CONTROL OF DISTRIBUTED GENERATION FOR GRID-CONNECTED AND
INTENTIONAL ISLANDING OPERATIONS

By

Irvin Joel Balaguer Álvarez

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Electrical Engineering

2011

ABSTRACT

CONTROL OF DISTRIBUTED GENERATION FOR GRID-CONNECTED AND
INTENTIONAL ISLANDING OPERATIONS

By

Irvin Joel Balaguer Álvarez

The current model for electricity generation and distribution in the United States is
dominated by centralized power plants. The power at these plants is typically combustion (coal,
oil, and natural) or nuclear generated. Centralized power models, like this, require distribution
from the center to outlying consumers. This system of centralized power plants has many
disadvantages. Electric utilities are becoming more and more stressed since existing transmission
and distribution systems are facing their operating constraints with growing load. Greenhouse
gas emissions have resulted in a call for cleaner renewable power sources. Under such
circumstances, distributed generation (DG) with alternative sources; such as fuel-cell, windturbine, bio-mass, micro-turbine and solar-cell systems; has been considered as a promising
solution to the above problems.
DG is defined as small, modular electricity generators located close to the end customer's
load connection point. DGs can enable utilities to decrease investment costs in transmission and
distribution system upgrades while still meeting increasing power demands. Also, DGs provide
customers with improved quality and reliability of energy supplies without imposing undesirable
effects on environment. In general, DG can be intended as small sized power plants that are
designed to be installed and operated within a local load center.

This research presents the development and test of a control strategy for DG capable of
working in both intentional islanding (stand-alone) and grid-connected modes. In the gridconnected mode of operation, the DG is connected to the utility. The utility, which is assumed to
be stiff, sets the voltage at the terminal of the DG inverter. The inverter controls the power being
injected into the grid by controlling the injected current. Thus, in this mode, the inverter operates
in the current control mode. In the stand-alone mode, the inverter supplies power to the load. It
has to maintain the voltage at the terminals of the load, irrespective of any changes in the load.
Thus, in this mode, the inverter operates in the voltage controlled mode.
The stand-alone control features an output voltage controller capable of handling deficit of
generated power (load shedding) and synchronization for grid reconnection with a seamless
transition from stand-alone to grid-connected operation modes. The grid-connected mode with
current control is also enabled for the case of power grid connection. This grid-connected control
features an output current controller capable of loss of main detection, synchronization with the
grid, and seamless transition from grid-connected to stand-alone operation modes with minimum
interruption to the load.
The operational principle and control method of the proposed system are explained in detail.
A 10kW DG inverter has been designed, built and set up for testing. Simulation and
experimental results are provided in order to verify the validity of the developed DG system.

To the only wise God our Savior, be glory and majesty, dominion and power, both now and ever.
Amen. (Jude 1:25 King James Version)

To my wife Raquel, my son Kevin, and my daughters Kelly and Kiara, for their patience,
unconditional love, and support.

iv

ACKNOWLEDGMENTS

First and foremost I would like to thank God for giving me the drive, ability and patience to
strive for the completion of this dissertation.
I am forever grateful to Dr. Fang Z. Peng for providing me the opportunity to work with him
and for his kind words of advice, guidance and encouragement throughout my stay at Michigan
State University.
I would also like to thank Dr. Robert Schlueter, Dr. Elias Strangas, and Dr. Robert Ofoli for
agreeing to be members of my doctoral guidance committee, for their invaluable comments and
time.
I extend a special thank you to Dr. Percy Pierre and Dr. Barbara O‟Kelly of the Sloan
Engineering Program in MSU's College of Engineering and to Professor Aníbal Romney,
Chairperson of the Department of Electronics Engineering Technology of the University of
Puerto Rico-Aguadilla Campus, for the generous financial support without which this work
would not have been possible.
I deeply appreciate the continued support, cooperation, and valuable discussions that I
engaged in with the Power Electronics and Motor Drives Laboratory colleagues who I was
involved with: Dr. Eduardo Ortiz, Dr. Lihua Chen, Dr. Miaosen Shen, Dr. Haiping Xu, Dr.
Heung-Geun Kim, Dr. Nam-Sup Choi, Dr. Yuan Li, Dr. Honnyong Cha, Dr. Yi Huang, Miss Qin
Lei, Mr. Uthane Supatti, Mr. Shuitao Yang, Mr. Craig Rogers, Mr. Matthew Gebben, Mr. Jorge
Cintrόn, Mr. Dong Cao, Miss Xi Lu, Miss Wei Qian, Mr. Varun Chengalvala, Mr. Richard
Badin, Mr. Alan Joseph, Mr. Joel Anderson, and Mr. Carlos Niño. This long list is still not
complete and I apologize to those not listed as you all contributed to my experience in the lab.

v

A special thanks to Miss Qin Lei, Mr. Shuitao Yang, Mr. Jorge Cintrόn, and Mr. Uthane
Supatti for all their help with the hardware and experimental setups. To my proofreaders Mr.
Craig Rogers, Mr. Matthew Gebben, Mrs. Deana Hutchins, Mr. Erick Rivas, Mrs. Aurelia Rivas,
Mr. Jason Lounds, Mr. Alex Fitzpatrick, and Mrs. Deb Fitzpatrick, thanks all you very much.
I would also like to express my gratitude to Mrs. Sheryl Hulet, former graduate secretary and
Mrs. Meagan Kroll, the current graduate secretary at the Department of Electrical and Computer
Engineering at Michigan State University for their tremendous help with all the procedural paper
work throughout my time in the Ph.D. program.
From the bottom of my heart, I‟m most grateful to my parents, Mr. Ramón Balaguer and
Mrs. Carmen Rita Álvarez, and my brothers, Victor and José, for their unwavering support,
constant encouragement, and extraordinary understanding throughout my graduate studies. I‟m
equally grateful to my parents-in-law, Mr. Adalberto Lebrón, Mrs. Esther Salas, and my
brothers-in-law, Adalberto Jr. and Marcos, for their good wishes, and specifically, for their faith
in my abilities. I truly believe that this work could only have been brought to completion via the
blessings and good wishes from all of them.
A special thank you goes out to all of our extended family from the Lansing Seventh-day
Adventist Church, Greater Lansing Adventist School, Lansing Spanish Seventh-day Adventist
Church, and the University Seventh-day Adventist Church in East Lansing.
Finally, words cannot articulate the companionship and support provided to me by my lovely
wife, Raquel, my son Kevin and my two daughters, Kelly and Kiara. I would have left this work
long ago without their presence in my life. Obtaining a Ph.D. is a complex undertaking. At times
it is uncomfortable and challenging, and at others utterly rewarding. There have been many
peaks and troughs along the way. Raquel has been my pillar through them all. She has always

vi

been willing to make sacrifices in her life to accommodate my work schedule. I could not have
asked for more, and I genuinely thank her for the role she has played in making this endeavor a
success.

vii

TABLE OF CONTENTS

LIST OF FIGURES .......................................................................................................................x
CHAPTER 1. INTRODUCTION .................................................................................................1
1.1. The Distributed Generation Concept ....................................................................................1
1.2. Benefits associated with DG .................................................................................................3
1.3. Issues associated with DG ....................................................................................................5
1.4. Scope of the Dissertation ....................................................................................................11
1.5. Outline of the Dissertation ..................................................................................................12
CHAPTER 2. LITERATURE REVIEW ...................................................................................13
CHAPTER 3. SYSTEM DESCRIPTION ..................................................................................37
3.1. Circuit Topology .................................................................................................................37
3.2. Voltage Source Inverter ......................................................................................................38
3.3. LCL filter ............................................................................................................................41
3.3.1. Specifications for the design of LCL filter ..................................................................42
3.3.2. Design of L ................................................................................................................43
I
3.3.3. Design of C f ..............................................................................................................44
3.3.4. Design of L ...............................................................................................................44
g
3.4. Simulation and Experimental Set-ups .................................................................................45
3.4.1. Simulation Set-up.........................................................................................................45
3.4.2. Experimental Set-up.....................................................................................................46
CHAPTER 4. PROPOSED CONTROL FOR GRID-CONNECTED OPERATION OF DG49
4.1. Introduction .........................................................................................................................49
4.2. Circuit Topology .................................................................................................................49
4.3. Controller ............................................................................................................................50
4.3.1. Synchronization Controller for Grid Reconnection: Proposed Algorithm ..................52
4.4. Transfer Functions ..............................................................................................................54
4.5. Simulation Results ..............................................................................................................56
4.6. Experimental Results ..........................................................................................................60
CHAPTER 5. PROPOSED CONTROL FOR INTENTIONAL ISLANDING OPERATION
OF DG WITH SEAMLESS TRANSITION FROM GRID CONNECTED OPERATION .63
5.1. Introduction .........................................................................................................................63
5.2. Grid Condition Detection ....................................................................................................64
5.3. Intelligent Load Shedding ...................................................................................................68
5.4. Transition from Grid-connected to Stand-alone: Proposed Controller ...............................73
5.5. Transfer Functions ..............................................................................................................75
5.6. Simulation Results ..............................................................................................................77
viii

5.7. Experimental Results ..........................................................................................................82
CHAPTER 6. CONCLUSIONS AND FUTURE WORKS ......................................................86
6.1 Conclusions ..........................................................................................................................86
6.2 Future Works .......................................................................................................................87
APPENDICES ..............................................................................................................................89
Appendix 1. Transfer Functions of the current controlled inverter ...........................................90
Appendix 2. Derivation of the Load Shedding Equations .......................................................100
Appendix 3. Transfer Functions of the voltage controlled inverter .........................................104
Appendix 4. Block Diagram of the 2407A DSP Controller ....................................................109
REFERENCES ...........................................................................................................................110

ix

LIST OF FIGURES

Fig. 2. 1 Real power compensator with synchronization function ............................................... 15
Fig. 2. 2 Reactive power compensator with synchronization function ......................................... 15
Fig. 2. 3 Overview of proposed unified controller........................................................................ 15
Fig. 2. 4 System configuration for simulated and experimental results........................................ 16
Fig. 2. 5 Islanding Detection Flowchart........................................................................................ 17
Fig. 2. 6 Re-closure Flowchart ...................................................................................................... 19
Fig. 2. 7 Proposed islanding detection algorithm ......................................................................... 21
Fig. 2. 8 Flowchart of the control strategy implemented to produce intentional islanding .......... 22
Fig. 2. 9 Block diagram of voltage control ................................................................................... 24
Fig. 2. 10 Block diagram of voltage control with positive feedback ............................................ 24
Fig. 2. 11 Diagram of magnitude of voltage feedback in dq frame .............................................. 29
Fig. 2. 12 Diagram of frequency feedback in dq frame ................................................................ 29
Fig. 2. 13 Islanding-detection scheme .......................................................................................... 30
Fig. 2. 14 Re-closure scheme ........................................................................................................ 31
Fig. 2. 15 Flowchart diagram of the modes of the VSI................................................................. 32
Fig. 2. 16 Block diagram of the whole proposed controller using the synchronization control
loops .............................................................................................................................................. 32
Fig. 3. 1 Schematic diagram of the grid-connected inverter system ............................................. 37
Fig. 3. 2 Typical diagram of micro-source generation system ..................................................... 38
Fig. 3. 3 DC to Three-Phase AC Inverter Diagram ...................................................................... 39
Fig. 3. 4 PWM Operation of the Bridge........................................................................................ 41

x

Fig. 3. 5 LCL Filter configuration circuit ..................................................................................... 42
Fig. 3. 6 Simulated system ............................................................................................................ 46
Fig. 3. 7 Experimental set-up ........................................................................................................ 48
Fig. 4. 1 Schematic diagram of the grid-connected inverter system ............................................. 50
Fig. 4. 2 Block diagram of the current controller for grid-connected ........................................... 51
Fig. 4. 3 Synchronization controller ............................................................................................. 54
Fig. 4. 4 Block diagram of the current controlled inverter ........................................................... 54
Fig. 4. 5 LCL Filter and parallel RLC load................................................................................... 55
Fig. 4. 6 Current controller for grid-connected operation ............................................................. 57
Fig. 4. 7 Phase voltages and currents during grid-connected operation ....................................... 58
Fig. 4. 8 Synchronization for grid re-connection .......................................................................... 59
Fig. 4. 9 Phase voltage without (top) and with (bottom) synchronization .................................... 60
Fig. 4. 10 Line to line voltages and phase current during grid-connected operation .................... 61
Fig. 4. 11 Transition from stand-alone to grid connected operation ............................................. 62
Fig. 5. 1 Simulation waveforms of load voltages and grid currents during the grid disconnection
....................................................................................................................................................... 63
Fig. 5. 2 PLL structure .................................................................................................................. 65
Fig. 5. 3 Loss of Main Detection .................................................................................................. 66
Fig. 5. 4 Voltage or frequency change at grid disconnection ....................................................... 67
Fig. 5. 5 Islanding Detection Algorithm ....................................................................................... 67
Fig. 5. 6 Voltage Transients under various Active Power Differences ........................................ 69
Fig. 5. 7 Frequency Transients under various Reactive Power..................................................... 70
Fig. 5. 8 System to implement load shedding ............................................................................... 71
Fig. 5. 9 System in per unit to implement load shedding ............................................................. 71

xi

Fig. 5. 10 Voltage controlled inverter ........................................................................................... 74
Fig. 5. 11 Block diagram of the voltage controlled inverter ......................................................... 75
Fig. 5. 12 Simulated systems ........................................................................................................ 78
Fig. 5. 13 From grid-connected to stand-alone operation with severe transients ......................... 79
Fig. 5. 14 From grid-connected to stand-alone operation without severe transients .................... 79
Fig. 5. 15 From grid-connected to stand-alone operation without severe transients .................... 80
Fig. 5. 16 Phase voltage Va without load shedding algorithm...................................................... 81
Fig. 5. 17 Phase voltage Va with load shedding algorithm ........................................................... 81
Fig. 5. 18 Transition from grid-connected to stand-alone operation with severe transients ......... 82
Fig. 5. 19 Transition from grid-connected to intentional islanding operation without severe
transients ....................................................................................................................................... 83
Fig. 5. 20 Line to line voltages and phase currents during intentional islanding operation ......... 84
Fig. 5. 21 DG line to line voltages and phase currents during intentional islanding operation .... 84
Fig. 5. 22 Implementation of the load shedding algorithm ........................................................... 85
Fig. A1. 1 Block diagram of the current controlled inverter ........................................................ 90
Fig. A1. 2 LCL Filter and parallel RLC load ................................................................................ 91
Fig. A2. 1 System to implement load shedding .......................................................................... 100
Fig. A3. 1 Block diagram of the voltage controlled inverter ...................................................... 104
Fig. A3. 2 LCL Filter and parallel RLC load .............................................................................. 105
Fig. A4. 1 Block diagram of the 2407A DSP controller ............................................................. 109

xii

CHAPTER 1. INTRODUCTION

The current model for electricity generation and distribution in the United States is
dominated by centralized power plants. The power at these plants is typically combustion (coal,
oil, and natural) or nuclear generated. Centralized power models like this require distribution
from the center to outlying consumers.
This system of centralized power plants has many disadvantages. Electric utilities are
becoming more and more stressed since existing transmission and distribution systems are facing
their operating constraints with growing load. Greenhouse gas emissions have resulted in a call
for cleaner renewable power sources. Under such circumstances, distributed generation (DG)
with alternative sources such as fuel-cell, wind-turbine, bio-mass, micro-turbine and solar-cell
systems, has been considered as a promising solution to the above problems.

1.1. The Distributed Generation Concept
DG is defined as small, modular electricity generators located close to the end customer's
load connection point. They can enable utilities to decrease investment costs in transmission and
distribution system upgrades while still meeting increasing power demands and provide
customers with improved quality and reliability of energy supplies without imposing undesirable
effects on environment [1-2]. In general, DG can be intended as small sized power plants that are
designed to be installed and operated within a local load center.
To effectively and efficiently connect any of the DG sources to the existing power systems
power electronics-based conversion systems need to be developed for the proper control and
conditioning of the energy to be delivered [3]. Specifically, with most of the DG sources such as

1

variable frequency AC microturbines, DC fuel cells, DC photovoltaic cells and low power
variable frequency AC wind turbines, electrical power is generated as DC voltage or converted
to DC voltage, then converted to AC using a voltage sourced inverter. This voltage sourced
inverter performs the interface function between the DC bus and the AC world. Through the
proper control and conditioning of the DG, benefits such as voltage support and improved power
quality, diversification of power sources, reduction in transmission and distribution losses,
transmission and distribution capacity release and improved reliability, among others, can
enhance the utility grid without having to add or replace the existing transmission/distribution
system.
Some issues and concerns must be addressed when dealing with DG systems. Particularly,
attention must be taken into account when a design is being done for the support of power
delivery to the utility and when incorporating the concepts of both grid-connected and standalone. During the grid-connected operation, each DG system is usually operated to provide or
inject pre-set power to the grid, which is the current control mode in stiff synchronization with
the grid [4-6]. When the main grid is cut off from the DG system, stand-alone operation or
intentional islanding, the DG system has to detect this islanding situation and must be switched
to a voltage control mode to provide constant voltage to the local sensitive loads [7-9]. The trend
is that they should be able to work in stand-alone mode but also connected to the power grid
(grid-connected) [10]. Thus some new challenges on the control side of the DG occurred. Among
these challenges are: reasonable voltage regulation in stand-alone mode, grid-connection mode
enabled, and automatic detection of grid disconnection. Also grid disconnection detection and an
automatic mode switching are required. In order to manage these challenges, relative complex
control strategies need to be developed.

2

1.2. Benefits associated with DG
In distribution systems, DG can provide benefits for the consumers as well as for the utilities,
especially in sites where there are deficiencies in the transmission system. Some of the expected
benefits of DG are [11-19]:


Green house emissions reductions: By the increase of the use of renewable energy units,
as well as high efficiency generation units, operated in an optimum manner, the green
house emissions will be decreased with respect to the conventional generation.



Energy efficiency: By an adequate planning and operation of the generation and storage
units of the DG, the electric and heat generation or combined heat and power (CHP) can
be mixed, increasing the energy efficiency of the installation. It can also be made in a
profitable way.



Reduced transmission and distribution investments: DG helps bypass „„congestion‟‟ in
existing transmission grids. DG could serve as a substitute for investments in
transmission and distribution capacity. DG can postpone the need for new infrastructure.
Because of opportunities for integration in buildings, DG development often occurs in the
same location as demand. In such cases, if production output is concurrent with demand –
such as demand for air-conditioning in hot regions – network reinforcement may be
unnecessary while generation remains in the same order of magnitude as demand.
Moreover, normal development of the grid in response to growing demand may also be
postponed or even avoided as DG has the net effect of decreasing demand in that area.



Minimization of the electric losses: On-site production reduces the amount of power that
must be transmitted from a centralized plant, and avoids resulting transmission losses and

3

distribution losses, as well as the transmission and distribution costs, a significant part of
the total electricity cost, due to the fact that generation buses and consumption are closer.


Network (voltage) support: The connection of distributed generators to networks
generally leads to a rise in voltage in the network.



Quality of supply improvement: In areas where voltage support is difficult, installation of
a distributed generator may improve quality of supply. As the demand for more and
better quality electric power increases, DG can provide alternatives for reliable, costeffective, premium power for homes and businesses.



New market opportunities and enhanced industrial competitiveness: DG can also
stimulate competition in supply; adjusting price via market forces. In a free market
environment, DG operator can buy or sell power to the electricity grid, exporting only at
peak demand and purchasing power at off-peak prices.



Reduction of the energy costs: Thanks to the intelligence and control capabilities of the
DG, its operator will schedule the operation of its generation and storage sources,
depending on the electricity and gas actual prices, climatic conditions and their forecast.



Locality, i.e. improved utilization of local resources: Distributed energy generation may
also promote local business opportunities, and develop products and services based on
local raw materials and labor. Local employment can be improved by creating new jobs
related to distributed energy generation. This, in turn, causes a need for high-quality
education. Locality also means the absence of transmission lines, large power plants, and
fuel storage, which spoil the landscape. The environmental load is also reduced due to the
avoidance of additional energy required to compensate transmission losses.

4

1.3. Issues associated with DG
Despite the above mentioned benefits provided by DG, there are technical limits regarding
the degree to which DG can be connected. Indiscriminate application of individual DG systems
can cause as many problems as it may solve [11]. This is because the distribution system was
intended to cope with the conventional load supply by central generation, where power flows
radially from the transmission network. Changing the power flow causes problems since DG
does not behave the same way as conventional load. The issues associated with DG can be
summarized as [14, 17, 19-27]:


Interface with AC System: The main DG requirement for interfacing with the utility
system is that it must not compromise the stability and reliability of the grid. The
interface must also guarantee compliance with already existing protection schemes.



Protection: DG needs to be retrofitted in its protection algorithms to include the
contributions of micro-sources. DG can impact a variety of levels of short-circuit current.
The DG systems have to provide enough fault current to operate the protective devices,
including circuit breakers, fuses, and fault-protection relays. The addition of DG on a
circuit may need to be studied to establish whether changes are needed for coordination
or protection equipment. Different hardware setups may be required: the rating of the
breakers responsible to implement protection may need to be revisited, and surely they
will have to be controlled with a different algorithm.



Power quality: DG can negatively affect power quality. Power quality refers to the degree
to which power characteristics align with the ideal sinusoidal voltage and current
waveform, with current and voltage in balance.
o Voltage Regulation: The primary objective of voltage regulation is to provide
each customer connected to the utility with voltage that conforms to limits voltage
5

range for normal operation. The operating window for DG systems is 106-132
Vrms on a 120 Vrms base, that is, 88 - 110% of nominal voltage [28].
o Harmonics: Due to the power electronics and digital methods used to form the AC
waveform from DC, inverter-based DG technologies produce various harmonics
of the power system frequency. Standards states that the total harmonic distortion
(THD) must not exceed 5% of the fundamental 60 Hz frequency, nor 3% of the
fundamental for any individual harmonic [28].
o Power Factor: Power factor measures the apparent power that is generated when
the voltage and current waveforms are out of synchronism. Power factor is the
ratio of true electric power (watts), to the apparent power (kVA). Although not
strictly the case, power factor problems can be thought of as contributing to utility
system inefficiencies [29]. The DG inverter should operate at a power factor >
0.85 (lagging or leading) [28]. Most DG inverters designed for utilityinterconnected service operate close to unity power factor. Specially designed
systems that provide reactive power compensation may operate outside of this
limit with utility approval.
o Frequency: DG systems have to operate in synchronism with the utility. DG
systems installed in North America should have a fixed operating frequency range
of 59.3 - 60.5 Hz [28]. Systems installed in another country should follow the
frequency operating window standards of that country.
o DC injection: DC injection occurs when an inverter passes unwanted DC current
into the AC or output side of the inverter. The DG inverter should not inject dc
current > 0.5% of rated inverter output current into the ac interface under either
normal or abnormal operating conditions [28]. Inverter manufacturers generally
use one of two methods to prevent the injection of dc current into the utility
interface. One method is to incorporate an ac output isolation transformer in the
inverter. The other method, which uses a shunt or dc-current sensor, initiates

6

inverter shutdown when the dc component of the current exceeds the specified
threshold.


Instantaneous power tracking: The requested power from the load coming on-line is a
step function, while the prime mover in the micro-source always takes a finite amount of
time to ramp up to the newly requested value. Micro-sources have a slow response to
changes in commands and the inverter interface by itself does not provide any kind of
internal form of energy storage. This inertia-less system is not well suited to handle step
changes in the requested output power. If the connection to the grid is missing due to a
temporary malfunction then the need for some sort of storage is manifest. Storage is
required to satisfy the instantaneous power balance as a new load comes on-line without
penalizing the quality of other network quantities, such as bus voltage magnitude. Load
changes resulting in fast transients that exceed the ramping capability of generation
require storage availability from which to draw the required transient energy.



Unidirectional Area Electric Power System (EPS) Relaying: Due to the traditional radial
nature of distribution systems, most protective devices on the EPS are unidirectional in
nature and respond to a given value of current without regard to the direction of flow of
that current. Because DG produces fault current of various magnitudes for faults on the
EPS, the traditional radial nature of the distribution system is disrupted and unidirectional
relays could operate improperly.



Paralleling DG: One of the selling points for DG is that the local generation follows a
scalable system model, where due to the typical small size of the units, one can install as
many units as needed to satisfy the requests of the loads, without having too much of
extra capacity sitting idle. But this concept requires that the micro-sources can be
installed in parallel without any restrictions.

7



Plug and Play Configuration: When looking into the future and envisioning microsources being installed by the thousands, the need for plug and play configuration
becomes manifest. The plug and play mode of operation implies simplicity of installation
and therefore speeds up the process of diffusion of the DG in the system. The ideal case
would be purchasing a unit and plugging it in a three-phase socket, having power injected
immediately (after synchronization).



Synchronization with the Grid: One of the most important issues of a DG system
connected to the utility network is the synchronization with the grid voltage vector. The
synchronization algorithm mainly outputs the phase of the grid voltage vector. The phase
angle of the utility voltage is a critical piece of information for grid connected systems.
This information can be used to synchronize the turning on/off of the power devices,
calculate and control the flow of active/reactive power or transform the feedback
variables to a reference frame suitable for control purposes. Because of these, the
accurate and fast detection of this phase angle is essential to assure the correct generation
of the reference signals.



Loss of Main Detection (Grid condition detection) or Islanding Detection: One of the
major concerns in operating DG systems connected to the grid is the possibility of
islanding due to grid disturbances, intentional disconnect for servicing, accidental
opening, intentional disconnect from the utility, and an act of nature, among others.
Islanding is the condition in which a portion of the utility system, which contains both
load and DG, is isolated from the remainder of the utility system and continues to
operate. Islanding is either due to preplanned (intentional) events or due to non-planned
or accidental (un-intentional) events [10]. Some distinctions of islanding are:

8

o non-intentional islanding occurs if it is not possible to disconnect the DG after the
fault, non-intentional islands must then be detected and eliminated as fast as
possible;
o intentional islanding refers to the formation of islands of predetermined or
variable extension; these islands have to be supplied from suitable sources able to
guarantee acceptable voltage support and frequency, controllability and quality of
the supply, and may play a significant role in assisting the service restoration
process;
o microgrids are seen as particular types of intentional islands basically operated in
autonomous mode, not connected to the supply system; the whole microgrid can
be seen from the distribution system as a single load and has to be designed to
satisfy the local reliability requirements, in addition to other technical
characteristics concerning frequency, voltage control and quality of supply.
In a deregulated market environment, current practices of disconnecting the DG
following a disturbance will no longer be a practical or reliable solution. As a result, the
IEEE Std. 1547-2003 states as one of its tasks for future consideration of the
implementation of stand-alone operation of DG (IEEE P1547.4: Guide for Design,
Operation, and Integration of Distributed Resource Island Systems with Electric Power
Systems) [28].


Transitions from grid-connected to stand-alone: One of the problems to face during the
transfer to stand-alone is to ensure minimal to none transients at all the load bus. The DG
inverter should operate in grid-connected and stand-alone modes in order to provide
power to the emergency load during system outages. However, grid current controller

9

(for grid-connected) and output voltage controller (for stand-alone) are switched between
the two modes, so the outputs of both controllers may not be equal during the transfer
instant, which will cause the current or voltage spikes during the switch process.


Load shedding: Another problem to face during the transfer to stand-alone is to
automatically readjust the power output of the units to compensate for the missing quota
of injected power from the utility system. This issue brings a challenge because of the
assumption that there is no previous knowledge of the loading levels as the system
transfer to island and also because of the assumption that no communication may exist
between the micro-sources to enforce a coordinated behavior during and after the transfer
to island.



Reclosing: Automatic circuit reclosers may also be deployed in the feeder circuit to
automatically clear faults and quickly restore service on the feeder. Reclosers reenergize
the circuit automatically at a predetermined time after a trip resulting from a feeder fault.
The response of the DG unit needs to be coordinated with the reclosing strategy and the
settings of the recloser isolation operations. Coordination and synchronization are
required to prevent possible damage to the equipment connected to the DG.



Transitions from stand-alone to grid-connected: When the grid-disconnection cause
disappears, the transition from stand-alone mode to grid-connected mode can be started.
The voltage amplitude and phase of the DG have to be synchronized with the grid to
avoid hard transients in the reconnection. Once the synchronization process is completed,
the DG can be reconnected to the grid.

10

1.4. Scope of the Dissertation
This research presents the development and test of a control strategy for DG capable of
working in both stand-alone and grid-connected modes. The stand-alone control features an
output voltage controller capable of handling excess or deficit of generated power and
synchronization for grid reconnection with a seamless transition from stand-alone to gridconnected operation modes. The grid-connected mode with current control is also enabled for the
case of power grid connection. This grid-connected control features an output current controller
capable of loss of main detection, synchronization with the grid, and seamless transition from
grid-connected to stand-alone operation modes with minimum interruption to the load.
A method to automatically switch between both modes of operation is described. This
method, based on a phase-locked loop (PLL), detects the power grid disconnection or recovery,
and switches the operation mode accordingly.
The proposed control strategy will have the following characteristics:
1. Interface with AC System
2. Power quality
a. Voltage Regulation
b. Harmonics
3. Synchronization with the Grid
4. Loss of Main Detection or Islanding
5. Transitions from grid-connected to stand-alone
6. Load shedding
7. Reclosing
8. Transitions from stand-alone to grid-connected

11

Operation modes as well as the involved voltage and current controllers will be described in
detail. The design of an LCL filter to achieve attenuation of the switching frequency ripple in the
output voltage will be also described. A PLL for grid synchronization and loss of main detection
will be presented. Also, a re-connection algorithm and automatic mode switching will be
delineated.

1.5. Outline of the Dissertation
A brief description of the Distributed Generation Concept is presented in this chapter.
Chapter 2 presents a literature review of the techniques used for the control of an inverter unit in
grid-connected and stand-alone modes. The system description including circuit topology,
voltage source inverter, LCL filter, simulation set-up, and experimental set-up are given in
Chapter 3. Chapter 4 discusses the proposed control for grid-connected operation of DG. The
proposed control for intentional islanding operation is presented in Chapter 5. Conclusions and
the scope for future work are presented in Chapter 6.

12

CHAPTER 2. LITERATURE REVIEW

This section summarizes the techniques used for the control of an inverter unit in gridconnected and stand-alone modes.
R. Tirumala, et al. [30] presented an algorithm for a utility interactive DG system with a
seamless transition between grid-tied (current controller) and off-grid (voltage controller) modes
of operation. A static transfer switch (STS) was used to disconnect and reconnect the load bus to
the grid. The control ensured a smooth voltage profile across the load when the grid was
disconnected or reconnected. The control algorithm ensured that the static transfer switch was
turned off before the inverter was shifted to the voltage-controlled mode. Also, the algorithm
ensured that the voltage applied across the load matched the load voltage just before
disconnection. The steps to perform this algorithm can be summarized as follows:
1. Detect a fault on the grid and give a turn off signal to the STS.
2. Monitor the magnitude and phase of the load voltage.
3. When the STS current goes to zero, switch the inverter to a voltage-controlled mode,
with the voltage reference being derived from the load voltage.
4. Ramp up the magnitude of the load voltage from its initial value to the rated value.
For the transfer between the voltage-controlled mode and the current controlled mode, the
inverter voltage matched the grid voltage both in magnitude and phase before the static transfer
switch was turned on. The STS would be turned on when there is essentially zero voltage across
it. Once the STS was turned on, the grid current would be slowly ramped up to prevent any
voltage spikes caused by the grid inductance. The steps to perform this algorithm can be
summarized as follows:

13

1. Detect that the grid is within nominal operating parameters.
2. Adjust the load voltage to match the magnitude and phase of the grid voltage.
3. Once the load voltage is equal to the grid voltage, turn on the STS and switch from
voltage-controlled mode to current-controlled mode, with the reference current being
equal to the load current.
4. Change the reference current slowly to the desired current (both magnitude and phase).
L. Yunwei, et al. [31] proposed a unified controller for use with DG system. By regulating
the output voltage, the proposed controller controlled power flow in the grid-connected mode of
operation, enabling the operation of DG when the system islands, and resynchronized the DG
with the utility before reconnecting them. The presented controller responded fast, allowing the
controlled DG to transit smoothly between the grid-connected and islanding modes without
disrupting critical loads connected to it. The resynchronization process when the utility grid
returned back to normal operating conditions form was achieved by aligning the voltage at the
DG and utility ends of a STS separation device. This process was implemented by adding two
synchronization compensators to the real and reactive power control loop, as shown in the
dashed frames of Fig. 2.1 and Fig. 2.2. To summarize, the final block diagram representation of
their proposed unified controller is shown in Fig. 2.3.

14

Fig. 2. 1 Real power compensator with synchronization function [31]

Fig. 2. 2 Reactive power compensator with synchronization function [31]

Fig. 2. 3 Overview of proposed unified controller [31]
15

T. Thacker, et al. [32-33] proposed a switched-mode control with detection and re-closure
algorithms scheme to regulate between the grid-connected and stand-alone modes of operation.
Their proposed system configuration can be seen in Fig. 2.4.

PCC control
Va_grid

VSI
va

ia

vb

ib

Vdc

vc

ic

PCC
Da

Dc

grid
load
ABC
2
DQ0



1  2
PLL 1  2 PLL
Vd

Io

Vq
control and
detection

Vo_g
Vq_g
Vd_g

Id
Iq



Vo



Dd
Dq
Do

DQ0
2
ABC

PCC control

Fig. 2. 4 System configuration for simulated and experimental results [32-33]
Their proposed detection scheme, Fig. 2.5, used passive sensing parameters (over/under voltage
& frequency, real/reactive power deviation) with a BPF loop being fed directly to the duty cycles
instead of being fed to the current references. The advantage of BPF going directly to the dutycycles is that the current limiters can still be implemented without special considerations. When
an islanding event was detected, the system was automatically disconnected from the grid and
switched to voltage mode control.

16

Measurements

V > 1.1 Vpu
or
V < 0.88 Vpu

no

Islanding? no

yes

no

ΔP > 20%

ΔQ > 20%

freq > 60.5
or
freq < 59.3

yes

Islanding? yes

Fig. 2. 5 Islanding Detection Flowchart [32-33]
17

Their proposed re-closing scheme is seen in Fig. 2.6. Like the detection algorithm, this algorithm
was autonomous and incorporated into the control of the DG. The idea was that by measuring
four key parameters: the grid voltage, VSI voltage, VSI frequency, and the line angle difference
between the grid and VSI, the system could safely reclose to the utility without having to deenergize the DG. The scheme first measured and detected if the grid voltage had been recovered
from its fault and was back in nominal operating conditions. With the grid back to nominal
conditions, the signal coordinate transforms and detection started to use the grid‟s line angle as a
reference. This caused the VSI‟s PLL to start tracking the grid. Next, the magnitudes of the VSI
voltage and grid voltage were compared to ensure that they were on the same order of magnitude
before re-closing. The VSI frequency was then checked to make sure that the VSI had not left the
nominal frequency range. Finally, the system checked to see that the phase angle difference
between the VSI and grid were near zero. Once all of these conditions were satisfied,
concurrently, the DG would re-close with the grid.

18

Measurements

Vg < 1.1 Vpu
or
Vg > 0.88 Vpu

yes

no

Islanding? yes

no

V ≈ Vg

yes

freq < 60.5
or
freq > 59.3

yes

VSI θ
≈
Grid θ

yes

Islanding? no

Fig. 2. 6 Re-closure Flowchart [32-33]
19

The work presented in [34] by H. Zeineldin, et al., proposed a control strategy to implement
intentional islanding of inverter based DG. The proposed method was based on designing two
control algorithms, one for normal operation and the other for islanded operation. The DG
provided constant power and constant voltage during normal operation. A hybrid passive
islanding detection method was implemented to detect DG islanding. The detection algorithm
sent a signal to declare an islanded operation and the DG switched to the voltage control mode.
To overcome a large delay in detecting islanding for matching load condition cases, the Rate of
Change of Frequency (ROCOF) was used, in parallel with the OFP/UFP, as another measure to
detect islanding. The algorithm stated by monitoring both the frequency and voltage at the PCC
and calculating the ROCOF. The time at which the frequency exceeded its thresholds and the
time when ROCOF exceeded its threshold were denoted by T1 and T2 respectively and were
stored. The difference between the actual time T and T1 and T2 respectively were calculated. If
the difference exceeded a certain predetermined delay time, islanding was declared and the DG
was operated in the islanded mode. The islanding detection algorithm was responsible for
sending a signal that switched the inverter to the suitable interface control. Once islanding was
detected, the DG switched to the voltage control interface. To assure safe islanded operation of
the DG, the output active power of the DG was monitored to assure that it was less than the DG
capacity. If the load on the island was greater than the DG capacity, the DG would become
overloaded and a signal was sent to disconnect it. Fig. 2.7 and Fig. 2.8 show the flowcharts of
their designed control strategy.

20

frequency and voltage
measurement

df/dt calculation

59.3 < f > 60.5
or
0.88 > Vpu > 1.1

no

store T1
df/dt > 0.1
Store T2

yes

no

yes
T-T1 > delay1
no
T-T2 > delay2
yes

yes

Islanding
detection

Fig. 2. 7 Proposed islanding detection algorithm [34]

21

no

frequency and voltage
measurement

Islanding detection
algorithm

Is the DG
Islanded

no

Operate DG
In
P-V mode

yes

Operate DG As
voltage
controlled VSI

DGactive power
no

> Prated
yes

Disconnect DG

Fig. 2. 8 Flowchart of the control strategy implemented to produce intentional islanding
[34]

22

In [14], a control strategy for grid-connected and islanded operation was designed and
implemented by Y. Zhou, et al. Their proposed controller solved the following issues: how to
detect system separation fast and accurately, how to control DG in an islanded power system to
stabilize frequency and voltage, and how the controller of the DG can be transferred through grid
connected operation to islanding operation and vice versa seamlessly in order to protect the
critical load. Voltage angle difference between the local power system and the main power grid
was measured. If the angle difference was increased to an abnormal value, which cannot happen
under grid connected operation, then it was determined that the local power system was
disconnected from the main power grid. Before synchronization, voltage magnitudes and phase
angles of the islanded system at the point of common coupling (PCC) and grid were measured.
When the magnitude and angle differences between the islanded system and the main grid
approached zero the synchronization began and the hybrid power system was connected with the
power grid again.
G. Fang and M. R. Iravani [35] reported a control strategy that provided control over
frequency and voltage permitting the operation of the DG unit in both grid-connected and
autonomous modes. The features of the control strategy presented were: it provided smooth
transition capability from grid-connected mode to autonomous (islanded) mode, and it included
an islanding detection capability. Reactive power control (upper path of Fig. 2.9), which drove
the system to an unstable condition during an autonomous mode of operation, was exploited for
islanding detection. To decrease the detection time, positive feedback based on the instantaneous
PCC voltage, was added to the controller as shown in Fig. 2.10. This positive feedback ensured
that the feedback process was only effective during transients, did not impact the dc steady state
error signal, and provided attenuations for high-frequency noise.

23

Fig. 2. 9 Block diagram of voltage control [35]

Fig. 2. 10 Block diagram of voltage control with positive feedback [35]

In [36], presented by G. Iwanski and W. Koczara, the loss of mains was detected using two
methods. The first method was based on the voltage amplitude calculation and the second
method, used for detection of grid voltage failures, was based on the monitoring of the frequency
of the stator voltage provided by the grid. The mains outage detection implicated soft
disconnection of the generator from grid by STS opening, and transition to standalone operation.

24

This way the selected load was supplied uninterruptedly. On the other hand, recovery of the grid
voltage caused that the stator voltage was synchronized with the grid and the generator was
softly connected to the grid by closing the STS. Their strategy for synchronization of the stator
and grid voltages was:
1. The angle between the stator voltage vector and the grid voltage vector was calculated.
2. This angle was reduced by iterative turning of the synchronously rotating frame in the
direction of the grid voltage vector.
3. The original transformation angle, calculated by integration of reference angular speed,
was decreased iteratively in every computation cycle and in each cycle a new angle was
determined.
4. When the stator voltage was synchronized with the power grid, two PLL structures
were operated simultaneously. During synchronization, the reference dq frame connected
with the stator voltage rotates with an angular speed Ω while the grid voltage vector
rotates synchronously with the reference synchronous speed of the dq frame ( * ).
s
5. The relative speed and position of the grid voltage vector and the synchronously
rotating frame were decreased to zero.
6. Thus, the synchronously rotating frame was synchronized with the grid voltage,
whereas the stator voltage was synchronized with the rotating frame controller and
consequently provided stator voltage and grid voltage synchronization.
7. If the angle was close to zero, the STS was closed and the generator was connected to
the grid.
They proposed two methods for the main outage detection and soft disconnection. The first
method was based on the voltage amplitude calculation. If the power of load connected between

25

the stator and breaking point was much higher or much lower than the power delivered to the
grid, the amplitude was increased or decreased rapidly after line breaking. This way the loss of
main was quickly detected. The second method used for detection of grid voltage failures was
based on the monitoring of the frequency of the stator voltage provided by the grid. The output
frequency could not be controlled using a power control method which was applied during the
grid connection operation. The frequency was continuously increased or decreased in case of the
main outage.
The aim of the research presented by R. Majumder, et al. [22, 37] was to set up a power
electronics interfaced DG system. A seamless transfer between islanded and grid connected
mode was proposed that uses an online load flow study. During resynchronization, the reference
voltage of the DG was changed to achieve the same voltage magnitude and angle at PCC as the
grid voltage while simultaneously supplying the total power demand of the DG in desired ratio.
Once the breaker was closed, the DG started to supply its rated power and the rest of the power
requirement was supplied by the grid. Their proposed sequence of control from a grid connected
operation to islanded mode and then again back to grid connected can be summarize as:
1. Detect the islanding by zero current in the breaker connecting the grid with the DG.
2. If islanded, switch to voltage control mode.
3. Calculate the reference voltage required for the DG to maintain the load power
requirement.
4. Check for the clearing of the fault.
5. If resynchronization is desired, detect the grid voltage and frequency.
6. Calculate the reference voltages for the DG to make the PCC voltage the same as the
grid voltage while continuing to supply the load requirement.

26

7. Calculate the change in angle required to match the phase for proper synchronization.
8. Change the voltage reference to the new calculated value.
9. Connect the breaker.
10. Switch to the state feedback control mode.
Aiming to solve the transition problem from grid-tied mode to off-grid mode, H. Shengli, et
al. [38] presented a control strategy based on a controlled voltage method whether connected to
the grid or stand-alone. In grid-tied mode, the inverter worked as a controlled voltage source by
controlling the phase and magnitude of the filter capacitor voltage, the injection current to the
grid was regulated indirectly, so the output active and reactive powers were also successfully
controlled. Once the grid failed, the inverter regulated its output voltage amplitude quickly, while
the voltage fluctuated within permissible levels during this period, the grid currents forced
through the STS decreased to zero at a highly accelerated rate. The controller cancelled all the
gate drive pulses of the STS and reduced the inverter output voltage lower than the grid voltage
simultaneously, which introduced a reverse voltage across the coupling inductor and forced the
grid current to decrease to zero quickly. As soon as the grid current reached zero, the STS was
turned off and the controller promptly regulated the inverter output voltage to its rated value.
After disconnection from the grid, the inverter recovered its voltage amplitude to a rated level.
Based on the SST forced turn-off strategy, the inverter operated as a controlled voltage source
whether grid-tied or not. By controlling the phase and magnitude of the filter capacitor voltage,
the grid current was regulated indirectly; accordingly the output active and reactive powers were
also successfully controlled.
C.-S. Wu, et al. [4] introduced a power supply system designed with grid-connected
operation and autonomous operation modes. Through a novel anti-island (AI) detection method,

27

the current status of the electricity network was detected quickly and the operation mode of the
inverter was ascertained. Based on analysis of transition between grid-connected operation and
autonomous operation modes, the output conditions of the inverter were adjusted optimally and a
seamless transition process was acquired. All transitions were conducted in zero-crossing in
order to reduce the voltage ripple of the sensitive load. Their seamless transition from
autonomous operation mode to grid-connected operation mode in detail is as follows:
1) Detects the voltage, frequency of the electricity network and judges the operation
status of the grid;
2) Adjusts the output voltage of the inverter, and makes it equal to those of the electricity
networks;
3) After adjusting, translates the operation mode of inverter (from voltage source to
current source) and closes the switch. In order to reduce the voltage ripple on the
sensitive load, the initial current is given as the current of the load;
4) Increases the output current step by step up to maximization.
Similar to the transition process described above, the seamless transition from grid-connected
operation mode to autonomous operation mode in detail is as followings:
1) Detect a fault in the electricity networks (by means of AI method introduced in next
chapter);
2) Set the output current to that of load in order to reduce the voltage ripple impact;
3) Open the switch and change the operation mode of inverter.
For the AI detection two positive feedback mechanisms were established. One was magnitude of
voltage feedback (Fig. 2.11); the other was frequency of voltage feedback (Fig. 2.12).

28

Vd sense

Id ref

P

V

Fig. 2. 11 Diagram of magnitude of voltage feedback in dq frame

ω sense

Iq ref

Q

ω

Fig. 2. 12 Diagram of frequency feedback in dq frame

A novel scheme for seamless transfer of MTG (Microturbine Generation) system operation
between grid-connected and islanding modes and vice versa was proposed by D. N. Gaonkar, et
al., [39]. The presented scheme used the estimated phase angle error obtained by the PLL for
islanding detection and re-synchronizing DG to grid. A converter control strategy for both gridconnected and islanding modes was presented. The proposed seamless transfer scheme consisted
of a passive islanding detection and re-closure method. The presented islanding detection method
used the phase angle estimated by the PLL to detect the islanding condition. Their algorithm
devised for the detection scheme is shown in Fig. 2.13. Their re-closure scheme continuously
monitored the phase angle and terminal voltage magnitude to determine whether or not the
disturbance in the grid was over. This was necessary in order to synchronize the MTG system
and to connect back to the grid without any down-time. The re-closure algorithm continuously
monitored the terminal voltage of the grid and MTG system. Both voltage magnitudes were
compared. Both voltages had to be approximately equal to avoid large transients during reconnection to grid. Once the voltages were approximately equal, the algorithm compared the Δθ
29

value obtained from the PLL with the set threshold limit. As long as these minimum
requirements were met (voltage and phase angle), there were no major issues in reconnection of
islanded systems to the utility. The re-closure algorithm for connecting the MTG system to the
grid, when the utility recovers from the disturbance, is shown in Fig. 2.14.

measurement

Is
Δθ > Δθmin

no

no
Islanding

yes

Transfer control to
islanding mode

Fig. 2. 13 Islanding-detection scheme [39]

30

measurement

Is
V < 1.1 pu and

no

V > 0.88 pu

yes
Is
Vdg ≈ Vgrid

no

yes

Is
Δθ > Δθmin

no

yes

Transfer control to
islanding mode

Fig. 2. 14 Re-closure scheme [39]
31

Islanding
exist

Synchronization
restoration
Islanding mode
operation

Grid-connected
mode
Grid failure
IBS disconnection

Fig. 2. 15 Flowchart diagram of the modes of the VSI [3]
E*
iPCC
X

+90

LPF

Qc

Q
+

-

Q*=0

o

VPCC
iPCC

X
VG

LPF

X

LPF

PI(s)

φs

+

+
+

GS

P/Q
decoupling

E

Pc

P
+-

Gq(s)

-

ES

Gp(s)

φ

+

E sin(ωt-φ)

Vref

+

P*

φs
θG

ZG

VG(rms) +

GS’

PI(s)

ES

-

Phase synchronization

VC(rms)

GS’

amplitude synchronization
Fig. 2. 16 Block diagram of the whole proposed controller using the synchronization
control loops [3]

32

The intent of the research that has been presented in [40] by C. Chien-Liang, et al., was to
introduce a practical inverter based DG system that ensured smooth mode transfer between
islanding and grid-tie modes while maintained accurate current sharing and high quality output
waveforms. The key features of the proposed DG system include: a single current loop controller
designed for a grid-tie operation to reduce the steady-state error while maintaining system
stability; for islanding operation, a dual-loop control system for outer voltage loop and a
controller for inner current loop control is proposed to limit peak current magnitude under
transient, enhance voltage loop stability, and reduce the voltage steady-state error; a phase
synchronization is implemented with PLL and an automatic phase adjustment to synchronize the
output currents among the inverters; and, a proper mode transfer procedure with smooth current
transition are suggested to minimize the excessive electrical stresses. Their proposed procedure
to change from grid-tie to islanding mode is summarized as follows.
1) The upper level controller detects the fault on the voltage grid and extracts the current
information.
2) Through a CAN bus, the upper level controller provides the current information and
commands the current-controlled inverters to change their outputs so that the current on
the STS can be minimized to avoid mode transfer transient.
3) The upper level controller provides the turn OFF signal for the STS after a certain
waiting time.
4) Through the CAN bus, the upper level controller commands a selected inverter to
change from current-controlled mode to voltage-controlled mode at the next zero
crossing.

33

5) That inverter regulates the bus voltage to a desired level and provides the output
current information.
Their procedure to change from islanding to grid-tie mode is summarized as follows.
1) The upper level controller detects if the grid voltage recovers, and keeps detecting the
grid voltage magnitude and phase information.
2) Through the CAN bus, the upper level controller provides the grid voltage information
and commands the inverter to adjust its voltage to track the grid voltage in both
magnitude and phase.
3) The upper level controller keeps monitoring both voltages. It turns on the STS once the
two voltages are synchronized in phase and magnitude.
4) Through the CAN bus, the upper level controller commands the inverter to change its
controller from voltage controlled mode to current-controlled mode at the next zero
crossing. It assigns the current references so that zero current goes through the STS
during transfer transient.
5) The current controlled inverters change the current reference to a desired level.
In [41], presented by L. Qin, et al., the transition from grid-connected to standalone operation
using a Solid State Relay (SSR) was discussed. A feed-forward that could boost the dynamic
response and benefited the transition from grid-connected to stand-alone was added to the
controller. They proposed to force the grid current to be zero by using a voltage amplitude
regulation method. Then, the SSR was turned off and the reference output voltage was recovered
to the rated value. The principle of zero current regulation was to retain the current control mode
in transition but change the current reference to zero. After the current dropped to zero, the SSR
was turned off and the system was switched to voltage control.

34

A seamless transfer of grid-interactive inverters between grid-connected and stand-alone
modes was proposed by Y. Zhilei, et al. [42]. In grid-tied mode, an output voltage controller was
used for compensating the filter capacitor current, and a grid current controller was used to
control the grid current. In stand-alone mode, the output voltage controller was used to regulate
the output voltage and to set the output of the grid current controller to zero. Therefore, the
transfer between the two controllers did not exist with their proposed method. In order to realize
a seamless transfer between grid-tied and off-grid modes, they proposed a controller that
matched the magnitude, frequency, and phase of the grid voltage before connecting to the utility.
The detailed process of their seamless transfer between the two modes is as follows:
1) Off-grid mode to grid-tied mode:
a) Detect that the grid is operating in nominal condition.
b) Adjust the reference voltage to match the frequency and phase of the grid
voltage.
c) Change the voltage reference to the grid voltage at the positive zero-crossing of
the output voltage, which makes the output voltage equal to the grid voltage, even
in polluted grid voltage.
d) Once the load voltage is equal to the grid voltage, the STS is turned on.
e) Increase the reference grid current slowly from zero to the desired value (both
magnitude and phase).
2) Grid-tied mode to off-grid mode:
a) Detect a fault on the utility.
b) Decrease the reference current to zero at zero crossing of the grid current.

35

c) Change the STS voltage from high level to low level at zero crossing of the
grid voltage. This will turned off the STS.
d) Synchronize the reference voltage with the grid voltage.
e) Change the reference voltage at zero-crossing of the grid voltage.
From this algorithm, the transfer between both modes was only the change of the reference
voltage between the two modes. The transfer between the output voltage controller and the grid
current controller did not exist in their proposed method.

36

CHAPTER 3. SYSTEM DESCRIPTION

3.1. Circuit Topology
Fig. 3.1 shows the proposed main circuit topology for grid-connected and stand-alone
operations voltage source inverter. The system consists of a DG unit that is modeled by a DC
source, a sinusoidal pulse-width-modulated (SPWM) voltage source inverter, an LCL filter to
achieve attenuation of the switching frequency ripple in the output voltage, a load, and the
controller needed to implement grid connected and stand-alone operations.

Voltage Source Inverter
Sb

Sa
Vdc

a
Sa’

VIa VIb

b
Sb’

VIc

Sc

Lg

LI

Ia

Utility
PCC Disconnect
Switch
VGa
VIa

c

Grid

Sc’

Ia

Cf
Ib

LCL Filter
Ic VI-ac VI-bc

Load
VI-ca VG-ab VG-bc VG-ca

Sa-a’
CONTROLLER

Sb-b’
Sc-c’

Fig. 3. 1 Schematic diagram of the grid-connected inverter system

The voltage source inverter performs the interface function between the DC bus and the three
phase AC world. The inverter consists of power electronics devices actuated by gate pulses:

37

these devices are high frequency static switches that periodically apply repetitive pulses with
different widths and polarities at the AC terminals, with the goal to create an AC waveform of
desired magnitude and phase.
The controller includes control for grid-connected and stand-alone operations, PLL,
coordinate transforms, parallel interconnection to the grid (represented by ideal, sinusoidal
voltage sources behind line impedances) through the Point of Common Coupling (PCC)
breakers. The loss of main detection, load shedding algorithm, and re-connection to the grid are
also included.

3.2. Voltage Source Inverter
A typical DG system based on micro-source is depicted in Fig. 3.2. There are two basic
elements: the part where the electricity is generated (micro-source) and the part that performs
the interface with the rest of the system (voltage source inverter).

Microsource

Three
Phase
Output

DC
Link

Voltage Source
Inverter
Fig. 3. 2 Typical diagram of micro-source generation system

38

All the power, DC or non-power frequency AC, generated by each DG must use an
electronic inverter (to convert DC voltage to a three-phase AC voltage with desired magnitude
and phase) to interface with the electrical power system. This power electronic interface provides
significant flexibility and permits the DG to function as a semi-autonomous power system [31].
There are two main requirements to convert DC voltage to a three-phase AC voltage: a
matrix of switches and a switching sequence. Fig. 3.3 shows the circuit that allows synthesizing
the AC voltage at the three-phase terminals starting from a DC voltage. From left to right, there
is the DC bus and then the matrix of six power electronics devices. Each device has bidirectional current flow capability. The flow of current out of the DC bus is regulated by signals
sent to the gates to each of the devices present in the inverter.

Fig. 3. 3 DC to Three-Phase AC Inverter Diagram

The operation of this bridge requires two restrictions. First, two devices on the same leg may
never be conducting. Second, at least one device per leg must be conducting. The first constraint

39

comes from the fact that if for example, devices numbered 1 and 2 are conducting at the same
time then the DC source is shorted, resulting in very high currents that will destroy both devices.
The second constraint stems from the fact that the current flowing in each of the phases on the
AC side must have a path where to flow: if for instance neither device numbered 1 and 2 is
closed, then the current flowing on the AC side in the „a‟ phase would have no path where to
flow.
Consider the switching sequence shown in Fig. 3.4, where devices 1, 4, and 5 are closed: this
configuration satisfies both the above constraints. The voltages at the AC terminals are:

V  V
ab
dc

(3.1)

V  V
bc
dc

(3.2)

V 0
ca

(3.3)

From Eq. 3.1 to Eq. 3.3 it can be noticed that the output voltages can be either V , V
dc
dc
or zero. By carefully selecting a switching sequence it is possible to make those three levels of
voltage appear in one particular phase. Furthermore, it is possible to create a three phase system
of sinusoidal voltages with desired amplitude and phase. This is called a six pulse operation of
the bridge. In reality the output waveform of the AC voltage is a squared wave with a particular
amplitude and phase at the fundamental frequency. In order to solve this problem, more complex
switching sequences with higher switching frequencies are needed.
One of these complex switching sequences is the pulse width modulation (PWM) technique.
This PWM technique works on an averaging effect using the switching frequency as a base
period where the averaging occurs. Fig. 3.4 shows how the basic principle of the PWM technique
works: it allows the instantaneous average output to be held closer to the desired fundamental

40

output. The voltage waveform is made of pulses of different widths: hence the name pulse width
modulation. The sinusoidal signal is compared with a sawtooth waveform (carrier). When the
carrier is less than the sinusoidal signal, the PWM signal will be in high state (1). Otherwise it
will be in the low state (0).

Fig. 3. 4 PWM Operation of the Bridge
(For interpretation of the references to color in this and all other figures, the reader is
referred to the electronic version of this dissertation)

3.3. LCL filter
For attenuating the current ripple produced at the output of the inverter, an LCL filter is
placed in between inverter and grid. An LCL filter can achieve reduced levels of harmonic

41

distortion with lower switching frequencies and with less overall stored energy [43]. Fig. 3.5
shows the LCL filter where L and L are inductors on inverter side and grid side respectively.
g
i

LCL Filter

Li

Inverter
+
Vdc
_

+
Vi
_

Cf

Lg
+
Vc
_

+

Vg
_

Fig. 3. 5 LCL Filter configuration circuit

Z = Ls
i
i

(3.4)

Z =L s
g
g

(3.5)

1
Z =
c sC

(3.6)
f

From the economical point of view, the design of the LCL filter is made in such a way that
the magnitude of the inductor should be minimum and the magnitude of the capacitor should be
maximum. By selecting large capacitor the filter volume is reduced [44-45].

3.3.1. Specifications for the design of LCL filter
The following are the parameters for the design of the LCL filter:
Output Power of inverter: P
 10 kW
i  3ø

42

Apparent Power of inverter: S  10 kVA
i
Output Voltage of Inverter: V  208 V
i
ll
Switching frequency: f  10 kHz
s

V  400 V
dc
Input DC voltage:
(V  V
/ 0.612  208 / 0.612  339.869 V )
dc
ll  rms
Grid Voltage: V  208 V
g
ll

P
ˆ  load  1  3.33kW  27.5 A  28 A
Inverter current: I
L V
120V
load  1

 

ˆ
ˆ
I  10%  (0.10) I  (0.10)(28)  2.8 A
L
L

Inverter ripple current:

Reactive Power storage at C : Q  5%
f

3.3.2. Design of L
I
The ripple current depends on the DC link voltage, inductance, and the switching frequency.
The DC link voltage and switching frequency are constant, thus the inductance can be calculated
using the following procedure:

ˆ
I
V L L
L
ˆT
s

(3.7)

ˆ
where  is the phase voltage duty cycle at maximum output and is given by:

ˆ 





2V
g  pk  1 2 208 2

 0.85
V
3(400)
dc

(3.8)

43

ˆ
V
V
ˆ
ˆ   L  1 dc
I
L
Lf
6 Lf
s
s

(3.9)

 V
L  (0.1416)  dc
ˆ
 I f
 L s

(3.10)








200
  1mH
L  (0.1416) 
 (2.8)(10 x103 ) 



(3.11)

3.3.3. Design of C f
Considering the capacitor stores 5% of the system power as reactive power, maximum
capacitance is:
Q  5%S

(3. 12)

Q  5%S
 (0.05)(10kVA)  500VA
3 

(3.13)

C

C

f

f



Q
3 V 2 
i



Q
500

 31 F
3  V 2   (3)(1202 )(2 60)
i

(3.14)

(3.15)

3.3.4. Design of L
g
As most of the ripple is filtered by L & C , grid side inductor value is taken as half the
I
f
value of L .
I
L  0.5L  L  0.5 1mH   0.5mH
g
I
g

(3.16)

44

3.4. Simulation and Experimental Set-ups
3.4.1. Simulation Set-up
The performance of the proposed control strategies will be evaluated by computer simulation
using SABER. Fig. 3.6 shows the simulated system. This system will be tested under the
following conditions:


Switching frequency, f , 10 kHz
s



Filter inductor, L , 1 mH
I



Filter inductor, L , 0.5 mH
g



Filter capacitor, C , 31  F
f



Output voltage 208 V
, 3 @ 60 Hz grid connection, with V  400 V
rms  ll
dc



Output capacity 10 kW from DG



Total load 10 kW

The load will be adjusted to consume 10 kW. The DG system will be simulated to supply 10
kW and zero reactive power. The system will be operated initially in grid-connected operation.

45

PCC

Voltage Source Inverter

Sa

Lg Ia

LI

a
Vdc
DG unit Sa’

b

VIa

Utility
Disconnect
Switch VGa

c
Cf
LCL Filter

Grid

Load

θ
Mode of Operation new
Controller for Grid-connected Operation gridDa
Switch
DQ
IDref +
connected
Db
current +
regulator + +
+
ABC Dc
IQref
+
ID IQ

VD VQ

Controller for intentional islanding operation

VDref +

-

VQref

+
-

VD

voltage
regulator

IDref +
-

IQref

+
-

or

current
regulator

K

ID IQ

VDpu VD < 0.88
f

intentional
+ islanding
- +
+
- +

f > 60.5
Switch Mode
or
of Operation
f < 59.3
Loss of Main Detection

VD VQ
Load shedding
algorithm

VIa VIb VIc

ABC θnew
DQ

ID IQ

K

VQ
VD > 1.1

Ia Ib Ic

S Sa-a’
P Sb-b’
W S
M c-c’

ABC


V
θnewV
PLL

VD VQ f θold
VI-acVI-bcVI-caVG-abVG-bcVG-ca
θold

Re-synchronization

θnew

Fig. 3. 6 Simulated system

3.4.2. Experimental Set-up
The hardware prototype of Fig. 3.6 will be implemented for experimental verification. The
control, PLL, grid condition detection, and re-closure algorithms will be programmed using a

46

universal DSP control board developed at the Power Electronics and Motor Drives Laboratory at
Michigan State University. The system will be tested under the following conditions to
experimentally verify the simulation results:


Switching frequency, f , 10 kHz
s



Dead time 3μs



Filter inductor, L , 1 mH
I



Filter inductor, L , 0.5 mH
g



Filter capacitor, C , 50  F
f



Simulated

Output

voltage

104 V
, 3 @ 60 Hz
rms  ll

grid

connection,

with

V  200 V
dc


Output capacity 2.5 kW from DG



Total load 2.5 kW

The reason for simulating the output voltage is to ensure the algorithms and controllers are
functioning properly under low-power tests; such that there is a reduced risk of operator and
equipment damage if the system fails.
Shown in Fig. 3.7 are the inverter, the DSP board, the filter, and the rectifier.

47

Fig. 3. 7 Experimental set-up

The DG will be started up in grid-connected operation mode, and then the separation device
will be opened. When the DG is disconnected from the grid it operates in stand-alone mode.

48

CHAPTER 4. PROPOSED CONTROL FOR GRID-CONNECTED OPERATION OF DG

4.1. Introduction
There are two modes of operation for the DG inverter – the grid-connected mode and the
stand-alone mode. Each mode has its own control requirements and control structure. In the gridconnected mode of operation, the DG is connected to the utility. The utility, which is assumed to
be stiff, sets the voltage at the terminal of the DG inverter [10]. The inverter controls the power
being injected into the grid by controlling the injected current. Thus, in this mode, the inverter
operates in the current control mode.
In the stand-alone mode, the inverter supplies power to the load. It has to maintain the
voltage at the terminals of the load, irrespective of any changes in the load. Thus, in this mode,
the inverter operates in the voltage controlled mode.
This chapter discusses the grid-connected mode of operation and its controller design, while
the stand-alone mode will be discuss in the next chapter.

4.2. Circuit Topology
Fig. 4.1 shows the main circuit topology. This system consists of the micro-source
represented by the DC source, the conversion unit which performs the interface function between
the DC bus and the three phase AC world, and the LCL filter that attenuates the current ripple
produced at the output of the inverter. The controller presented provides constant DG output and
maintains the voltage at the PCC before and after the grid is disconnected.

49

Voltage Source Inverter
Sb

Sa
Vdc

a

b
Sb’

Sa’

VIa

VIb

VIc

Sc
c
Sc’

Ia

Lg

LI

Ia

Utility
PCC Disconnect
Switch
VGa
VIa
Grid

Cf
Ib

LCL Filter
Ic VI-ac VI-bc

Load
VI-ca VG-ab VG-bc VG-ca

Sa-a’
CONTROLLER

Sb-b’
Sc-c’

Fig. 4. 1 Schematic diagram of the grid-connected inverter system

4.3. Controller
For grid-connected operation, the controller shown in Fig. 4.1 is designed to supply constant
current output in order to provide a pre-set power to the main grid [46]. An important aspect to
consider in grid-connected operation is the synchronization with the grid voltage [47]. For unity
power factor operation, it is essential that the grid current reference signal be in phase with the
grid voltage. This grid synchronization can be carried out by using a PLL [48-49]. Also, the PLL
is used to determine the frequency and angle reference of the PCC [3]. Fig. 4.2 shows the control
topology used.

50

VIc

VIb

VIa

ABC
V

PLL

new

old

Ic

Ib

Ia

ABC

Current
Regulator

+
+ +
+

VQ

new

VD

DQ
IQ

ID

IDref+ IQref +


V

Synchronization
controller
new

Sa-a’

Da SPWM
Sb-b’
Db
ABC
Sc-c’
Dc

DQ

Fig. 4. 2 Block diagram of the current controller for grid-connected
When using the current control, the output current from the filter, which has been
transformed into a synchronous frame by Park‟s transformation (Eq. 4.1) and regulated in DCquantity, is fed back and compared with reference currents I

DQref

. This generates a current

error that is passed to the current regulator (PI controller) to generate voltage references for the
inverter. In order to get a good dynamic response V
is fed forward. This is done because the
DQ
terminal voltage of the inverter is treated as a disturbance and the feed-forward is used to
compensate for it. The voltage references in DC-quantities, V
, are transformed into a
DQref

51

stationary frame by the inverse of Park‟s transformation (Eq. 4.2) and utilized as command
voltages for generating high frequency pulse width modulated (PWM) voltages.

X 
  cos 
 D
 X   2  sin 
 Q 3
 1/ 2



 X0 



 
 cos(  2 / 3)  cos(  2 / 3)   X a 
sin(  2 / 3)
sin(  2 / 3)   X 
 b
X 
1/ 2
1/ 2

 c

(4.1)

where θ = ωt and ω is the frequency of the electric system.



X 
 cos 
sin 
1/ 2   X D 
 a 
 X     cos(  2 / 3) sin(  2 / 3) 1/ 2   X 
 Q
 b 
  cos(  2 / 3) sin(  2 / 3) 1/ 2  
X  
 X 
 b
 0



(4.2)

4.3.1. Synchronization Controller for Grid Reconnection: Proposed Algorithm
When the DG is in islanded mode operation and the grid-disconnection cause disappears, the
transition from stand-alone to grid-connected mode can be started [42]. To avoid hard transients
in the reconnection, the DG has to be synchronized with the grid voltage [50-52]. The DG is
operated in synchronous island mode until both systems are synchronized. Once the voltage in
the DG is synchronized with the utility voltage, the DG is reconnected to the grid and the
controller will pass from voltage control mode to current control mode. This synchronization is
achieved by implementing the following algorithm:
o

Assume that the phase difference between grid voltage and inverter voltage is given by:

  V  V
G

o

(4.3)

I

In order to obtain information of  , two sets of voltage values are used:

3
k  V V  V V  V V   cos( )
Ia Ga Ib Gb Ic Gc 2

(4.4)

52

3
g  V V  V V  V V   cos( )  3 sin( ) 

Ia Gb Ib Gc Ic Ga 4 

(4.5)

where,

V V
sin(t )
Ga
Gm
V
V
sin(t  120o )
Gb
Gm
V V
sin(t  120o )
Gc
Gm

V  V sin(t   )
Ia
Im
V  V sin(t  120o   )
Ib
Im
V  V sin(t  120o   )
Ic
Im

Using the variables k and g, sin( ) can be found as:

4
2
g k
3
sin( )  3
3

(4.6)

Fig. 4.3 shows how sin( ) is used to obtain the compensated phase angle for which the grid
voltage and the DG voltage are synchronized. When the grid is recovered, a PLL observer,
whose output will generate the grid frequency and phase, processes the grid phase voltages. If
the amplitude and frequency of the voltages are within the limits defined by standards, a
synchronizing signal will be generated. When the sine of the phase error is between -0.04 and
0.04 radians, the voltages are considered to be synchronized and the control of the supply-side
inverter will be switched from stand-alone to grid-connected control mode.

53

sync

sin  

+_

PI



X

+

comp

+
1/s

-0.04  sin  0.04 Synchronization

sin desired 

PLL

Voltage
Controller

Grid
condition

signal
Grid
recovered

Fig. 4. 3 Synchronization controller

4.4. Transfer Functions
Fig. 4.4 shows the block diagram of the DG interface control for grid-connected operation.

D

Vd

+
+ Vin

+ e K + K I1
P1
Id-ref _
s V*

1

Vin

F(s)

Filter

Id

Z(s)

Load

Vd

Id
Fig. 4. 4 Block diagram of the current controlled inverter

The PI controller produces a signal that is proportional to the time integral of the controller.
The transfer function of the PI controller is given by:

DK

P1

where K



P

K

I1
s

(4.7)

is the proportional gain and K the integral gain.
I

The inverter stage does not have any significant transient time associated with it and hence it
is modeled as an ideal gain. This ideal gain can be given by G  s   1 .
I

54

The schematic circuit of the filter stage is shown in Fig. 4.5. It consists of an LCL filter and a
parallel RLC load.

L1

L2

Vx

Vin

Id
+
Vd

Cf

RL LL CL

Filter: F(s)

Load: Z(s)

Fig. 4. 5 LCL Filter and parallel RLC load

The transfer function of the filter is given by:
I (s)
1
F ( s)  d

V ( s) s3C L L  s 2C L Z  s L  L  Z
in
f 1 2
f 1
1 2





(4.8)

The transfer function of the load, Z(s), is given by:
V (s)
1
Z (s)  d

1
1
I (s)

 sC
d
L
R
sL
L
L

(4.9)

This can be re-expressed as:

Z ( s) 

sL R
L L
2 R C L  sL  R
s
L L L
L
L

(4.10)

Using Fig. 4.4 and equations (4.7), (4.8) and (4.10), the transfer function of the current controlled
system is derived as:

55

V ( s)
FZD
d

I
( s) 1  FZ  FD 
d - ref

H ( s) 

Z (s) 

F (s) 

(4.11)

651.466 s

(4.12)

s 2  150.454 s  142117



6.4516 x1010 s 2  150.454s  142117



s5  150.454s 4  9.8219 x107 s3  1.456 x1010 s 2  5.5783x1013 s  0.4187

D  0.8 

H (s) 

25
s

(4.13)

(4.14)

3.365 x1013 s 2  1.051s
(4.15)
s6  150.108s5  9.83x107 s 4  6.62 x1010 s3  2.31x1013 s 2  7.58 x1015 s  2.28x1017

where R  4.33 , L  4.584mH , C  1.535mF , L  1mH , L  0.5mH , C  31 F ,
f
L
L
L
1
2

K

P1

 0.8 , K

I1

 25

4.5. Simulation Results
The performance of the proposed control strategies was evaluated by computer simulation
using SABER. Fig. 4.6 shows the simulated system.

56

Utility
PCC Disconnect
Switch
VIa
VGa

Voltage Source Inverter

Vdc
DG unit

Sa Sb
a

Sc
b

Sa’

Sb’

Lg

LI

c
Sc’

Ia

Grid
Cf
Load

LCL Filter
Controller for Grid-connected Operation
IDref +

current
regulator

- +
IQref

θnew

Mode of Operation Switch
Grid-connected

+

Da
DQ

++
intentional
islanding

+

Db
ABC Dc

SPWM

VIa VIb VIc

Ia Ib Ic
θnew

Voltage controller for
stand alone operation

ABC



DQ
ID

Sb-b’
Sc-c’

VD VQ

ID IQ

ABC

Sa-a’

VI-ac VI-bc VI-ca VG-ab VG-bc VG-ca

IQ

Re-synchronization
θold

θnew

V
θnew

V
PLL

VD VQ f θold
Fig. 4. 6 Current controller for grid-connected operation

The R load was adjusted to consume 10 kW. The DG system was designed to supply 10 kW
and zero reactive power. The system was operated initially in grid-connected operation. Fig. 4.7
shows the voltages and currents at the PCC during grid-connected operation.

57

V:t(s)
va

V

200.0

vb
vc

0.0

-200.0

A:t(s)
ia

A

50.0

ib
ic

0.0

-50.0

V:t(s)
grid_condition

V

4.0
2.0
0.0
0.0 25.0m

75.0m

0.125

t(s)

0.175

0.225

0.275

0.325

Fig. 4. 7 Phase voltages and currents during grid-connected operation

When the grid-disconnection cause disappears, the transition from stand-alone mode to gridconnected mode can be started. The DG was operated in synchronous island mode until both
systems were re-synchronized. While in synchronous island mode, the synchronization controller
decreases or decreases the frequency to a limited value, as seen in Fig. 4.8. Also seen in that
figure are the voltages of the DG and grid; here the DG voltage can be seen to synchronize with
the grid and when the phase angle between the two voltages are approximately equal, the
algorithm reconnects the system to the utility and switches the mode of control from voltage
control to current control. As can be seen, the proposed algorithm successfully forces the voltage
at the DG to track the voltage at the grid.

58

(V)

200.0

Vg_a

(V) : t(s)
Vg_a
Va

Va

0.0

-200.0
6.0

(V) : t(s)

(V)

4.0

Grid-connected

grid_condition

2.0
Intentional-islanding

0.0
0.6

0.61 0.62

0.63

0.64 0.65
t(s)

0.66 0.67 0.68 0.69

0.7

Fig. 4. 8 Synchronization for grid re-connection
Once the synchronization was completed, the DG was reconnected to the grid and the
controller was switched from voltage control mode to current control mode. Fig. 4.9 shows the
phase voltage V without and with the synchronization algorithm implemented. As can be
a
noticed, the transients are minimal and virtually negligible indicating that the algorithm avoids a
hard transient in the reconnection from stand-alone operation to grid-connected operation.

59

(V) : t(s)
Va(w/o sync.)

(V)

200.0
0.0

-200.0
(V) : t(s)
Va(w sync.)

(V)

200.0
0.0

-200.0
0.50 0.52 0.54 0.56 0.58 0.60 0.62 0.64 0.66 0.68
t(s)
Fig. 4. 9 Phase voltage without (top) and with (bottom) synchronization

4.6. Experimental Results
A hardware prototype has been implemented for experimental verification. The control, PLL,
grid condition detection, and re-closure algorithms have been programmed using a universal
DSP control board developed at the Power Electronics and Motor Drives Laboratory at Michigan
State University. The DG is started up in grid-connected operation mode. Fig. 4.10 demonstrates
how the system line to line voltage and phase current behaves during grid-connected mode.

60

Fig. 4. 10 Line to line voltages and phase current during grid-connected operation

Fig. 4.11 shows the process of synchronization where the line to line voltage at both ends of
the separation device is illustrated. At the beginning of the synchronization, both voltages are out
of phase. As can be seen, the proposed algorithm successfully forces the voltage at the DG to
track the voltage at the grid until the synchronization process is completed. Also shown is the
smooth transition of the currents.

61

Fig. 4. 11 Transition from stand-alone to grid connected operation

62

CHAPTER 5. PROPOSED CONTROL FOR INTENTIONAL ISLANDING OPERATION
OF DG WITH SEAMLESS TRANSITION FROM GRID CONNECTED OPERATION

5.1. Introduction
The control of the DG system is important in both grid-connected and stand-alone modes and
the system stability becomes very crucial during the transfer between these two modes. If the
system does not have a proper transfer procedure, severe transient voltages or currents will
occur, which may damage the entire system [40]. Fig. 5.1 shows a waveform showing this
situation after grid disconnection at time t . A seamless transfer can ensure smooth operation
1
and quick attainment of steady state.

Fig. 5. 1 Simulation waveforms of load voltages and grid currents during the grid
disconnection [38]

63

In order to solve this transition problem, this chapter presents the development and test of a
control strategy for DG capable of working in intentional islanding connection mode with a
seamless transition from grid-connected to stand-alone operation modes. The control scheme
proposed is based on a voltage-controlled method for the stand-alone DG inverter. The standalone mode with voltage control is featured with a grid condition detection algorithm to detect
the instant at which the DG is cut from the main grid, a load shedding algorithm to disconnect
part of the load in order to steer the power system from potential dangers, and a voltage
controller with seamless transition from grid-connected to stand-alone operation modes.

5.2. Grid Condition Detection
The instant at which the DG is cut off from the main grid must be detected in order for the
system to change between grid-connected to stand-alone modes [53]. This detection is achieved
by using a PLL which consists of Clarke‟s transformation (Eq. 5.1), Park‟s transformation (Eq.
5.2), a PI regulator, and an integrator [5, 54]. The schematic of the PLL is illustrated in Fig. 5.2.
V   2 3 1 3  V 
ab 
 

V   0 1 3  V 
 bc 
 

(5.1)

V    cos 
 d
Vq   sin 
 

(5.2)

sin   V 
 
cos   V 
 

64

Va b c
abc




Vα β

'
Vq

dq0

K p+ k I / s

ω ω'
+
+

ωs e t

1/s

'

Test switch mode
voltage of operation
1/ (2)
f ' and
frequency
Vd = E '

Fig. 5. 2 PLL structure

The lock is realized by setting V to zero. A PI regulator can be used to control this variable
q
and the output of this regulator is the grid frequency [55]. As can be noticed in Fig. 5.1, in
addition to the frequency, the PLL is capable of tracking the magnitude of its input signals ( V
d
and V ), e.g. the grid voltages. These two parameters, frequency or voltage magnitude, are used
q
in the loss of main detection algorithm to detect the grid condition [28]. The algorithm sends a
signal that switches the inverter to the suitable interface control.
Fig. 5.3 shows the implementation of this algorithm. The output of a comparator block
activates a monostable circuit. If the monostable circuit stays in on-state for 0.16 seconds,
corresponding to 10 cycles, this is considered as an abnormal condition [28]. This abnormal
condition sends a signal that switches the inverter to the suitable interface control.

65

Loss of Main Detection

Vd

f

Vdp.u. > 1.1
or
Vdp.u. < 0.88
f > 60.5
or
f < 59.3

YES
monostable
YES

Switch
Mode of
Operation

Fig. 5. 3 Loss of Main Detection

This switching between grid-connection and stand-alone operation modes is done by using an
over/under frequency method (OFP/UFP) or an over/under voltage method (OVP/UVP) that
cause the DG inverter to switch if the frequency or amplitude of the voltage stays outside of
prescribed limits. When the grid is disconnected, this causes that the voltage amplitude or
frequency changes, as shown in Fig. 5.4. When these changes in voltage or frequency exceed
certain thresholds, grid disconnection is considered and the operation mode is consequently
switched. The algorithm is shown in Fig. 5.5.

66

Fig. 5. 4 Voltage or frequency change at grid disconnection

voltage or frequency
measurement

Vdpu < 0.88
or
Vdpu > 1.1

YES

NO

Intentional islanding
operation
Fig. 5. 5 Islanding Detection Algorithm
67

f < 59.3
or
f > 60.5

YES

While serving as good indications for islanding detection, the quick voltage or frequency
variations lead to a serious concern: the DG would operate out of the allowable voltage or
frequency range quickly after islanding occurs [56]. To avoid this, intelligent load shedding
algorithms need to be implemented in a DG system to make sure that the demand is within
available generation by disconnecting some least important loads [57].

5.3. Intelligent Load Shedding
Load shedding is defined as the process in which a part of the system load is disconnected
according to a certain priority in order to steer the power system from potential dangers [58-59].
During the grid connected operation, the DG is operated to provide the optimum power to the
grid according to many factors such as the availability of energy, energy cost, and so on [39].
The main grid is supplying or absorbing the power difference between the DG and local load
demand. When the main power grid is out (power outage), the DG that continues to inject predetermined optimum power can cause voltage and frequency transients depending on the degree
of power difference. The power difference makes the voltage and frequency drift away from the
nominal values [37]. When the voltage and frequency drifts have reached certain levels, it is
deemed that an islanding is occurring. This methodology is enough for islanding detection.
However, it is not enough for intentional islanding operation because often the local DG is either
less or greater than local load demand, and intelligent load shedding is needed. Therefore, it is
essential to have an analytical solution of the voltage and frequency transients locally for the DG
to have information and make decisions, and for intelligent load shedding to secure energy
delivery to sensitive loads.

68

To develop the load shedding algorithm, a constant impedance load is used. Fig. 5.6 shows
the theoretical voltage transients for a constant impedance load under various active power
differences (from -50% to +50%) after main power outage, while Fig. 5.7 shows the theoretical
frequency transients under various reactive power differences. As seen from Figs. 5.6 and 5.7,
with no load shedding it would be insufficient for keeping the voltage or frequency within the
limits required.

Fig. 5. 6 Voltage Transients under various Active Power Differences

69

Fig. 5. 7 Frequency Transients under various Reactive Power

The challenge is how to switch the DG inverter system to voltage control mode and bring the
voltage back to the normal range (0.88 – 1.1 Vpu) for intentional islanding operation. The
analytical solution of the simple case scenario shown in Fig. 5.6 provides a possible solution to
this challenge. Fig. 5.6 shows that the voltage change rate is related to the power differences
between the DG and load demand. The approach proposed is to detect the voltage change rate
and profile after the power outage and determine how much load shedding is needed before
going to the intentional islanding operation and switching to the voltage control mode. In order
to accomplish this, the system shown in Fig. 5.8 has been analyzed.

70

S1

S2
R1

Id

R2

Vg

Fig. 5. 8 System to implement load shedding
To determine the amount of load to be disconnected the following algorithm, based on Fig.
5.9, is proposed:

Id

S2
R1

R2

Idpu

Rpu=R1//R2

Fig. 5. 9 System in per unit to implement load shedding
o

Obtain the voltage amplitude expression for load shedding:

Using the circuit shown in Fig. 5.9, the expressions for the load voltages V
,V
, and V
cpu
apu bpu
can be found:
V
I
R sin(t   )
apu
dpu pu

(5.3)

2 

V
I
R sin  t   

bpu
dpu pu
3 


(5.4)

71

2 

V
I
R sin  t   

cpu
dpu pu
3 


(5.5)

Using V
,V
, and V
an expression for the voltage amplitude can be found,
cpu
apu bpu
V

V

V

pk

pk

pk



2
V 2 V 2 V 2
3 ab bc ca

(5.6)



2




3I
R
cos2  t      cos2 t     sin 2  t    
dpu pu
3
3
6



(5.7)





R
cos2  t      cos2 t     sin 2  t    
dpu pu
3
6



(5.8)

 2I

o

Derive the slope of the voltage amplitude

d  V (t ) 
 pk 

s 
dt

o

I

dpu

Derive I



 2I

R K
dpu pu





cos2  t      cos2 t     sin 2  t    
3
6



(5.9)

dpu





 s 2 cos 2  t      cos 2 t     sin 2  t    
3
6


2 R

pu

(5.10)

K

Using
R

pu

R
/ /R
1 pu
2 pu

(5.11)

72

and solving for R , where R represents the load to be shed,
1
1

R

1 pu

 2 I

dpu

K





s cos 2  t      cos 2 t     sin 2  t      2 I
K
dpu
3
6



(5.12)

where
 

 



K  sin  t     cos  t      sin  t     cos  t      sin t    cos t   
3
3
6
6





(5.13)

5.4. Transition from Grid-connected to Stand-alone: Proposed Controller

The proposed voltage closed loop control for stand-alone operation with seamless transition
is shown in Fig. 5.10. The control works as voltage regulation through current compensation.
The controller uses voltage compensators to generate current references for the current
regulation.

73

VIc

VIb

VIa

ABC


V

V
PLL

new

old

new

IDref
Voltage +
- +
Regulator
IQref -

Current _+
++
Regulator
_ +
K
K
ABC
Ib

Ic

DQ

DQ

Sa-a’
Da
SPWM
Sb-b’
ABC Db
Dc
Sc-c’

VQ

new

VD

ID
IQ

VDref
VQref +

new

Load Shedding
Algorithm
Rload shedding

Ia

VQ

VD

+ -

Synchronization
controller

Fig. 5. 10 Voltage controlled inverter
As shown, the load voltage, V and V , are forced to track their references ( V
and
Q
Dref
D
V
) by using a voltage regulator (PI compensator). The outputs of this compensator, I
Qref
Dref

and I

Qref

, are compared with the load current ( I

D

and I ), and the error is fed to a current
Q

regulator (PI compensator). The output of the current regulator acts as the voltage reference
signal that is fed to the sinusoidal pulse-width modulator (SPWM) to generate the high frequency
gating signals for driving the three-phase voltage source inverter. The current loop is included to
stabilize the system and to improve the system dynamic response by rapidly compensating for
near-future variations in the load voltages [11]. In order to get a good dynamic response V
is
DQ

74

fed forward. This is done because the terminal voltage of the inverter is treated as a disturbance
and the feed-forward is used to compensate for it [60].
A compensation coefficient, K, is added to the current control loop as a feedforward control
unit. This feedforward control achieves accurate tracking of the sinusoidal reference. The
compensation coefficient processes the magnitude of the input voltage of the PWM modulator
and counterattacks the severe transitions influenced by the grid disconnection. Then, this input
voltage is fed to the PWM modulator to produce the drive signals for the inverter switches.
Therefore, the modulated wave does not include the transient components that resulted from the
grid disconnection.

5.5. Transfer Functions
Fig. 5.11 shows the block diagram of the DG interface control for intentional islanding
operation.

D

E
Vd-ref +

_
Vd

e

Vd

+
+ Vin

K I1 + b K + K I2
P2
K P1+ Id-ref _
s V*
s

1

Vin

F(s)

Filter

Id

K

Fig. 5. 11 Block diagram of the voltage controlled inverter

75

Id

Z(s)

Load

Vd

The PI controllers produce a signal that is proportional to the time integral of the controller.
The transfer functions of the PI controllers are given by:

EK

P1

DK



P2

where K



P

K

I1
s

K

(5.14)

I2
s

(5.15)

are the proportional gains and K the integral gains.
I

The inverter stage does not have any significant transient time associated with it and hence it is
modeled as an ideal gain. This ideal gain can be given by G  s   1 .
I
The transfer function of the LCL filter is given by:
I (s)
1
F ( s)  d

V ( s) s3C L L  s 2C L Z  s L  L  Z
in
f 1 2
f 1
1 2





(5.16)

The transfer function of a parallel RLC load, Z(s), is given by:

Z ( s) 

sL R
L L
2 R C L  sL  R
s
L L L
L
L

(5.17)

Using Fig. 5.11 and equations (5.14) to (5.17), the transfer function of the current controlled
system is derived as:

H ( s) 

V ( s)
FZDE
d

V
(s) 1  KF  FZ  FD  FZDE 
d - ref

(5.18)

By using K  0.9425 , R  4.33 , L  4.584mH , C  1.535mF , L  1mH , L  0.5mH ,
L
L
L
1
2
C

f

 31 F , K

P1

 0.8 , K

I1

 25 , K

P2



1
1
, K  , then,
I 2 25
0.8

76

E  0.8 

25
s

D  1.25 

H ( s) 

(5.19)

1
25s

(5.20)





4.203x1013 s 2  31.282s  1

s6  150.454s5  9.8219 x107 s 4  1.5601x1011 s3  7.7068 x1013 s 2  2.1418 x1016 s  4.0878x1014

(5.21)

5.6. Simulation Results
The performance of the proposed control strategy was evaluated by computer simulation
using SABER. Fig. 5.12 shows the simulated system.
The R load was adjusted to consume 10 kW. The DG system was designed to supply 10 kW
and zero reactive power. The system was operated initially in grid-connected operation. The grid
was disconnected at 0.3 seconds. After the island was detected the control mode was changed
from current controlled to voltage controlled operation. Fig. 5.13 shows the currents at the PCC
before and after grid disconnection without the seamless transition controller implemented, while
Fig. 5.14 shows the currents at the PCC before and after grid disconnection with the seamless
transition controller implemented.

77

PC
C
Lg Ia VIa

Voltage Source Inverter

LI

Sa

a

Vdc

DG unit

b

Sa’

c

Cf

Ia Ib Ic

Mode of Operation Switch θnew

IQ

intentional
islanding

Controller for intentional islanding operation

VDref
+

VQref

- +
-

VD VQ

voltage
regulator

IDref +
IQref

- +
-

current
regulator
K

+
- ++
+

VQ

K

ID IQ

Da

Grid-connected

Controller for
Grid-connected
Operation

ABC
DQ θnew

ID

Load

LCL Filter

VD

DQ Db SPWM
ABC Dc

Re-synchronization

Fig. 5. 12 Simulated systems

78

Sc-c’

Load shedding
VIa VIb VIc
algorithm
Rload shedding ABC


VI-acVI-bcVI-caVG-abVG-bcVG-ca
θold

Sa-a’
Sb-b’

θnew

V V
PLL

θnew
VD VQ f θold

100.0

(V)

(V)

0.0

stand-alone

grid-connected

200.0

(V) : t(s)
Va
Vb
Vc

0.0

(V) : t(s)
grid_condition

-200.0

(A)

-100.0
100.0

stand-alone

grid-connected

Ic

0.0

-100.0

(A) : t(s)
Ia
Ib
grid_condition

0.36

0.38

0.40

t(s)

0.42

0.44

0.46

Fig. 5. 13 From grid-connected to stand-alone operation with severe transients

100.0
(V)

200.0
0.0

grid-connected

stand-alone

0.0

grid_condition

-200.0

(A)

-100.0

100.0

grid-connected

stand-alone

0.0
-100.0

(V) : t(s)
Va
Vb
Vc

(A) : t(s)
Ia
Ib
Ic
grid_condition

0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 0.52
t(s)

Fig. 5. 14 From grid-connected to stand-alone operation without severe transients

79

Fig. 5.15 shows a line-to-line voltage and a phase current at the PCC before and after grid
disconnection with the seamless transition controller implemented. As can be noticed, the
proposed controller successfully suppresses the severe transients caused by the disconnection of
the grid.

0.0

(V)

(V)

500.0 100.0

stand-alone

(V) : t(s)
grid_condition

0.0

-500.0 -100.0
100.0

(A)

grid-connected

(V) : t(s)
Vca

grid-connected

stand-alone

(A) : t(s)
Ic
grid_condition

0.0

-100.0
0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.4 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49
t(s)
Fig. 5. 15 From grid-connected to stand-alone operation without severe transients
To keep the magnitude of the voltage in its normal operational range when there is a power
mismatch, the load shedding algorithm proposed was implemented. Fig. 5.16 shows the
theoretical voltage transients under a power difference without the load shedding algorithm
implemented. For this case, when the voltage is out of the normal operating point, the load

80

shedding algorithm cut off the power difference from the load and the voltage was brought back
to the normal range. Fig 5.17 shows that the suitable load disconnection results in voltage
recovery, compared to the case of “no load shedding”.
200.0

(V) : t(s)
Va

Va

150.0
100.0

(V)

50.0
0.0

-50.0
-100.0
-150.0
-200.0
0.2

0.22

0.24

0.26

0.3
t(s)

0.28

0.32

0.34

0.36

0.38

Fig. 5. 16 Phase voltage Va without load shedding algorithm

200.0

(0.304,169.21)

(V) : t(s)
Va

(0.457,169.78)

150.0
100.0

(V)

50.0
0.0
-50.0
-100.0
-150.0
-200.0
0.2

0.24

0.32

0.28

0.36

t(s)

Fig. 5. 17 Phase voltage Va with load shedding algorithm
81

5.7. Experimental Results

The DG is started up in grid-connected operation mode, and then the separation device is
opened. When the DG is disconnected from the grid it operates in stand-alone mode. Fig. 5.18
shows a voltage and phase currents when the disconnection device is opened and the seamless
controller from grid-connected to stand alone is not implemented.

Fig. 5. 18 Transition from grid-connected to stand-alone operation with severe transients
Fig. 5.19 shows the grid voltage, the DG line to line voltage, and the phase current before
and after grid disconnection with the seamless transition controller implemented. As can be
noticed, the proposed controller successfully suppresses the severe transients caused by the
disconnection of the grid.

82

grid-connected

stand-alone
V_DG
V_grid

Voltages (L-L)
100v/div

current

Fig. 5. 19 Transition from grid-connected to intentional islanding operation without severe
transients
Fig. 5.20 shows the line to line voltage for the grid and the DG when the system is operating
in the islanding mode. Also shown are the load currents for the same type of operation. Fig. 5.21
shows the line to line voltages of the DG and the phase currents when the system is operating in
the islanding mode. As can be seen, the proposed control scheme is capable of maintaining the
voltages within the designed levels.

83

Fig. 5. 20 Line to line voltages and phase currents during intentional islanding operation

Voltages (L-L)
100v/div

current

Fig. 5. 21 DG line to line voltages and phase currents during intentional islanding operation

84

To test the load shedding algorithm, a test case where the islanded network is supplying
330W and importing 330W of active power from the grid was analyzed. Starting from this point,
in steady-state, the DG is disconnected and the network will become islanded. As shown in Fig.
5.22 it can be noticed that the suitable load disconnection results in voltage recovery. A total load
of around 640 W is curtailed to 320 W through load shedding, which is within the DG
capabilities. It can also be noticed from Fig. 5.21 that the load shedding assists the voltage to
reach acceptable values above the threshold selected.

Fig. 5. 22 Implementation of the load shedding algorithm

85

CHAPTER 6. CONCLUSIONS AND FUTURE WORKS

6.1 Conclusions

This research presented the development and test of a control strategy for DG capable of
working in both intentional-islanding (stand-alone) and grid-connected modes. The stand-alone
control featured an output voltage controller capable of handling excess or deficit of generated
power and synchronization for grid reconnection with a seamless transition from stand-alone to
grid-connected operation modes. The grid-connected mode with current control was also enabled
for the case of power grid connection. This grid-connected control featured an output current
controller capable of loss of main detection, synchronization with the grid, and seamless
transition from grid-connected to stand-alone operation modes.
An automatic mode switch method based on a PLL controller was described in order to
detect the power grid disconnection or recovery and switch the operation mode accordingly.
The proposed control strategy has the following characteristics:


Interface with AC System



Power quality



Synchronization with the Grid



Loss of Main Detection or Islanding



Transitions from grid-connected to stand-alone



Load shedding



Reclosing

86



Transitions from stand-alone to grid-connected

The simulation results showed that the detection algorithm can distinguish between islanding
events and changes in the loads and apply the load shedding algorithms when needed. The
experimental results showed that the proposed control schemes are capable of maintaining the
voltages within the standard permissible levels during grid-connected and islanding operation
modes. In addition, it was shown that the re-closure algorithm causes the DG to resynchronize
itself with the grid. Also, the simulation and experimental results show that seamless transfer has
been achieved.

6.2 Future Works

There are some issues that could be explored in the future related to this work:


Throughout this thesis, the DG unit was modeled by an ideal DC source and therefore,
the dynamic of the input source was neglected. As a future work, the effect of these
dynamic on the islanding detection and control of islanded systems can be studied.



A situation particular to the three-phase signals is the concept of unbalance. The threephase signals are unbalanced if they either have unequal magnitudes or phasedisplacements unequal to 120 degrees. The performance of the three phase PLL
algorithm presented is not good when the utility voltage presents voltage unbalances. If
these unbalances are not taking into account, the information of the utility voltage,
obtained from PLL structures, can present undesired errors. Based on the theory of
symmetrical components, an unbalanced set of signals can be decomposed into positive-,
negative- and zero-sequence components. The positive-sequence component is a

87

balanced set of signals. To eliminate the distorted utility voltage effects, a positive
sequence computation block can be used with good performance. This situation can be
considered as a future work.


One of the selling points for DG is that the local generation follows a scalable system
model, where due to the typical small size of the units, one can install as many units as
needed to satisfy the requests of the loads, without having too much of extra capacity
sitting idle. This concept requires that DGs can be installed in parallel without any
restrictions.



Storage need to be incorporated to satisfy the instantaneous power balance as a new load
comes on-line without penalizing the quality of other network quantities, such as bus
voltage magnitude. Load changes resulting in fast transients that exceed the ramping
capability of generation require storage availability from which to draw the required
transient energy. This inertia-less system presented is not well suited to handle step
changes in the requested output power.

88

APPENDICES

89

Appendix 1. Transfer Functions of the current controlled inverter

Fig. A1.1 shows the block diagram of the DG interface control for grid-connected operation.

D

Vd

+
+ Vin

+ e K + K I1
P1
Id-ref _
s V*

1

Vin

F(s)

Filter

Id

Z(s)

Load

Vd

Id
Fig. A1. 1 Block diagram of the current controlled inverter

The PI controller produces a signal that is proportional to the time integral of the controller.
The transfer function of the PI controller is given by:

DK

P1



K

I1
s

(A1.1)

where kp is the proportional gain and kI the integral gain.
The inverter stage does not have any significant transient time associated with it and hence it
is modeled as an ideal gain. This ideal gain can be given by GI(s) = 1.
The schematic circuit of the filter stage is shown in Fig. A1.2. It consists of an LCL filter and
a parallel RLC load.

90

L1

L2

Vx

Vin

Id
+
Vd

Cf

RL LL CL

Filter: F(s)

Load: Z(s)

Fig. A1. 2 LCL Filter and parallel RLC load

The transfer function of the filter is given by:

I (s)
F (s)  d
V (s)
in

(A1.2)

By Kirchhoff Current Law, the following expression is obtained:

V V
x in  sC V  I ( s )  0
f x d
sL
1

(A1.3)

Equation (A1.3) can be re-expressed as:

V

V
x  in  sC V  I ( s )  0
f x d
sL sL
1
1

(A1.4)

91

Using Ohm‟s Law, the current Id is given by:

V 0
x
I (s) 
d
sL  Z ( s )
2

(A1.5)

From equation (A1.5), the voltage Vx is given by:

V  I (sL  Z )
x d 2

(A1.6)

Substituting equation (A1.6) into equation (A1.4)

I ( sL  Z ) V
d 2
 in  sC I ( sL  Z )  I ( s )  0
f d 2
d
sL
sL
1
1





(A1.7)

Equation (A1.7) can be re-expressed as:

sI L
I Z V
d 2  d  in  I  s 2C I L  sC I Z  0
d
f d 2
f d
sL
sL
sL
1
1
1

(A1.8)


Z L2  Vin
I  s 2C L  sC Z 

 1 
d
f 2
f
sL
L
sL

1
1 

1

(A1.9)

92



V
L
in  sL  s 2C L  sC Z  Z  2  1
1
f 2
f
I
sL
L
d

1
1 




(A1.10)



V
in  s3C L L  s 2C L Z  s L  L  Z
f 1 2
f 1
1 2
I
d

(A1.11)

Then, the transfer function of the filter, F(s), is given by:

I (s)
1
F ( s)  d

V ( s) s3C L L  s 2C L Z  s L  L  Z
in
f 1 2
f 1
1 2





(A1.12)

The transfer function of the load, Z(s), is given by:

V (s)
Z (s)  d
I (s)
d

(A1.13)

By Kirchhoff Current Law:

I I
I
I
d
R
L
C
L
L
L

(A1.14)

V
V
I  d  d  sC V
d R
L d
sL
L
L

(A1.15)

93

Equation (A1.15) can be re-expressed as:

 1

1
I V 

 sC 
d
d R
L
sL
 L
L


(A1.16)



d   1  1  sC 
L
V
R
sL
d  L

L


(A1.17)

I

Then, the transfer function of the load, Z(s), is given by:

V (s)
1
Z (s)  d

1
1
I (s)

 sC
d
L
R
sL
L
L

(A1.18)

This can be re-expressed as:

Z ( s) 

sL R
L L
2 R C L  sL  R
s
L L L
L
L

(A1.19)

Using Fig. A1.2 and equations (A1.12) and (A1.19), the transfer function of the current
controlled system is derived as:

H ( s) 

V ( s)
d
I
( s)
d  ref

(A1.20)

94

I

d  ref

I e
d

(A1.21)

eD  V *

(A1.22)

V* V  V
d
in

(A1.23)

V FI
in
d

(A1.24)

I Z V
d
d

(A1.25)

From equation (A1.25),

V
I  d
d
Z

(A1.26)

Substituting equation (A1.25) into equation (A1.24)

V
V F d
in
Z

(A1.27)

Equation (A1.27) can be re-expressed as:

V
V  d
in FZ

(A1.28)

95

Substituting equation (A1.27) into equation (A1.23)

V
V* V  d
d FZ

(A1.29)

Substituting equation (A1.22) into equation (A1.29)

V
eD  V  d
d FZ

(A1.30)

From equation (A1.30)

V
1
e   d V 
dD
 FZ



(A1.31)

From equation (A1.31)

I

V
 1
V
 d 
 1 d
d  ref
Z  FZ  D

(A1.32)

Equation (A1.32) can be re-expressed as:

I

d  ref



V
V
V
d  d  d
FZD D
Z

(A1.33)

96

I

1 1
 1

  V
 FZD D Z  d

d  ref

I

I

(A1.34)

1
1 1
d  ref

 
V
FZD D Z
d

(A1.35)

d  ref 1  ZF  FD

V
FZD
d

(A1.36)

Then, the transfer function of the voltage controller, H(s), is given by:

H ( s) 

V ( s)
FZD
d

I
( s) 1  FZ  FD 
d  ref

(A1.37)

Where

Z ( s) 

F (s) 

CK

sL R
L L
2 R C L  sL  R
s
L L L
L
L

1





s3C L L  s 2C L Z  s L  L  Z
f 1 2
f 1
1 2

P1



K

I1
s

97

R  4.33
L

L  4.584mH
L

C  1.535mF
L

L  1mH
1

L  0.5mH
2

C

K

K

f

 31 F

P1

I1

 0.8

 25

Z (s) 

F (s) 

651.466 s
s 2  150.454 s  142117



6.4516 x1010 s 2  150.454s  142117



s5  150.454s 4  9.8219 x107 s3  1.456 x1010 s 2  5.5783x1013 s  0.4187

98

D  0.8 

25
s

3.365 x1013 s 2  1.051s
H (s) 
s6  150.108s5  9.83x107 s 4  6.62 x1010 s3  2.31x1013 s 2  7.58 x1015 s  2.28x1017

99

Appendix 2. Derivation of the Load Shedding Equations

The approach proposed is to detect the voltage change rate and profile after the power outage
and determine how much load shedding is needed before going to the intentional islanding
operation and switching to the voltage control mode. In order to accomplish this, the system
shown in Fig. A2.1 has been analyzed.

Id

S2
R1

R2

Idpu

Rpu=R1//R2

Fig. A2. 1 System to implement load shedding
o

Obtain the voltage amplitude expression before load shedding. The expressions for the

load voltages V
,V
, and V
can be found:
cpu
apu bpu
V
a  I sin(t   )
d
R

(A2.1)

V
b  I sin  t    2 


d
R
3 


(A2.2)

V
c  I sin  t    2 


d
R
3 


(A2.3)

In per unit:

V
apu
I
sin(t   )
dpu
R
pu

(A2.4)

100

V
2 
bpu

I
sin  t   

dpu
R
3 

pu

(A2.5)

V
2 
cpu

I
sin  t   

dpu
R
3 

pu

(A2.6)

Solving for the voltages:
V
I
R sin(t   )
apu
dpu pu

(A2.7)

2 

V
I
R sin  t   

bpu
dpu pu
3 


(A2.8)

2 

V
I
R sin  t   

cpu
dpu pu
3 


(A2.9)

o

V

Using V
,V
, and V
an expression for the voltage amplitude can be found,
cpu
apu bpu

pk



2
V 2 V 2 V 2
3 ab bc ca

(A2.10)

2 

V
V
V
I
R sin(t   )  I
R sin  t   

abpu
apu bpu
dpu pu
dpu pu
3 


(A2.11)


2 

V
I
R sin(t   )  sin  t   

abpu
dpu pu 
3 



(A2.12)


 

V
I
R
3 sin  t    
abpu
dpu pu 
6 



(A2.13)



V
 3I
R sin  t    
abpu
dpu pu
6


(A2.14)

2 
2 


V
V
V
I
R sin  t   
  I dpu R pu sin  t   

bcpu
bpu cpu
dpu pu
3 
3 


 
2 
2  

V
I
R
sin t   
  sin  t   

bcpu
dpu pu  
3 
3 

 


101

(A2.15)
(A2.16)

V
I
R   3 cos t    

bcpu
dpu pu 

(A2.17)

V
  3I
R cos t   
bcpu
dpu pu

(A2.18)

2 

V
V
V
I
R sin  t   
R sin(t   )
I
capu
cpu
apu
dpu pu
3  dpu pu


(A2.19)

 
2
V
I
R sin  t   
capu
dpu pu  
3

(A2.20)



  sin(t   ) 




 

V
I
R  3 cos  t     
capu
dpu pu 
3 


(A2.21)



V
 3I
R cos  t    
capu
dpu pu
3


(A2.22)



V2
 3I 2 R 2 sin 2  t    
abpu
dpu pu
6


(A2.23)

V2
 3I 2 R2 cos2 t   
bcpu
dpu pu

(A2.24)



V2
 3I 2 R 2 cos 2  t    
capu
dpu pu
3


(A2.25)

V2
V 2
V 2
abpu bcpu
capu


 


 3I 2 R 2 cos 2  t      cos 2 t     sin 2  t     
dpu pu 
3
6 



(A2.26)

V2
V 2 V 2
abpu bcpu capu





 3I
R
cos 2  t      cos2 t     sin 2  t    
dpu pu
3
6


V

pk



2
V 2 V 2 V 2
3 ab bc ca

(A2.27)

(A2.28)

102

V

V

pk

pk

2




3I
R
cos2  t      cos2 t     sin 2  t    
dpu pu
3
3
6





(A2.29)





R
cos2  t      cos2 t     sin 2  t    
dpu pu
3
6



(A2.30)

 2I

o

Derive the slope of the voltage amplitude

d  V (t ) 
 pk 

s 
dt

s

(A2.31)
 2I

R K
dpu pu





cos 2  t      cos 2 t     sin 2  t    
3
6



(A2.32)

where
 

 



K  sin  t     cos  t      sin  t     cos  t      sin t    cos t   
3
3
6
6





(A2.33)
Solving for I

I

dpu







 s 2 cos 2  t      cos 2 t     sin 2  t    
3
6


2 R

Using R

R

1 pu

dpu

pu

pu

(A2.34)

K

 R / / R and solving for R , where R represents the load to be shed,
1
2
1
1
 2 I

dpu

K





s cos 2  t      cos 2 t     sin 2  t      2 I
K
dpu
3
6



103

(A2.35)

Appendix 3. Transfer Functions of the voltage controlled inverter

Fig. A3.1 shows the block diagram of the DG interface control for intentional islanding
operation.

D

E
Vd-ref +

+
+ Vin

K I1 + b K + K I2
P2
K P1+ Id-ref _
s V*
s

e

_

Vd

1

Vin

F(s)

Filter

Id

Z(s)

Load

Vd

Id

Vd

K

Fig. A3. 1 Block diagram of the voltage controlled inverter
The PI controllers produce a signal that is proportional to the time integral of the controller.
The transfer functions of the PI controllers are given by:

EK

P1

DK



P2



K

I1
s

K

(A3.1)

I2
s

(A3.2)

The inverter stage does not have any significant transient time associated with it and hence it
is modeled as an ideal gain. This ideal gain can be given by GI(s) = 1.
The schematic circuit of the filter stage is shown in Fig. A3.2. It consists of an LCL filter and
a parallel RLC load.
104

L1

L2

Vx

Vin

Id
+
Vd

Cf

RL LL CL

Filter: F(s)

Load: Z(s)

Fig. A3. 2 LCL Filter and parallel RLC load

The transfer function of the filter is given by:
I (s)
1
F ( s)  d

V ( s) s3C L L  s 2C L Z  s L  L  Z
in
f 1 2
f 1
1 2





(A3.3)

The transfer function of the load, Z(s), is given by:

Z ( s) 

sL R
L L
2 R C L  sL  R
s
L L L
L
L

(A3.4)

Using Fig. A3.9 and equations (A3.3) to (A3.4), the transfer function of the current controlled
system is derived as:

H ( s) 

V ( s)
d
V
( s)
d  ref

(A3.5)

V
V  e
d  ref
d

(A3.6)

eE  I

(A3.7)

d  ref

105

eE  I  b
d

(A3.8)

bD  V  KI  V
d
d
in

(A3.9)

V FI
in
d

(A3.10)

I Z V
d
d

(A3.11)

From (A3.11),

V
I  d
d
Z

(A3.12)

(A3.12) in (A3.10)

V
V F d
in
Z

(A3.13)

From (A3.13)

V
V  d
in FZ

(A3.14)

106

(A3.14) in (A3.9)

V
V
bD  V  K d  d
d
Z
FZ

(A3.15)

From (A3.15)

K1
 1
b V 
1 
d  FZ
Z D

(A3.16)

(A3.16) and (A3.12) in (A3.8)

V
K V
 1
eE  d  
1  d
Z  FZ
Z D

(A3.17)

From (A3.17)

K
1 1 V
 1
e

   d
 FZD ZD D Z  E

(A3.18)

(A3.18) in (A3.6)

V
 e V
d  ref
d

(A3.19)

107

K
1
1
 1

V




1 V
d  ref  EFZD EZD ED ZE  d



(A3.20)

From (A3.0)

H (s) 

V ( s)
FZDE
d

V
( s) 1  KF  FZ  FD  FZDE 
d  ref

(A3.21)

Using K  0.9425 , R  4.33 , L  4.584mH , C  1.535mF , L  1mH , L  0.5mH ,
L
L
L
1
2
C

f

 31 F , K

I1

 25 , K

P2



1
1
, K  , then,
I 2 25
0.8

651.466 s

Z (s) 

(A3.22)

s 2  150.454 s  142117

F (s) 



6.4516 x1010 s 2  150.454s  142117

25
s

D  1.25 

H (s) 



s5  150.454s 4  9.8219 x107 s3  1.456 x1010 s 2  5.5783x1013 s  0.4187

E  0.8 

H ( s) 

P1

 0.8 , K

(A3.23)

(A3.24)

1
25s

(A3.25)

V ( s)
FZDE
d

V
( s) 1  KF  FZ  FD  FZDE 
d  ref



(A3.26)



4.203x1013 s 2  31.282s  1

s6  150.454s5  9.8219 x107 s 4  1.5601x1011 s3  7.7068 x1013 s 2  2.1418 x1016 s  4.0878x1014

(A3.27)

108

Appendix 4. Block Diagram of the 2407A DSP Controller

Fig. A4.1 shows the block diagram of the basic configuration for the LF2407A DSp
controller. The major interfaces of the board include the target RAM, SRAM memory, analog
interface, analog signals interface, PWM output signal interfaces, among others functions.

Fig. A4. 1 Block diagram of the 2407A DSP controller

109

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