, that is, x(t). The “(t)” is dropped for ease.

For 0 < t ≤ DTs

During this interval, switch Q1 is ON and Q2 is OFF. The expressions that result are:

vL1 = L1d〈iL1〉Ts

dt= 〈vg〉Ts


dt=〈vc1〉Ts

n− 〈vc2〉Ts − 〈vg〉Ts + 〈vPV 〉Ts

iC1 = C1d〈vC1〉Ts

dt= −〈iL2〉Ts

n


dt= 〈iL2〉Ts

iCout = Coutd〈vg − vPV 〉Ts

dt= 〈iL2〉Ts − 〈iPV 〉Ts

Where 〈〉Ts represents averaging over one switching period.

For DTs < t ≤ Ts

During this interval, switch Q1 is OFF and Q2 is ON. The expressions that result are:


dt= 〈vg〉Ts − 〈vc1〉Ts + n〈vc2〉Ts


dt= −〈vg〉Ts + 〈vPV 〉Ts


dt= 〈iL1〉Ts


dt= −n〈iL1〉Ts

iCout = Coutd〈vg − vPV 〉Ts

dt= 〈iL2〉Ts − 〈iPV 〉Ts


The equations in the previous sections must be perturbed and linearized about an

operating point. That is each component, 〈x(t)〉Ts, is considered to have a DC component

and an ac component:

〈x(t)〉Ts ≈ X + x, (4.3)

where X is the dc component, and x is the ac component. All the variables are perturbed

and linearized to obtain the ac small-signal expressions. In addition, each variable is

multiplied by the relevant duty command (d(t) or d’(t)) to obtain the average over one

switching cycle. The resultant ac terms for the small-signal model are:

L1d îL1dt

= vg −D′vc1 + nD′vc2 + Vc1d− nVc2d

L2d îL2dt

=D

nvc1 +

Vc1nd−Dvc2 − Vc2d− vg + vPV

C1dvc1dt

= −Dn

îL2 −IL2nd+D′ îL1 − IL1d

C2dvc2dt

= D îL2 + IL2d− nD′ îL1 + nIL1d

Coutd(vg − ˆvPV )

dt= îL2 +

ˆvPV

Req

The next step is to form the state-space representation of the entire system. For the

purposes of obtaining the transfer function, the perturbation on the input, vg , is set to

zero. The state-space form of the equations is:

x = Ax+Bu, (4.4)


where the state variables and inputs are:

x =

d îL1dt

d îL2dt

dvc1dt

dvc2dt

d ˆvPV

dt

x =

îL1

îL2

vc1

vc2

ˆvPV

u =[d]

The system matrices for buck mode are found to be:

A =

0 0 −D′

L1

nD′

L1

0

0 0D

nL2

−DL2

1

L2

D′

C1

− D

nC1

0 0 0

−nD′

C2

D

C2

0 0 0

0 − 1

Cout

0 0 − 1

ReqCout


B =

Vc1 − nVc2L1

Vc1n− Vc2L2

−(IL2n

+ IL1)

C1

IL2 + nIL1C2

0

The goal is to determine the control-to-output transfer function. The output, y, is found

to be:

y = Cx+Du, (4.5)

where the matrix C is chosen to have ˆvPV as the output. There is no direct coupling

from input to output, so the matrices become:

C =[0 0 0 0 1

], D =

[0],

The control-to-output transfer function, GV pv,d(s) can then be found using:

GV pv,d(s) =[C(sI − A)−1B +D

]T(4.6)

The expression in (4.6) is evaluated in MATLAB to obtain the transfer function. The

symbolic form is expressed in (4.7):

GV pv,d(s) =A(s) +B(s) + C(s)

D(s) + E(s) + F (s) +G(s) +H(s)(4.7)

where

A(s) = (C1C2L1ReqVc2n2 − C1C2L1ReqVc1n)s2

B(s) = (C1DIL1L1Reqn3 + C1DIL2L1Reqn

2 + C2DIL1L1Reqn+ C2DIL2L1Req)s


C(s) = C1ReqVc2D′2n4 − C1ReqVc1D

′2n3 + C2ReqVc2D′2n2 − C2ReqVc1D

′2n

+ C1DReqVc2D′n4 − C1DReqVc1D

′n3 + C2DReqVc2D′n2 − C2DReqVc1D

′n

D(s) = (C1C2CoutL1L2Reqn2)s4

E(s) = (C1C2L1L2n2)s3

F (s) = (C1CoutL2ReqD′2n4 + C2CoutL2ReqD

′2n2 + C1CoutL1ReqD2n2

+ C2CoutL1ReqD2 + C1C2L1Reqn

2)s2

G(s) = (C1L2D′2n4 + C2L2D

′2n2 + C1L1D2n2 + C2L1D

2)s

H(s) = C1ReqD′2n4 + C2ReqD

′2n2

A similar analysis can be done for boost mode, where the converter is analyzed for (S2,

S3) on. The B, C, and D matrices remain the same as buck mode, and the A matrix

becomes:

A =

0 0 −D′

L1

nD′

L1

0

0 0D

nL2

−DL2

− 1

L2

D′

C1

− D

nC1

0 0 0

−nD′

C2

D

C2

0 0 0

01

Cout

0 0 − 1

ReqCout

The symbolic expression for boost mode becomes:

GV pv,d(s) =A(s) +B(s) + C(s)

D(s) + E(s) + F (s) +G(s) +H(s)(4.8)

where

A(s) = (−C1C2L1ReqVc2n2 + C1C2L1ReqVc1n)s2

B(s) = (−C1DIL1L1Reqn3 − C1DIL2L1Reqn

2 − C2DIL1L1Reqn− C2DIL2L1Req)s


C(s) = −C1ReqVc2D′2n4 + C1ReqVc1D

′2n3 − C2ReqVc2D′2n2 + C2ReqVc1D

′2n

− C1DReqVc2D′n4 + C1DReqVc1D

′n3 − C2DReqVc2D′n2 + C2DReqVc1D

′n

D(s) = (C1C2CoutL1L2Reqn2)s4

E(s) = (C1C2L1L2n2)s3

F (s) = (C1CoutL2ReqD′2n4 + C2CoutL2ReqD

′2n2 + C1CoutL1ReqD2n2

+ C2CoutL1ReqD2 + C1C2L1Reqn

2)s2

G(s) = (C1L2D′2n4 + C2L2D

′2n2 + C1L1D2n2 + C2L1D

2)s

H(s) = C1ReqD′2n4 + C2ReqD

′2n2

The steady-state DC values are found in Table 4.3. Note that the direction of IL2 is

reversed in boost mode due to the power reversal within the converter during this mode.

Table 4.3: Component DC steady-state values for converter analysis.

Parameter Buck Boost

Vc1 VBATT VBATT

Vc2 −∆V −∆V

IL1D

D′IL2n

D

D′IL2n

IL2 IPV −IPV

4.2.2 Control Design

The converter plant is analyzed for different points on the IV curve. For simplicity, STC

conditions are considered (G = 1000 W/m2, T = 25◦C). The operating points under

study on the IV curve are shown in Fig. 4.6 to model Voc, MPP, and Isc regions. The

goal is to determine the frequency and phase response of the converter. This is achieved

by replacing Veq and Req in Fig. 4.5 with a non-linear model. The frequency range under

consideration is 100 Hz to 40 kHz (fs/5). Table 4.4 summarizes the list of parameters

assumed for the Cuk converter used for simulation.


Table 4.4: Parameters used for Isolated Cuk analysis

Parameter Value Unit

L1 274 µH

L2 100 µH

C1 4.4 µF

C2 6.6 µF

Cout 6.6 µF

0 50 100 150 200 250 300 350 4000

1

2

3

4

5

6 X: 321.1Y: 6.194

V [V]

I [A

]

X: 353.7Y: 5.912

X: 384.9Y: 4.685

Figure 4.6: IV curve points under consideration.

Model Validation

The modeling approach is verified by a PLECS simulation using the model in Fig. 4.7.

The simulation uses a 1% perturbation in duty cycle to determine GV pv,d(s). A compari-

son of phase and frequency response is shown in Fig. 4.8 for for buck mode (VBATT = 400

V) at the MPP point and in Fig. 4.9 for boost mode (VBATT = 288 V). The responses

match very closely.


Vbatt

L1

FET1c1

c1

NOT

LogicalOperator

C1

Trn: [2 -1]

C2FET2 Cout

L2

c2

c2

Sawtooth PWM

smC

D

++

VVpv ~

Vpv_hat

~

d_hat

1DTable

IV-Curve

IVVm5

Saturation

Figure 4.7: PLECS simulation model to verify transfer function.


102

103

104

105

106

10

20

30

40

50

60

70

80

Frequency [rad/s]

Gai

n [d

B]

Calculated GvdSimulated Gvd

(a)

102

103

104

105

106

−400

−300

−200

−100

0

100

200

Frequency [rad/s]

Pha

se [d

egre

es]


(b)

Figure 4.8: Validation of GV pv,d(s) model for buck mode using PLECS simulation (a)frequency response (b) phase response.


102

103

104

105

106

10

20

30

40

50

60

70

80

Frequency [rad/s]

Gai

n [d

B]


(a)

102

103

104

105

106

−250

−200

−150

−100

−50

0

Frequency [rad/s]

Pha

se [d

egre

es]


(b)

Figure 4.9: Validation of GV pv,d(s) model for boost mode using PLECS simulation (a)frequency response (b) phase response.


Buck Mode

The behaviour of the plant is studied under buck mode with VBATT = 400 V. The duty

cycle is changed accordingly to meet the operating points in Fig. 4.6. The frequency

and phase responses are shown in Fig. 4.10. The pole-zero plot is shown in Fig. 4.11.

The converter exhibits a 540 degree phase drop over a narrow frequency range, making

the converter difficult to control at high bandwidth irrespective of operating point. The

initial phase of the system is 180 degrees, implying that changes in the duty cycle result

in opposite changes in the voltage. This means that the compensator needs to have a

180 degree phase reversal term to obtain sufficient phase margin. Compensation for buck

mode can be implemented using a simple PI control in the form

Gc(s) = −(Kp +KI

s), (4.9)

where the negative sign (180 degrees phase shift) is necessary to obtain positive phase

margin. Note that a higher order controller would be required to obtain high bandwidth

due to the large phase drop. The system can be compensated at lower bandwidth by

crossing before the resonant frequency, obtaining a phase margin of 90◦. The compen-

sated system is shown in Fig. 4.12 for Kp = 0, KI = 0.5.


102

103

104

105

106

10

20

30

40

50

60

70

80

Frequency [rad/s]

Gai

n [d

B]

Voc Region − 384.94 VMPP − 353.6 VIsc Region − 321 V

(a)

102

103

104

105

106

−400

−300

−200

−100

0

100

200

Frequency [rad/s]

Pha

se [d

egre

es]


(b)

Figure 4.10: Plant response of buck mode at remarkable points of IV curve (a) frequencyresponse (b) phase response.


−6000 −5000 −4000 −3000 −2000 −1000 0 1000−6

−4

−2

0

2

4

6x 10

4

Real Axis (seconds−1)

Im A

xis

(sec

onds−

1 )384.9 V − Voc353.6 V − MPP321 V − Isc

Figure 4.11: Pole-Zero plot for buck mode.

−100

−80

−60

−40

−20

0

20

Mag

nitu

de (

dB)

102

103

104

105

−360

−180

0

180

360

Pha

se (

deg)

System: IscPhase Margin (deg): 90Delay Margin (sec): 0.00807At frequency (rad/s): 195Closed loop stable? Yes

Frequency (rad/s)

VocMPPIsc

Figure 4.12: Compensated system for buck mode, Kp = 0, KI = 0.5.


Boost Mode

A similar analysis is conducted in boost mode with VBATT = 288 V. The duty cycle is

changed accordingly to meet the operating points in Fig. 4.6. The frequency and phase

responses are shown in Fig. 4.13. The pole-zero plot is shown in Fig. 4.14. It is observed

that the phase drop is only 180 degrees around the resonant frequency, however it is

sensitive to the operating condition, where in Isc mode there is a significant phase drop

which occurs. This means that it is possible to compensate the converter in boost mode

using a higher bandwidth controller within a specific operating range. Compensation for

boost mode is possible using a lead-lag controller and PI compensator

Gc(s) = K(1 +

s

ωz1

)(1 +s

ωz2

)

s(1 +s

ωp1

)(1 +s

ωp2

), (4.10)

where the aim is to obtain a phase-boost around the resonant frequency whilst achieving

high bandwidth. An example of the compensated system is shown in Fig. 4.15, with

parameters found in Table 4.5

Table 4.5: Control parameters for lead-lag controller used in boost mode compensation.

Control Parameter Value

K 100

wp1 1e6 rad/s

wp2 1.2e6 rad/s

wz1 1e4 rad/s

wz2 2e4 rad/s


102

103

104

105

106

10

20

30

40

50

60

70

80

Frequency [rad/s]

Gai

n [d

B]


(a)

102

103

104

105

106

−350

−300

−250

−200

−150

−100

−50

0

Frequency [rad/s]

Pha

se [d

egre

es]


(b)

Figure 4.13: Plant response of boost mode at remarkable points of IV curve (a) frequencyresponse (b) phase response.


−3500 −3000 −2500 −2000 −1500 −1000 −500 0 500−5

−4

−3

−2

−1

0

1

2

3

4

5x 10

4

Real Axis (seconds−1)

Im A

xis

(sec

onds−

1 )384.9 V − Voc353.6 V − MPP321 V − Isc

Figure 4.14: Pole-Zero plot for boost mode.

−10

0

10

20

30

40

50

60

Mag

nitu

de (

dB)

102

103

104

105

−315

−270

−225

−180

−135

−90

−45

0

45

Pha

se (

deg)

System: MPPPhase Margin (deg): 62.4Delay Margin (sec): 6.69e−06At frequency (rad/s): 1.63e+05Closed loop stable? Yes

Frequency (rad/s)

VocMPPIsc

Figure 4.15: Compensated system for boost mode using higher order controller.



The design of the partial power processing isolated Cuk converter has been discussed

for both steady state and dynamic operation. In terms of steady-state operation, it is

possible to select the components and achieve benefits such as lower costs and component

ratings with sufficiently low ∆V . It is possible to compensate the converter at a high

bandwidth in boost mode over a limited operating range, allowing for faster convergence

and smaller settling time. High bandwidth may be more challenging in buck mode due

to the significant phase drop at the resonant frequency. In addition, it is necessary to

insert a phase reversal term in buck mode to obtain sufficient phase margin.

References

[1] R. W. Erickson and D. Maksimovic, Fundamental of Power Electronics, 2nd Edition.

Springer Science+Business Media, LLC, 2004.

[2] “2001 magnetics design handbook,” Texas Instruments, Tech. Rep. MAG100A, 2001.

[3] G.-B. Koo, “Design guidelines for rcd snubber of flyback converters,” Fairchild Semi-

conductor, Tech. Rep. AN-4147, 2006.

[4] M. Villalva, T. de Siqueira, and E. Ruppert, “Voltage regulation of photovoltaic

arrays: small-signal analysis and control design,” Power Electronics, IET, vol. 3,

no. 6, pp. 869–880, Nov 2010.

70

Chapter 5

System Implementation

A prototype of a partial power processing isolated Cuk converter is built to interface

between the aircraft PV array and battery bus. The converter is part of a larger 10 kW

modular system shown in Fig. 5.1. Each converter connects to a 2 kW PV string; the

system input power level can be increased by adding one converter for each added string.

The Aux board controls startup and input capacitor pre-charge of the connected dc-dc

converter boards. The commands to the Aux board are issued via a CAN network by

the aircraft central controller (not shown). Active cooling is achieved through the use

of four 3.5 W fans controlled by the Aux board. The fuse and contactor provide extra

measures of protection.

The converter is shown in Fig. 5.2. The prototype specifications are listed in Table 5.1.

The converter weighs 604 g and contains no electrolytic capacitors to extend lifetime and

increase reliability [1]. The inductors and transformer have been chosen to minimize the

overall mass and volume, increasing power density. Silicon Carbide MOSFETs rated for

1.2 kV are used forQ1 andQ2 to obtain high efficiency at the 200 kHz switching frequency.

An optional RCD snubber is added on the high-voltage side to increase reliability by

suppressing ringing. A mass distribution of the components is shown in Fig. 5.3. The

magnetics (transformer, inductors) are 34% of the mass, while heatsinks (MOSFET,

Unfolder) are 19%.

The prototype uses a high-voltage side isolated from a low-voltage auxiliary side.

Sensing of voltage and current is performed through isolated optical sensors and hall

effect sensors, respectively. The Cuk converter is controlled using an on-board Texas

Instruments TMS320F28035 microcontroller. The commands to the converter are sent

via CAN through two control boards. An example of the connected setup is shown in

Fig. 5.4.

71

Chapter 5. System Implementation 72

2 kW

2 kW

2 kW

2 kW

2 kW

Aux

Board

DC-DC

Converter

DC-DC

Converter

DC-DC

Converter

DC-DC

Converter

DC-DC

Converter

900 VDC/100 A

Contactor

60A

Fuse

Terminal

Block

VBATT (+/-)

12 V (+/-)

CAN

Fan

3.5 WFan

3.5 W

Fan

3.5 W

Fan

3.5 W

Figure 5.1: Converter connected as part of a larger 10 kW system.


Optional

RCD SnubberLpri

Lsec

Cpri Csec

Q1

Q2

Unfolder

Bridge

Auxiliary

Side

Figure 5.2: Converter prototype.

Transformer

18%

Lpri

8%

Lsec

8%

MOSFET

Heatsinks

8% Unfolder

Heatsinks

11%

Other (PCB, parts,

etc..)

47%

Figure 5.3: Mass distribution of the converter.


Table 5.1: Converter Prototype Specifications


Maximum Battery Voltage, VBATT,max 400 V

Minimum Battery Voltage, VBATT,min 288 V

Maximum Voltage Difference ∆Vmax 110 V

Minimum Voltage Difference ∆Vmin 20 V

Switching Frequency, fs 200 kHz

Turns ratio, n1/n2 2

Primary-side Inductance, Lpri 274 µH

Secondary-side Inductance, Lsec 100 µH

Primary-referred Magnetizing Inductance, Lm 2 mH

Leakage Inductance, Llk 1.76 µH

Input Capacitance, CIN 4.4 µF

Output Capacitance, COUT 6.6 µF

Primary-side Capacitance, Cpri 4.4 µF

Secondary-side Capacitance, Csec 6.6 µF

PV Input Capacitance, CPV 2.04 µF


Control

Boards

Programmer

Figure 5.4: Converter connected setup.

5.1 Efficiency

The converter is tested at different levels of ∆V at both extremes of the battery voltage

range. In order to measure the efficiency, the PV is replaced by a constant voltage source

using a high power DC power supply, the battery is implemented using an electronic

load, and the snubber is not included. The converter operates in the forward and reverse

direction for buck and boost modes, respectively. The measured system efficiency for

buck and boost modes is shown in Fig. 5.5.

The efficiency drops for increasing ∆V due to the higher processed power. The light-

load efficiency could be further improved by operating the Cuk converter using light-load

efficiency improvement techniques such as burst-mode [2, 3] below PPV = 400 W. The

system efficiency is 98.8% in buck mode for a maximum power of PPV = 2.7 kW and

minimum ∆V = 30 V. This corresponds to a processed power of PP = 250 W. The


efficiency in the reverse direction for ∆V = 82 V is 97.6% at PPV = 2.7 kW. This

corresponds to a processed power of PP = 602 W.

60

65

70

75

80

85

90

95

100

0 400 800 1200 1600 2000 2400 2800

Sys

tem

Effi

cien

cy (%

)

PV Power (W)

30 V

70 V

110 V

ΔV =

(a)

60

65

70

75

80

85

90

95

100

0 400 800 1200 1600 2000 2400 2800

Sys

tem

Effi

cien

cy (%

)

PV Power (W)

22 V

42 V

82 V ΔV =

(b)

Figure 5.5: Converter efficiency in (a) buck mode at the maximum battery voltage,VBATT,max = 400 V (b) boost mode at the minimum battery voltage, VBATT,min = 288 V.


5.2 Thermal Performance

The thermal performance of the converter is examined. The goal is to observe the effect

of increased processed power on the converter. The operating modes are summarized in

Table 5.2. Thermal captures are taken within a few minutes of converter operation, and

no active cooling (e.g. fan, airflow) is utilized. The captures are shown in Fig. 5.6.

Table 5.2: Operating modes for thermal performance.

Mode VBATT Vsupply ∆V Isupply

Buck 400 V 370 V 30 V 6.75 A

Buck 400 V 300 V 100 V 6.75 A

Boost 340 V 370 V 30V 6.75 A

Boost 270 V 370 V 100 V 6.75 A

The following observations are made:

• As ∆V increases, the decrease in efficiency is shown through the increase of temper-

ature of additional components. For example, the snubber and inductors increase

in temperature compared to the lower ∆V case.

• The unfolder bridge losses are predominantly due to the diodes. The difference

between buck and boost modes is also shown through the on-state of the switches

in the respective modes.

• The primary MOSFET, Q1 in buck mode exhibits greater switching losses since it

is under a larger voltage stress.

• The RCD snubber exhibits losses as the switch voltage stresses increase.


(a) (b)

(c) (d)

Figure 5.6: Thermal performance in buck mode (a) ∆V = 30 V (b) ∆V = 100 V and inboost mode (c) ∆V = 30 V (d) ∆V = 100 V. No active cooling is used.


5.3 Operation Waveforms

The converter is tested using commercial rooftop panels at The University of Toronto

during the month of October. The specifications of the PV string are found in Table 5.3,

where a string consists of 10 panels. The converter performs MPPT using the perturb-

and-observe (P&O) method [4] and a tuned digital compensator.

Figure 5.7: Roof panel setup at The University of Toronto.

Table 5.3: Commercial PV string specifications for 10 series panels.


String Open Circuit Voltage, VPV,oc 376 V

String Short Circuit Current, IPV,sc 8.22 A

String MPP Voltage, VPV,MPP ∆Vmax 300.6 V

String MPP Current, IPV,MPP ∆Vmax 7.87 A

Converter steady-state waveforms of the input PV voltage, VPV , high voltage switch-

ing MOSFET, VQ1, secondary side inductor iL,sec, and auxiliary side driving waveform

from the microcontroller for Q1, VPWM,1, were obtained for buck (VBATT = 400V) and

boost mode (VBATT = 250 V). The waveforms obtained for PPV around 1.2 kW are shown

in Fig. 5.8, and PPV around 300 W are shown in Fig. 5.9. Note that VBATT = 250 V

is used for boost mode, since the 288 V operating point is very close to the commercial

MPP voltage of the rooftop commercial panels (300.6 V), and the snubber is introduced

for increased reliability.


Several insights are drawn from the waveforms:

• The peak-peak inductor current, iL,sec,pk−pk in buck mode is always around double

than that of boost mode. This is because the voltage difference, ∆V is around 100

V in buck mode compared to around 40 V in boost mode.

• The DC value of iL,sec in buck mode is positive, while in boost mode it is negative.

This is because there is a reverse in power flow for boost mode within the converter.

• The switch voltage stress on the primary MOSFET Q1 in buck mode is larger than

boost mode since VBATT,buck = 400 V, and VBATT,boost = 250 V.

The converter startup waveforms converging to MPPT are shown in Fig. 5.10 for PPV

= 1.65 kW and PPV = 1.1 kW. The time taken to reach MPPT is around 70 ms for the

1.65 kW case and 200 ms for the 1.1 kW case. This can be attributed to the additional

cloud cover and disturbances present in the lower power case. A zoomed in capture in

AC-coupled mode of a dynamic step during MPPT is shown in Fig. 5.11. The inner loop

loop regulates to the reference within 400 µs.


iLsec

VQ1

VPV

VPWM, Q1

(a)

iLsec

VQ1

VPV

VPWM, Q1

(b)

Figure 5.8: Steady-state operating waveforms at PPV 1.2 kW for (a) buck ∆V = 120 Vand (b) boost mode ∆V = 30 V.


iLsec

VQ1

VPV

VPWM, Q1

(a)

iLsec

VQ1

VPV

VPWM, Q1

(b)

Figure 5.9: Steady-state operating waveforms at PPV 300 W for (a) buck ∆V = 100 Vand (b) boost mode ∆V = 40 V.


IPV

PPV

VPV

(a)

IPV

PPV

VPV

(b)

Figure 5.10: MPPT Startup waveforms for PPV (a) 1.65 kW (b) 1.1 kW.


IPV

VPV

Figure 5.11: Dynamic step during MPPT operation.



An experimental verification of a Partial Power Processing Isolated Cuk Converter is

presented. The converter is digitally controlled, weighs 0.604 kg, uses only two active

switching Silicon Carbide switching MOSFETs with no electrolytic capacitors. The ex-

perimental prototype achieves high efficiency (> 98%) at high frequency (200 kHz) using

the partial power concept. Results show that efficiency degrades as more power is pro-

cessed with the increase in ∆V . Dynamic operation is presented, where the converter

performed MPPT using the P&O method in both buck and boost modes on a commercial

high voltage PV string.

References

[1] G.-S. Seo, B.-H. Cho, and K.-C. Lee, “Electrolytic capacitor-less pv converter for full

lifetime guarantee interfaced with dc distribution,” in Power Electronics and Motion

Control Conference (IPEMC), 2012 7th International, vol. 2, June 2012, pp. 1235–

1240.

[2] J. ho choi, D.-Y. Huh, and Y. seok Kim, “The improved burst mode in the stand-by

operation of power supply,” in Applied Power Electronics Conference and Exposition,

2004. APEC ’04. Nineteenth Annual IEEE, vol. 1, 2004, pp. 426–432 Vol.1.

[3] B. Wang, X. Xin, S. Wu, H. Wu, and J. Ying, “Analysis and implementation of

llc burst mode for light load efficiency improvement,” in Applied Power Electronics

Conference and Exposition, 2009. APEC 2009. Twenty-Fourth Annual IEEE, Feb

2009, pp. 58–64.

[4] T. Esram and P. Chapman, “Comparison of photovoltaic array maximum power point

tracking techniques,” Energy Conversion, IEEE Transactions on, vol. 22, no. 2, pp.

439–449, June 2007.

86

Chapter 6

Conclusions

6.1 Thesis Summary and Contributions

The objective of this work is to present 1) a system level analysis of a PV powered

electric vehicle system, using the Solarship as the application example, 2) the design and

verification of a lightweight partial power processing dc-dc converter.

In Chapter 2, the system level simulation of a solar powered vehicle applied to the

Solarship example is presented. It is found that the Solarship is able to achieve its

objectives of 200 km range and 200 kg payload for specific designs under a specific set

of environmental conditions (e.g. irradiance level) and mechanical parameters (e.g. CD).

The novel contributions of this chapter include:

• Presentation of a method that uses historical averaged data to determine the

amount of irradiance (compared to clear sky conditions) that is most suitable for

a given application.

• Implementing a system level simulation model that determines the appropriate

wingspan of the Solarship based on variation of mechanical parameters such as

coefficient of drag and speed.

In Chapters 3, 4, and 5 the design and implementation of a Partial Power Processing Iso-

lated Cuk converter is presented. The component specifications are presented, in addition

to design considerations specific to the partial power scheme. The novel contributions of

these chapters include:

• The experimental implementation of a Partial Power Processing Isolated Cuk con-

verter. Achieved high efficiency (> 98%) at high frequency operation (200 kHz),

small mass (0.604 kg), with no electrolytic capacitors.

87

Chapter 6. Conclusions 88

• Small-signal ac model of the Partial Power Processing Isolated Cuk Converter used

for control design.

The results show high efficiency (> 98%) in addition to successful experimental imple-

mentation of MPPT using the P&O method on a commercial high-voltage PV string

in both buck and boost modes of operation. The results also verify the theory of op-

eration of the partial power concept, where an increase in processed power results in a

degradation of efficiency.

6.2 Future Work

Based on the research work in this thesis, there are several additional avenues that can

be pursued:

• Experimental verification of the Solarship simulation model. Obtaining experimen-

tal data from the Solarship in flight is needed to verify the simulation results of the

model.

• Experimental verification of the compensation analysis for each mode of operation.

The small-signal analysis shows that the plant phase response is different in buck

mode compared to boost mode. Each mode of operation exhibits a different phase

drop around the resonant frequency, requiring different controller designs to com-

pensate at high bandwidth. This work did not experimentally implement different

control schemes for each mode.

• Light-load efficiency can be improved using methods such as burst-mode.

• The expansion of the partial power concept to soft-switching topologies such as

LLC or Dual Active Bridge (DAB). This work only investigated the hard-switching

isolated Cuk converter in partial power processing mode.

• Silicon Carbide MOSFETs are used in this work’s experimental prototype. With

advances in Gallium Nitride (GaN) technology, it is worthwhile to look into GaN

MOSFETs to determine whether they lead to improved efficiency.

lightweight dc-dc converter with partial power processing ... · pdf filelightweight dc-dc...

Documents