Design and Implementation of a PV Converter for DC ...

Design and Implementation of a PV Converter for DC

Microgrid with Fast and Accurate MPP Tracking Strategy

using Boundary Controller

by

Yang Zhou

A Thesis submitted to the Faculty of Graduate Studies of

The University of Manitoba

in partial fulfilment of the requirements of the degree of

MASTER OF SCIENCE

Department of Electrical and Computer Engineering

University of Manitoba

Winnipeg

Copyright © 2017 by Yang Zhou

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Abstract

Photovoltaic (PV) is an important application of solar energy that widely used in microgrid

systems. This thesis proposes a fast and accurate Maximum Power Point Tracking (MPPT)

algorithm used for PV application where a dp/dv tracker and a second-order switching surface

control technique are applied to perform fast switching in a boost-type converter. A fast action of

tracking Maximum Power Point (MPP) and stable operation at the point are achieved as soon as

the environmental conditions are changed. The operating principles of the proposed control

technique and mathematical derivations of the control law and steady state characteristics are

presented. Simulation result shows that the proposed controller has a dramatic improvement in

terms of dynamic response comparing with conventional PI based MPPT controller. A 280 W

prototype for the proposed controller is built and tested with PV panels. Experiment results show

a good agreement with the derived theory.

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Publications from This Thesis

Conference Papers

[1] Y. Zhou, C. Ho, “A review on Microgrid architectures and control methods,” IEEE ECCE-

Asia, Hefei, China, 2016, pp. 3149 – 3156.

[2] Y. Zhou, C. Ho and K. M. Siu “A Fast and Accurate MPPT Control Technique using

Boundary Controller for PV Applications, IEEE Applied Power Elec. Conf. and Ex. (APEC)

Tampa, US, 2017.

Transaction Papers

[1] Y. Zhou, C. Ho and K. M. Siu “A Fast and Accurate MPPT Control Technique using

Boundary Controller for PV Applications, IEEE Transactions on Power Electronics.

(Submitted)

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Acknowledgments

Firstly, I would like to thank my supervisor Dr. Ngai Man (Carl) Ho for his valuable

guidance throughout my entire master program. It is him who brought me into the research field

of power electronics where I am able to work on the meaningful and exciting projects. I also

learned a lot from him both knowledge and professionalism, also his attitude towards research

inspire me to concur the difficulties with faith.

I would like to express my great gratitude to my RIGA lab mates who offered lots of help

during my two years’ study, especially Mr. Mandip Pokharel, Mr. King Man (Ken) Siu and Mr.

Dong Li who provided their valuable experiences on the simulation, hardware and controller

design. I also owe thank to Ms. Radwa Abdalaal and Mr. Isuru Jayawardana for sharing their

knowledge to help me to better understand the theory of power electronics that used in my project.

I also really appreciate the help of my other lab mates for their help suggestions and comments on

my thesis. I would also thank to all my fellows and friends in Department of Electrical Engineering

and Computer, especially Mr.Erwin Dirks for technical support.

Last but not the least, I would like to thank my family for their unconditional love and

support all the time, I would not have the opportunity to come to Canada and conduct further

research without their understanding and support.

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Dedications

To my beloved mother, father, my sister and her husband and the lovely child and my girlfriend

Zhuang Zhang.

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Table of Contents

Publications from This Thesis ....................................................................................................... iii

Acknowledgments.......................................................................................................................... iv

Dedications ......................................................................................................................................v

Table of Contents ........................................................................................................................... vi

List of Tables ............................................................................................................................... viii

List of Figures ................................................................................................................................ ix

List of Abbreviations ..................................................................................................................... xi

Chapter 1 Introduction ..............................................................................................................1

1.1 Microgrid Overview.............................................................................................................1

1.1.1 Structure of DC Microgrid .......................................................................................3

1.1.2 Power Converters Used in Microgrid ......................................................................5

1.1.3 Review of Converter Control Techniques .............................................................10

1.2 MPPT Control Technique Used in DC Microgrid .............................................................12

1.3 Motivation of the Thesis ....................................................................................................16

1.4 Organization of the Thesis .................................................................................................17

1.5 Contributions of the Research ............................................................................................19

Chapter 2 Operation Principles of the Proposed MPPT Controller........................................21

2.1 dp/dv tracker algorithm ......................................................................................................22

2.2 Control Laws of Boundary Controller ...............................................................................28

2.3 Overall Controller ..............................................................................................................32

Chapter 3 Steady State Characteristics and Analysis of the Proposed MPPT Controller ......33

3.1 PV Array Characteristics – V-I curve ................................................................................33

3.2 PV Array Characteristics – V-P curve ...............................................................................35

3.3 Voltage of PV Array at MPP .............................................................................................35

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3.4 Capacitor Voltage Ripple ...................................................................................................36

3.5 PV Output Current Ripple .................................................................................................36

3.6 Duty Ratio ..........................................................................................................................36

3.7 Inductor Current Ripple .....................................................................................................36

3.8 Switching Frequency .........................................................................................................37

Chapter 4 Simulation Results of the Proposed MPPT ............................................................38

4.1 Steady-State Operation ......................................................................................................38

4.2 Transient Performance .......................................................................................................42

Chapter 5 Experimental Verifications ....................................................................................45

5.1 Experimental Setup ............................................................................................................45

5.2 Experimental Results – Steady State .................................................................................48

5.3 Experimental Results – Transient Performance .................................................................50

5.4 Experimental Results – Quantifying of PV Converter Efficiency .....................................53

Chapter 6 Conclusion and Suggestion for Future Research ...................................................55

6.1 Conclusion .........................................................................................................................55

6.2 Suggestion for Future Research .........................................................................................56

References ......................................................................................................................................57

Appendix ........................................................................................................................................63

A. Derivation of (4) and (6) ......................................................................................................63

B. Derivation of (10) and (11) ..................................................................................................64

C. Derivation of (13) .................................................................................................................65

D. Derivation of (17) .................................................................................................................65

E. Derivation of (18) .................................................................................................................66

F. Derivation of (19) .................................................................................................................66

viii

List of Tables

Table 1-1 Commonly Used Converters Technique in Microgrid ................................................... 6

Table 4-1 Parameters of Calculating Theoretical Values ............................................................. 40

Table 4-2 Steady State Simulation and Theoretical Values.......................................................... 41

Table 4-3 Comparison of Simulation Parameters and Results ..................................................... 42

Table 5-1 Specification of the PV Converter Prototype ............................................................... 47

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List of Figures

Fig. 1-1 Illustration of Topology for Future Smart Grid. [3] ............................................... 2

Fig. 1-2 Structure of A DC Microgrid .................................................................................. 4

Fig. 1-3 A Typical PV Converter in an AC Microgrid. ........................................................ 7

Fig. 1-4 PV System with Energy Storage in A DC Microgrid. ............................................ 9

Fig. 1-5 Current/Voltage and Power/Voltage Characteristic of PV array. ......................... 13

Fig. 1-6 Fast Moving Vehicle with PV Panel On-top Under Rapidly Changing Irradiance.

16

Fig. 2-1 Structure of the Proposed Control Scheme with a Boost-type PV Converter. ..... 21

Fig. 2-2 PV V-P Characteristic and Pinciple of Maximum Power Point Tracker. ............. 25

Fig. 2-3 Flow Chart of dp/dv Tracker. ................................................................................ 26

Fig. 2-4 Slope of P-V curve of PV when (a) 𝑑𝑝/𝑑𝑣𝑐 > 0 (b) 𝑑𝑝/𝑑𝑣𝑐 ≅ 0 (c) 𝑑𝑝/𝑑𝑣𝑐 <

0. 27

Fig. 2-5 State of PV Converter When Switch (a) ON and (b) OFF. .................................. 28

Fig. 2-6 Capacitor Voltage and Current Waveforms in Steady State. ................................ 29

Fig. 2-7 Flow Chart of Boundary Controller. ..................................................................... 31

Fig. 3-1 The Single-diode Model Equivalent Circuit of a PV Cell [51]. ........................... 33

Fig. 3-2 An Ideal PV V-I Curve. ........................................................................................ 34

Fig. 4-1 Simulation Waveforms in Steady State. ............................................................... 39

Fig. 4-2 Dynamic Response of PI and Proposed MPPT Controllers.................................. 44

Fig. 5-1 Test Bed Setup (a) Schematic of Test Bed, and (b) Laboratory Setup. ................ 46

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Fig. 5-2 Experimental Steady State Waveforms ................................................................ 49

Fig. 5-3 Experimental Results in (a) V-I Curve, and (b) V-P Curve in Steady State. ........ 49

Fig. 5-4 Experiment Results of Step Change of (a) Switched from 2 to 4 Panels, and (b)

Vice Versa. 51

Fig. 5-5 Power and Inductor Current Trajectory for Fig. 5-4 (a). ...................................... 52

Fig. 5-6 Topology of Converter for Quantifying Efficiency .............................................. 53

Fig. 5-7 Converter Efficiency In Regard to Input Power and Voltage When Switching

Frequency is 5 kHz ....................................................................................................................... 54

xi

List of Abbreviations

MPPT Maximum Power Point Tracking

MPP Maximum Power Point

DG Distributed Generation

DER Distributed Energy Resources

ESS Energy Storage System

AC Alternating Current

DC Direct Current

PCC Point of Common Coupling

PV Photovoltaic

PQ Power Quality

EV Electric Vehicle

LED Light-Emitting Diode

PFC Power Factor Correction

UPS Uninterruptible Power Supply

PWM Pulse Width Modulation

SEPIC Single-Ended Primary-Inductor Converter

NPC Neutral-Point Clamped Converter

MMC Modular Multi-Level Converter

xii

DBI Dual Buck Inverter

AVG Active Virtual Ground

CM Common Mode

VG Virtual Ground

PLL Phase Locked Loop

VSI Voltage Source Inverter

P&O Perturb and Observe

INC Incremental Conductance

PI Propositional Integral

DSP Digital Signal Processor

1

Chapter 1 Introduction

1.1 Microgrid Overview

Centralized power generation has been nominated in power system for centuries.

Emerging distributed generation (DG) has recently challenged this situation as a consequence

of increment of public environment awareness, supply reliability issues, power quality (PQ)

requirements and its economic merits [1]. As an important family of DGs, renewable energy

such as solar, wind and small hydro have been enlarged in the percentage of power generation

market due to its environment friendly features [2]. However high penetration of renewable

resources has addressed challenges to operations and stability of power systems due to their

non-linear and intermittent characteristics. Also the fact that vast amount of renewable energy

being used leads to a change of conventional power system structure. Thus, proper microgrid

architectures and corresponding control techniques are important to regulate distributed energy

resources (DERs) to ensure stability and safety of power systems.

With a cluster of various distributed generators, energy storage, power consumers,

power electronics interfaces and controllers, a microgrid can work as a self-managed cell of

power systems and be capable of controlling its internal components to minimize negative

effects on external network. One attractive feature of microgrid is the capability of working in

both grid-connected and islanded operating modes. Fig. 1-1 shows a conceptual topology of

future smart grids connecting to a small residential microgrid [3].

2

Fig. 1-1 Illustration of Topology for Future Smart Grid. [3]

In case of power system contingency such as outage, voltage sag or frequency variation

which causes failure of upstream distribution network, a microgrid can be disconnected from

the main grid and work in an islanded mode and be supported by the local DERs and energy

storage systems (ESSs) [2]. This feature ensures supply reliability and power quality of its

internal power consumers. Furthermore, a microgrid is able to provide surplus power to

external power consumers by involving in the distribution reconfiguration process when faults

occur in upstream distribution network [4]. However, appropriate coordination of internal

components is essential for a microgrid to gain such functionality, in this sense, proper control

techniques are necessary to achieve above objectives.

Debate over AC versus DC which is better never ends, even though AC plays the

A Microgrid

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majority parts of power system since 19th century, DC power system has re-raised people’s

interests thanks to the fast development of power electronic technology [5]. As an important

part integrated with distribution power system, an AC microgrid mainly inherits technologies

of conventional AC power system [5] and therefore problems within AC power system such

as power quality issues and synchronization issues still exist in an AC microgrid. And these

drawbacks lead to the complexity to control a microgrid, also conversion efficiency of

converters in an AC microgrid is another concern. Even there are still many problems unsolved,

AC microgrid has exposed numerous merits.

1.1.1 Structure of DC Microgrid

DC microgrid is an emerging technology due to the increment of modern DC loads

such as electric vehicle (EV), light-emitting diode (LED) lighting and that the majority of

electronic devices are DC, as well as DC storage elements and DERs. In this sense, DC

microgrid has shown its vast potential appliance. Similar to AC microgrid, a DC microgrid

connects to a host grid via the point of common coupling (PCC) which enables microgrid to

connect and disconnect transition. DC micro-sources such as PV, energy storage and DC loads

can easily connect to a DC bus via a single stage DC-DC converter. AC loads such as rotating

machine and AC generators such as wind turbine only requires rectifiers with controllers to

integrate with the DC bus. With less conversion process than AC counterpart, DC microgrid is

considered to be more reliable and topology is simpler [6]. A loss comparison between DC

microgrid and AC microgrid in residential houses is made and the author found out that DC

microgrid is more efficient in terms of power conversion losses, furthermore, reduction loss of

DC microgrid can be significant compared to AC counterpart when an energy storage system

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(ESS) is applied [7]. DC microgrid tends to be more efficient than AC microgrid if DC source

and DC loads are in a major percentage [8].

However there are drawbacks of DC microgrid such as standardization is a concern

and these needs to be addressed [6]. DC breaker is difficult to achieve in an economic way

which slowing down the usage of DC microgrid as DC current cannot be zero at any moment

[8]. Nevertheless, currently there are a few applications which employ DC distribution system

such as spaceship, tractions, telecommunication, and data centers and LED lighting system [6].

An example of DC microgrid structure is shown in Fig. 1-2.

Fig. 1-2 Structure of A DC Microgrid

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1.1.2 Power Converters Used in Microgrid

Power converters play an important role in microgrid as they bridge different energy

resources and transfer energy seamlessly among various microgrid components regardless of

AC or DC. Semiconductors such as diodes, switches and passive devices such as resistors,

inductors and capacitors are the basic components to construct a converter. Not only convert

energy, converters with proper controllers also keep the power quality of microgrid towards

expected objective. Table 1-1 summarizes the common converters used in microgrids in terms

of applications, control methods and topologies.

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Table 1-1 Commonly Used Converters Technique in Microgrid

Converter

Category

Applications in

Microgrid

Control Methods

Commonly Used

Commonly Used

Topology

DC-DC

Energy storage systems

(e.g. battery or

capacitor), DC loads

(e.g. EV chargers and

LED lightings), DC

generators (e.g. PV)

Voltage mode control,

current mode control,

boundary control,

power control, MPPT

control, duty ratio

control.

Buck, boost, buck-

boost, SEPIC, Ćuk,

Zeta, full bridge DC

converter.

AC-DC

Main converter in DC

microgrid, power

supply in AC microgrid

for DC loads, DC motor

drive, Power Factor

Correction (PFC)


current mode control,

boundary control,

power control.

Single (three) phase

diode bridge rectifier,

single (three) phase

controlled rectifier.

DC-AC

Motor drive,

Uninterruptible Power

Supply (UPS), active

power filter


Current mode control,

Reactive power control,

Hysteresis control.

Half-bridge inverter,

full-bridge inverter,

NPC inverter, MMC,

DBI.

AC-AC Air conditioning

compressor. [9]

ON/OFF Control,

Phase-Angle Control,

PWM AC Chopper

Control. [10]

Cyclo converter, matrix

converters [9]

AC-DC-

AC

Wind turbine, micro

turbine.

Wind speed control,

voltage model control,

power and reactive

power control. [11]

Back-to-back converter,

rectifier-inverter

converter. [11]

7

Fig. 1-3 A Typical PV Converter in an AC Microgrid.

Fig. 1-3 shows a typical topology for a PV generator with a MPPT controller injecting

power into the AC bus through an inverter. The boost converter controls the PV panel to

operate at the Maximum Power Point and the inverter shapes the current to an AC form which

is synchronized with the grid voltage. For the MPPT controller, sometimes more advanced

topologies would be used for various power ratings and different applications. For example an

interleaving boost converter is typically used for relatively high power applications [12], [13].

Those two converters work 180 degree phase shifted and in parallel. It can share the current

and minimize the current ripple of the PV panel. On the other hand, a low-power micro-inverter

typically uses a flyback converter instead of a boost converter [14], since flyback converter

can give a galvanic isolation and a high boosting ratio by adjusting the high frequency

transformer turns ratio. The inverter topology selections are limited by the common mode

8

(CM) voltage issues [15]. The CM issues generates a high frequency leakage current to reduce

the life time of PV panels. Thus, some single phase PV inverter topologies have been invented

to deal with the problem, such as the H5 topology [16], the Heric topology [17] and the latest

proposed topology, of the Active Virtual Ground topology (AVG) [18]. Although the

topologies are based on a full-bridge inverter, the differences are to add a block device

disconnecting the leakage current path, a branch bypassing the free-wheeling current and a

path returning the high frequency current, respectively. 3 phase 4-wire topology is the typical

topology to solve the CM voltage issue by connecting the capacitor bank middle point to the

Neutral of the grid [19]. It makes the potential difference between the PV panel and the grid

network is always constant. 2-level (simple half-bridge) and 3-level (Neutral Point Clamped)

topologies can be used. However, the drawback is that a high dc-link voltage is required to

supply which causes high switching losses in the both power stages, of the MPPT converter

and the inverter. The Virtual Ground (VG) topology has been proposed recently [20]. The

inverter works like a 3 phase 3-wire system but the mid-point of the capacitor bank is controlled

as the same voltage potential as the grid neutral point. The high frequency leakage current is

not created and the DC link voltage can be reduced effectively. The PV inverter topology is

critical for AC microgrids, since the high frequency leakage current not only shortens the PV

panel life time but also creates interference to other grid connected devices and shortens their

life time of components. However, DC microgrids employing boost converter does not need

worry the leakage current problem as the output of boost converter is DC link.

9

PV Array

Load

Battery

Fig. 1-4 PV System with Energy Storage in A DC Microgrid.

Fig. 1-4 illustrates a system which is a DG supported microgrid with energy storage

systems as part of DC microgrid. The system is typically used in solar energy powered lighting

networks [21] and solar energy powered EV changing stations [22]. The MPPT controller is

used to maximize the power output of PV such as the function in Fig. 1-3. Boost converter is

utilized in this topology and also an energy storage system is connected to DC bus to absorb

or output power when output power of PV fluctuates during day and night. The arrangement

can always balance the input and output power. Besides, the system can work as in the

islanding mode [3].

Nevertheless, no matter in DC or AC microgrids, boost converter is always in the front

power stage of PV converter with a MPPT controller.

10

1.1.3 Review of Converter Control Techniques

1.1.3.1 Boundary Control

The boundary control family includes first order switching surface such as sliding mode

control and hysteresis control and second order switching surface, however, dynamic

performance robustness of first order switching surface is limited [23]. Furthermore, boundary

control with first order switching surface such as hysteresis exhibits poor steady state in the

discontinuous conduction mode, operation point is altered as load is changed, however

boundary control with the second order switching surface avoids this problem [24]. Sliding

mode control is widely used in power converters, however, the control parameters are hard to

be unified due to the stability in transient are determined by load [25]. Boundary control with

second order switching surface is aimed to have inductor current trajectory moving along the

natural switching surface of the converter in the successive switching actions so that the target

operating point is reached in minimum time which can be two switching actions under load

disturbance [26]. The necessary conditions of determining the moment to perform switching

actions are derived from the converter operating in the target equilibrium state [27]. A detail

derivation of boundary control law of a boost converter for PV application is described in

chapter 2.2.

11

1.1.3.2 Voltage Mode Control

Voltage mode control is a single loop feedback control, which can regulate duty ratio

of converter to adjust output voltage to objective value. Author in [28] raises a voltage clamp

control method in the application of DC microgrid which composes of an energy storage

system and multiple DGs. The energy storage system charges and discharges alternatively to

maintain DC link voltage in grid-connected mode and as a microgrid works in the islanded

mode, energy storage system discharges when insufficient power generated from DGs and be

charged when the amount of energy in the energy storage element is below a reference point.

A PI controller is commonly employed in controllers of power converters in microgrid due to

the easiness to realize. In a voltage mode control, a proper gain of PI controller is necessary to

be chosen in order to regulate voltage towards target value. The trial and error method is widely

seen in tuning PI gain, however, it is time consuming and the chosen gain may not be the

optimized one [29].

12

1.2 MPPT Control Technique Used in DC Microgrid

MPPT techniques are commonly used in renewable energy generations such as

photovoltaic and wind turbine generators. Due to the non-linear V-I characteristics and also

the fact that variation of solar irradiation intensity, cloud coverage and temperature can lower

down the utilization efficiency of output power of PV, the MPP is necessary to be tracked by

a MPPT controller to ensure PV system is operating at this point [30]. With a MPPT controller,

maximum power can be extracted from PV panels, hence conversion efficiency of PV is

boosted and cost of PV produced energy is therefore reduced [31]. Furthermore, the dynamic

MPPT performance is limited according to varying irradiance sequence specified in EN50530

[32]. A typical current/voltage and power/voltage characteristics of PV array is illustrated in

Fig. 1-5

13

(a)

(b)

Fig. 1-5 Current/Voltage and Power/Voltage Characteristic of PV array.

MPP

MPP

MPP

MPP

14

Various MPPT algorithms are researched in literature within which Perturb and

Observe (P&O) algorithm is one of the most popular one used in the industry due to its

simplicity and economic merits of implementation [33]. However, this method cannot track

the maximum power point precisely as operation point will oscillate around MPP and it

exhibits feature of wrong MPP tracking direction when irradiance level suddenly change [34].

Furthermore, the step size perturbation determines the trade-off of accuracy and speed of MPP

tracking [35]. An adaptive P&O method is introduced to address this concern and step size is

minimized when operation point is close to MPP and MPP tracking direction is ensured by

applying a band to limit PV terminal voltage [36]. Another well-known MPPT control

technique is incremental conductance (INC), which is believed to be more accurate to track

MPP and eliminate oscillation at MPP than the P&O counterpart according to a research study

[37]. However, P&O and INC are proved to be no difference both in theory and experimental

test in [38]. A modified variable-step INC algorithm is proposed in [39] which shows less

system oscillations at MPP comparing with conventional method, the tracking speed of MPP

is also improved. Another variable-step INC method is proposed in [40] to avoid the division

calculation by canceling the voltage perturbation. However, both of abovementioned variable-

step INC methods still have room to improve the MPP tracking speed. Constant voltage is a

simple method to realize MPP tracking, voltage at MPP is approximated by a certain

percentage of open circuit voltage of PV panels, however this method has the limit of

temperature change [41]. Fuzzy Logic Control is an emerging MPPT control technique which

has good accuracy in tracking MPP even in a varying environment, nevertheless this control

technique may track the MPP in an incorrect direction under the variation of irradiance [42].

In a PV converter, MPPT controller is commonly used in coordination with a Proportional or

15

Propositional Integral (PI) controller which modulate duty ratio to control the switch.

However, the dynamic response of PI controller in transient period is not satisfied [43].

Especially for fast moving objects such as solar panels on vehicle or a spacecraft, the MPP

does not stay at one point and irradiation received depends on shading and facing angle to the

sun. Since the object moves very fast and unpredictable, received irradiation changes

accordingly which causes a difficulty for the conventional MPPT controller, such as P&O, to

track the MPP. It reduces the MPPT power efficiency due to the poor tracking accuracy.

This thesis proposes a fast and accurate MPPT control scheme based on a boost type

DC-DC converter to maximize energy generation from PV panels. For the control part, dp/dv

slope of PV power curve is used to track MPP and boundary controller is utilized for fast

modulating PV output voltage. This innovative combination of control loops provides a rapid

response during irradiation transient and a stable operation during steady state. Furthermore,

the new boundary control law for boost converter with input voltage control and overall system

steady state characteristics have been found. The principle of operation, controller design,

simulation and experimental verifications will be discussed in the following chapters.

16

1.3 Motivation of the Thesis

Conventional PI based MPPT controller cannot track MPP under rapidly changing

irradiance conditions due to its slow response. Fig. 1-6 illustrates one of PV applications with

MPPT that a fasting moving vehicle with mounted PV panels driving on urban area where

shadows of buildings cause rapidly changing of irradiance on PV panels. It is obviously that a

slow MPPT cannot maximize solar energy transferring due to the slow dynamic response.

Fig. 1-6 Fast Moving Vehicle with PV Panel On-top Under Rapidly Changing

Irradiance.

Efficiency of MPPT controller is another concern, faster MPPT means shorter time of

MPP tracking which enable PV converter to be fast-responding in transient period. This can

reduce power loss comparing to a slow MPPT controller.

17

Furtherly, the fast MPPT technique can be extended to microgrid applications to

provide high MPPT efficiency according to EN 50530.

In conclusion, a fast MPPT with certain accuracy is needed to be researched.

1.4 Organization of the Thesis

Six chapters are included in the thesis, each of which is described as follows:

Chapter 1 gives a literature review on Microgrids which introduces DC

microgrid topology and control technique state of art. Particularly MPPT

control techniques used in DC microgrid are reviewed and compared.

Contribution of the thesis are highlighted in the last part of this chapter.

Chapter 2 explains theory being used in the proposed MPPT controller for PV

applications. Operation principle of dp/dv tracker as outer loop controller is

explained on how to track MPP. Control law of boundary control is derived

with turn-on and turn-off criteria determined.

Chapter 3 presents steady state characteristic of the proposed MPPT controller.

A single diode based mathematical model is built to calculate steady state

results which are later compared with simulation results. Major indices of

steady state of the proposed MPPT controller are calculated in detail in this

chapter.

Chapter 4 demonstrates simulation result of the proposed MPPT in terms of

steady state and dynamic response. Transient response of the proposed MPPT

18

is compared with three different MPPT controllers which include a combination

of P&O and dp/dv tracker as outer loop and PI, boundary controller as inner

loop control. Steady state characteristics of simulation results are compared

with theoretical counterparts, results are summarized and listed in the table.

Chapter 5 evaluate system performance of the proposed MPPT controller in

both steady state and transient state experimentally. The architecture of

experiment test bed, experiment waveforms and detail procedures of

conducting test are presented in this chapter. Power and inductor current

trajectories during operation point changing in a transient period are illustrated

and explained.

Chapter 6 draws the conclusion of this thesis and also suggestions for future

research work are listed in the final part of this chapter.

19

1.5 Contributions of the Research

This thesis proposed a new control technique to achieve MPPT for PV application used

in DC microgrid. The major contributions of this thesis is summarized as following:

A literature review has been conducted with respect to DC microgrid as well as

control techniques including boundary control, voltage mode control and MPPT

control. Various MPPT techniques are compared.

A boost type converter is designed and implemented in printed circuit board

(PCB) board. Theory employed in the proposed MPPT control technique

including MPP tracker and boundary control law is derived and explained based

on designed topology. The development of control algorithm in a based Digital

Signal Processor (DSP) controllers is presented in procedures.

The proposed MPPT control technique has been verified both in simulation and

experimentally by using a 2*2 Siemens SP75 PV panels, which is in agreement

with delivered theory.

Steady state of the proposed MPPT controller is studied and PV model is

characterized by using a diode model, calculated steady state parameters are

compared with simulation results.

Dynamic response of the controller is evaluated experimentally and

demonstrated by plotting inductor current trajectory when operation point is

switched in transient.

20

These contributions led to the following publications in journals and

conferences.

Conference Papers

[1] Y. Zhou, C. Ho, “A review on Microgrid architectures and control

methods,” IEEE ECCE-Asia, Hefei, China, 2016, pp. 3149 – 3156.

[2] Y. Zhou, C. Ho and K. M. Siu “A Fast and Accurate MPPT Control

Technique using Boundary Controller for PV Applications, IEEE

Applied Power Elec. Conf. and Ex. (APEC) Tampa, US, 2017.

Journal Papers

[1] Y. Zhou, C. Ho and K. M. Siu “A Fast and Accurate MPPT Control

Technique using Boundary Controller for PV Applications, IEEE

Transactions on Power Electronics. (Submitted)

Contribution of each author is summarized in following table.

Contributor Statement of Contribution

Yang Zhou Manuscript writing, experiments implementation, data analysis,

theory and characteristics deriving

Ngai Man (Carl) Ho Review of manuscript, providing guidance of theory and

experiment

King Man (Ken) Siu PCB design and controller programing and implementation

guidance

21

Chapter 2 Operation Principles of the Proposed MPPT Controller

Converter topology is important to realize MPPT and energy storage is commonly used

to store the energy generated from PV as PV panels cannot generate power during night. Boost

type converter is a commonly used topology [13]. It is because 1) the simplicity and easiness

to implement, 2) the typical output voltage of converter, for example dc link voltage, is higher

than PV string voltage [13] and 3) input current of boost converter is continuous which can

reduce input filter size [44].

Fig. 2-1 Structure of the Proposed Control Scheme with a Boost-type PV Converter.

PV Panels

Boundary

controllerdp/dv Tracker

PWM

𝑝𝑃𝑉 𝑝

𝑉𝐷𝐶

+

𝑉𝐷𝐶

𝑖𝑃𝑉 𝑖𝑃𝑉

𝑖𝐿

𝑣𝐶

+

𝑖𝐶

𝑣𝑃𝑉

+

𝑣𝐶

𝑖𝐶

𝑣𝐶,ref

L

C

D

S

22

Fig. 2-1 shows a typical boost type DC-DC PV converter with MPPT in the proposed

control scheme block diagram [45]. System input is a PV cell which gives a typical PV

characteristics. System output is a voltage source which can be a dc grid, dc link capacitors or

a voltage source inverter (VSI) connected with an AC grid. The proposed MPPT controller

composes of two main control loops, which are namely “dp/dv tracker” as outer loop and

“boundary controller” as inner loop. The dp/dv tracker is used to determine the MPP along the

PV characteristic based on the slope of the curve. It gives a voltage reference to the inner

controller to control the converter operating at or around the point. The inner controller is based

on boundary controller concept, it gives very fast dynamic response to reach the operating

point. Therefore, the combined controller can track the MPP quickly and accurately.

2.1 dp/dv tracker algorithm

Slope of power and voltage curve is used to track the maximum power point of PV

panels. Sensor circuit senses the instantaneous output voltage and current of the PV cell and

therefore power array power 𝑝𝑃𝑉 is acquired in following equation,

𝑝𝑃𝑉 = 𝑣𝑃𝑉 × 𝑖𝑃𝑉. (1)

where 𝑝𝑃𝑉, 𝑣𝑃𝑉, and 𝑖𝑃𝑉 are output power, output voltage and output current of PV panels,

respectively, and they are defined in Fig. 2-1.

The boost converter in Fig. 2-1 connects to the PV panel directly. The time-varying

input capacitor voltage, 𝑣𝐶(𝑘) and input power of the converter, 𝑝(𝑘), are identical to the

23

output voltage, 𝑣𝑃𝑉, and output power, 𝑝𝑃𝑉, of the PV panels, respectively. Fig. 2-2 shows an

ideal PV cell characteristic. A perturbation of PV capacitor voltage is applied, meanwhile,

input power of the converter, 𝑝(𝑘), is calculated by product of 𝑣𝐶(𝑘) and PV output current,

𝑖𝑃𝑉(𝑘), i.e.

𝑝(𝑘) = 𝑣𝐶(𝑘) ∙ 𝑖𝑃𝑉(𝑘). (2)

then it is compared with previous value 𝑝(𝑘 − 1). If 𝑝(𝑘) is greater than 𝑝(𝑘 − 1) as a result

of output voltage increment, which means operation point is at the left side of MPP and moving

up and towards MPP so in order to reach MPP, the next perturbation of capacitor voltage will

be a positive increment. On the contrary, if 𝑝(𝑘) is less than 𝑝(𝑘 − 1) while 𝑣𝐶(𝑘) is less than

𝑣𝐶(𝑘 − 1), which means operation point is still on the left of MPP but moving away, thus a

positive perturbation of output voltage will be applied in the next step. Similarly, when 𝑝(𝑘)

is less than previous value 𝑝(𝑘 − 1) while 𝑣𝐶(𝑘) is greater than 𝑣𝐶(𝑘 − 1), which means

operation point is on the right side of MPP, but moving away from MPP, thus, a negative

perturbation shall be applied by the controller to force operation point go back to MPP. The

fourth scenario is when 𝑝(𝑘) is greater than 𝑝(𝑘 − 1) and 𝑣𝐶(𝑘) is less than 𝑣𝐶(𝑘 − 1) which

indicating operation point is on the right side of MPP but moving towards it, so the capacitor

voltage is required to decrease so as to force operation point continue to move towards MPP.

In summary, capacitor voltage needs to decrease no matter operation point is moving towards

or away to MPP when it is on the right side of MPP, following the same rule, capacitor voltage

is required to increase when operation point is on the left side of MPP . Eventually, the MPP

is reached, capacitor voltage, 𝑣𝐶(𝑘), will be kept at or around the point. Above cases can be

differentiated by three slope values of the PV Voltage-Power (V-P) characteristic curve. The

24

MPP tracker characteristics on the PV V-P curve is shown in Fig. 2-2 and the corresponding

logic flow is shown in Fig. 2-3. The slope of V-P curve can be obtained based on the two-point

form. The general equation is,

∆𝑝

∆𝑣𝐶=

𝑝(𝑘)− 𝑝(𝑘−1)

𝑣𝐶(𝑘)−𝑣𝐶(𝑘−1) (3)

where, 𝑣𝐶(𝑘) and 𝑣𝐶(𝑘 − 1) represent capacitor voltage, 𝑝(𝑘) and 𝑝(𝑘 − 1) is the output

power of PV panels in current moment and previous moment respectively. By taking

approximation, the continuous-time signal is the same as the interpolation of the discrete

signal, i.e. 𝑑𝑝

𝑑𝑣𝑐=

∆𝑝

∆𝑣𝐶.

An integrator is used to bring the error of the slope variation at the MPP to zero with a

proper chosen gain 𝐾𝑖.

25

Fig. 2-2 PV V-P Characteristic and Principle of Maximum Power Point Tracker.

MPP

v

P

0

∆𝒑

∆𝒗𝑪> 𝟎

∆𝒑

∆𝒗𝑪< 𝟎

∆𝒑

∆𝒗𝑪= 𝟎

∆𝒗𝑪

∆𝒑

𝒗𝑪(𝐤), 𝒑(𝐤)

𝒗𝑪(𝐤 − 𝟏), 𝒑(𝐤 − 𝟏)

26

START

Yes

No

No No

YesYes

∆𝑝

∆𝑣𝐶

=𝑝(𝑘) − 𝑝(𝑘 − 1)

𝑣𝐶(𝑘) − 𝑣𝐶(𝑘 − 1)

Increase 𝑣𝐶(𝑘)

∆𝑝

∆𝑣𝐶

= MAX ∆𝑝

∆𝑣𝐶

= MIN Decrease

𝑣𝐶(𝑘)

∆𝑝

∆𝑣𝐶

≤ MIN ∆𝑝

∆𝑣𝐶

≥ MAX

∆𝑝

∆𝑣𝐶

> 0

Sense 𝑣𝐶(𝑘), 𝑖(𝑘) Calculate 𝑝(𝑘)

Fig. 2-3 Flow Chart of dp/dv Tracker.

27

k-1 k k+1 k-1 k k+1 k+2 k-1 k k+1

𝑣𝐶

𝑝

𝑇𝑆 𝑇𝑆

𝑣𝐶

𝑝

𝑣𝐶

𝑝

𝑇𝑆 𝑇𝑆 𝑇𝑆 𝑇𝑆 𝑇𝑆

(a) (b) (c)

Fig. 2-4 Slope of P-V curve of PV when (a) 𝑑𝑝

𝑑𝑣𝑐> 0 (b)

𝑑𝑝

𝑑𝑣𝑐≅ 0 (c)

𝑑𝑝

𝑑𝑣𝑐< 0.

There are three possible scenarios,

0<𝑑𝑝

𝑑𝑣𝑐< MAX - the slope is positive and the controller should increase the capacitor

voltage, this scenario is shown in Fig. 2-4 (a).

𝑑𝑝

𝑑𝑣𝑐≅ 0 - MPP is reached as shown in Fig. 2-4 (b).

MIN <𝑑𝑝

𝑑𝑣𝑐< 0 - the slope is negative and the controller should decrease the capacitor

voltage as shown in Fig. 2-4 (c).

where MAX and MIN are the maximum and minimum slope rate that operation points can

reach. The integration of 𝑑𝑝

𝑑𝑣𝑐 with properly selected 𝐾𝑖 is given to inner loop as voltage reference

to calculate the boundary control law.

28

2.2 Control Laws of Boundary Controller

The inner loop aims for fast and precise control towards targeting output voltage. Thus,

a boundary controller with second order switching surface is used in this thesis as it provides

fast dynamic response in transient conditions [46]-[49]. The detail derivation of operation

principle of boundary control with second order switching surface is described in following.

(a)

(b)

Fig. 2-5 State of PV Converter When Switch (a) ON and (b) OFF.

+ 𝑉𝐷𝐶

𝑖𝑃𝑉

𝑖𝐶

𝑖𝐿 L

C

D

S 𝐶𝐷𝐶 𝑣𝐶

+

+

+ 𝑉𝐷𝐶

𝑖𝑃𝑉

𝑖𝐶

𝑖𝐿 L

C

D

S 𝐶𝐷𝐶 𝑣𝐶

+

+

29

0 A

t

S = OFF S = ONS = ON

𝑣𝐶,ref (𝑡)

𝑖𝐶(𝑡)

𝑣𝐶(𝑡)

ΔV

ΔV

𝑣𝐶,𝑚𝑎𝑥

𝑣𝐶,𝑚𝑖𝑛

𝑡1 𝑡2 𝑡3 𝑡4

Fig. 2-6 Capacitor Voltage and Current Waveforms in Steady State.

Schematic of PV converter with MPPT controller is shown in Fig. 2-1. In order to

evaluate operating modes of the converter, it can be divided into two equivalent circuits when

the switch S is turned ON and OFF, which are shown in Fig. 2-5 (a) and Fig. 2-5 (b),

respectively. The controller is based on the steady-state characteristics on the turned ON and

OFF operating modes to determine switching actions. Fig. 2-6 shows ideal input capacitor

waveforms of a boost converter. The controller senses the capacitor current and voltage at 𝑡1

or before and determine the right turning off moment by predicting the capacitor current

reaching zero and the capacitor voltage reaching 𝑣𝐶,𝑚𝑖𝑛 at the same time, e.g. at 𝑡2, using the

converter characteristics. Thus, the Turn-Off criteria can be derived as,

𝑣𝐶(𝑡) ≤ 𝑣𝐶,𝑚𝑖𝑛 + [𝐿

2𝐶

1

𝑣𝐷𝐶−𝑣𝐶] 𝑖𝐶

2(𝑡) (4)

and 𝑖𝐶(𝑡) ≤ 0 (5)

Similarly, the controller senses the capacitor current and voltage at 𝑡3 or before and determine

30

the right turning on moment by predicting the capacitor current reaching zero and the capacitor

voltage reaching 𝑣𝐶,𝑚𝑎𝑥 at the same time, e.g. at 𝑡4, using the converter characteristics. Thus,

the Turn-On criteria can be expressed as,

𝑣𝐶(𝑡) ≥ 𝑣𝐶,𝑚𝑎𝑥 − [𝐿

2𝐶

1

𝑣𝐶] 𝑖𝐶

2(𝑡) (6)

and 𝑖𝐶(𝑡) ≥ 0 (7)

A detailed derivation of (4) and (6) is given in the Appendix.

The Turn-Off and Turn-On criteria in (4) – (7) are inequality, they can be implemented

by digital controller [48]. And the inner control algorithm of the Turn-on and Turn-off criteria

for aforementioned boost-type PV converter under boundary control laws is shown in the flow

chart of Fig. 2-7.

31

Fig. 2-7 Flow Chart of Boundary Controller.

START

S is ON?YesNo

S is ON S is OFF

Yes

Yes

Yes

Yes

RETURN

No

No

No

NoEqn.(6)? Eqn.(4)?

Sense 𝑣𝐶(𝑘), 𝑖𝐶(𝑘), 𝑣𝐶,𝑟𝑒𝑓 (𝑘), 𝑣𝐷𝐶 (𝑘)

𝑖𝐶 ≥ 0 𝑖𝐶 ≤ 0

32

2.3 Overall Controller

The boundary controller with second-order switching surface follows the energy

balancing theory to regulate the input capacitor voltage. And it gives very fast dynamic

response during transients and tracking the input capacitor voltage reference accurately. Thus,

the control bandwidth of outer loop can be increased to speed up the whole control process.

And unlike conventional proportional-integral (PI) controllers, boundary control does not need

to be tuned [50], thus it shortens the duration to design a controller for engineers. Typically,

the control bandwidth of output loop is one-tenth of that of inner loop in order to avoid

interference between the loops. Thus, fast and accurate MPP tracking can be achieved. The

flow charts in Fig. 2-3 (outer loop) and Fig. 2-7 (inner loop) are implemented serially such as

shown in the control block diagram in Fig. 2-1. The outer loop provides a reference voltage to

the inner loop to maintain the input capacitor voltage to reach the desired operating point in a

short period of time. The implementation of the controllers can be simply sensing the

corresponding voltage and current signals and determines the MPP and makes switching action

decisions based on the equations of (3) - (7) by using a DSP controller.

33

Chapter 3 Steady State Characteristics and Analysis of the Proposed MPPT Controller

This section is aimed to present steady state analysis of the proposed scheme.

Mathematical modeling of a PV cell based on a single diode model [51], which is shown in

Fig. 3-1, is described and applied in the analysis.

Fig. 3-1 The Single-diode Model Equivalent Circuit of a PV Cell [51].

3.1 PV Array Characteristics – V-I curve

For the sake of simplicity of calculation, equivalent series resistance 𝑅𝑆 and equivalent

parallel resistance 𝑅𝑃 are neglected in this thesis and therefore V-I characteristic of PV array

in nominal working condition where irradiance of sun 𝐸𝑛 = 1000𝑊/𝑚2 and temperature 𝑇𝑛 =

25 is constituted in following equation [52].

𝑖𝑃𝑉 = 𝑁𝑝𝐼𝑠𝑐,𝑛 − 𝐼0,𝑛 [exp (𝑣𝑃𝑉

𝑁𝑠𝑎𝑉𝑇,𝑛) − 1] (8)

where 𝑖𝑃𝑉 and 𝑣𝑃𝑉 are output current and voltage of PV panels, 𝑁𝑝 is number of PV panels in

parallel and 𝑁𝑠 is number of PV panels in series, 𝐼𝑠𝑐,𝑛 is nominal short-circuit current, 𝐼0,𝑛 is

saturation current of photovoltaic. Equation for 𝐼0,𝑛 is given in Appendix to this thesis, 𝑎 is

the ideality factor of diode and is usually in between 1 to 2 and is chosen as 1 in this thesis for

𝑅𝑆 𝑅𝑃 𝐼𝐷 𝐼𝐶𝑒𝑙𝑙

𝑖𝑃𝑉 𝑣𝑃𝑉

34

the ease of calculation, 𝑉𝑇,𝑛 is thermal voltage. By taking the approximation that the

exponential term is much higher than 1, i.e. exp (𝑉𝑃𝑉

𝑁𝑠𝑎𝑉𝑇,𝑛) ≫ 1, (8) can be simplified as,

𝑖𝑃𝑉 = 𝑁𝑝𝐼𝑠𝑐,𝑛 − 𝐼0,𝑛 exp (𝑣𝑃𝑉

𝑁𝑠𝑎𝑉𝑇,𝑛). (9)

Fig. 3-2 An Ideal PV V-I Curve.

A typical PV V-I curve is shown in Fig. 3-2 and it can graphically represent the

equation in (9). Point 1 is approximately at the MPP of the PV cell and the small-signal slope

can be determined by the following equations which are based on (9),

1

𝑟𝑃𝑉=

𝑑𝑖𝑝𝑣

𝑑𝑣𝑝𝑣= −

𝐼0,𝑛

𝑁𝑠𝑎𝑉𝑇,𝑛exp (

𝑉𝑃𝑉

𝑁𝑠𝑎𝑉𝑇,𝑛) (10)

or 1

𝑟𝑃𝑉=

𝑑𝑖𝑝𝑣

𝑑𝑣𝑝𝑣=

𝐼𝑃𝑉−𝑁𝑝𝐼𝑠𝑐,𝑛

𝑁𝑠𝑎𝑉𝑇,𝑛 (11)

A detailed derivation of (10) and (11) is given in the Appendix to this thesis.

In principle, (10) and (11) are valid for the whole curve, such as points 2 and 3, in Fig.

0 VOC

ISC

1/𝑟𝑃𝑉

1/𝑟𝑃𝑉

I

VVPV

IPV

1/𝑟𝑃𝑉 Point 1

Point 2

Point 3

35

3-2 by simply inputting a steady-state value of 𝑉𝑃𝑉 or 𝐼𝑃𝑉, respectively, with some constant

physical parameters. From (10), it can be seen that the relationship of the change of 𝑣𝑃𝑉 and

𝑖𝑃𝑉 is negative, thus it can be estimated that ripple polarities of voltage and current are opposite.

3.2 PV Array Characteristics – V-P curve

Instantaneous output power f PV can be re-expressed by putting (9) into (1),

𝑝𝑃𝑉 = 𝑣𝑃𝑉𝑁𝑝𝐼𝑠𝑐,𝑛 − 𝑣𝑃𝑉𝐼0,𝑛 exp (𝑣𝑃𝑉


The rate of change of V-P characteristic is

𝑑𝑝𝑝𝑣

𝑑𝑣𝑝𝑣= 𝑁𝑝𝐼𝑠𝑐,𝑛 − 𝐼0,𝑛 (1 +

𝑉𝑃𝑉

𝑁𝑠𝑎𝑉𝑇,𝑛) exp (

𝑉𝑃𝑉


A detailed derivation of (13) is given in the Appendix.

The equation represents the slope and output voltage relationship in a V-P curve of PV array

such as one in Fig. 2-2.

3.3 Voltage of PV Array at MPP

When a PV array reaches the MPP, the slope of V-P curve is zero. Thus, (13) can be

simplified as,

𝑁𝑝𝐼𝑠𝑐,𝑛 = 𝐼0,𝑛 (1 +𝑉𝑃𝑉,MPP


𝑉𝑃𝑉,MPP


where 𝑉𝑃𝑉,MPP is output voltage at the MPP. It can be seen that from (14), the voltage at the

MPP can be solved by the equation with some physical parameters. However, it is not practical

to control the voltage by simply using the equation since it is well known that the physical

parameters change with operating conditions. Thus, the outer controller is used to determine

the MPP reference voltage value and provide it to the inner controller to control the converter

36

to operate at that point.

3.4 Capacitor Voltage Ripple

For the boundary controller, as ∆𝑉 is a fixed value which defines the band of capacitor

voltage, it is shown in Fig. 2-6, the actual peak-to-peak voltage ripple ∆𝑉𝐶 may be the addition

of ∆𝑉𝑟𝑒𝑓 and ∆𝑉.

∆𝑉𝐶 = (∆𝑉𝑟𝑒𝑓 + ∆𝑉) × 2 (15)

When the integrator gain Ki is properly chosen, steady error will be zero, thus ∆𝑉𝑟𝑒𝑓 ≅ 0, so

capacitor voltage ripple is actually the band defined as parameter of controller.

3.5 PV Output Current Ripple

The ripple current amplitude of PV panels is related to the PV V-I characteristics.

According to Fig. 3-2 and (10), when 𝑣𝑃𝑉 has a positive increment, then 𝑖𝑃𝑉 has a negative

increment. Thus the ripple current amplitude can be obtained based on (10),

∆𝐼𝑃𝑉 = ∆𝑉𝑐𝐼0,𝑛

𝑁𝑠𝑎𝑉𝑇,𝑛exp (

𝑉𝑃𝑉


3.6 Duty Ratio

According to Fig. 2-6, inductor current ripple remains the same during ON and OFF

switching circle in steady state, thus duty ratio, D, can be found as

𝐷 =𝑉𝐷𝐶−𝑣𝐶

𝑉𝐷𝐶 (17)


3.7 Inductor Current Ripple

Inductor current ripple is defined as the peak-to-peak value of the ripple current which

37

is carried on the dc current. It can be expressed by,

∆𝑖𝐿 =𝑣𝐶𝐷

𝑓𝐿 (18)


3.8 Switching Frequency

One of the characteristics of boundary controller is varying switching frequency, since

there is no clock to govern the switching period. The switching frequency of switch is

expressed as

𝑓 = √𝑣𝐶𝐷

8𝐿𝐶∆𝑉𝐶 (19)


38

Chapter 4 Simulation Results of the Proposed MPPT

4.1 Steady-State Operation

Computer simulation of the proposed topology is implemented in PLECS. The

topology of simulated converter is shown in Fig. 2-1. The converter uses a boost type topology

with capacitor installed in the power input side. Different than classical boost converter, a

constant voltage source is used in output side to represent a DC link. For the controller part, c-

script is used in dp/dv tracker block to realize tracking slope of V-P curve of PV module.

Boundary controller functions as inner loop giving duty ratio to the switch according to voltage

reference provided by outer loop.

With 2 × 2 PV panels as input, capacitor voltage, PV output current, inductor current

and gate signal at steady state are illustrated in Fig. 4-1. By given parameters listed in Table

4-1, steady state values are calculated by equations presented in previous section. Table 4-2

shows the comparison of theoretical values and simulation results of steady state. The table

indicates that the simulation values are very similar with the values from the derived theoretic

equations.

39

200µs

t

3V

0.56A

1.99A

Fig. 4-1 Simulation Waveforms in Steady State.

40

Table 4-1 Parameters of Calculating Theoretical Values

Parameters Values

𝑁𝑝 2

𝑁𝑠 2

𝐼𝑠𝑐,𝑛 3.99A

𝑉𝑜𝑐,𝑛 22.05V

𝑉𝑇 1.852V

𝑎 1

𝐿 2.4mH

𝐶 15µF

∆𝑉𝐶 3V

41

Table 4-2 Steady State Simulation and Theoretical Values

Parameter Simulation Results Theoretical Values

𝑉𝑀𝑃𝑃 34.88V 35.374V

𝐼𝑀𝑃𝑃 7.38A 7.22A

∆𝑉𝐶 3V 3V

∆𝐼𝑃𝑉 0.56A 0.61A

duty ratio 0.708 0.705

∆𝐼𝐿 1.99A 1.93A

𝑓 5263Hz 5373Hz

42

4.2 Transient Performance

Transient performance of the proposed controller is evaluated and compared with three

different MPPT controllers in simulation, which are P&O tracker as outer loop and boundary

controller as inner loop, dp/dv tracker and PI controller, P&O and PI controller. Parameters of

4 controllers are listed in Table 4-3.

Table 4-3 Comparison of Simulation Parameters and Results

MPPT Controller

Type

dp/dv +

Boundary

MPPT

P&O +

Boundary

MPPT

dp/dv +

PI

MPPT

P&O +

PI

MPPT

Inductance 2.4mH

Capacitance 15 µF

Output voltage 120V

Sun irradiance change From 50% to 100%

Simulation time 0.04s

Voltage ripple (p-p) 3V

Switching frequency 4761-5032Hz 4758-5043Hz 5000Hz 5000Hz

Inner loop PI

parameters - -

Kp:0.008, Ki:20 Kp:0.008, Ki:20

Step Size - 0.01V - 0.01V

Settling time (2%) 236 µs 263 µs 1.8ms 2.2ms

43

4 different MPPT controllers with combination of dp/dv tracker, P&O tracker as outer

loop controller and PI, boundary controller as inner loop controller are compared in terms of

dynamic response in simulations. A step change of irradiance of sun is applied to all MPPT

controllers at the same time. The comparison of dynamic response of all 4 controllers are

explicated in Fig. 4-2 where the yellow color waveforms are generated by the proposed

controller, blue color waveforms are created by the P&O tracker as outer loop and boundary

controller as inner loop, green color waveforms represent dp/dv tracker and PI controller and

P&O + PI controller output red color waveforms. All controllers can successfully track the

MPP after the irradiation changes. However, the group of controllers utilizing PI as inner loop

needs much more switching circles and longer transient time to reach new MPP, since the

converter passive component responses are included in the transfer functions in the control

loop. Another conclusion can be drawn from Fig. 4-2 is that both MPPT controller using

boundary controller as inner loop have very fast dynamic response, however the dp/dv tracker

is slightly faster than P&O one. This slow response characteristic leads to lower MPPT

efficiency occurring during the transient. On the other hand, the proposed controller can

response at once to govern the converter to achieve maximum power extraction, besides it can

also be seen from Fig. 4-2, PI controller experiences a few oscillations to stabilize.

44

t 1ms

P&O + Boundary Controller

Proposed Controller

P&O + PI Controller

dp/dv Tracker + PI Controller


P&O + PI Controllerdp/dv Tracker + PI Controller

Proposed Controller


dp/dv Tracker + PI Controller

P&O + PI Controller

Proposed Controller

Fig. 4-2 Dynamic Response of PI and Proposed MPPT Controllers.

45

Chapter 5 Experimental Verifications

5.1 Experimental Setup

A 280W boost type PV converter prototype with DSP based MPPT controller has

been implemented to experimentally verify the proposed concept. Fig. 5-1 (a) shows the

schematic and connections of the testbed, and Fig. 5-1 (b) shows the input are 2 × 2 PV

panels (Siemens SP75 solar panels) connected to converter by 10 meters long cable, each

of PV panels has rated power of 75W, the output are resistors and a dc voltage source

connected in parallel. The dc voltage source represents a DC link to keep output stable and

the resistors are used to consume the power either generating by the dc voltage source or

the PV panels. As PV output power are varying when environment variable of PV changes,

DC voltage source can vary output power accordingly. Circuit parameters, PV panel

parameters at nominal conditions and controller parameters are listed in Table 5-1

46

(a)

LoadConverter DC source

PV panels

(b)

Fig. 5-1 Test Bed Setup (a) Schematic of Test Bed, and (b) Laboratory Setup.

DC

sourc

e

C S

L D2×

2 P

V p

anel

s

switch

Cable

Cable

𝐶𝐷𝐶 𝑅𝐿

PV Converter

47

Table 5-1 Specification of the PV Converter Prototype

Circuits parameters Nominal values

Input capacitance C1 15 µF

Output capacitance C2 470 µF

Inductance L 2.4 mH

Resistance R 33.3 Ω

DC source voltage 120V

PV panel parameters Values

Number of series cells 36

Maximum power rating Pmax 75W

Rated current IMPP 4.4A

Rated voltage VMPP 17.0V

Short circuit current ISC 4.8A

Open circuit voltage VOC 21.7V

Controller parameters Values

CPU clock frequency 200 MHz

ADC sampling frequency 3.5 MHz

Switching frequency 3.7-5 kHz

48

The experimental setup is aiming to evaluate the steady and transient performance of

MPPT controller. The test of MPPT controller (whole system test) is conducted in following

procedures, firstly, a set of 1 × 2 PV panels is generating power then the second step follows

suddenly switching on the switch connected to the spare 1 × 2 PV panels and finally 2 × 2 PV

panels are generating power. It emulates the sudden change of sun irradiation. The MPPT

controller is expected to keep at maximum power point as soon as switch is closed and provide

fast tracking from one operation point to the other. Finally, waveforms are observed in

oscilloscopes and data are saved for further analysis.

5.2 Experimental Results – Steady State

Power from the 2 × 2 PV panels are used as input to the booster converter to evaluate

steady state performance of the proposed MPPT controller. The major procedures of the

proposed experimented test for the proposed MPPT controller is as follows:

1. Set up a set of 1 × 2 PV panels (75W each) for generating power.

2. Connecting the spare 1 × 2 PV panels (75W each) by closing the switch

resulting in 2 × 2 PV panels generating power.

Fig. 5-2 shows capacitor voltage, PV output current, inductor current and gate signal

from top to bottom. MPP is reached with an average capacitor voltage is about 26.5V and PV

output current approximately 7.7A.

49

Fig. 5-2 Experimental Steady State Waveforms

(a)

(b)

Fig. 5-3 Experimental Results in (a) V-I Curve, and (b) V-P Curve in Steady State.

50

Fig. 5-3 shows the experimental results in Fig. 5-2 plotting in X-Y mode with the

estimated V-I and V-P curve of the PV strings based on the single diode model. The result

indicates that MPP is reached and operating stably with parameters as shown in Table 5-1.

5.3 Experimental Results – Transient Performance

Fig. 5-4 shows dynamic response of the PV system from a 1 × 2 PV panels setting to

a 2 × 2 PV panels settings by suddenly closing the switch connecting the 1 × 2 PV panels.

Schematic of test circuit is shown in Fig. 5-1 (a), transient response of MPPT controller is

evaluated by switching on and off of one PV string branch. Once the other PV string is in

operation, new MPP is supposed to be immediately reached from the previous one. Fig. 5-4

(a) and (b) explicate system output as a result of number of PV module suddenly changing,

where red waveform is the inductor current waveform and blue waveform is the PV output

current, pink waveform is the capacitor voltage at input while green waveform is waveform of

the gate signal. From Fig. 5-4 (a) PV output current suddenly rises to its double quantity when

the second PV string is switched on. From capacitor voltage waveform, it can be found that

new MPP is getting stabilized in a few switching circles around 1ms. Scenario that operation

point switched from 2×2 to 1×2 PV array is shown in Fig. 5-4 (b), where the capacitor voltage

is stabilized in a few switching actions while input current experience a dramatic drop to 50%

of previous value approximately. Switching trajectory is shown in Fig. 5-5 (a) that the inductor

current in yellow colour manages to catch the new operation point in one switching action on

the estimated V-I curve while Fig. 5-5 (b) shows new maximum power point is reached with

estimated V-P curve after one set of switch on and off actions.

51

(a)

(b)

Fig. 5-4 Experiment Results of Step Change of (a) Switched from 2 to 4 Panels, and

(b) Vice Versa.

52

Fig. 5-5 Power and Inductor Current Trajectory for Fig. 5-4 (a).

MPP2

MPP1

V-P Curve 1

V-P Curve 2

(𝒑, 𝒗𝑪)

MPP2

MPP1

V-I Curve 1

V-I Curve 2

(𝒊𝑳, 𝒗𝑪)

Cu

rren

t (A

)

53

5.4 Experimental Results – Quantifying of PV Converter Efficiency

Efficiency of prototype PV converter is measured in this chapter, the converter

topology is shown in Fig. 5-6 where a DC voltage source is used as input and resistor load is

connected as output. Procedures of conducting this test is as follows:

1. The output voltage of PV converter is fixed at 120V.

2. Resistance of load is changed in order to achieve change of input power.

3. Input voltage change is realized by altering duty ratio.

4. Converter efficiency at each operation point is measured and recorded by using a

YOKOGAWA WT1800 power analyzer.

C

L D

𝐶𝐷𝐶 𝑅𝐿

PV Converter

V

A

V

A

Pin Pout

S

Fig. 5-6 Topology of Converter for Quantifying Efficiency

54

5 different input voltage of PV converter are considered in the converter efficiency

evaluation, 53V, 63V, 83V, 99V and 112 V as shown in Fig. 5-7. This figure also illustrates

the power and efficiency trend when different input voltage are given with switching frequency

5 kHz. The highest efficiency of this converter is approximately 95% with input power 430W

and input voltage 112V. From this figure, it can also be observed efficiency is boosted with

higher capacitor voltage and higher power.

Fig. 5-7 Converter Efficiency In Regard to Input Power and Voltage When Switching

Frequency is 5 kHz

80%

82%

84%

86%

88%

90%

92%

94%

96%

Co

nve

rter

Eff

icie

ncy

Input Power(W)

VC=53V VC=63V VC=83V VC=99V VC=112V

55

Chapter 6 Conclusion and Suggestion for Future Research

6.1 Conclusion

In this thesis, a review of state of art microgrid architecture and control methods of PV

converters are presented in the first chapter. Despite of the drawbacks due to the less

development, DC microgrid shows a promising future as its characteristics of high efficiency,

relatively simple designing and controlling than AC counterpart and the promising future of

DC load applications. And a simple boost converter can be used as an interface between the

grid and PV panels.

Based on a simple boost converter structure, the design and implementation of a fast

and accurate MPPT control scheme for PV applications has been presented in this thesis. There

are two control loops in the controllers, outer loop - dp/dv tracker algorithm is used to track

maximum power point and provide voltage reference to inner loop, which is based on boundary

control theory to provide fast dynamic response. The controller has shown a significant

improvement comparing with conventional PI based MPPT controllers in simulations. The

controller also increases the control bandwidth to extract more energy from PV cells during

irradiation changes. The concept of the proposed MPPT controller were explained in details.

The boundary control laws of boost converter with input voltage control and the whole system

steady state characteristics have been determined. A laboratory prototype has been built based

on a boost type converter with a DSP controller applied with delivered theory. Experimental

results have demonstrated the performance of the proposed controller, which can accurately

56

extract energy from the PV strings at the MPP and responds quickly during transients to locate

at the new MPP. The results confirmed the conceptual idea and the derived theory.

6.2 Suggestion for Future Research

There are following suggestions for future research regarding this project:

Switching frequency of prototype converter is limited by the DSP performance, a high

performance DSP controller can improve the dynamic response of MPPT.

Since the non-linear characteristic of PV model, the small signal model is necessary to

build furtherly to evaluate the stability and PV system performance of the proposed

MPPT controller.

Dynamic response of the proposed controller is limited by the outer loop-dp/dv tracker,

where an integrator is employed to generate the voltage reference for inner loop –

boundary controller, one of alternative solutions is to merge two loops into one and

predict MPP by evaluating the capacitor voltage ripple variation which is related to PV

characteristic.

A simple diode model with only nominal condition is used to evaluate steady state of

MPPT, however, it might not be accurate enough to match the actual case.

Mathematical modeling of PV can be improved by considering environmental variants

such as temperature and irradiance level. Also equivalent series resistance of and

equivalent parallel resistance of PV array should also be calculated to have a more

accurate model.

57

References

[1] N. Lidula and A. D. Rajapakse, “Microgrids research: A review of experimental

microgrids and test systems,” Renewable and Sustainable Energy Reviews, vol. 15, no.

1, pp. 186–202, 2011

[2] T. S. Ustun et al., “Recent developments in microgrids and example cases around the

world—A review,” Renewable and Sustainable Energy Reviews, vol. 15, no. 8, pp.

4030–4041, 2011.

[3] A. Timbus, A. Oudalov and C. Ho, “Islanding detection in smart grids”, IEEE ECCE10,

Sept. 2010.

[4] P. Costa and M. Matos, 'Assessing the contribution of microgrids to the reliability of

distribution networks', Electric Power Systems Research, vol. 79, no. 2, pp. 382-389,

2009.

[5] J. J. Justo, F. Mwasilu, J. Lee, and J.-W. Jung, “AC-microgrids versus DC-microgrids

with distributed energy resources: A review,” Renewable and Sustainable Energy

Reviews, vol. 24, pp. 387–405, Aug 2013.

[6] A. T. Elsayed, A. A. Mohamed, and O. A. Mohammed, “DC microgrids and distribution

systems: An overview,” Electric Power Systems Research, vol. 119, pp. 407–417, 2015.

[7] H. Kakigano, M. Nomura, T. Ise, “Loss Evaluation of DC Distribution for Residential

Houses Compared with AC System,” Proc. IPEC, pp. 480-486, 2010.

[8] E.Planas, J.Andreu, J.I.Gárate, I.M.D.Alegría and Edorta Ibarra, “AC and DC

technology in microgrids: A review,” Renewable and Sustainable Energy Reviews, vol.

43(2015), pp. 726-749, 2015.

[9] P. Szczes´niak, J. Kaniewski and M. Jarnut, “AC–AC power electronic converters

without DC energy storage: A review,” Energy Conversion and Management, vol.92,

pp. 483–497, 2015.

[10] F. L. Luo, H. Ye, and M. H. Rashid, Digital Power Electronics and Applications. New

York: Elsevier Academic Press, 2005.

58

[11] E. Hossain, E. Kabalci, R. Bayindir and R. Perez, “A comprehensive study on microgrid

technology,” International Journal of Renewable Energy Research, vol. 4, no. 4 pp.

1094-1107, 2014

[12] C. Ho, H. Breuninger, S. Pettersson, G. Escobar, L. Serpa, and A. Coccia, “Practical

design and implementation procedure of an interleaved boost converter using SiC diodes

for PV applications”, IEEE Trans. on Power Electronics, Vol. 27, No. 6, pp. 2835 –

2845, Jun. 2012.

[13] C. Ho, H. Breuninger, S. Pettersson, G. Escobar and F. Canales, "A comparative

performance study of an interleaved boost converter using commercial Si and SiC diodes

for PV applications", IEEE Trans. on Power Electronics, Vol. 28, No. 1, pp. 289 – 299,

Jan. 2013.

[14] Z. Zhang, X. F. He and Y. F. Liu, "An Optimal Control Method for Photovoltaic Grid-

Tied-Interleaved Flyback Microinverters to Achieve High Efficiency in Wide Load

Range," in IEEE Trans. on Power Electronics, vol. 28, no. 11, pp. 5074-5087, Nov. 2013.

[15] C. Ho, “Challenges and design considerations of PV inverters in the future Smart Grids,”

IET APSCOM12, Nov. 2012.

[16] M. Victor, F. Greizer, S. Bremicker, and U. Hübler, “Method of converting a direct

current voltage from a source of direct current voltage, more specifically from a

photovoltaic source of direct current voltage, into a alternating current voltage”, US

Patent, No. US7411802 B2, 12/08/2008.

[17] H. Schmidt, C. Siedle, and J. Ketterer, “DC/AC converter to convert direct electric

voltage into alternating voltage or into alternating current,” US Patent, No. US7046534

B2, 16/05/2006.

[18] R. Li and C. Ho, “Active Virtual Ground: Single Phase Grid-Connected Voltage Source

Inverter Topology,” Proc. IEEE APEC16, Mar. 2016.

[19] S. Saridakis, E. Koutroulis and F. Blaabjerg, "Optimal Design of Modern

Transformerless PV Inverter Topologies," in IEEE Trans. on Energy Conversion, vol.

28, no. 2, pp. 394-404, June 2013.

59

[20] G. Escobar, N. Ho, and S. Pettersson, “Method and apparatus for zero sequence damping

and voltage balancing," US Patent, No US9030854 (B2), 12/05/2015.

[21] H. J. Chiu, Y. K. Lo, C. J. Yao and S. J. Cheng, "Design and Implementation of a

Photovoltaic High-Intensity-Discharge Street Lighting System," IEEE Trans. Power

Electron, vol. 26, no. 12, pp. 3464-3471, Dec, 2011.

[22] N. Liu, Q. Chen, X. Lu, J. Liu and J. Zhang, "A Charging Strategy for PV-Based Battery

Switch Stations Considering Service Availability and Self-Consumption of PV Energy,"

IEEE Trans. Ind. Electron, vol. 62, no. 8, pp. 4878-4889, Aug, 2015.

[23] Messikh, T., Rahim, N., Saad, M.: ‘Boundary control of dual-output boost converter

using state-energy’, IET Power Electron., Vol. 7, pp. 2310–2321, Sep. 2014.

[24] K. S. Leung and H. S. H. Chung, “A comparative study of the boundary control of buck

converters using first- and second-order switching surfaces–Part II: Discontinuous

conduction mode,” in Proc. IEEE PESC, 2005, pp. 2126–2132.

[25] H. Wang, H. Chung, and J. Presse, “A unified derivation of second-order switching

surface for boundary control of dc-dc converters,” in Proc. IEEE Energy Convers.

Congr. Expo., Sep. 2009, pp. 2889–2896.

[26] K. K. S. Leung and H. S. H. Chung, “Derivation of a second-order switching surface in

the boundary control of buck converters,” IEEE Power Electron. Lett., vol. 20, no. 2, pp.

63–67, Jun. 2004.

[27] W. W. Burns, III and T. G. Wilson, “System-state and operating condition sensitive

control method and apparatus for electric power delivery systems,” U.S. Patent 4084103

A, Apr 11, 1978

[28] H. Kakigano, Y. Miura, and T. Ise “Low-voltage bipolar-type DC microgrid for super

high quality distribution,” IEEE Trans. Power Electron., vol. 25, no. 12, pp. 3066–3075,

Dec. 2010.

[29] R.N. Tripathi, T.Hanamoto, “FRIT based optimized PI tuning for DC link voltage control

of grid connected solar PV systems,” Proc. of IEEE Conf. on Indus. Electro., pp. 1567-

1572, Nov. 2015

60

[30] H. Patel and V. Agarwal, “Maximum power point tracking scheme for PV systems

operating under partially shaded conditions,” IEEE Trans. Ind. Electron, vol. 55, no. 4,

pp. 1689–1698, Apr. 2008.

[31] M. Metry, M.B. Shadmand, R. S. Balog and H. A. Rub, “MPPT of Photovoltaic Systems

Using Sensorless Current-Based Model Predictive Control” IEEE Trans. Ind. Electron,

vol. 53, no. 2, pp. 1157-1167, 2016.

[32] EN 50530: Overall efficiency of grid connected photovoltaic inverters, April 2010.

[33] E. Mamarelis, G. Petrone, G. Spagnuolo, “A two-steps algorithm improving the P&O

steady state MPPT efficiency,” Applied Energy, vol. 113, pp. 414–21, Jan 2014.

[34] N. Femia, G. Petrone, G. Spagnuolo, and M. Vitelli, “Optimization of perturb and

observe maximum power point tracking method,” IEEE Trans. Power Electron., vol. 20,

no. 4, pp. 963–973, 2005.

[35] H. A. Sher, A. A. Rizvi, K. E. Addoweesh and K. Al-Haddad, “A Single-Stage Stand-

Alone Photovoltaic Energy System With High Tracking Efficiency,” IEEE Trans.

Sustainable Energy., vol. 8, no. 2, pp. 755–762, 2017.

[36] J. Ahmed and Z. Salam, “A Modified P&O Maximum Power Point Tracking Method

With Reduced Steady-State Oscillation and Improved Tracking Efficiency,” IEEE

Trans. Sustainable Energy., vol. 7, no. 4, pp. 1506 - 1515, 2016.

[37] I. S. Kim, M. B. Kim, and M. J. Youn, “New maximum power point tracker using sliding-

mode observer for estimation of solar array current in the grid-connected photovoltaic

system,” IEEE Trans. Ind. Electron., vol. 53, no. 4, pp. 1027–1035, 2006

[38] D. Sera, L. Mathe, T. Kerekes, S. Spataru, and R. Teodorescu, “On the perturb-and-

observe and incremental conductance MPPT methods for PV systems,” IEEE J.

Photovoltaics, vol. 3, no. 3, pp. 1070–1078, Jul. 2013.

[39] F. Liu, S. Duan, F. Liu, B. Liu, and Y. Kang, “A variable step size INC MPPT method

for PV systems,” IEEE Trans. Ind. Electron., vol. 55, no. 7, pp. 2622–2628, Jul. 2008.

61

[40] N. E. Zakzouk; M. A. Elsaharty; A. K. Abdelsalam; A. A. Helal and B. W. Williams;

"Improved performance low-cost incremental conductance PV MPPT technique," IET

Renew. Power Gener, vol. 10; no. 4, pp. 561-574, 2016.

[41] M. A. G. de Brito, L. Galotto, L. P. Sampaio, G. de Azevedo e Melo, and C. A. Canesin,

“Evaluation of the main MPPT techniques for photovoltaic applications,” IEEE Trans.

Ind. Electron., vol. 60, no. 3, pp. 1156–1167, Mar. 2013.

[42] B. Alajmi, K. Ahmed, S. Finney, and B. Williams, “Fuzzy logic controlled approach of

a modified hill climbing method for maximum power point in microgrid stand-alone

photovoltaic system,” IEEE Trans. Power Electron., vol. 26, no. 4, pp. 1022–1030, Apr.

2011.

[43] M. A. Elgendy, B. Zahawi, and D. J. Atkinson, “Assessment of perturb and observe

MPPT algorithm implementation techniques for PV pumping applications,” IEEE Trans.

Sustain. Energy, vol. 3, no. 1, pp.21–33, Jan. 2012.

[44] W. Xiao, N. Ozog, and W. G. Dunford, “Topology study of photovoltaic interface for

maximum power point tracking,” IEEE Trans. Ind. Electron, vol. 54, no. 3, pp. 1696–

1704, Jun. 2007.

[45] C. Ho, H. Breuninger, S. Pettersson, G. Escobar, L. Serpa, and A. Coccia, “Practical

design and implementation procedure of an interleaved boost converter using SiC diodes

for PV applications”, IEEE Trans. on Power Electron, Vol. 27, No. 6, pp. 2835 – 2845,

Jun. 2012.

[46] W. W. Burns, III and T. G. Wilson, “System-state and operating condition sensitive

control method and apparatus for electric power delivery systems,” U.S. Patent 4084103

A, Apr 11, 1978

[47] K. K. S. Leung and H. Chung, “State trajectory prediction control for boost converters”

Proc. IEEE ISCAS '04, vol. 5, pp. 556-559, May 2004.

[48] K. Au, C. Ho, H. Chung, W.H. Lau and W.T. Yan “Digital implementation of boundary

control with second-order switching surface for inverters”, IEEE PESC07, Jun. 2007.

62

[49] C. Ho, H. Chung, and K. Au, “Design and implementation of a fast dynamic control

scheme for capacitor-supported dynamic voltage restorers,” IEEE Trans. Power

Electron., vol. 23, no. 1, pp. 237-251, Jan. 2008.

[50] W W Burns and T. G. Wilson, "A state-trajectory control law for dc-to-dc converters,"

IEEE Trans. on Aerospace and Electronic Systems, vol. AES-14, pp. 2-20, 1978.

[51] M. G. Villalva, J. R. Gazoli, and E. R. Filho, “Comprehensive approach to modeling and

simulation of photovoltaic arrays,” IEEE Trans. Power Electron., vol. 24, no. 5, pp.

1198–1208, May 2009.

[52] H. Cai, J. Xiang, and W. Wei. Modelling, analysis and control design of a two-stage

photovoltaic generation system. IET Renew. Power Gener., DOI:10.1049/iet-

rpg.2015.0514, 2015.

63

Appendix

A. Derivation of (4) and (6)

In the Turn-ON equivalent circuit is in Fig. 2-5 (a), the switch S is in ON state and the

diode D is in OFF state. Thus, inductor L is charging up from the PV source and part of PV

output current goes to 𝐶1 according to KCL [25]. As a result, following equations can be

derived.

𝑖𝐿 = 𝑖𝑃𝑉 − 𝑖𝐶 (A1)

And 𝑣𝐿 = 𝑣𝐶 (A2)

where 𝑖𝐿, 𝑖𝑃𝑉 and 𝑖𝐶 are inductor current, PV output current and capacitor current respectively.

And 𝑣𝐿 is voltage over inductor and 𝑣𝐶 is voltage of capacitor 𝐶. Since 𝑖𝑃𝑉 is assumed as a DC

current, derivative of (A1) can result in following equations,

𝑑𝑖𝐿(𝑡)

𝑑𝑡≅ −

𝑑𝑖𝐶(𝑡)

𝑑𝑡 (A3)

𝑣𝐿(𝑡) = 𝐿𝑑𝑖𝐿(𝑡)

𝑑𝑡 (A4)

By combining (A2) – (A4), capacitor voltage can be rearranged as follows.

𝑣𝐶 =1

𝐶∫ 𝑖𝐶(𝑡)𝑑𝑡 + 𝑣𝐶(0) (A5)

where 𝑣𝐶(0) represents capacitor initial voltage. (A4) can be rearranged as

𝑑𝑡 = |𝐿𝑑𝑖𝐶

𝑣𝐶| (A6)

As capacitor voltage equals to the initial voltage, the instantaneous voltage at 𝑡3, plus

with the integration of capacitor current from 𝑡3 to 𝑡4 which is the triangular shadow area in

capacitor current waveform within the time interval of 𝑡3 and 𝑡4 in Fig. 2-6. Therefore, integral

of capacitor current can be simplified as,

64

∫ 𝑖𝐶(𝑡)𝑑𝑡𝑡4

𝑡3=

1

2𝑖𝐶(𝑡3)∆𝑡 (A7)

Where ∆𝑡 = 𝑡4 − 𝑡3 , the crest value of capacitor voltage waveform can be obtained by putting

(A6) and (A7) into (A5), as such

𝑣𝐶,𝑚𝑎𝑥 = 𝑣𝐶(𝑡4) = [𝐿

2𝐶

1

𝑣𝐶] 𝑖𝐶

2(𝑡3) + 𝑣𝐶(𝑡3) (A8)

where 𝑣𝐶,𝑚𝑎𝑥 is upper peak reference capacitor voltage. Therefore, turn-on criteria of S must

fulfill (A8), thus an inequality (6) can be derived.

Similarly, in the Turn-OFF equivalent circuit in Fig. 2-5 (b), the switch S is in OFF state and

the diode D is in ON state. Thus, inductor L is discharging and delivering to the output

capacitor 𝐶𝐷𝐶 and the output source such as a dc grid. Thus, the voltage across the inductor is

the difference of input voltage,𝑣𝐶 , and output voltage, 𝑣𝑑𝑐, The value of capacitor voltage

𝑣𝐶,𝑚𝑖𝑛 can be derived as.

𝑣𝐶,𝑚𝑖𝑛 = 𝑣𝐶(𝑡2) = − [𝐿

2𝐶

1

𝑣𝑑𝑐−𝑣𝐶] 𝑖𝐶

2(𝑡1) + 𝑣𝐶(𝑡2) (A9)

where 𝑣𝐶,𝑚𝑖𝑛 is lower peak reference capacitor voltage. Therefore, turn-off criteria of S must

fulfill (A9), thus an inequality (4) can be derived.

B. Derivation of (10) and (11)

By using (9), and introducing small signals,

𝐼𝑃𝑉 + 𝑖𝑝𝑣 = 𝑁𝑝𝐼𝑠𝑐,𝑛 − 𝐼0,𝑛 exp (𝑉𝑃𝑉+𝑣𝑝𝑣

𝑁𝑠𝑎𝑉𝑇,𝑛) (A10)

By taking the derivative,

𝑑𝑖𝑝𝑣

𝑑𝑣𝑝𝑣= −

𝐼0,𝑛

𝑁𝑠a𝑉𝑇,𝑛exp (

𝑉𝑃𝑉


𝑣𝑝𝑣


Assume the small signal of 𝑣𝑝𝑣 is much smaller than the steady state voltage 𝑉𝑃𝑉, i.e. 𝑣𝑝𝑣 ≪

𝑉𝑃𝑉, thus, (10) can be obtained. By putting (9) into (10), then (11) can be obtained. Where

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𝐼0,𝑛 =𝑁𝑝𝐼𝑠𝑐,𝑛

exp(𝑉𝑜𝑐,𝑛𝑎𝑉𝑇,𝑛

)−1 (A12)

C. Derivation of (13)

By using (12), and introducing small signals,

𝑃𝑃𝑉 + 𝑝𝑝𝑣 = (𝑉𝑃𝑉 + 𝑣𝑝𝑣)𝑁𝑝𝐼𝑠𝑐,𝑛 − (𝑉𝑃𝑉 + 𝑣𝑝𝑣)𝐼0,𝑛 exp (𝑉𝑃𝑉+𝑣𝑝𝑣


By taking the derivative,

𝑑𝑝𝑝𝑣

𝑑𝑣𝑝𝑣= 𝑁𝑝𝐼𝑠𝑐,𝑛 − 𝐼0,𝑛 (1 +

𝑉𝑃𝑉+𝑣𝑝𝑣


𝑉𝑃𝑉+𝑣𝑝𝑣


Assume the small signal of 𝑣𝑝𝑣 is much smaller than the steady state voltage 𝑉𝑃𝑉, i.e. 𝑣𝑝𝑣 ≪

𝑉𝑃𝑉, thus, (13) can be obtained.

D. Derivation of (17)

According to Fig. 2-5, when switch is ON, inductor voltage is expressed by

𝑣𝐿 = 𝐿𝑑𝑖𝐿

𝑑𝑡 (A15)

Since 𝑣𝐿 = 𝑣𝐶 during ON state of switch, (A15) can be re-arranged as

𝑑𝑖𝐿 =1

𝐿𝑣𝐶𝑇𝑂𝑁 (A16)

where 𝑇𝑂𝑁 is turn-on time. And further as

𝑑𝑖𝐿 =1

𝐿𝑣𝐶𝐷 ∙ 𝑇 (A17)

where 𝐷 is duty ratio and 𝑇 is switching period. Similarly, inductor current ripple during switch

OFF can be derived as

𝑑𝑖𝐿 =1

𝐿(𝑣𝐶 − 𝑣𝑑𝑐)(1 − 𝐷)𝑇 (A18)

So 𝐷 can be acquired by solving (A17) and (A18).

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E. Derivation of (18)

(A15) can be re-arranged as

𝑣𝐶 = 𝐿∆𝑖𝐿

𝐷∙𝑇 (A19)

Thus (18) is obtained by re-arranging (A19)

F. Derivation of (19)

From Fig. 2-6 the peak-to-peak capacitor voltage is shown as

∆𝑉𝐶 =1

𝐶∫ 𝑖𝐶𝑑𝑡

𝑡4

𝑡2 (A20)

The integral of 𝑖𝐶 from 𝑡2 to 𝑡4 (T/2) is actually the triangular shadow area in the waveform of

𝑖𝐶 and time span, so

∫ 𝑖𝐶𝑑𝑡𝑡4

𝑡2=

𝑇

2.∆𝑖𝐿

2

2 (A21)

By putting (18) and (A21) into (A20),

∆𝑉𝐶 =𝑣𝐶𝐷

8𝐿𝐶𝑓2 (A22)

Thus 𝑓 can be acquired by re-arranging (A22).

Design and Implementation of a PV Converter for DC ...

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