Islanding and Seamless Reconnection of Multiple Solid-State Transformers Based On Droop Control

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ABSTRACT

CHO, YONGHWAN. Islanding and Seamless Reconnection of Multiple Solid-State Transformers Based On Droop Control. (Under the direction of Subhashish Bhattacharya.)

Solid state transformer (SST) is an emerging power electronics-based technology that

can replace traditional distribution transformers and actively manage renewable energy

resources, energy storage devices, and residential loads. The SST has been focused on due to

its low volume and weight which is achieved by using high-frequency AC-link transformer

instead of 50/60 Hz. Moreover, SST itself has features of reactive power compensation,

har-monic current filtering, and fault ride through capability while the conventional distribution

system needs additional equipments such as static synchronous compensator (STATCOM),

unified power flow controller (UPFC), unified power quality conditioner (UPQC), etc.

The SST is a core component of a smart distribution system, Future Renewable Electric

Energy Delivery and Management (FREEDM) system. By taking advantage of DC bus that

SST provides, DC microgrid can be easily integrated to the SST-based distribution system.

The renewable energy sources or energy storage devices of the DC microgrid can be used for

saving energy and more reliable operation of the distribution system, for example, islanding

operation. Wireless communication and power management system of the FREEDM also

improves the stability and controllability of the distribution system.

Among many functionalities of the FREEDM system, the autonomous islanding is

investigated in this thesis to attain fault ride-through capability when the system is islanded

from the utility. Moreover, a method is developed to achieve smooth reconnection to the grid

after a fault is cleared. The main component of the proposed control strategy is the control

of the high-voltage side converter of the SST, which is based on a combination of droop

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(DAB), Distribued Energy Storage Device (DESD), and the Distributed Renewable Energy

Resources (DRER) are also developed and presented in detail. The harmonic compensation

scheme of the SST is also presented including a novel hybrid harmonic compensation

(HHC) method. The novel virtual impedance is also developed to cope with the wide range

of the grid impedance. A low-voltage scaled SST system is introduced, and the controllers

of the converters within the system are described. The proposed control strategy has been

tested in simulation and experimentally on a low-voltage scaled testbed.

The stability of the system that consists of the parallel connected voltage source inverters

is analyzed and a framework for the stability analysis is provided. The impedance based

models of the voltage source inverters are derived from large signal models. Solving the

impedance based circuit diagram of the overall power system, the current of the inverter

can be expressed by the sum of the transfer functions. The stability of the system can be

determined by analyzing the poles and zeros of the transfer functions. It is shown that the

grid impedance and the line impedance between SSTs can degrade the damping ratio of

the system and even make the system unstable if the controller bandwidth of the inverter

and the damping resistance are not selected propely with enough design margin. The

impedance based model and the criterion to determine the stability of the system are

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Islanding and Seamless Reconnection of Multiple Solid-State Transformers Based On Droop Control

by Yonghwan Cho

A dissertation submitted to the Graduate Faculty of North Carolina State University

in partial fulfillment of the requirements for the Degree of

Doctor of Philosophy

Electrical Engineering

Raleigh, North Carolina

2017

APPROVED BY:

David Lubkeman Mesut Baran

Xiangwu Zhang Subhashish Bhattacharya

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DEDICATION

To my parents Mr. Sung-Il Cho and Mrs. Aisa Kang, and my brother Mr. Soohwan Cho.

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BIOGRAPHY

Yonghwan Cho was born in Seoul, the capital of South Korea. He received his Bachelor of

Science degree in Electrical Engineering from Seoul National University, Seoul, Korea, in

2012. In 2012, he joined the Department of Electrical and Computer Engineering at North

Carolina State University, Raleigh, North Carolina as a Ph.D. Scholar. His research interests

include Power Electronics, Solid-State Transformers, Grid-connected Converters, DC/DC Converters, Renewable Energy Integration, Motor Drives. He also worked as a Research

Assistant at the NSF FREEDM Systems Center and a Teaching Assistant of NCSU.

From 2008 to 2011, he was with MELFAS Inc, Seoul, South Korea, as a Research Engineer

in the Advanced Technology Department working on Automated Test Equipment that

verifies the functionality of capacitive touch sensor ICs. From May to August 2014, he

worked as an intern in Power Electronics Team of TESLA, Palo Alto, California, conducting

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ACKNOWLEDGEMENTS

Thank my God that he sent me to this beautiful place. Though I sometimes had a hard

time pursuing a doctoral degree, I learned not only academical knowledge but also the

knowledge of God. I appreciate to all of the memebers of the youth group of Duraleigh

Presbyterian Church and Hanmaum Church. I realized later that I had much love and

comfort from the communities that I could stay strong.

I would like to express my sincere gratitude to my Ph.D. advisor, Dr. Subhashish

Bhat-tacharya, who gave me the opportunity of pursuing Ph.D. in Power Electronics and

sup-ported me during the past five years. I could grow as an independent researcher under

his guidance and support working on interesting and challenging projects related to the

Solid-State Transformer. I feel thankful for his consistant trust and encouragement.

I got many help from faculties and staffs in the FREEDM system center. I appreciate

especially my committee members, Dr. David Lubkeman and Dr. Mesut Baran for their

suggestions and feedbacks to deepen and improve my research and dissertation. Thanks

Dr. Xiangwu Zhang from the college of textiles for serving as the graduate representative in

my Ph.D. committee. I would like to thank Ms. Karen Autry for her kindness and love, Mr.

Hulgize Kassa and Dr. Leonard White for their help in lab and funny jokes.

I would like to extend my sincere thanks to Dr. Sungmin Kim, Dr. Yongsu Han, and Dr.

Byeongheon Kim for their guidance, ideas, and discussions. It was my great honor to meet

them. I learned a lot from them, not only Power Electronics but also their attitudes and

interests toward research. I also give thanks to Dr. Kuijun Lee for his advice and kindness.

Thanks to many nice and smart colleagues in the FREEDM system center. I would like to

thank Dr. Sachin Madhusoodhanan, Dr. Ankan De, and Richard Byron Beddingfield who I

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their kindness and academic discussions with me.

My gratitude goes to Dr. Woongje Sung, Dr. Inhwan Ji, Dr. Seunghun Baek, Dr. Kibok

Lee, Kijeong Han, Jaehyuk Won and Heonyoung Kim. It was fun to talk and hang out with

them in and out of the FREEDM system center. Thank Jongbeom Park and Shinyoung Kwag

for the time we prayed and shared our lives .

Lastly, I would like to thank my parents and brother for their love and support. Though I

lived away from them during my Ph.D. studies, I know their pray, advice, and encouragement

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LIST OF TABLES

Table 1.1 Components of the Flexible AC Transmission System (FACTS). . . 5

Table 3.1 Testbed Parameters . . . 44

Table 3.2 Parameters of the proposed droop method. . . 60

Table 3.3 Parameters of the capacitor voltage controller . . . 64

Table 3.4 Simulation parameters of the harmonic compensation scheme of the islanding SST. . . 70

Table 3.5 Simulation parameters of the hybrid harmonic compensation (HHC) scheme of the load SST. . . 88

Table 3.6 Simulation parameters of the five-SST system used to verify the island-ing operation. . . 106

Table 4.1 Parameters of the current controlled inverter . . . 140

Table 4.2 Parameters of the voltage controlled inverter . . . 146

Table 4.3 Simulation parameters of the low-voltage scaled testbed . . . 155

Table 4.4 Simulation parameters of the low-voltage scaled testbed operating in islanded mode . . . 162

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LIST OF FIGURES

Figure 1.1 Block diagram of the power system of the United States. . . 3

Figure 1.2 Block diagram of the Solid-State Transformer (SST). . . 3

Figure 1.3 The architecture of the Future Renewable Electric Energy Delivery and Management (FREEDM) system. . . 7

Figure 2.1 The active and reactive power flow through an inductor. . . 17

Figure 2.2 Droop characteristics of the synchronous generator. (a) Character-istic of speed and active power. (b) CharacterCharacter-istic of voltage and reactive pwoer. . . 18

Figure 2.3 Circuit diagram of voltage source inverter (VSI) for single-phase sys-tem. (a) LC-filtered VSI. (b) LCL-filtered VSI. . . 19

Figure 2.4 Conventional droop method. (a) frequency droop method. (b) mag-nitude droop method. . . 21

Figure 2.5 Block diagram of the conventional droop controller. . . 23

Figure 2.6 Block diagram of the multiloop controller of the LCL-filtered converter. 25 Figure 2.7 The virtual impedance implementation technique. . . 27

Figure 2.8 Block diagram of the microgrid and utility interfaced with static trans-fer switch (STS). . . 28

Figure 2.9 Block diagram of the synchronization controller. (a) Phase synchro-nization controller. (b) Voltage magnitude synchrosynchro-nization controller. 29 Figure 2.10 Block diagram of the current-controlled method (CCM) of the LCL-filtered converter with harmonic compensators. (a) Singleloop struc-ture. (b) Multiloop strucstruc-ture. . . 32

Figure 2.11 Circuit diagram of the dual active bridge (DAB). . . 35

Figure 2.12 Waveforms of the dual active brid (DAB) during one switching cycle. 36 Figure 2.13 Block diagram of the singleloop controller of the DAB. . . 39

Figure 2.14 Block diagram of the multiloop controller of the DAB. . . 39

Figure 3.1 Circuit diagram of the low-voltage scaled testbed. . . 42

Figure 3.2 Circuit diagram of the grid-connected SST and the DESD integrated into the low-voltage side DC link of the SST. . . 44

Figure 3.3 Three operation modes of the FREEDM system and the transitions of the operation modes. . . 45

Figure 3.4 Flow chart of the operation of the SST based system. (a) Flow chart of the FID. (b) Flow chart of the islanding SST. (c) Flow chart of the load SST. . . 47

Figure 3.5 The overall control strategy of the islanding SST. . . 48

Figure 3.6 The overall control strategy of the load SST. . . 50

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Figure 3.8 The characteristic of the voltage magnitude droop curve. . . 54

Figure 3.9 Proposed droop method. (a) frequency droop method. (b) magnitude droop method. . . 56

Figure 3.10 Flow chart for generating the reference of the real power of the is-landing SST which is used for the autonomous isis-landing operation with the proposed droop method. . . 57

Figure 3.11 Block diagram of the proposed droop method. . . 59

Figure 3.12 Circuit diagram of the LCL filter of the AC/DC stage of the SST. . . 61

Figure 3.13 Block diagram of the singleloop capacitor voltage controller. . . 62

Figure 3.14 Bode diagram of the loop gain of the capacitor voltage controller. . . 64

Figure 3.15 Bode diagram analysis to verify the controller design. (a) Bode dia-gram of theTv c/(1+Tv c). (b) Bode diagram of theGg/(1+Tv c). . . 65

Figure 3.16 Step response of the active and reactive power of the proposed droop method and the capacitor voltage controller. . . 67

Figure 3.17 Block diagram of the current harmonic compensators of the islanding SST. . . 68

Figure 3.18 Simulation results without the harmonic compensation scheme. (a) Grid current waveform. (b) FFT of the grid current. . . 68

Figure 3.19 Simulation results with the harmonic compensation scheme. (a) Grid current waveform. (b) FFT of the grid current. . . 69

Figure 3.20 Circuit diagram of the dual active bridge (DAB). . . 70

Figure 3.21 Block diagram of the proposed controller of the DAB. . . 70

Figure 3.22 Step responses of the proposed DAB controller with three different controller bandwidths. . . 74

Figure 3.23 Circuit diagram of the bidirectional buck/boost converter of the is-landing SST. . . 75

Figure 3.24 Outer DC link controller of the buck/boost converter of the islanding SST. . . 75

Figure 3.25 Inner battery current controller of the bidirectional buck/boost con-verter of the islanding SST. . . 76

Figure 3.26 Step responses of the buck/boost controller with three different band-widths of the DC link controller. . . 78

Figure 3.27 Block diagram of the battery power controller of the islanding SST. . 78

Figure 3.28 Charging and discharging of the battery using the battery power controller. . . 79

Figure 3.29 Block diagram of the proposed multiloop controller of the LCL-filtered converter with a hybrid harmonic compensation scheme and a novel virtual impedance method. . . 82

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Figure 3.32 Bode diagrams of the loop gains of the harmonic compensation sys-tems. (a) Loop gain of the harmonic current compensation (HCC) system. (b) Loop gain of the harmonic voltage compensation (HVC)

system. . . 86

Figure 3.33 Waveform of the grid current with the harmonic compensation of the 23rd harmonic current. (a) Grid current with the HCC of the outerloop. (b) Grid current with the HVC of the innerloop. . . 87

Figure 3.34 Simulation results with the hybrid harmonic compensation (HHC) scheme. (a) Grid current waveform. (b) FFT of the grid current. . . 88

Figure 3.35 Block diagram of the proposed virtual impedance method. . . 90

Figure 3.36 The step responses of the DC-link voltage and the grid current. (a) Without the grid impedance. (b) With the grid impedance. (c) With the grid impedance and only the feed forward of the virtual impedance method. (d) With the grid impedance and the whole virtual impedance method. . . 91

Figure 3.37 Step responses of the proposed DAB controller with three different controller bandwidths. . . 93

Figure 3.38 Step response of the battery current controller of the DESD of the load SST. . . 94

Figure 3.39 Circuit diagram of the DRER of the load SST. . . 95

Figure 3.40 Outer PV voltage controller of the DRER of the load SST. . . 95

Figure 3.41 Inner PV current controller of the DRER of the load SST. . . 96

Figure 3.42 Step response of the PV voltage controller of the DRER of the load SST. 97 Figure 3.43 I-V and P-V characteristics of the PV array used in the simulation. . . 98

Figure 3.44 Bidirectional power flow of the load SST with DRER. . . 99

Figure 3.45 Transient responses of the islanding of the low-voltage scaled testbed. (a) Transient response of the PCC current. (b) Transient response of the active and reactive power. (c) Transient response of the DC link voltages. (d) Transient response of the battery current. . . 101

Figure 3.46 Simulation results of the autonomous islanding with communication delay. (a) With communicaion delay of 100 msec. (b) With communi-cation delay of 200 msec. . . 103

Figure 3.47 Simulation results of the islanding operation when the power of the load SST varies due to the DRER. . . 105

Figure 3.48 Circuit diagram of the five AC/DC stages of the SST connected parallel to the utility grid through FID. . . 107

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Figure 3.50 Simulation result of the islanding of the five-SST system when the sum of the power references of the islanding SSTs are larger than required. . . 110 Figure 3.51 Simulation result of the islanding of the five-SST system when the

sum of the power references of the islanding SSTs are smaller than required. . . 111 Figure 3.52 Circuit diagram of the five AC/DC stages of the SST connected parallel

to the utility grid through FID when line impedance exist between the islanding SSTs. . . 113 Figure 3.53 Simulation waveforms during the transition from the grid connected

mode to the islanding mode when line impedance exist between the islanding SSTs. . . 114 Figure 3.54 Simulation waveforms during the transition from the grid connected

mode to the islanding mode when islanding SSTs were drawing dif-ferent amount of actual power. . . 116 Figure 3.55 Simulation waveforms during the transition from the grid connected

mode to the islanding mode with three different inductance of the grid side inductor of the LCL filter. . . 118 Figure 3.56 Circuit diagram of the four AC/DC stages of the SST connected

paral-lel to the utility grid when line impedance exist between the islanding SSTs. . . 120 Figure 3.57 Circuit diagram of the four AC/DC stages of the SST operating in

islanded mode when line impedance exist between the islanding SSTs.122 Figure 3.58 Output power of the islanding SST1 and the islanding SST2 according

to different inductance of the grid side inductor of the LCL filter. (a)

LL1=LL2=1m H. (b)LL1=1m H andLL2=3m H. . . 123

Figure 3.59 Block diagram of the seamless reconnection method of the islanding SST located nearest to the PCC. . . 124 Figure 3.60 Block diagram of the seamless reconnection method of the islanding

SST connected in parallel with the SST located nearest to the PCC. . 125 Figure 3.61 Transient responses of the seamless reconnection of the low-voltage

scaled testbed. (a) Transient response of the PCC current. (b) Tran-sient response of the active and reactive power. (c) TranTran-sient response of the DC link voltages. (d) Transient response of the battery current. 128 Figure 3.62 Zoomed-in simulation results of the seamless reconnection. . . 130 Figure 3.63 Circuit diagram of the five AC/DC stages of the SST connected parallel

to the utility grid through FID. . . 131 Figure 3.64 Simulation result of the seamless reconnection of the five-SST system.132 Figure 3.65 Simulation waveform of the grid side current of the islanding SSTs

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Figure 4.1 Circuit diagram of the AC/DC stage of the SST connected to the utility grid. . . 137 Figure 4.2 The block diagram of the singleloop current controller of the

LCL-filtered voltage source inverter in single-phase system. . . 137 Figure 4.3 The impedance based model of the current controlled AC/DC stage

of the SST. . . 139 Figure 4.4 The steady-state and transient response of the current controller of

the AC/DC stage of SST. (a) The grid current waveform when the controller bandwidth is 700 Hz. (b) The grid current waveform when the controller bandwidth is 1300 Hz. . . 141 Figure 4.5 The migration of poles and zeros of the internal resonance transfer

functionRc c when the controller bandwidth is changed from 500 Hz

to 1300 Hz. (500 Hz, 700 Hz, 900 Hz, 1100 Hz, 1300 Hz) . . . 142 Figure 4.6 The migration of poles and zeros of the internal resonance transfer

functionRc c when the grid impedance is increased from 0.1 mH to 5

mH. (0.1 mH, 1 mH, 3 mH, 5 mH) . . . 142 Figure 4.7 The migration of poles and zeros of the internal resonance transfer

functionRc c when the damping resistance is decreased to 1Ω. The

grid impedance is increased from 0.1 mH to 5 mH. (0.1 mH, 0.5 mH, 1 mH, 5 mH) . . . 143 Figure 4.8 Circuit diagram of the AC/DC stage of the SST connected to the utility

grid. . . 144 Figure 4.9 The block diagram of the singleloop voltage controller of the

LCL-filtered voltage source inverter in single-phase system. . . 144 Figure 4.10 The impedance based model of the voltage controlled AC/DC stage

of the SST. . . 145 Figure 4.11 The migration of poles and zeros of the internal resonance transfer

functionRv c when the controller bandwidth is changed from 500 Hz

to 1300 Hz. (500 Hz, 700 Hz, 900 Hz, 1100 Hz, 1300 Hz) . . . 147 Figure 4.12 The migration of poles and zeros of the internal resonance transfer

functionRv c when the grid impedance is increased from 0.1 mH to

10 mH. (0.1 mH, 1 mH, 5 mH, 10 mH) . . . 148 Figure 4.13 The migration of poles and zeros of the internal resonance transfer

functionRv c when the damping resistance is decreased to 2Ω. The

grid impedance is increased from 0.1 mH to 10 mH. (0.1 mH, 1 mH, 5 mH, 10 mH) . . . 148 Figure 4.14 The steady-state waveform of the grid current of the voltage

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Figure 4.15 Admittance model of the low-voltage scaled testbed connected to

the utility grid. . . 150

Figure 4.16 Poles and zeros of the resonance functions of the grid-side current of the current controlled inverter. (a) Poles and zeros of the internal resonance function,R3. (b) Poles and zeros of the parallel resonance function,P3,1. (c) Poles and zeros of the series resonance function,S3. 154 Figure 4.17 Pole-zero map of the internal resonance function of the testbed when Lg r i d =Ll1=Ll2=0.1m H andLg r i d =Ll1=Ll2=2.0m H. (a) Pole-zero map of the internal resonance function,R3. (b) Zoomed in pole-zero map of the internal resonance function,R3. . . 156

Figure 4.18 Simulation waveform of grid side current of the current controlled inverter. (a) Grid side current whenLg r i d =Ll1=Ll2=0.1m H. (b) Grid side current whenLg r i d=Ll1=Ll2=2.0m H. . . 156

Figure 4.19 Pole-zero map of the internal resonance function of the testbed with different grid impedance and cable impedance. (a) Pole-zero map of the internal resonance function whenLg r i d =Ll1=Ll2=0.1m H. (b) Pole-zero map of the internal resonance function whenLg r i d = 5.0m H andLl1 = Ll2 =0.1m H. (c) Pole-zero map of the internal resonance function whenLl1=5.0m H andLg r i d =Ll2=0.1m H. (d) Pole-zero map of the internal resonance function whenLl2=5.0m H andLg r i d =Ll1=0.1m H. . . 158

Figure 4.20 Admittance model of the low-voltage scaled testbed operating in islanded mode. . . 160

Figure 4.21 Pole-zero map of the internal resonance function of the testbed oper-ating in islanded mode with different cable impedance. (a) Pole-zero map of the internal resonance function whenLl1=Ll2=0.1m H. (b) Pole-zero map of the internal resonance function whenLl1=5.0m H andLl2=0.1m H. (c) Pole-zero map of the internal resonance func-tion whenLl2=5.0m H andLl1=0.1m H. (d) Pole-zero map of the internal resonance function whenLL1=Ll2=5.0m H. . . 163

Figure 5.1 The low-voltage scaled testbed built in the lab. . . 166

Figure 5.2 The hardware structure of the islanding SST. . . 167

Figure 5.3 The battery pack and the power stage of the islanding SST. . . 167

Figure 5.4 The ZigBee module and the DSP board of the SST. . . 167

Figure 5.5 Instability phenomenon of the 13th harmonic compensator of the conventional single-loop current controller. . . 169

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Figure 5.7 The step responses of the DC-link voltage and the grid current. (a) Without the grid impedance. (b) With the grid impedance. (c) With the grid impedance and only the feed forward of the virtual impedance method. (d) With the grid impedance and the whole virtual impedance method. . . 171 Figure 5.8 Step response of the active and reactive power of the AC/DC stage of

the islanding SST. . . 172 Figure 5.9 Step response of the proposed DAB controller and the conventional

small-signal based controller. . . 173 Figure 5.10 (a) Step response of the battery power controller. (b) Waveforms of

low-voltage side DC bus and the battery voltage. . . 174 Figure 5.11 The transient responses during the transition period of the operation

from grid-connected mode to islanding mode. (a) PCC current (FID current). (b) Grid powers. (c) MV DC link voltages. (d) LV DC link voltages. (e) DESD battery voltages. (f ) DESD battery currents. . . 176 Figure 5.12 Transient responses of the active power of the SSTs during the

transi-tion from grid-connected mode to islanded mode when the commu-nication delay exists. . . 178 Figure 5.13 Transient responses of the SSTs during the transition from grid-connected

mode to islanded mode when line impedance between islanding SSTs is 5mH. (a) Transient responses of the active power of the SSTs . (b) Transient responses of the medium-voltage side DC bus. . . 179 Figure 5.14 Transient responses of the SSTs during the transition from grid-connected

mode to islanded mode when line impedance between islanding SSTs is 5mH and the droop slope is increased for 150 msec. (a) Transient responses of the active power of the SSTs . (b) Transient responses of the medium-voltage side DC bus. . . 180 Figure 5.15 The transient responses during the transition period of the operation

from islanding mode to grid-connected mode. (a) PCC current (FID current). (b) Grid powers. . . 182 Figure 5.16 The transient responses during the transition period of the operation

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CHAPTER

1 INTRODUCTION

1.1 Research background

The semiconductor power devices have been developed widely after the initial replacement

of vacuum tubes by solid-state devices in the 1950s[1]. The first development was bipolar power device, such as bipolar transistors and thyristors made from silicon. Due to

advan-tages of using the power devices over vacuum tube, many efforts have been made aiming to

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switching speed and replaced bipolar transistors at applications for high switching speed.

To overcome the issues of bipolar devices and power MOSFETs, insulated gate bipolar

tran-sistor (IGBT) was developed in 1980s which has huge advantage in increasing voltage and

current ratings of the device. Today the power devices are being more and more efficient by

using wide bandgap materials, such as silicon carbide (SiC) and gallium nitride (GaN).

Along with the advancement of the power device technology, research on power

elec-tronics has been focused on to improve many aspects of power conversion using the power

devices. Due to the fast switching capability and low on-resistance of the power devices,

the volume of the power converter is reduced and the efficiency is increased. Moreover,

power electronics provide controllability of voltage and current and thus, can be used

for wide range of applications meeting the system requirement. For example, the speed

of the electric motors can be controlled accurately and the state of charge (SOC) of the

battery of the electric vehicle can be managed by controlling the current and voltage of the

battery charger. Also high-voltage direct current (HVDC) is developed for transmitting large

amounts of electricity over long distances which converts several hundreds of kilovolts of

AC to DC.

Solid-state transformer (SST) is an emerging technology which is for replacing

tradi-tional distribution level power transformer with converters made up of the solid-state

devices[2],[3]. Fig. 1.1 shows the block diagram of the power system of the United States [4]. The transmission level of several hundreds of kilovolts are stepped down to distribution level of several tens of kilovolts. It is again stepped down to residential level of 120/240 V by distribution level power transformer. The SST is not only able to interface the distribution

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Generating station Generator Transmission substation Distribution substation Customer 120/240V Transmission line customer Subtransmission customer Generator step-up transformer Step-down power transformer Step-down power transformer Distribution transformer (1~20 customers) Main transmission

138kV, 230kV, 345kV, 500kV, 765kV

Sub-transmission 115/121kV, 60/69kV

Distribution 11/12kV, 13.8kV, 35kV

Figure 1.1Block diagram of the power system of the United States.

AC DC DC AC AC DC DC AC Medium-frequency

isolated DC/DC stage

Figure 1.2Block diagram of the Solid-State Transformer (SST).

has many advantages coming from power electronics technology.

The SST typically consists of 3 stages of power converters, AC/DC, DC/DC and DC/AC, as shown in Fig. 1.2. While the conventional transformer operates with 50/60 Hz, the SST uses medium-frequency (10-20 kHz) in its DC/DC stage. Since the volume of the transformer is inversely proportional to the cube of the frequency, the volume and weight of the SST

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the efficiency of this stage can be increased to 99%. If the SiC devices are used, the overall

efficiency of the SST can be competitive with that of the traditional distribution level power

transformer.

Besides the advantage of the volume and weight, the SST can provide controllability

to the distribution power system, such as power factor correction and current harmonics

compensation. While the traditional passive transformer does not have any functionality

other than the voltage step down and the galvanic isolation, the SST itself has many power

electronics based features. For example, Flexible AC Transmission System (FACTS) requires

different types of equipments as shown in Table 1.1. The FACTS is a power electronics based

system which is meant to increase power transfer capability by controlling the reactive

power of the power transmission system[9]. Since the traditional power transformers are passive components, the active components are needed : Static Synchronous Compensator

(STATCOM), Static Var Compensator (SVC), Unified Power Flow Controller (UPFC), etc.

However, if the SSTs are used instead of the conventional transformer, those equipments

are not needed and the SSTs themselves provide the controllability of the reactive power.

Due to the 3-stage structure, the SST provides DC bus of both the medium-voltage (MV)

and low-voltage (LV). It is another advantage of using SSTs in the distribution level power

system. Since the renewable energy sources (RESs) and energy storage systems (ESSs), such

as photovoltaics (PV) and battery, produce DC, it is more simple and easy to connect those

devices to the DC grid than the AC grid.

When electricity began to be used, there was a debate on selecting the transmission type

between AC and DC. It resulted in using AC system since stepping up the high-voltage to

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Table 1.1Components of the Flexible AC Transmission System (FACTS).

Connection Types

Parallel

Static Synchronous Compensator (STATCOM) -Static Synchronous Generator (SSG)

-Battery Energy Storage System (BESS)

-Superconducting Magnetic Energy Storages (SMES) Static Var Compensator (SVC)

-Thyristor Controlled Reactor (TCR) -Thyristor Switched Reactor (TSR) -Thyristor Switched Capacitor (TSC)

Series

Static Synchronous Series Compensator (SSSC) Interline Power Flow Controller (IPFC)

Thyristor Controlled Series Capacitor (TCSC) Thyristor Switched Series Capacitor (TSSC) Thyristor Controlled Series Reactor (TCSR) Thyristor Switched Series Reactor (TSSR) Combination of

Parallel and Se-ries

Unified Power Flow Controller (UPFC)

Thyristor Controlled Phase Shifting Transformer (TCPST) Interphase Power Controller (IPC)

transformer windings. The invention of the induction motor expanded the AC system even

to the distribution level and the residential level.

DC power system has been expanded recently especially in the transmission level

high-voltage power system. The improvement of the ratings of the power devices and modular

multi-level converter (MMC) enabled the conversion of the high-voltage AC to DC. DC

system is also more efficient than AC system in transmitting large amount of electricity over

long distances. Thus, HVDC electric power transmission system is now being widely used.

However, DC grid of distribution level and residential level is not formed widely.

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installed widely because most of the residential devices are based on AC and it takes a lot of

cost and effort to replace the whole AC system with DC system. Considering those aspects,

the SST can be a solution which both maximizes the usage of the current AC power system

and provides DC grid. The RESs and ESSs of either distribution level or residential level can

be connected to the DC links of the SSTs.

With the many merits of the SST, a SST-based microgrid system is proposed in 2008,

which is called Future Renewable Electric Energy Delivery and Management (FREEDM)

system. Fig. 1.3 shows the architecture of the FREEDM system. The MV grid is connected

to the SST through the fault isolation device (FID). The FID is a solid-state based circuit

breaker which is more efficient and has faster response than the conventional mechanical

circuit breaker[10],[11]. It isolates the SST from the MV grid when any fault is occured. The response time of the FID is nearly 100µs while that of the conventional one is 1-2

ms. The Distribued Renewable Energy Resources (DRERs) are the devices which interface

the RESs with the DC grid that the SST forms. Similarly, the Distributed Energy Storage

Devices (DESDs) connect the ESSs to the DC grid. DRER and DESD consist of DC/DC power converters. The distributed grid intelligence (DGI) is a software embedded in ARM

processor. Each component of the FREEDM system, FID, SST, DESD, and DRER, has both

ARM processor based board and DSP board. DSP board is for controlling the power stage and

the ARM board handles higher level control and communication among each component

of the FREEDM system to improve reliability and controllability of the system. Lastly, the

residential area AC loads, distributed AC generators, and solar micro-inverters can be

connected to the residential level AC grid of the SSTs.

(25)

Figure 1.3The architecture of the Future Renewable Electric Energy Delivery and Management (FREEDM) system.

into the current AC power grid system in the form of distributed generation (DG)[12]. These RESs-based DG system is typically installed with ESSs and forms AC microgrid at MV

distribution level or LV residential level. When the microgrid is operating in grid-connected

mode, RESs lessen the burden of the power grid by feeding a large portion of the system

loads and can even feed the power grid when the amount of power RESs produce exceeds

the system load. Moreover, another feature of the microgrid is autonomous islanding mode

in which the microgrid is operated solely by the RESs and ESSs without any interruption

when it is islanded from the power grid intentionally or unintentionally. Each DG unit

(26)

of the microgrid and benefits both the utility and customers.

The SST also has autonomous islanding mode for residential-level grid. The DRERs

and DESDs which are integrated into the LV side DC link (LVDC) of the SST can supply

power required in both the DC grid and the residential-level AC grid (LVAC) when the MV

AC grid is disconnected from the SST. In this operation mode, the AC/DC stage of the SST connected to the MV side and the medium-frequency isolated DC/DC stage are turned off, and only DRERs, DESDs, and AC/DC stage of the LV side operate.

However, if the SST does not have enough DRERs or DESDs, the residential are fed by the

SST will experience an outage. In this case, the typical solution is to restore the MV grid or

the LV grid with generating units, which is called black start. Black start is “a bottom-up type

of restoration that uses preselected generating units in the case of a widespread blackout,

whereas a top-down type of restoration is assisted by neighboring power grids only when a

portion of the power system experiences outages"[13]. The United States Department of Energy, in[14], has defined the black start capability as “the ability to go from a shutdown condition to an operating condition delivering electric power without assistance from the

electric system".

The black start operation of the SSTs has been introduced and the control methods

for a grid-connected operation and black start operation have been proposed in the

litera-ture[15]. In[16], SSTs are differentiated as master or slave and are controlled by proposed sequences by taking advantage of the communication capability of the FREEDM system.

Those methods restore the MV AC grid using the DRERs and DESDs. However, these

meth-ods change the controllers of the SSTs according to their operation modes, which results

(27)

pe-riod. Thus, more reliable and practical strategies are required to achieve uninterruptible

SST-based microgrid system.

The islanded microgrid needs to be reconnected seamlessly maintaining the power flow

of the microgrid when the power grid is restored and ready to be used[17]–[20]. The voltage at each end of the static transfer switch (STS) or the FID should be actively synchronized to

prevent overcurrent or overvoltage due to the voltage difference. A wireless communication

based method is proposed in[17]and a synchronization controller is presented in[18] for multiple DG units connected in parallel. Seamless reconnection strategy for FREEDM

system is needed where multiple SSTs operate in parallel.

With the increasing penetration of power electronics based power conversion such

as UPSs, DG systems, etc., regulating harmonic current has been an important issue and

admissible harmonic currents are limited according to standards, e.g. IEEE Std 519-1992.

The LCL-filtered voltage-source converter (VSC) has drawn much attentiondue to its better

attenuation of switching frequency current harmonics compared to L-filtered VSC[21]–[23]. However, the low-order harmonic current should be removed by harmonic

compen-sators (HCs) in order to prevent the grid from being polluted[24]–[26]. The HC is a resonant controller which is widely used in grid-connected converters and especially in

single-phase system[27]. The resonant controller is used in stationary reference frame while the synchronous PI controller is designed in synchronous reference frame. It is proved that

pro-portional+resonant (PR) regulator in the stationary reference frame and the synchronous PI regulator have same transient and steady-state performance[28]. The harmonic current can be regulated by adding the HCs for harmonic frequencies of interest in parallel with the

(28)

compen-sation is to add enough number of HCs to meet the THD standards and guarantee stability

of the converter at the same time. The maximum frequency of the HC is limited since the

phase margin of the harmonic compensation loop decreases as its harmonic frequency

increases. Moreover, the stability is worse if the grid impedance is large due to long cable or

transformer[24],[29].

In most cases, the SST is also connected to the MV power grid through the LCL filter.

Thus, it is important to design not only the controller of the LCL-filtered AC/DC stage at the grid fundamental frequency but also the HCs for regulating grid harmonic currents.

1.2 Research purpose

As mentioned in the previous section, the SST is an emerging technology that can replace

the traditional distribution-level power transfomer. The volume and weight of the SST can

be reduced due to the medium-frequency isolated DC/DC stage. With the advent of wide bandgap power devices and nanocrystalline core material, the efficiency of the SST is as

high as the conventional power transformer. By taking advantage of using power electronics

based converters, reactive power can be controlled without any other auxiliary equipments

used in FACTS, such as SVC, STATCOM, and UPFC.

The FREEDM system maximizes the advantage of using SST. The FID, DRER, DESD, and

DGI are other components of the FREEDM system and provide controllability and reliability

of the system. For example, the DRERs can produce power and feed the residential loads

reducing the power usage of the power grid. The DESDs can be used for peak shaving to

“reduce the amount of energy purchased from the utility company during peak hours when

(29)

Among the many functionalities of the FREEDM system, the autonomous islanding

operation of the FREEDM system of multiple SSTs is studied in this thesis. There are two

types of the autonomous islanding operation of the FREEDM system. One is the islanding

of the DC grid integrated into the DC link of the SST[31]. When the MV power grid is disconnected intentionally or unintentionally and the DC microgrid cannot be enabled by

the SST, the DRERs and DESDs autonomously form the DC grid with their energies and also

feed the residential AC system. The autonomous islanding of the DC grid is based on v-i

droop control which is implemented to the DESDs. The DRERs do not directly regulate the

DC grid but support the grid by producing renewable energy. The other type is the islanding

operation of the MV grid. If a SST has not enough power rating of DRERs and DESDs, it

needs to be fed by other sources connected to the point of common coupling (PCC) of the

MV power grid. The sources can be auxiliary generators or other SSTs tied to the PCC of

the MV. As mentioned before, the black start operation of the SSTs are presented in the

literatures[15],[16]. After the shutdown of the MV power grid, the restoring process of the MV line initiates using the SSTs which have large capability of the DRERs and DESDs. The

controller of the SSTs and DESDs changes according to the operation mode, grid-connected

or black start, or complicated communication is needed which result in unavoidable delays

of the power system restoration during the mode transition period. In this thesis, a new

control strategy is developed to maintain the MV at PCC without any blank time when the

FREEDM system is islanded so that SSTs without enough DRERs and DESDs can even be

operated in the autonomous islanding mode and the residential load can be fed without

facing the outage. The SSTs with abundant energy sources behave like UPSs to support

(30)

proposed and controllers for each stage of the SST and DESD are presented in detail.

In order for the islanded FREEDM system to be reconnected to the power grid after it is

recovered, a seamless reconnection scheme is needed. The voltages at both ends of the FID

should be actively synchronized firstly while maintaining the islanding operation and then

be reconnected without overcurrent or overvoltage issues. A novel seamless reconnection

scheme is studied to provide more reliable and practical method.

Regarding the harmonic current compensation, a major challenge is to add enough

number of HCs to meet the THD standards and guarantee stability of the converter at the

same time. To overcome the instability issue, phase compensation methods are presented

in[24],[32]. In those methods, conventional resonant HC is modified to have trigonometric terms to compensate the phase of it. In this thesis, a multi-loop controller is presented as a

possible replacement for the conventional grid current controller to have enough phase

margin at high harmonic frequencies without using trigonometric terms and to achieve

sufficient harmonics attenuation by implementing both harmonic current compensation

(HCC) and harmonic voltage compensation (HVC), namely a hybrid harmonic

compensa-tion (HHC). Convencompensa-tional multi-loop controller has an inner-loop of filter capacitor current

or converter-side inductor current to improve dynamic performance and achieve active

damping[22],[23],[25]. However, the proposed multi-loop controller has an inner-loop of filter capacitor voltage to provide not only the HHC but also a straightforward criteria of

setting the controller gain of the outer-loop. It should be noted that active damping is also

feasible with the proposed multiloop frame by using a feed forward method presented in

(31)

1.3 Thesis structure

This thesis has the following structure.

Chapter 1 is the introduction. It describes the background of the research, the purpose

of the research, and the structure of the thesis.

In chapter 2, the literature review of the islanding, seamless reconnection, and

har-monic compensation is presented and their limitations are discussed. The strategies for the

black start operation of the SSTs are shown firstly. Then the conventional droop method is

presented which is widely used in the DG systems and UPSs for the autonomous islanding

operation. Several schemes for the active synchronization and seamless reconnection are

depicted. Lastly, the harmonic current compensation schemes are reviewed.

Chapter 3 proposes novel strategies for the islanding, seamless reconnection, and

har-monic compensation. The structure of the controller of SST and DESD is described and the

design of the controller is also presented. New methods for both the seamless transition

from grid-connected mode to islanded mode, and from islanded mode to grid-connected

mode are suggested. A novel harmonic compensation scheme is described and compared

with the conventional strategy. All the strategies are verified through simulation results.

Chapter 4 shows experimental results to verify the proposed strategies. A low-voltage

scaled testbed is built to represent the FREEDM system with multiple SSTs. The testbed

with multiple SSTs is operated using wireless communication. The strategies are digitally

implemented in DSP controllers and the proposed schemes are verified experimentally.

(32)

CHAPTER

2 REVIEW AND ANALYSIS OF EXISTING

(33)

2.1 Black start operation of SST-based system and

autonomous islanding of microgrid

2.1.1 Strategies for black start operation of SST-based system

In the FREEDM system with multiple SSTs operating in parallel, the PCC voltage can be

restored by the black start operation using the DESDs and DRERs[15],[16]. In order to restore the PCC voltage, the controller of each stage of the SST and DESD is switched according to

the operation modes in[15]. During the grid-connected mode, the MV side AC/DC stage regulates the MV DC link by controlling the current of the MV grid. The dual active bridge

(DAB) controls the LV DC link. Provided the LV DC link, the DRER controls the voltage

of the PV panel according to the maximum power point tracking (MPPT) algorithm. The

DESD makes the current of the battery follow the reference value determined by a battery

management system (BMS). Once the system is islanded and the black start operation

initiates, the DESD controls the LV DC link, not the battery current. Provided the LV DC

link, the DAB regulates MV DC link. Finally, the MV side AC/DC stage controls the capacitor voltage of the LCL filter to restore the PCC voltage. To adjust power sharing of the SSTs

connected in parallel, the conventional voltage-frequency (V-f ) droop method is used to

calculate the reference of each capacitor voltage. The controller of the MV side AC/DC, DAB, and DESD, changes to achieve the black start operation and the delay between the

instance of the grid disconnection and black start restoration is unavoidable.

(34)

using the droop method. The slave SST works in the same way as the SST in grid-connected

mode which is described in[15]. The master and slave SSTs are controlled by proposed sequences by taking advantage of the communication capability of the FREEDM system.

However, the droop method is not used and no sequence for the parallel operation of the

master SSTs is presented.

2.1.2 Strategies for autonomous islanding of microgrid

The autonomous islanding is the key feature of the microgrid. It enables the uninterruptible

operation of the microgrid and increase reliability of the microgrid system. It benefits both

the utility and customers. For the islanding operation, the PCC voltage can be directly

controlled as proposed in[33]. In the paper, the MV side grid current is controlled during the grid-connected mode. When the islanding is detected, the PCC voltage controller is

enabled as an outer loop of the grid current controller. The output of the PCC voltage

controller determines the reference of the grid current which is necessary to regulate the

PCC voltage. However, this method occurs high current at the instance of the islanding

due to the sudden initiation of the outer loop. Moreover, it does not provide strategy for

operating multiple converters connected in parallel.

Changing the controller of the converter according to the operation mode is not

suit-able to achieve seamless mode transition and the droop method has been widely used

as a solution for the UPSs and the DG systems[12],[34]–[38]. It was firstly used for the parallel operation of the synchronous generators in power system, but extended to the

grid-connected power converters so that they can mimick the operation. The droop method

(35)

0

2



E

X

_R





1

E

Q

P

,

Figure 2.1The active and reactive power flow through an inductor.

phase and voltage difference across the inductor determine the active and reactive power

as shown in Eq. 2.1 and Eq. 2.2.

P = E1

R2+_X2[(R(E1−E2cos(δ) +X E2sin(δ))]≈

E1E2

X δ (2.1)

Q= E1

R2+_X2[(X(E1−E2cos(δ)−R E2sin(δ))]≈

E1

X (E1−E2) (2.2)

As shown above, if the reactance is much larger than the resistance and the phase

difference is small enough, the active power and the reactive power are decoupled and they

are proportional to the difference of the phase and the magnitude, respectively. The droop

method is based on those decoupled characteristics.

In the electrical power generation system, the droop speed control and droop voltage

control are used to share electric loads among synchronous generators in proportion to

their power rating when they are connected to a power grid in parallel[39]. The droop characteristics are shown in Fig. 2.2. fn l andff l denote the speed reference of the prime

mover at no load and full load, respectively.Pf l denotes the active power of the generator

drawn from the grid. Likewise,En l andEf l are the back-EMF (electromotive force) of the

(36)

P

fl

f

nl

f

fl

f

P

(a)

Q

fl

E

nl

E

fl

E

Q

(b)

Figure 2.2Droop characteristics of the synchronous generator. (a) Characteristic of speed and

active power. (b) Characteristic of voltage and reactive pwoer.

drawn from the grid. When the load is increased, the speed reference of each generator is

decreased according to the droop characteristic to share the increased amount. The droop

characteristic is determined by the speed at no load and the slope of the droop. The slope

is defined as

S PP =

fn l−ff l

ff l

×100%. (2.3)

It is typically in the range 2%-4%. Each generator has a governor which monitors the power

load variation and adjusts the speed reference of a prime mover. The reactive power is shared

by automatic voltage regulator (AVR)[40]. The excitation of the synchronous generator is controlled by the AVR.

The droop method has been adopted to grid-connected converters to achieve the power

(37)

vg

Li

C

vi

Rd

Ri

ig

vc

ii

ic

(a)

vg

Lg C Li

vi

Rg

Rd

Ri

ig

vc

ii

ic

(b)

Figure 2.3Circuit diagram of voltage source inverter (VSI) for single-phase system. (a) LC-filtered

VSI. (b) LCL-filtered VSI.

feasible and thus, is widely being used for the UPSs. Today it is extending its range of

application to the DG systems to increase the reliability of the microgrid. When the droop

method is used in the grid-connected converters, the capacitor voltage of the input filter of

the converters are controlled instead of the speed and the back-EMF of the synchronous

(38)

single-phase power system, LC-filtered and LCL-filtered voltage source inverter (VSI). The higher

order input filters have better performance than the L-filter in preventing the harmonic

current of switching-frequency level polute the grid. In addition, the total inductance can

be reduced compared to the L-filter, which results in the reduction of the volume, weight,

and cost of the input filter[41],[42]. Other advantage of using LC or LCL filter is that the capacitor voltage can be used as a voltage source, e.g. a generator. Thus, LC or LCL-filtered

VSI are used for not only the dynamic voltage restorer (DVR) but also the DG generating

units with droop method.

Fig. 2.4 shows the conventional droop method which is applied to the LC or LCL-filtered

grid-connected converters. Each figure has two different droop curves which are for two

converters operating in parallel. Fig. 2.4a shows the relationship between the frequency of

the capacitor voltage and the active power which each converter provides to the load. The

droop characteristic is determined by the normal operating point,Pg∗, and the droop slope,

mP. When the microgrid is islanded, the frequency of the capacitor voltage is dropped and

converged to a value,ω_{i s l a n d e d}, according to the droop characteristic of the two converters. The droop curve should be determined considering the power sharing of the two

convert-ers. Fig. 2.4b shows the relationship between the magnitude of the capacitor voltage and

the reactive power of the two converters. The droop characteristic is determined by the

normal operating point,Qg∗, and the droop slope,mQ, like the droop curve in Fig. 2.4a. The

manitude of the capacitor voltage is dropped when the microgrid is islanded. It can be seen

that the converters mimick the operation of the synchronous generators by applying the

droop method to the capacitor voltage of the input filter.

(39)

P

g

[W]

ω

c

[rad/s]

m

P1

ω

normal

ω

islanded

P

g1

P

g2

P

g1*

P

g2*

m

P2

(a)

Q

g

[VAr]

V

c

[rad/s]

m

Q1

V

normal

V

islanded

Q

g1

Q

g2

Q

_g1*

Q

_g2*

m

Q2

(b)

Figure 2.4Conventional droop method. (a) frequency droop method. (b) magnitude droop

(40)

above, the reference of the frequency of the capacitor voltage is calculated by the “real

power versus frequency (P-ω)" droop control, and the reference of the magnitude of the

capacitor voltage is calculated by the “reactive power versus voltage (Q-E)" droop control

[34]. The droop characteristic can be expressed as

ωc∗=ωg+mP(Pg∗−Pg) (2.4)

Vc∗=Vg+mQ(Qg∗−Qg) (2.5)

where theωg and theVg denote the frequency and magnitude of the grid voltage,

repec-tively, calculated by phase- locked loop (PLL). These value can be replaced with any fixed

dispatched value. If the PLL value is used, any fixed value should replace those when the

microgrid is islanded.

The droop control enables the power sharing of the converters connected in parallel.

In addition to the power sharing, the microgrid can operate in the autonomous islanding

mode without any wireless communication among the converters. However, if there is a

wide variation of the power during the grid connected operation such as the SST, the droop

characteristic changes and the power is shared in unexpected way when the microgrid is

islanded. For example, in Fig. 2.4a, if the second converter draws more power from the grid,

which meansPg2∗decreases, its droop curve shifts to the left side of the graph. It means

that the amount of power the second converter is supposed to provide for the islanding

operation is decreased. If the first converter cannot afford to compensate the decreased

amount, the autonomous islanding fails. One possible way to solve this problem is to

adjust the droop slope according to the change of the power during the grid-connected

(41)

Pg_max

-Pg_max

Pg [W] ωc [rad/s]

ωc_max

ωc_min

Qg_max

-Qg_max

Qg [VAr]

Vc [V]

Vc_max

Vc_min

mP

mQ

Pg , Pg*

v

g

PLL

ω

g

mP

ωc*

θc*

Qg , Qg*

VC*

mQ

vc*

* *

( )

c g m PP g Pg

   

* *

( )

c g Q g g

V V m Q Q

1

s * * *

cos( )

c c c

v V 

V

g

Figure 2.5Block diagram of the conventional droop controller.

the wide variation of the operating point. Moreover, it is still difficult to estimate the exact

amount of the power to be shared among the converters if the operating point of each

converter is deviated from the normal point. The autonomous islanding is not guaranteed.

As shown in Fig. 2.5, the droop controller determines the reference of the capacitor

voltage of the LC or LCL filter. Therefore, a capacitor voltage controller is needed to

synthe-size the reference voltage. Typically, the LC filter is used to regulate the capacitor voltage,

(42)

autonomous islanding is not the requirement of the system, the LCL-filtered converter is

controlled by a typical grid current controller. On the other hand, the LCL-filtered converter

is controlled by the capacitor voltage controller if the autonomous islanding operation is

needed.

The most widely used compensator for the grid-connected converter is the

propor-tional+resonant (PR) controller. As mentioned previously, it is used in the stationary ref-erence frame. While the synchronous PI controller is designed in the synchronousd-q

reference frame by transforming the stationary variables to thed-qvariables, the PR

con-troller can be directly designed in the stationary reference frame with the same steady

state and transient performance as the synchronous PI controller. The PR regulator can be

expressed as

G =KP+

2KIωcs

s2+₂ω

cs+ωf2

(2.6)

whereω_f is the system fundamental frequency, ω_c is cutoff bandwidth,KP is the

pro-portional gain andKI is the integral gain. The resonant controller is used to control the

fundamental frequency component by setting theω_f as the system fundamental frequency. It can be used to control the current or voltage at the frequency of interest and thus,

low-order harmonic components of the current or voltage can also be regulated by using the

resonant controller, which is called the harmonic compensator (HC). The HC is expressed

as

Gh=

X

h

2KI hωc hs

s2+₂ω

c hs+ωh2

(43)

P

g*

Droop

Controller

v

c*

G

outer

PWM

v

i *

v

c

P

g

_Gating

v

i

Q

g *

Q

g

G

inner

i

inner

i

inner*

v

c

v

g

v

PCC

Figure 2.6Block diagram of the multiloop controller of the LCL-filtered converter.

whereωh is the low-order harmonic frequency,ωc h is cutoff bandwidth for the harmonic

frequency,KI his the integral gain for the harmonic frequency. The HC for each low-order

harmonic frequency can be added in parallel with the PR controller for the fundamental

frequency. Since the resonant regulator provides harmonic compensation functionality,

the PR controller is preferred to the synchronous PI controller when the converter is used

with the grid, especially with the single-phase grid.

The typical structure of the controller of the LCL-filtered converter is shown in Fig. 2.6.

As shown above, the outer loop and the inner loop are used, which is called multiloop

controller. The outer loop controls the capacitor voltage of the LCL filter. It is for reference

tracking performance at steady-state[22]. The outer loop compensator can be expressed as

Go u t e r=KP v+

2KI vωc vs

(44)

whereω_f is the system fundamental frequency,ω_{c v} is cutoff bandwidth,KP v is the

propor-tional gain andKI vis the integral gain. The inner loop regulates either the capacitor current

or the converter current. The role of the inner loop is to improve dynamic performance of

the system and to provide damping effect. Therefore, only a proportional controller is used

Gi n n e r =KP i (2.9)

whereKP i denotes the proportional gain.

A major challenge of the droop method is the coupling of the active and reactive power.

It is due to the high resistance of the cable used in distribution level or residential level. The

cable used in transmission level is mainly inductive. However, in the distribution level or

the low voltage level, the resistance of the cable is not ignorable and thus, the active and

reactive power is coupled. This power coupling affects the accuracy of the power control

and may induce the oscillation of the power. A rotational transformation is proposed in

[37]to decouple the active and reactive power by using the ratio between the resistance and the reactance of the cable. However, it is hard to be used for the power sharing of the

parallel converters when islanded.

A virtual impedance method is another solution for the power decoupling[12],[23], [43]. It is to add virtual impedance, which is mainly inductive, between the grid and the capacitor of the input filter of the converter to make the cable more inductive. Fig. 2.7 shows

a block diagram of the virtual impedance implementation technique presented in[12]. The virtual resistanceRv and the virtual inductanceLv are implemented by subtracting

the voltage across the virtual impedancevvαβfrom the reference of the capacitor voltage

(45)

Droop

Controller

v

c*

Virtual Impedance

-

ω

L

v

ω

L

v

R

v

R

v

i

α

i

gαβ

i

β

v

α

v

β

v

vαβ

P

g

Q

g

v

c

G

outer

Figure 2.7The virtual impedance implementation technique.

inductance jωLvig, considering only the virtual inductance at the fundamental frequency.

The implementation in the box of Fig. 2.7 comes from the stationary reference frame

derivation,v_α+j v_β = jωLv(iα+j iβ) =ωLv(−iβ+j iα). In[23], another implementation

technique is presented which can cover not only the fundamental frequency but also

the low order harmonic frequency of interest. However, a proportional gain is ignored to

prevent a differentiation term from amplifying high-frequency noise, which may degrade

the accuracy of the fundamental frequency controller.

2.2 Active synchronization methods and seamless

reconnec-tion of microgrid

Fig. 2.8 shows the DG microgrid connected to the utility at the PCC through a static transfer

Islanding and Seamless Reconnection of Multiple Solid-State Transformers Based On Droop Control

ABSTRACT

DEDICATION

BIOGRAPHY

ACKNOWLEDGEMENTS

TABLE OF CONTENTS

LIST OF TABLES

LIST OF FIGURES

CHAPTER

1

INTRODUCTION

1.1

Research background

1.2

Research purpose

1.3

Thesis structure

CHAPTER

2

REVIEW AND ANALYSIS OF EXISTING

2.1

Black start operation of SST-based system and

autonomous islanding of microgrid

2.1.1

Strategies for black start operation of SST-based system

2.1.2

Strategies for autonomous islanding of microgrid

0



E

X

R





E

Q

P

,

P

f

f

f

P

Q

E

E

E

Q

P

[W]

ω

[rad/s]

m

ω

ω

P

P

P

P

m

Q

[VAr]

V

[rad/s]

m

V

V

Q

Q

Q

Q

m

v

PLL

ω

V

P

Droop

Controller

v

_R

_Gating