Interactions between Distributed Energy Resources in a Balanced Three-Phase Microgrid.

ABSTRACT

RAVURI, LIKHITA. Interactions between Distributed Energy Resources in a Balanced Three-Phase Microgrid . (Under the direction of Dr. Srdjan M Lukic.)

The penetration of Distributed Energy Resources (DER) at medium and low voltages (MV and

LV), both in utility networks and downstream of the meter, is increasing worldwide. While the

application of DERs can potentially reduce the need for traditional system expansion, controlling

a huge number of DERs create a whole new challenge for operating and controlling the network

safely and efficiently. This challenge can be partially addressed by microgrids, that are localized

grids that can disconnect from the traditional grid to operate autonomously and help mitigate grid

disturbances to strengthen grid resilience. This research mainly focuses on two main concerns in

microgrids: 1. The interactions between various DERs in a microgrid and improving the power

quality, and 2. The system response to faults by abiding to IEEE-1547 standards defined by the

utlility.

Studying the interactions between multiple inverter interfaced DERs when tied together is

absolutely important, given their predominance in many microgrids. In order to avoid the need

for any communication among modules in a paralleled inverter system, the power-sharing control

loops are based on the P/Q droop method. The output impedance of the closed-loop inverter affects the power sharing accuracy and determines the droop control strategy. Furthermore, the

proper design of this output impedance can reduce the impact of the line-impedance unbalance. In

order to program a stable output impedance, the virtual impedance concept is increasingly used for

the control of power electronic systems, as an additional degree of freedom for active stabilization,

improved power quality and disturbance rejection. Methods to estimate the optimal values for these

virtual impedances have been explored.

Synchronous generators are one of the most common types of DERs, and this research focuses on

interactions between inverter based DERs and synchronous generators in microgrids. When voltage

inertia is observed to change the system dynamics when compared to the most common

inverter-based microgrids. The operating characteristics of such microgrid systems have been explored for

different modes of operation.

Instead of trying to mitigate inverter overloads and thus allow larger voltage and frequency

transients, it is often preferable to allow the inverter to provide as much support as possible, and

simply current limit when necessary. Also, according to the new IEEE-1547 standards, the smart

in-verters in microgrids are expected to stay online and operate in Low Voltage Ride Through (LVRT)

mode. Current limiting in the presence of other grid-forming DER is complicated for voltage

con-trolled inverters. The use of simple current reference saturation is shown to cause instability. Virtual

impedance current limiting is implemented to provide improved transient stability during current

limiting with faults. Current limiting performance during faults in islanded and grid connected

mode is investigated, and it is shown that virtual impedance current limiting provides improved

transient stability during current limiting in the presence of synchronous generators compared to

traditional current limiting methods.

The methods implemented in this thesis for mitigating the problems with multiple component

interactions in microgrids will allow for more reliable and cost effective application of inverter based

DERs with synchronous generators in the microgrid, even during faults. The analysis was carried

out by modeling the microgrid system using PLECS and MATLAB software platforms. Hardware

validation for the same have been initialized through designing and building a robust DC storage

©Copyright 2017 by Likhita Ravuri

Interactions between Distributed Energy Resources in a Balanced Three-Phase Microgrid

by Likhita Ravuri

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

in partial fulfillment of the requirements for the Degree of

Master of Science

Electrical Engineering

Raleigh, North Carolina

2017

APPROVED BY:

Dr. Iqbal Husain Dr. David Lubkeman

DEDICATION

To my dear parents, Lakshmi and Satyanarayana Ravuri

BIOGRAPHY

Likhita Ravuri was born on May 27, 1995 to Lakshmi Devi and Satyanarayana V.V. Ravuri,

in the city of Bhimavaram (Andhra Pradesh), India. She received the Bachelor of Engineering

(B.E.) with Honors in Electrical and Electronics Engineering from Birla Institute of Technology

and Science (BITS) Pilani, Hyderabad in 2015.

Likhita joined the Electrical and Computer Engineering Department of North Carolina State

University in August 2015 to pursue the Master of Science (M.S.) degree in Electrical

Engineer-ing. She has been working with the Future Renewable Electric Energy Delivery and Management

(FREEDM) Systems Center under the guidance of Dr. Srdjan M. Lukic for the past two years,

during the course of her master’s degree.

Her research interests include Power Electronics and Microgrids. After her graduation, she

plans to join VoltServer as an Electrical Design Engineer and pursue a career in the industry in an

ACKNOWLEDGEMENTS

I would like to thank my advisor, Dr. Srdjan Lukic for giving me the opportunity to work on this

thesis under his guidance. I owe my progress in this work to him for his knowledgeable mentorship

and his ever encouraging belief in me. His leadership, support, attention to detail, and hard work

have set an example I hope to match some day. I sincerely thank him for understanding my

con-straints and supporting me throughout the past 2 years, this wouldn’t have been possible if not for

the confidence he had in me.

My sincere thanks to Dr. Iqbal Husain for efficiently leading the FREEDM Systems Center as

the Director and for his efforts in making the center one of the best Power Electronics research

centers in the world. My heartfelt thanks to Dr. David Lubkeman for his contributions as the leader

for GEH Testbed. I thank him for all the insightful discussions in the course of our preparation

for the NSF Site Visit-2017, it was a one-of-a-kind experience. Special thanks to Dr. Wensong

Yu for leading the LV-SST hardware team for GEH Testbed and for his very informative and

knowledgeable Power Electronics training sessions.

Thank you Hao, for being patient and helping me through the DESD prototyping, especially

with the communication protocols. Thank you for introducing me to the concept of fault analysis in

smart inverters. It was a great pleasure working with you and I am thankful for finding a good friend

in this process. Thanks Awal and Siyuan for all the great ideas to make the site-visit demonstration

a huge success, we make a great team together. Thanks Samir for helping me with the synchronous

generator design. Thanks Ashish for all your help with LaTeX. This is a perfect opportunity to

thank Karen, Hulgize and Rebecca for their efforts to make FREEDM a safe, friendly and exciting

place.

Sravani and Gopi, you guys motivated and pushed me all the way from India. We have come a

long way together. Manila, thanks for always being there no matter what. Radha, FREEDM gave

me an amazing, funny and caring soul-sister, always stay the same. Siddharth and Zhao, I never

I am immensely grateful to all the people who made this research and my graduate study at

NC State a wonderful experience for me, I’m very glad that our paths crossed. I wish everyone of

you, the best.

Chinna Mavayya and Chinnatta, you guys left no stone unturned to ensure my happiness

throughout the past two years. Thank you for being the most caring and awesome uncle and aunt

ever. Tejas, one smile from you would brighten up my day. I express my sincere appreciation to my

extended family, this wouldn’t have been possible without you all.

Amma and Daddy, I am extremely grateful to have you both as my parents. Thank you for

all the sacrifices and your unconditional love. Daddy, the confidence you had in me is what drives

me even today. Thank you for setting up the best example to working hard and staying content.

Amma, I know how hard it has been for you to take care of everything all by yourself for the past

three years, thank you for being strong and motivating me to chase my dreams. Pandu, you are

TABLE OF CONTENTS

LIST OF TABLES . . . .viii

LIST OF FIGURES . . . ix

Chapter 1 Introduction . . . 1

1.1 Big Picture-Microgrids . . . 1

1.2 Problem Statement . . . 3

1.2.1 Component Interactions . . . 3

1.2.2 IEEE 1547 standards during faults (Low Voltage Ride Through) . . . 3

1.3 Objectives . . . 5

1.4 Outline of Chapters . . . 5

Chapter 2 Modeling and Control of Distributed Energy Resources in Microgrid . 7 2.1 Three Phase Battery Energy Storage System . . . 7

2.1.1 Overview of Energy Storage Systems in microgrids . . . 7

2.1.2 Three Phase Inverter Plant . . . 9

2.1.3 DC/DC Stage - Modeling . . . 21

2.1.4 Battery Interface . . . 30

2.2 Inverter based Distributed Generator Emulation . . . 31

2.3 Synchronous Generator Model . . . 32

2.3.1 Modeling . . . 32

2.3.2 Control . . . 32

2.3.3 Permanent Magnet SG Vs. Wound Field SG . . . 38

Chapter 3 Component Interactions in Three-Phase Microgrids . . . 39

3.1 System at Test . . . 39

3.2 Paralleled Inverter System . . . 40

3.2.1 Operation . . . 41

3.2.2 Challenges . . . 45

3.2.3 Virtual Impedance . . . 46

3.2.4 Stability . . . 47

3.3 Generators in microgrids . . . 48

3.3.1 Operation . . . 48

3.3.2 Machine dynamics in a microgrid . . . 48

3.3.3 Effect on Inverters . . . 51

3.4 Connection Type . . . 52

3.4.1 Grid Connected Mode . . . 54

3.4.2 Islanded Mode . . . 58

Chapter 4 Fault Current Limiting in Three-Phase Microgrids . . . 63

4.2.1 Before FCLs . . . 64

4.2.2 Fault Current Limiters . . . 65

4.3 Virtual Impedance based FCL . . . 66

4.3.1 Strategy-1 [1] . . . 67

4.3.2 Strategy-2 [2] . . . 69

4.3.3 Simulation Results . . . 71

Chapter 5 Hardware Development . . . 85

5.1 Hardware Prototyping . . . 85

5.1.1 Converter Hardware . . . 85

5.1.2 Auxiliary Power Supply . . . 87

5.1.3 Final Hardware Prototype . . . 88

5.2 Battery Pack . . . 89

5.2.1 Battery Management System (BMS) . . . 90

5.3 Protection Mechanisms . . . 92

5.3.1 Protection Hardware . . . 92

5.3.2 Software Protection . . . 94

5.4 Experimental Results . . . 94

Chapter 6 Conclusion . . . 99

6.1 Accomplishments . . . 99

6.2 Recommended Future Work . . . 100

6.2.1 Secondary control for Inverters . . . 100

6.2.2 Active current threshold calculation during faults . . . 100

6.2.3 Stability analysis and bounds forZf cl . . . 101

References. . . .102

Appendix . . . .107

Appendix A Virtual Impedance Value Optimization . . . 108

A.1 Virtual Impedance for Real and Reactive Power Decoupling . . . 108

LIST OF TABLES

Table 2.1 Three Phase Inverter-Model Parameters . . . 17

Table 2.2 Interleaved DC/DC Boost Converter-Model Parameters . . . 30

Table 2.3 100kVA Synchronous Generator-Controller Parameters [1] . . . 36

LIST OF FIGURES

Figure 1.1 Microgrid, Adapted from [3] . . . 2

Figure 1.2 Voltage Interconnection and Ride Through requirements, Adapted from [4] . . . 4

Figure 1.3 Frequency Interconnection and Ride Through requirements, Adapted from [4] . . 5

Figure 2.1 3-phase ESS block diagram . . . 8

Figure 2.2 Three Phase Inverter Circuit Diagram . . . 10

Figure 2.3 Three Phase Inverter Controller Block Diagram . . . 17

Figure 2.4 PWM Switching Sequence . . . 18

Figure 2.5 3-Phase Inverter Output Voltage Waveforms . . . 19

Figure 2.6 Three Phase Output Current Waveforms . . . 19

Figure 2.7 Three Phase Inverter Voltage Waveform during Load Change . . . 20

Figure 2.8 Three Phase Inverter Current Waveform during Load Change . . . 20

Figure 2.9 Boost Converter circuit diagram . . . 21

Figure 2.10 Boost Converter - ON State . . . 22

Figure 2.11 Boost Converter - OFF State . . . 22

Figure 2.12 Designed Interleaved DC Energy Storage Device circuit diagram . . . 25

Figure 2.13 DC-DESD current controller bode plot . . . 26

Figure 2.14 Bode plot to determine voltage controller bandwidth . . . 27

Figure 2.15 DC-DESD control loop simulation block diagram . . . 28

Figure 2.16 DC DESD inductor current waveforms: (a)Step response of inductor currents, (b)DC-DESD inductor current ripple in each interleaved phase . . . 29

Figure 2.17 DC DESD battery current ripple . . . 29

Figure 2.18 Battery Model Circuit Diagram [5] . . . 31

Figure 2.19 Synchronous Generator Block Diagram, Adapted from [1] . . . 33

Figure 2.20 Governor Control Circuit Block Diagram . . . 34

Figure 2.21 Governor following the Speed Reference . . . 34

Figure 2.22 AVR Control Circuit Block Diagram . . . 35

Figure 2.23 AVR following the Voltage Reference and applying the corresponding Vf . . . 37

Figure 2.24 3-phase SG terminal voltage and current waveforms during load change . . . 37

Figure 3.1 Microgrid System under test . . . 40

Figure 3.2 Parallel voltage sources concept illustration, Adapted from [6] . . . 41

Figure 3.3 Real Power-Frequency (P-f) and Reactive Power-Voltage (Q-V) Droop charac-teristics . . . 42

Figure 3.4 Three Phase paralelled inverter voltages at PCC . . . 43

Figure 3.5 Three Phase paralelled inverter voltages at PCC . . . 44

Figure 3.6 Power Sharing in Paralleled 3-phase Inverters . . . 45

Figure 3.7 Virtual Impedance Concept [7] . . . 46

Figure 3.8 Paralleled Inverter-Generator voltage waveforms at PCC . . . 49

Figure 3.9 Paralleled Inverter-Generator current waveforms at PCC . . . 49

Figure 3.10 Paralleled Inverter-Generator Real power sharing . . . 50

Figure 3.12 System settling time delay due to SG’s inertia . . . 52

Figure 3.13 Simulated Microgrid System in PLECS . . . 53

Figure 3.14 DER Voltages in Grid connected mode . . . 54

Figure 3.15 DER Currents in Grid connected mode . . . 55

Figure 3.16 Grid Voltage and Currents . . . 55

Figure 3.17 Governor following the Speed Reference in Grid connected mode . . . 56

Figure 3.18 AVR following the Voltage Reference and applying the correspondingVf in Grid connected mode . . . 57

Figure 3.19 Power sharing in DERs in Grid connected mode . . . 57

Figure 3.20 Real power shared by the Grid . . . 58

Figure 3.21 DER Voltages in Islanded mode . . . 59

Figure 3.22 DER Currents in Islanded mode . . . 60

Figure 3.23 Governor following the Speed Reference in Islanded mode . . . 61

Figure 3.24 AVR following the Voltage Reference and applying the corresponding Vf in Is-landed mode . . . 61

Figure 3.25 Power sharing in DERs in Islanded mode . . . 62

Figure 4.1 High-Temperature superconducting FCL [8] . . . 65

Figure 4.2 Solid-state FCL [9] . . . 66

Figure 4.3 Virtual Impedance based Fault current limiting . . . 67

Figure 4.4 Virtual impedance based Fault current limiting strategy . . . 69

Figure 4.5 Phasor Diagram for Impedance . . . 70

Figure 4.6 Three-phase balanced fault at PCC in the current microgrid . . . 71

Figure 4.7 Droop Output for 3-phase balanced fault at t=5.85s to t=6.2s . . . 72

Figure 4.8 DER Voltages during 3-phase Fault at PCC in Islanded mode . . . 73

Figure 4.9 DER Currents during 3-phase Fault at PCC in Islanded mode . . . 74

Figure 4.10 Overall Virtual Impedance in the system during Fault-Islanded mode . . . 75

Figure 4.11 RMS currents in Inverter during 3-phase Fault-Islanded mode . . . 76

Figure 4.12 Power sharing in DERs during 3-phase Fault in Islanded mode . . . 76

Figure 4.13 PWM Generation during Fault . . . 77

Figure 4.14 Governor during Fault in Islanded mode-Speed reference generator . . . 78

Figure 4.15 AVR during Fault in Islanded mode-Applied field voltage . . . 79

Figure 4.16 DER Voltages and Currents during a 3-phase fault at PCC . . . 80

Figure 4.17 RMS currents in Inverters during 3-phase balanced fault at PCC . . . 80

Figure 4.18 Virtual Impedance in the system with a 3-phase balanced fault triggered at t=16.7s to t=17.85s . . . 81

Figure 4.19 Power sharing in DERs during 3-phase balanced fault at PCC in Grid connected mode . . . 82

Figure 4.20 PWM generation during 3-phase balanced Fault at PCC . . . 83

Figure 4.21 Governor following speed reference in Grid-connected mode during 3-phase bal-anced fault at PCC . . . 83

Figure 5.1 SiC Power Module (CCS050M12CM2) [10] . . . 86

Figure 5.2 Interfacing board mounted on top of the Gate Driver board from Cree . . . 86

Figure 5.3 Power Board for DESD . . . 87

Figure 5.4 Auxiliary Power Supply . . . 88

Figure 5.5 Final Converter Hardware with all the auxiliary circuitry . . . 88

Figure 5.6 Battery Module Operation [11] . . . 89

Figure 5.7 Toshiba LTO Battery pack used for the current DESD application . . . 90

Figure 5.8 Battery Management System . . . 91

Figure 5.9 DC-DC Converter Hardware in the DESD rack . . . 92

Figure 5.10 State Machine Algorithm for software protection . . . 94

Figure 5.11 Output Voltage and Currents at No Load operation- Worst Case . . . 95

Figure 5.12 No Load Closed-loop transient of DESD-StepUp . . . 95

Figure 5.13 No Load Closed-loop transient of DESD-StepDown . . . 96

Figure 5.14 3kW load Closed-loop response of DESD . . . 96

Figure 5.15 Inductor Current Ripple for a 3kW Load . . . 97

Figure 5.16 Transient Response of DESD with a 3kW Load . . . 98

Figure A.1 Optimization of virtual impedance for decoupling P and Q . . . 109

Chapter 1

Introduction

1.1

Big Picture-Microgrids

Economic, technology and environmental incentives are revolutionizing electricity generation and

transmission. The generating facilities are slowly moving towards more distributed energy resources

rather than centralized generation. Distributed Energy Resources (DER) include a wide range of

prime mover technologies, such as gas turbines, microturbines, internal combustion (IC) engines,

Photo-Voltaic (PV) systems, fuel cells, wind-power and storage devices. These emerging

technolo-gies have lower emissions and the potential to have lower cost negating traditional economies of

scale [12]. Few applications include power support at substations, deferral of transmission and

dis-tribution upgrades, use of renewable energy, higher power quality and smarter disdis-tribution systems.

Thus, distribution system provides major opportunities for smart grid concepts.

According to a recent research at University of Puerto Rico as part of the GridEd consortium

[13], today’s electricity system is considered to be 99.97% reliable, but still allows for power outages

and interruptions costing Americans at least $150 billion each year — about $500 per person. Since

1982, growth in peak demand for electricity – driven by population growth, bigger houses, bigger

TVs, more air conditioners and more computers – has exceeded transmission growth by almost

Figure 1.1: Microgrid, Adapted from [3]

permanently eliminating the fuel and greenhouse gas emissions from 53 million cars. Clearly, there

are terrific opportunities for improvement.

Also, due to the increased interference of digital systems and sophisticated controls, many

in-dustrial, commercial and residential customers now require a high level of power quality. Power

quality, availability and reliability are important issues to all customers. These customers are

espe-cially sensitive to momentary voltage sags caused by remote faults. It has been found that, in terms

of energy source security, that multiple small generators are more efficient than relying on a single

large one for lowering electric bills [14]. Small generators are better at automatic load following and

help avoid large standby charges seen by sites using a single generator.

This introduces the concept of microgrids. Microgrids are electricity distribution systems

con-taining loads and distributed energy resources, (such as distributed generators, storage devices, or

controllable loads) that can be operated in a controlled, coordinated way either while connected to

if extra generation is available, makes the chance of all-out failure much less likely.

1.2

Problem Statement

1.2.1 Component Interactions

Most emerging technologies such as microturbines, photovoltaic systems, fuel cells and ac storage

have an inverter to interface with the electrical distribution system, thus forming an inverter

dom-inated microgrid. However, since internal combustion engine driven synchronous generators (SGs)

are the most common type of DER with a combined installed capacity exceeding 100,000 MW [15],

mostly in backup power applications, it is expected that synchronous generators will play a major

role in microgrid installations. From the Fig. 1.1, it is therefore important to study the interactions

between the inverter interfaced sources with synchronous generators and battery energy storage

devices when tied together, thus leading to working on the interactions between multiple DERs in

a microgrid setup.

1.2.2 IEEE 1547 standards during faults (Low Voltage Ride Through)

The second focus of this thesis is the realistic applicability of the developed microgrid model on

real time systems. To achieve this, it’s extremely important to abide by the rules of the IEEE-1547

standards for interconnection and interoperability of Distributed Energy Resources (DER) with

associated Electric Power Systems (EPS) interfaces [16].

According to the revised 1547 draft from 2016 [17], one of the main updates in the smart inverter

design and operation requirements include voltage and frequency trip and ride-through settings.

1. Voltage Interconnection and Trip Requirements

• Should not superimpose a voltage or current upon the grid

• Can actively regulate the voltage at PCC

Figure 1.2: Voltage Interconnection and Ride Through requirements, Adapted from [4]

• Ride Through during Disturbances:

– Stay connected while the grid is within “Ride through until” voltage-time range in the corresponding operation mode as shown in Fig. 1.2

– ForHV1 (1.1,1.2)pu, power output can be reduced as f(V) under mutual agreement

– If ride through is not exited, and system recovers, inverters should restore to con-tinuous operation within 2 seconds

– If system doesn’t exit LVRT region, and returns fromLV3(<50) toLV2 [0.5,0.7)pu orLV1 [0.7,0.88) pu, Smart inverter restores available current in<= 2 seconds

2. Frequency Interconnection and Trip Requirements

• In [60.2,61.5]Hz, smart inverter can reduce power until it ceases to export power by

61.5Hz and the remaining requirements are mentioned in Fig. 1.3

Figure 1.3: Frequency Interconnection and Ride Through requirements, Adapted from [4]

1.3

Objectives

The objective of this research is to investigate the component interactions between Distributed

Generators in a microgrid and work towards mitigating the power sharing and inertia issues and

implement the respective control strategies. Inverter current-limiting in the presence of synchronous

generators is analyzed and virtual impedance current limiting is implemented to provide stable

current limiting during overloads and three-phase faults in both grid connected and islanded mode

operation.

1.4

Outline of Chapters

point (PCC) in microgrids. A detailed analysis on both grid-connected and islanded mode operation

have been performed and described in this chapter. The challenges involved with current limiting

in the presence of synchronous generators are described in Chapter 4 and virtual impedance based

current limiting algorithms are implemented to provide stable current limiting and Low-Voltage

Ride Through (LVRT) operation during balanced three-phase faults. In Chapter 5, as a first step

towards hardware development, a prototype for a DC Distributed Energy storage Device (DESD)

is designed, developed and tested for efficiency, robustness and performance. Finally, conclusions,

Chapter 2

Modeling and Control of Distributed

Energy Resources in Microgrid

This chapter discusses the modeling and control of all the DERs considered for this thesis so that

the findings from the next chapters can be validated through simulations.

2.1

Three Phase Battery Energy Storage System

Due to the penetration of renewable energy sources into the present day power systems, the use of

energy storage systems in power system management is growing. The evolution of the concept of

energy storage systems undoubtedly offers new opportunities, challenges, and numerous advantages.

Over the past few decades, many new advances have been made in this field of energy storage

systems. To analyze the dynamics introduced by the energy storage system (ESS) in the system of

interest, a simplified model is developed in PLECS.

2.1.1 Overview of Energy Storage Systems in microgrids

Energy Storage Systems (ESS) technologies have existed for quite a long time and are becoming of

overcome some of the limitations of electricity generation from renewable energy sources (the major

one being intermittent nature of generation). Besides, they also offer a number of advantages like

frequency regulation, transient stability, voltage support, flicker compensation, spinning reserve,

uninterrupted power supply, load leveling, and peak shaving among others. Utilization of energy

storage systems begins at the transmission level where large scale storage devices are the best

options to be used. Next, the small scale energy storage devices are the ones that are used at the

consumer’s end.

Battery Energy Storage systems (BESS) is the most commonly used category of energy storage

systems with the renewable energy sources. Battery Energy Storage Systems play a significant role

in the integration of small scale renewable energy sources into the main power system network

(a.k.a. smart grid). They can be seen as the distinct and most viable solution for small scale

renewable energy integration due to their remarkable properties like high energy density, technology

up-gradation, power density, discharge time, life cycle, response time, cost and efficiency etc. [18]

L_fa L_ca

L_fb L_cb

L_fc L_cc

CfaCfbCfc

Since the main focus of this thesis is on three phase systems, a three phase energy storage device

is considered to be integrated into the microgrid system. As shown in Fig. 2.1, a three phase AC

energy storage device is modeled in 2 stages,

• Three Phase Inverter Stage - To convert DC power to AC

• DC/DC Stage - To maintain the DC bus voltage at the inverter’s input. This stage interfaces

the batteries with the inverter stage.

2.1.2 Three Phase Inverter Plant

A three phase inverter and it’s characteristics are studied in order to analyze a DC microgrid

connected to an AC load. The operating principle of the inverter can be explained as a switch

rapidly switched back and forth to allow current to flow. The body-diode/ anti-parallel diodes

connected in parallel with the switch provide a path for the inductive load current when the switch

is turned off. The alternation of the direction of current in the inductor produces AC current on

the output side. Thus power gets converted from AC to DC.

Additionally, an LCL filter is used to filter the waveform for the fundamental component of

the waveform to pass to the output while limiting the passage of the harmonic components. If the

inverter is designed to provide power at a fixed frequency, a resonant filter can be used. For an

adjustable frequency inverter, the filter must be tuned to a frequency that is above the maximum

fundamental frequency. [19] The circuit diagram for a three-phase voltage source inverter with an

LCL filter is shown in Fig. 2.2.

A three phase inverter system can be modeled as a system using state-space analysis. Since the

input side differs in the ground point from the output side, the potential difference between the

two ground points needs to be considered. Also, since the inverter terminals are delta-connected,

S_au

S_al

S_bu

S_bl

S_cu

S_cl

V

L_fa L_ca

Lfb Lcb

Lfc Lcc

C_faC_fbC_fc

Figure 2.2: Three Phase Inverter Circuit Diagram

Thus,

R∆= 3RY (2.1)

L∆= 3LY (2.2)

C∆= 1

3CY (2.3)

From the inductor Volt-Seconds balance,

L1 diL1

dt =VL1 =mVdc−Vcap (2.4)

L2diL2

dt =VL2 =Vcap−Vout (2.5)

From the capacitor-charge balance,

CdVcap

1. Steady-state analysis

Considering the DC components of above equations for computing steady-state values,

VL1 =DVDC−Vcap (2.7)

Since, volt-seconds of the inductor,L1 are balanced at steady-state,

VL1 = 0

D= Vcap

VDC

Similarly, balancing the volt-seconds of inductor,L2 at steady state,

VL2 =Vcap−Vout (2.8)

VL2 = 0

Vcap=Vout

Thus, duty cycle,

D= Vout

VDC

(2.9)

From the capacitor-charge balance at steady state,

Ic=IL1 −IL2 (2.10)

Ic= 0

Thus, at steady-state, the output voltage of the inverter is same as the voltage across the filter

capacitor. Similarly, from the above derived equations, the average current flowing through

the capacitor at steady-state is zero, thus the current through both the inductors is the same.

Given this, controlling the capacitor voltage, Vcap and the inductor current,IL1 ensures full

control over the inverter’s output voltage and current at steady-state.

2. Small-signal analysis

To analyze the dynamic performance of the inverter, small signal analysis is performed. This

analyzes the system for small perturbations in different variables that effect the system performance.

Thus, perturbing the variables in (2.4), (2.5) and (2.6) for small-signal analysis,

mVdc= ˆdVDC+ ˆVdcD+DVDC (2.11)

Vcap= ˆvcap+Vcap (2.12)

iL1 = ˆiL1+IL1 (2.13)

iL2 = ˆiL2+IL2 (2.14)

Vout= ˆvout+Vout (2.15)

Substituting these parameters in the inductor-voltage and capacitor-charge equations and

con-sidering only the AC-small signal components,

dˆiL1

dt = ( ˆdVDC−ˆvcap) 1 3L1

(2.16)

dˆiL2

dt = (ˆvcap−ˆvout) 1

3L2 (2.17)

dˆvcap

dt = (ˆiL1 −ˆiL2)

3

dq0 transformation

The phase quantities in abc/stationary reference frame are generally sinusoidal in nature. Thus the

conventional control methods designed for regulating DC quantities doesn’t work very well in this

setup. However, if the reference frame is rotated at the operating frequency, the positive sequence

phase quantities become constant. Transforming the control variables from abc/ stationary reference

frame to dq0 reference frame,

Xabc=T−1Xdq0 (2.19)

where, T = r 2 3      

cos(wt) cos(wt− 2π

3 ) cos(wt+ 2π

3 )

−sin(wt) −sin(wt−2π

3 ) −sin(wt+ 2π 3 ) 1 √ 2 1 √ 2 1 √ 2       Thus, TdT −1 dt T

−1 ₌

     

0 −w 0

w 0 0

0 0 0

     

Neglecting the zero-sequence components, from (2.16), (2.17) and (2.18):

dˆiL1_dq

dt =

1 3L1

( ˆddqVDC−vˆcapdq)−ˆiL1_dq 

 

0 −w

w 0





 (2.20)

dˆiL2_dq

dt =

1

3L2(ˆvcapdq −vˆoutdq)−ˆiL2_dq 

 

0 −w

w 0





 (2.21)

dvˆcapdq

dt =

3

C(ˆiL1_dq −ˆiL2_dq)−vˆcapdq



 

0 −w

w 0





 (2.22)

vcapd,vcapq is, d dt                

ˆ_iL

1_d

ˆ_iL

1q

ˆ_iL

2_d

ˆ_iL

2q

ˆ vcapd

ˆ vcapq

                =                

0 −w 0 0 ₃−_L1

1 0

w 0 0 0 0 ₃−_L1

1

0 0 0 −w _3L1

2 0

0 0 w 0 0 _3L1

2

3

C 0

−3

C 0 0 −w

0 _C3 0 0 −w

                               

ˆ_iL

1_d

ˆ_iL

1q

ˆ_iL

2_d

ˆ_iL

2q

ˆ vcapd

ˆ vcapq

                +                 VDC

3L1 0

0 VDC

3L1

0 0 0 0 0 0 0 0                    dd dq   +                 0 0 0 0 −1 3L2 0

0 ₃−_L1

2 0 0 0 0                   

voutd

voutq



 

This is of the form, ˙x = Ax+Bu. Thus, the control inputs of the six-state system are the d

and q parameters of the duty cycle, i.e., dd and dq.

From this, we can derive the transfer functions of any of the control states with respect to the

control inputs depending on the requirement of the controller.

Controller Design - Dual Loop Control

Two control schemes of the DER unit can be characterized into two types, namely,

• Current Controlled Method (CCM)

• Voltage Controlled Method (VCM)

While CCM has the advantage of superior harmonic compensation performance, using this

strategy leads to difficulties when DER units switch to autonomous islanding operation. On the

other hand, VCM has been considered as an attractive solution for dual-mode (grid-connected mode

and islanded mode) microgrid applications.

Voltage and current regulators are used in voltage-source inverters to control the output current

and/or voltage. There are many types of regulators, and different types of regulators are applied in

different reference frames. The most common are synchronous frame proportional-integral(PI)

have been developed such as predictive deadbeat, hysteresis, and sliding mode [13, 28, 29]. Since

this thesis focuses on balanced operating conditions, only synchronous frame PI control has been

implemented [1].

1. Controller Types

(a) Synchronous Frame PI controller

A PI (Proportional-Integral) controller consists of a proportional and integral term, and

is capable of eliminating steady state error at dc. The transfer function for a PI controller,

G(s) and discretized version G(z) at a (Ts = 100×10−6) sampling period, is given in

(2.23).

G(s) =Kp+

Ki

s & G(z) =

zKp,z+Ki,z

z−1 (2.23)

PI controllers have been applied for voltage and current regulation in the natural abc

frame or stationaryαβ frame, but are generally considered unsatisfactory because of the

significant steady state error due to the PI controller’s finite gain at non-zero frequencies

[20].

PI regulators have infinite gain at dc, and thus can be used to track reference sinusoids

with zero steady state error in the synchronous dq frame. However, components which

are not rotating at the synchronous frequency, such as negative sequence or harmonics,

are not dc in the synchronous frame. Since PI regulators have significant steady state

er-ror at non-zero frequencies, modifications are necessary if negative sequence or harmonic

components need to be controlled. One way of doing it is to have multiple dq

transforma-tions rotating at the frequencies of interest, i.e., (n−1)ωfor positive sequence harmonics,

(n+ 1)ω for negative sequence harmonics, 2ω for negative sequence fundamental, and

nωfor zero sequence harmonics. Alternatively, proportional-integral-resonant controllers

may be used.

similar to a synchronous PI controller transformed into the stationary frame [20]. The

transfer function for a non-ideal PR regulator is given in (2.24).

G(s) =Kp+Kr

2ωcs

s2_{+ 2ω}

cs+ω20

(2.24)

The PR controller has infinite gain at the controller resonant frequency, ω, and thus

can be used to track a reference sinusoid in the stationary frame with zero steady state

error [20]. In practical applications, the infinite gain at the resonant frequency can lead

to numerical stability problems, and so a damped version of the resonant controller can

be used that has a large, finite gain at the resonant frequency [20].

2. Dual Loop Control

(a) Voltage Control Loop

DQ PI control is also commonly used for voltage control of inverters. A typical

imple-mentation of dq voltage control is shown in Fig. 2.3. The control in Fig. 2.3 is composed

of an outer voltage loop and an inner current loop, and is referred to as multi-loop

volt-age control. The voltvolt-age control also includes virtual impedance, where the voltvolt-age drop

across a virtual impedance is subtracted from the voltage reference. Virtual impedance

is discussed in more detail in Ch 4.

(b) Current Control Loop

DQ PI control is commonly used for current control in inverters. A typical

implemen-tation of dq0 current control is shown in Fig. 2.3, which includes output voltage

feed-forward and decoupling terms. Thedq0 frame aligns the q-axis with the grid voltage by

converting the grid voltage todq0, driving the d-axis voltage to zero with a PI controller,

and feeding the integral of the PI output back as the dq0 transformation angle.

By feeding-forward the output voltage and the inductor voltage drop coupling term,

the current controller can be made into a single-input-single-output transfer function,

Sau

Sal

Sbu

Sbl

Scu

Scl Vdc

L1a L2a

L1b L2b

L1c L2c

Ca CbCc

Figure 2.3: Three Phase Inverter Controller Block Diagram

and decoupling terms commonly used indq0 current control have been implemented in

this control as well.

The inverter control parameters have been adapted from a Three phase, 100kW Schneider

inverter available off the shelf.

Table 2.1: Three Phase Inverter-Model Parameters

Parameter Value

Inverter-side filter inductor (L1) 750µH

Filter capacitor (C) 70µF

Grid-side filter inductor (L2) 1.7mH

Voltage Controller (kpv,Z) 0.17

Voltage Controller (kiv,Z) -0.158

Current Controller (kpi,Z) 2.5

Current Controller (kii,Z) -2.46

Frequency Droop Gain (mp) -1/100000

3. PWM Modulation Scheme

Space Vector PWM Modulation have been used to increase the output voltage range of the

converter for a given input [21].

PWM Comparison

Duty Cycle -1.0

-0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

Time (s)

1.988 1.992 1.996 2.000 2.004 2.008 2.012 2.016

D

u

ty

(

d

) 0

0

0

Reference Signal Sa Sb Sc

Duty_a Duty_b Duty_c

Figure 2.4: PWM Switching Sequence

Simulation Results

Implementing the switching model in PLECS, the inverter is observed to be stable and dual

loop-voltage control is implemented to control the inverter output loop-voltage of each phase to be same as

the grid phase voltage., i.e., 277√2 in dq0 reference frame.

Since the inverter is rated for 100kW, simulation results for the corresponding current through

Standalone Inverter_Vout

time (s)

1.304 1.306 1.308 1.310 1.312 1.314 1.316 1.318 1.320 1.322 1.324 1.326 1.328 1.330

V o lt ag e (V ) -400 -350 -300 -250 -200 -150 -100 -50 0 50 100 150 200 250 300 350 400 _{Vinv_a} Vinv_b Vinv_c

Figure 2.5: 3-Phase Inverter Output Voltage Waveforms

StandaloneInverter_Iout

time (s)

1.080 1.082 1.084 1.086 1.088 1.090 1.092 1.094 1.096 1.098 1.100 1.102 1.104 1.106

C u rr en t (A ) -200 -180 -160 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 120 140 160 180 200 _{Iinv_a} Iinv_b Iinv_c

Standalone Inverter_Vout

time (s)

1.990 1.995 2.000 2.005 2.010 2.015 2.020 2.025 2.030

V o lt ag e (V ) -400 -350 -300 -250 -200 -150 -100 -50 0 50 100 150 200 250 300 350 400 _{Vinv_a} Vinv_b Vinv_c

Figure 2.7: Three Phase Inverter Voltage Waveform during Load Change

StandaloneInverter_Iout

time (s)

1.990 1.995 2.000 2.005 2.010 2.015 2.020 2.025 2.030 2.035

C u rr en t (A ) -200 -180 -160 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 120 140 160 180 200 _{Iinv_a} Iinv_b Iinv_c

To check the controller bandwidth, the inverter’s response to a step change in load from 50kW

to 100kW can be seen in Fig. 2.7 and Fig. 2.8 and the results show that the controller bandwidth

is high-enough.

2.1.3 DC/DC Stage - Modeling

Distributed Energy Storage Devices(DESDs) are a very vital part of any kind of microgrids. During

an outage from the utility, the battery based energy storage device acts as a slack bus in the

microgrid and thus maintains the DC bus voltage in the system. Thus in a DC-DESD, the battery

bus is interfaced with a current controlled DC-DC converter.

S

V

_dc

Load

D

L

C

V

_dc

Figure 2.9: Boost Converter circuit diagram

The interfacing circuit between the battery and the DC-port of the 3-phase AC Storage Device

is basically a boost converterto step up the voltage level as required, the same is shown in Fig. 2.9.

To derive the transfer function of the converter,

1. Steady-state analysis

At steady-state, the volt-seconds of the inductor should be balanced and the charge balance

During ON State,

V

_dc

Load

L

C

V

₀

I_s

Figure 2.10: Boost Converter - ON State

VL=L

diL

dt =Vbatt (2.25)

ic=C

dvcap

dt =−

Vcap

R (2.26)

During OFF State,

V

_dc

Load

L

C

V

_dc

Figure 2.11: Boost Converter - OFF State

VL=L

diL

dt =Vbatt−Vcap (2.27)

ic=C

dvcap

dt =IL−

Vcap

At steady state, for inductor Volt-Seconds (V.s) balance, LdiL

dt = 0

Thus,

D(Vbatt) + (1−D)(Vbatt−Vcap) = 0 (2.29)

This implies that,

Vcap=

Vbatt

1−D (2.30)

At steady-state, for capacitor-charge (q.C) balance, Cdvcap

dt = 0

Thus,

D(Vcap

R ) + (1−D)(IL− Vcap

R ) = 0 (2.31)

This implies that,

IL=

Vcap

(1−D)R (2.32)

2. Small-signal analysis

Perturbing a small value for each time varying parameter:

˜

vL=VL+L

dˆiL

dt (2.33)

˜_ic=Ic+Ldˆvcap

dt (2.34)

˜

vbatt =Vbatt+ ˆvbatt (2.35)

˜

vcap=Vcap+ ˆvcap (2.36)

˜

d=D+ ˆd (2.37)

˜

The small signal analysis can be performed as follows: From volt-seconds balance:

˜

vL= ˜vbattd˜+ (˜vbatt−˜vcap) ˜d 0

(2.39)

cz Considering only the transient AC components,

LdˆiL

dt = ˆvbatt+Vcap ˆ

d−ˆvcapD 0

(2.40)

In Laplace domain,

sLˆiL(s) + ˆvcap(s)D 0

= ˆvbatt(s) +Vcapdˆ(s) (2.41)

From capacitor-charge balance:

˜_ic=−v˜cap

R d˜+ (˜iL− ˜ vcap

R ) ˜d

0

(2.42)

Considering only the transient AC components,

Cdvˆcap

dt =−

ˆ vcap

R +Vcapdˆ−ILdˆ+ ˆiLD

0

(2.43)

In Laplace domain,

(sC+ 1

R)ˆvcap(s) = (1−D)ˆiL(s)−IL ˆ

d(s) (2.44)

From (2.41) and (2.44); defining the system in matrix form,



 

sL D0

D0 −(sC+_R1)

     

ˆ_iL(s)

ˆ vcap(s)

   =    Vcap IL    ˆ

d(s) +

   1 0  

vˆbatt(s)

Thus, the transfer function of the inductor current with respect to the duty variable can be

Gid =

ˆ_iL(s) ˆ d(s) =

(cVcap)s+ 2D 0

IL

LCs2₊L

Rs+ (D

0

)2 (2.45)

Transfer function of output voltage with respect to the inductor current can be derived as,

Gvi =

ˆ vcap(s)

ˆ_iL(s) =

D0Vcap−(LIL)s

(CVcap)s+ 2D 0

IL

(2.46)

Transfer function of the output voltage with respect to the duty cycle can be derived as,

Gvd =

ˆ vcap(s)

ˆ

d(s) =

D0Vcap−(LIL)s

LCs2₊ L

Rs+ (D

0

)2 (2.47)

Four switches have been used in the designed energy storage system along with the source

in-ductor split into two halves that make the system an ”Interleaved Bi-directional DC-DC converter”

as shown in Fig. 2.12

Vbatt

S

audc

S

aldc

S

budc

S

bldc

L adc

L bdc

Controller Design - Dual Loop Control

A boost converter can be controlled for it’s output capacitor voltage or it’s input inductor current.

Dual loop control is implemented for the current application, the outer voltage loop would maintain

the DC bus in the DESD at 400V and the inner interleaved current loops will maintain the current

through each inductor in each leg of the DESD depending on the load requirement.

1. Current Loop

Thus, considering (2.46) for the transfer function of inductor current to voltage, and since

all parameters are DC, using a PI controller should help control the current in a current

controlled boost converter.

The transfer function of the PI controller can be realized as,

Gci=Kpi+

Kii

s (2.48)

Magnitude (dB)

-20 -10 0 10 20 30 40 50 60

100 101 102 103 104 105

Phase (

deg)

-135 -90 -45 0 45 90

Current Controller Bandwidth (DC DESD) Gm = Inf , Pm = 85 deg (at 1.45e+04 rad/s)

Frequency (rad/s)

So the loop gain can be realized as,

GLGi =GidGci (2.49)

From MATLAB, the values of Kp and Ki can be derived and the bode plot of the loop gain

GLGi is as shown in Fig. 2.13,

2. Voltage Loop

A PI controller is used to control theDC bus voltage. Since the DESD is bi-directional, the controller bandwidth is modeled such that it can operate both in buck and boost mode at

the commanded DC bus voltage. The voltage loop bandwidth can be seen from the bode-plot

of the loopgain GLGv below,

Gcv =Kpv+

Kiv

s (2.50)

Magnitude (dB)

-100 -80 -60 -40 -20 0 20 40 60 80 100

100 101 102 103 104 105 106 107

Phase (

deg)

90 135 180 225 270 315

Voltage Controller Bandwidth (DC DESD)

Gm = 39.6 dB (at 6.38e+04 rad/s) , Pm = 91.8 deg (at 2.95e+03 rad/s)

Frequency (rad/s)

Since this is the outer loop to the current controller loop, the voltage controller loop gain would

be as follows and the bode-plot to show the voltage-controller bandwidth can be observed in

Fig. 2.14

GLGv = (

GLGi

1 +GLGi

Gvi)Gcv (2.51)

Vbatt

S

audc

S

aldc

S

budc

S

bldc L_adc

L_bdc

Figure 2.15: DC-DESD control loop simulation block diagram

Simulation Results

Bipolar modulation is used for the Pulse Width Modulation (PWM) to generate the gate

pulses to all four switches. Due to the interleaved design, the triangular waves used for the

modulation in each interleaved controller leg are aligned 180◦ apart as shown in Fig. 2.15

For a load change from 1.25kW to 5kW, using the controller parameters defined in Table.

2.2, the inductor currents on the input side for the interleaved operation can be observed to

Inductor Currents

Time (s)

1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75

C u rr en t (A ) 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 Ind. Current_a Ind. Current_b Inductor Currents Time (s)

1.568014 1.568018 1.568022 1.568026 1.568030 1.568034 1.568038 1.568042 1.568046

C u r r e n t ( A ) 16.5 17.0 17.5 18.0 18.5 19.0 19.5 20.0 20.5 21.0 21.5 22.0 22.5 23.0 23.5 24.0 24.5 25.0

25.5 Ind. Current_a

Ind. Current_b

Figure 2.16: DC DESD inductor current waveforms: (a)Step response of inductor currents, (b)DC-DESD inductor current ripple in each interleaved phase

The inductor current ripple on the input side is shown in Fig. 2.16, The peak-to-peak ripple

of each inductor is around 9A at full-load, i.e., around 40% of full-load average current in

each inductor.

Source Current (I_batt)

Time (s)

2.509480 2.509490 2.509500 2.509510 2.509520 2.509530

C ur re nt ( A ) 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54

55 Source current

Figure 2.17: DC DESD battery current ripple

Table 2.2: Interleaved DC/DC Boost Converter-Model Parameters

Parameter Value

Battery-side inductor (L1 and L2) 120µH

Battery-side capacitor (Cbatt) 22µF

DC bus-side capacitor (CDC) 60µH

Voltage Controller (kpv) 0.6299

Voltage Controller (kiv) 70.8

Current Controller (kpi) 4.054×10−3

Current Controller (kii) 6.6856

profile of the batteries. The peak-to-peak current ripple here is around 3A at full-load, i.e.,

around 7% of full-load current. Thus, the current is much smoother here providing a much

better charging and discharging transient, Fig. 2.17 shows the simulation result for the same.

2.1.4 Battery Interface

There are basically three types of battery models reported in the literature, specifically:

experi-mental, electrochemical and electric circuit-based. Experimental and electrochemical models are

not well suited to represent cell dynamics for the purpose of state-of-charge (SOC) estimations of

battery packs [22]. Electric circuit-based models can be useful to represent electrical characteristics

of batteries. The most simple electric model consists of an ideal voltage source in series with an

internal resistance. The open circuit voltageVOC gives the voltage across the ideal battery, whereas

the voltage across the ideal battery and resistance Rb gives the terminal voltage of the batteryVb.

The true internal resistance of the battery is highly related to the State-Of-Charge (SOC) and

the electrolyte concentration of the battery bank. To take recognition of the role of the state of

charge, this battery model varies the resistance of the battery, i.e. Rb is a function of the state of

charge (SOC). This model assumes the same characteristics for the charge and the discharge cycles.

The open voltage source is calculated with a non-linear equation based on the actual SOC of the

battery [5]. The controlled voltage source is described by,

VOC =VOC0−K

Q

Q−R

idt +Ae

−BR

VOC=f(Ibatt,t)

Internal Resistance

Rb

Ibatt

VOC _Controlled

Voltage Science

Vbatt

Figure 2.18: Battery Model Circuit Diagram [5]

Vbatt=VOC −RbIbatt (2.53)

whereVOC is the no load battery voltage (V),Kis the polarization voltage (V),Qis the battery

capacity (Ah), A is the exponential zone amplitude (V), B is the exponential zone time constant

inverse (Ah−1), Vbatt is the battery voltage (V), Rb is the battery internal resistance (Ω), Ibatt is

the battery current (A), and R

idt is the charge supplied and drawn by the battery (Ah).

The model has a non-linear term equal to K_Q−QR

idt. This term represents a non-linear voltage

that changes with the amplitude of the current and the actual charge of the battery. So when the

battery is almost completely discharged and no current is flowing, the battery voltage increases

to nearly E0. As soon as a current circulates again, the voltage falls abruptly. This behaviour is representative of a real battery.

2.2

Inverter based Distributed Generator Emulation

Most of the DC distributed sources connecting to a three-phase AC line would need a similar power

electronic interface with a three-phase inverter in cascade. Thus, more DERs can be emulated in

the current system at test by connecting more such inverters in parallel. Thus, the overall system

lot of research is going on in this regard [23, 24, 25, 26] but that is beyond the scope of this thesis.

2.3

Synchronous Generator Model

Synchronous machines are AC machines that have a field circuit supplied by an external DC source.

In a synchronous generator, a DC current is applied to the rotor winding producing a rotor magnetic

field. The rotor is then turned by external means producing a rotating magnetic field, which induces

a 3-phase voltage within the stator winding. Field windings on rotor produce the main magnetic

field and the voltage is induced in the armature windings of stator.

The rotor of a synchronous machine is a large electromagnet. The magnetic poles can be either

salient or non-salient construction.

2.3.1 Modeling

By definition, in synchronous generators, the frequency of the electricity produced by synchronous

generators is synchronized with the mechanical rotational speed.

For a 4-pole machine, since the electrical frequency for the system is 60Hz, the synchronous

speed of the generator can be calculated as,

Nm=

120∗fe

p (2.54)

Thus, the synchronous speed of the machine is 1800rpm.

2.3.2 Control

This research is focused on residential microgrids and thus, the synchronous generators under

con-sideration are in the range of hundreds of kW. Thus the controller is mainly based on modern

electronic governor and automatic voltage regulator (AVR) control systems used for internal

com-bustion engine driven generators. The basic control diagram for a synchronous generator is as

Figure 2.19: Synchronous Generator Block Diagram, Adapted from [1]

1. Governor

The governor measures the shaft speed and adjusts the engine throttle position to regulate the

speed to the desired set point. Following figure shows the basic model for the diesel engine and

governor. The reference speed command comes from the corresponding real-power command

through the power sharing loop using a P-f droop curve or from an automatic generator

control (AGC). The simplified governor control is emulated through a PID control, and the

diesel engine is modeled as an actuator time constant and time delay [1]. The output of the

PID controller sets the torque command on the generator mechanical shaft.

The available synchronous generator model in PLECS library is used with the parameters

in Table. 2.4. For a 100kVA standalone synchronous generator with an RC load, since the

frequency is maintained at the nominal value (the P-f droop curve is defined as the same for

the inverter), the speed of the machine is always maintained at 1800rpm.

Fig. 2.21 shows the controller response to a load change from 50kW to 100kW. It can be

w

w

PI

control

1

1+sT

e

T

T

w

1

B+sH

Figure 2.20: Governor Control Circuit Block Diagram

P_offset from nominal (100kW)

Frequency Reference- From Droop curve (f_ref)

Speed Reference (w_ref)

Measured Speed (w_mea) × 1e5 P o w er ( W ) -1.0 -0.5 0.0 F re q u en c… 60.0 60.5 61.0 S p ee d ( rp m ) 1800 1810 1820 1830 Time (s)

0 2 4 6 8 10 12 14 16 18

S p ee d ( rp m ) 0 1000 2000 P_error f_ref w_ref w_mea

is maintained at the corresponding frequencies according to the Active Power-Frequency droop

curve.

2. Automatic Voltage Regulator (AVR)

The DC excitation system for the synchronous generator that controls the terminal voltage

comprises of an Automatic Voltage Regulator (AVR) and a brushless exciter. The AVR gets

a reference command for terminal voltage through a power-system stabilizer or a Q-V droop

curve with respect to voltage. Using a simplified PID control to emulate the modern digital

AVRs [1], the exciter is supplied to, through a power amplifier. The simplified brushless exciter

here is emulated using a simple first order-transfer function with a time constant,TE and an

exciter gain,KE.

V

V

PID

control

1

1+sT

Amplifier

1

sT

K

S

Figure 2.22: AVR Control Circuit Block Diagram

For the generator parameters shown in Table. 2.4, Fig. 2.23 shows the controller response to a

load change from 50kW to 100kW. It can be observed that the transient during the dynamic

load change is small and the generator’s terminal voltage is maintained at the corresponding

value according to the Reactive Power-Voltage droop curve. The nominal voltage i.e., 240VL−L

From the figure above, the reactive power of 4kVA generated in the system is due to the

capacitive load and since the slope of the droop curve is very small, the deviation in the terminal

voltage from nominal value is very low. Thus, the generator can maintain the terminal voltage close

to 240VL−Lat any load condition.

From Table. 2.3, the PID controller gains in the governor for the 100kVA generator in the current

application are chosen such that the commanded power sharing is met at the corresponding rotor

speed. Similarly, to maintain the terminal voltage, proper gains in AVR are chosen corresponding

to the reactive power sharing. These controller gains are adapted from [1].

Table 2.3: 100kVA Synchronous Generator-Controller Parameters [1]

Parameter Value

AVR (kp) 1.62

AVR (ki) 10.4

AVR (kd) 0.05

AVR (Td) 0.1

AVR (TE) 0.01

AVR (KE) 1

AVR (SE) 0

Governor (kp) 7

Governor (ki) 57

Governor (kd) 0

Governor (Td) 0

Engine (T1) 0 s

Engine (T2) 0 s

The initial transient in the voltage and speed waveforms is due to the generator’s inertia. The

steady-state response of the generator terminal voltage and the generator phase currents as load

increases from 50kW to 100kW is shown in Fig. 2.24, The amplitude of generator phase currents

Q_offset from nominal (0kVA)

Terminal Voltage Reference- From Droop curve (Vt_ref)

Measured Terminal Voltage (Vt_mea)

Applied Field voltage (Vf)

P o w er ( V A ) -8000 -6000 -4000 -2000 0 V o lt ag e (V ) 138.56 138.57 138.58 138.59 V o lt ag e (V ) 0 100 200 Time (s)

0 2 4 6 8 10 12 14 16 18

V o lt ag e (V ) 0 200 400 600 Q_error Vt_ref Vt_mea Vf

Figure 2.23: AVR following the Voltage Reference and applying the corresponding Vf

Generator Terminal Voltage (Vt)

Time (s)

9.635 9.640 9.645 9.650 9.655 9.660 9.665 9.670 9.675 9.680 9.685 9.690 9.695 9.700

V o lt a g e ( V ) -340 -320 -300 -280 -260 -240 -220 -200 -180 -160 -140 -120 -100-80 -60 -40 -200 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 V_terminal

Phasor Currents_Sync Gen (I_abc)

Time (s)

9.650 9.654 9.658 9.662 9.666 9.670 9.674 9.678 9.682 9.686

C u r r e n t ( A ) -340 -320 -300 -280 -260 -240 -220 -200 -180 -160 -140 -120 -100-80 -60 -40 -200 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 Ia_SG Ib_SG Ic_SG

Table 2.4: 100kVA Synchronous Generator-Model Parameters

Parameter Value

Stator Resistance (Rs) 0.0166Ω

Stator Leakage Inductance (Lls) 148.014µH

Unsat. Magn. Inductance-d (Lmd0) 2.922mH Unsat. Magn. Inductance-q (Lmq0) 1.382mH Saturated Magn. Inductance-d (Lmdsat) 2mH

Saturated Magn. Inductance-d (Lmqsat) 2.922mH

Saturating Magnetizing flux (PsiT) 1

Field Resistance (R0_f) 1.3Ω Field Leakage Inductance (L0_lf) 124.247µH

Damper resistance-d (R0_kd) 0.00237Ω

Damper resistance-q (R0_kq) 0.0025Ω

Damper leakage inductance-d (L0_lkd) 140.322µH Damper leakage inductance-q (L0_lkq) 179.315µH

Inertia (J) 0.1

Friction Co-efficient (F) 0

Number of pole-pairs (p) 2

2.3.3 Permanent Magnet SG Vs. Wound Field SG

In a Permanent Magnet Synchronous Generator (PMSG), the reactive power cannot be controlled

since the rotor is a permanent magnet and thus, no external DC field excitation is required. Since

the terminal voltage of the generator cannot be regulated in a PMSG, the fault response we see in

this case might not justify the system stability in terms of fault-tolerance. But in a full Synchronous

generator, the real and reactive power are always controlled and thus, the actual power sharing

and impacts on each of the sources can be seen well. Thus, for the current purpose of testing fault

Chapter 3

Component Interactions in

Three-Phase Microgrids

After modeling all the three different types of DERs in Ch 2, they are interconnected and connected

to the superimposed power grid with loads, to study the interactions between them. Any component

may be connected and fed directly into any other component. The energy of the battery storage can

be fed to both the load and the host network, and from the superimposed grid, in turn, the charging

of the storage is possible. Furthermore, the load can be fed directly from the host network. From

this general fully-interconnected model, a specific model can be derived, required for the simulation

of the real microgrid. It is also necessary to incorporate technical or regulatory constraints that

may limit the flow of energy.

3.1

System at Test

The system under consideration in this thesis is a simplified inverter and generator based microgrid

model (Fig. 3.1) to demonstrate the interactions between each other when connected. The impact

on overall system stability is also discussed to an extent when multiple generators are tied together.

this work is as follows,

SG IM Drive

Load 277V 3ph Grid

Diesel Engine Emulator

Sync Gen.

240V 3ph

Figure 3.1: Microgrid System under test

3.2

Paralleled Inverter System

The growing penetration of power-electronic-based renewable energy sources into the modern power

system, such as solar and wind energy, efficiently reduces the total consumption of the fossil fuels.

Thus, renewable energy power plants are becoming a main conversion scheme to accomplish the

green and clean electricity generation. For these applications, grid-tied inverters are extensively

employed as flexible and efficient grid interfaces to connect the renewables to the grid [27]

Inverters connecting DC power supplies to AC systems occur in numerous applications.

Pho-tovoltaic power plants and battery storage installations are examples of such applications. Since

many such distributed generators needs to be tied together with an inverter interface in a real-world

implementation of microgrids, the stability and control of paralleled inverters become a crucial case

3.2.1 Operation

Although inverter topologies used for power transmission have traditionally been current sourced, in

recent years, voltage source inverters (VSI) have been increasingly used for high-power applications

like electric traction and mill drives, PV power systems and battery storage systems. Control scheme

for VSI used in this research have been explained in detail in Ch 3.

Figure 3.2: Parallel voltage sources concept illustration, Adapted from [6]

It is well known that stable operation of a power system needs good control of the real power

flow, P and the reactive power flow, Q. Thus, when multiple sources are tied together in a microgrid,

power sharing between the sources is of high-priority. Traditionally, the communication link between

all the inverters connected together sends the corresponding power dispatch command to each

inverter to maintain the load. Recent advancements in control of Uninterrupted Power supply (UPS)

systems make possible, their independent parallel operation, avoiding communication links between

the units. The advantages of such power configuration include high reliability and no restriction on

the physical location of the UPS units [28]. To achieve this special kind of parallel operation, the

droop method is often adopted. The droop method is based on a well-known concept in large-scale

power systems that consists of drooping the frequency of the ac-generator when its output power

increases. Control of a distributed system without communication can only be achieved at the price

of permitting a small error. The small droop is generally considered acceptable as long as the error

Usually, the inverter output impedance is assumed to be inductive due to both the high-inductive

component of the line-impedance and the large inductor of the output filter [6]. Based on this

as-sumption, the relation between real and reactive power to frequency and output voltage magnitude

respectively, can be determined as follows,

P = U1

R2_+X2[R(U1−U2cosδ) +XU2sinδ] (3.1)

Q= U1

R2_+X2[−RU2sinδ+X(U1−U2cosδ)] (3.2)

So for overhead lines, sinceX R,Rcan be neglected. Assuming the power angleδto be small,

sinδ =δ and cosδ= 1.

Thus, above equations become,

P ∼= U1U2

X δ (3.3)

Q∼= U1(U1−U2)

X (3.4)

Thus, for an inductive system, the power angle depends predominantly on P, whereas the

voltage difference depends predominantly on Q.

Real Power

Frequency

Reactive Power

V

oltage

Q_min Q0 Qmax

Vmax

V_min

V0 mq

P_min P₀ Pmax

f_max

fmin

f0 mp

Thus, the frequency and voltage droop curve for the inverter can be determined as,

f−f0=−kp(P −P0) (3.5)

U1−U0 =−kq(Q−Q0) (3.6)

f0 and U0 are rated frequency and grid voltage respectively, and P0 and Q0 are the momentary

set points for active and reactive power of the inverter. The frequency and voltage droop control

characteristics are shown graphically in Fig. 3.3

Inverter Voltages (Paralleled)

Time (s)

1.108 1.110 1.112 1.114 1.116 1.118 1.120 1.122 1.124 1.126 1.128 1.130 1.132 1.134

V

o

lt

ag

e

(V

)

-280 -260 -240 -220 -200 -180 -160 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280

I II

Vinv1_a Vinv1_b Vinv1_c Vinv2_a Vinv2_b Vinv2_c

Figure 3.4: Three Phase paralelled inverter voltages at PCC

Droop control loop gives the system frequency reference from the generated real power (P) and

the inverter output voltage magnitude from the reactive power (Q) generated in the system. When

droop control is included to generate the voltage reference to the inverter controller, the power

sharing can be observed depending on the corresponding droop curves. To prove the concept, the