Placing of VSC-HVDC Lines in a Meshed AC-Network · PDF filePlacing of VSC-HVDC Lines in a...
65
Jin Shuai Placing of VSC-HVDC Lines in a Meshed AC-Network Master Thesis PSL1202 EEH – Power Systems Laboratory Swiss Federal Institute of Technology (ETH) Zürich Examiner: Prof. Dr. Göran Andersson Superviosr: Markus Imhof & Roger Wiget Zürich, August 29, 2012
Transcript of Placing of VSC-HVDC Lines in a Meshed AC-Network · PDF filePlacing of VSC-HVDC Lines in a...
Jin Shuai
Placing of VSC-HVDC Lines in a Meshed AC-Network
Master Thesis
PSL1202
EEH – Power Systems Laboratory
Swiss Federal Institute of Technology (ETH) Zürich
Examiner: Prof. Dr. Göran Andersson
Superviosr: Markus Imhof & Roger Wiget
Zürich, August 29, 2012
ii
Abstract Many existing High Voltage Alternating Current (HVAC) bulk transmission systems, e. g
in Europe and North America, have reached their capability limits and a significant
increase of transmission capacities is foreseen within the next decades. There are
several reasons calling for an upgrade, where the most significant is the expected
overall increase in consumption of electric energy. Furthermore, the fluctuating nature
of many renewable energy sources, like wind and solar, requires higher transmission
capacities in order to provide the regulating power from other power plants.
The recent developments in semiconductors and control equipment have made the
Voltage Source Converter Based High Voltage direct current (VSC-HVDC) feasible. Due
to the use of VSC technology and Pulse Width Modulation (PWM), VSC-HVDC has a
number of potential advantages as compared with classical HVDC, such as short circuit
current reduction, rapid and independent control of active and reactive power, etc.
With those advantages VSC-HVDC will likely be widely used in future transmission and
distribution systems.
In this thesis, two different algorithms with the objectives to place VSC-HVDC line in
order to reduce power flow contingencies and inter-area oscillations in AC power
system are developed and their effectiveness and validity on both small and complex
AC grid are investigated in the Matlab program.
In chapter2, the thesis studies the causes and possible solutions of power flow
contingencies, an algorithm is developed to identify the optimal placement for VSC-
HVDC line in order to reduce the power flow contingencies in a given AC grid, in
addition, not only the economical optimization of the whole system but also the line
capacity of the VSC-HVDC can be calculated by the algorithm. Its functionality is
verified by testing IEEE14 and IEEE118 bus systems.
Chapter3 describes different oscillation modes in power system, and an algorithm is
developed to specify optimal placement for VSC-HVDC line in order to reduce the inter-
area oscillation in a given AC grid, the algorithm is tested on Kundur second order
system and IEEE Two Area RTS-24 system. The weak connections in testing system are
specified by this algorithm and the oscillation modes in both testing system are
analyzed.
Chpater4 demonstrates some valuable work which is worth to do in the future due to
time limits for this thesis.
iii
iv
Contents
ABSTRACT.......................................................................................................................................... II
CONTENTS ........................................................................................................................................ IV
LIST OF FIGURES ............................................................................................................................... VI
LIST OF TABLES ...............................................................................................................................VIII
LIST OF ABBREVIATION ..................................................................................................................... X
PREFACE .......................................................................................................................................... XII
CHAPTER1
INTRODUCTION .................................................................................................................................. 1
1.1 BACKGROUND ................................................................................................................................ 1
1.2 CURRENT SOURCE CONVERTER HVDC .............................................................................................. 1
1.2.1 Configurations of Current Source Converter HVDC ......................................................... 1
1.2.2 Application of Classic HVDC .............................................................................................. 3
1.3 ADVANTAGES & DISADVANTAGES .................................................................................................... 4
1.3.1 Advantages of HVDC ......................................................................................................... 4
1.3.2 Disadvantages of HVDC ................................................................................................... 5
1.4 VSC-HVDC .................................................................................................................................. 6
1.4.1 Components of VSC-HVDC system ................................................................................... 6
1.4.2 Control Strategy of VSC-HVDC .......................................................................................... 7
1.4.3 VSC-HVDC vs. Classical HVDC ........................................................................................... 8
1.4.4 Applications of VSC-HVDC ................................................................................................ 9
CHAPTER2
OPTIMAL PLACEMENT OF VSC-HVDC LINK TO REDUCE POWER FLOW CONTINGENCIES .............. 11
2.1 INTRODUCTION ............................................................................................................................. 11
2.1.1 Causes of Power Flow Contingencies .............................................................................. 11
2.1.2 Possible Solutions ............................................................................................................. 11
2.2 ALGORITHM ............................................................................................................................. 12
2.3 SIMULATION RESULTS ............................................................................................................... 17
2.3.1 Simulation Results on IEEE14 ........................................................................................... 17
2.3.2 Simulation Results on IEEE118 ......................................................................................... 21
2.4 CONCLUSION ........................................................................................................................... 24
CHAPTER3 OPTIMAL PLACEMENT OF VSC-HVDC LINK TO REDUCE INTER-AREA OSCILLATIONS ..................... 25
3.1 INTRODUCTION ............................................................................................................................. 25
3.2 ALGORTHIM ............................................................................................................................. 27
3.2.1 Concept of slow coherency .............................................................................................. 27
3.2.2 Analytical expression ....................................................................................................... 28
3.3 SIMULATION RESULTS ................................................................................................................ 32
3.3.1 Simulation results on Kundur second order system ....................................................... 32
3.3.2 Simulation result on IEEE Two Area RTS-24 system ....................................................... 35
3.4 CONCLUSION ............................................................................................................................ 37
v
CHAPTER4
CONCLUSIONS AND FUTURE WORK ............................................................................................... 38
4.1 CONCLUSIONS .............................................................................................................................. 38
4.2 FUTURE WORK .............................................................................................................................. 38
APPENDIX A..................................................................................................................................... 40
REFERENCE ....................................................................................................................................... 49
vi
List of Figures Figure 1-1
(a) Monopolar Long-Distance Transmissions with ground return path [3]
(b) Monopolar Long-Distance Transmissions with metallic return path [3] …………………………………..2
Figure 1-2
(a) Bipolar Transmissions system with ground return [3]
(b) Bipolar Transmissions system without electrodes [3]
(c) In monopolar metallic return operation due to pole failure [3]
(d) In monopolar metallic return operation due to converter failure [3] ............................................... 2
Figure 1-3 Back-to-back converter [3] .......................................................................................................... 3
Figure 1-4 Cost structure [7] .......................................................................................................................... 5
Figure 1-5 A 12-pulse converter for HVDC ................................................................................................... 6
Figure 1-6 A VSC HVDC back-to-back system [8] ...................................................................................... 6
Figure 1-7 A bi-polar two level PWM converter [9] .................................................................................... 7
Figure 1-8 Overall control structure of the VSC-HVDC [10] ....................................................................... 8
Figure 2-1 Example AC system ..................................................................................................................... 13
Figure 2-2 Example system used to clarify BLR ........................................................................................ 14
Figure 2-3 (a),(b) and (c) The relationship of these three factors with Bus Sensitivity Index ............. 16
Figure 2-4 Flow Chart of the Algorithm ..................................................................................................... 17
Figure 2-5 Power flow of IEEE14 system in normal operation ................................................................ 18
Figure 2-6 Power flow of IEEE14 system after installing VSC-HVDC line from Bus1 to Bus3 .............. 19
Figure 2-7 Equivalent treatment to the first VSC-HVDC line .................................................................. 19
Figure 2-8 Power flow of IEEE14 system after installing VSC-HVDC lines from Bus1 to Bus and Bus1
to Bus9 ................................................................................................................................................. 20
Figure 2-9 Generation centre, load centre and power flow of the IEEE118 bus system ...................... 22
Figure 2-10 Overloaded area of the IEEE118 bus system .......................................................................... 22
Figure 2-11 Overloaded area of the IEEE118 bus system with VSC-HVDC .............................................. 24
Figure 3-1 Flow chart of the algorithm ..................................................................................................... 28
Figure 3-2 Norton equivalent input current of generator .................................................................... 29
Figure 3-3 Eigenvalue and stability of system ........................................................................................... 31
Figure 3-4 Kundur second order system [31] ............................................................................................. 33
Figure 3-5 (a) and (b) Participation factor of Kundur second order system ......................................... 35
Figure 3-6 IEEE Two Area RTS-24 system [33] ........................................................................................... 36
vii
viii
List of Tables Table 1-1 HVDC projects list around the world during 2000-2010[14] .................................................... 4 Table 1-2 Projects lists of VSC-HVDC .......................................................................................................... 10 Table 2-1 Bus Sensitivity Index for each bus based on the example system ......................................... 15 Table 2-2
(a) Simulation result for the first VSC-HVDC line by Algorithm
(b) Simulation result for the second VSC-HVDC line by Algorithm ....................................................... 18 Table 2-3
(a) Part of Simulation result for the first VSC-HVDC line by verifying method
(b) Part of Simulation result for the second VSC-HVDC line by verifying method .............................. 21
Table 2-4 Simulation results comparison of the developed algorithm and verifying method ......... 21 Table 2-5
(a) A part of load rates of transmission lines in overloaded area without VSC-HVDC line
(b) A part of load rates of transmission lines in overloaded area with VSC-HVDC line from Bus10 to
Bus1 ....................................................................................................................................................... 23 Table 2-6 The simulation results of likely starting and ending terminals............................................ 23 Table 2-7 Part of the simulation results from verifying method ........................................................... 24 Table 3-1 Generating parameters ............................................................................................................... 33 Table 3-2 Simulation results on operation case one ................................................................................ 33 Table 3-3 Simulation results on operation case two ............................................................................... 34 Table 3-4 Oscillation modes in kundur second order system ................................................................. 35 Table 3-5 Part of simulation result on IEEE Two Area RTS-24 system ................................................... 36 Table A - 1 Parameters of VSC-HVDC line in IEEE14 ................................................................................. 40
Table A - 2 Parameters of VSC-HVDC line in IEEE118 ................................................................................ 41 Table A - 3 Simulation Results of after first HVDC line on IEEE14 by verifying method...................... 42 Table A - 4 Simulation Results after installing second HVDC line on IEEE14 by Verifying method ... 43 Table A - 5 Line load rate of IEEE118 before installing VSC-HVDC line .................................................. 44 Table A - 6 Line load rate of IEEE118 after installing VSC-HVDC from Bus10 to Bus 1 ......................... 45 Table A - 7 Simulation Results of IEEE118 by the proposed algorithm .................................................. 46 Table A - 8 Simulation Results of IEEE Two Area RTS-24 system............................................................ 47 Table A - 9 Dynamic data of generators and line parameters for Kundur system ............................ 48
ix
x
List of Abbreviation
AVR Automatic Voltage Regulators
BLR Bus Load Rate
CSI Composite Security Index
DGLC Distribution of Generator and Load Center
GTO Gate Turn-off Thyristor
HVAC High Voltage Alternating Current
HVDC High Voltage Direct Current
IGBT Insulated Gate Bipolar Transistor
IGCT Integrated Gate Commutated Thyristors
LFIO Low Frequency Inter-area oscillations
MMC Modular Multilevel Converter
PSS Power System Stabilizer
POD Power Oscillation Damping
PWM Pulse Width Modulation
SVC Static Var Compensator
VSC Voltage Source Converter
xi
xii
Preface The research work was carried out at the Power Systems Laboratory of the Department
of Information Technology and Electrical Engineering of the Swiss Federal Institute of
Technology, Zürich (ETH Zürich).
First I would like to thank my supervisors Mr. Markus Imhof and Mr. Roger Wiget at ETH
Zürich and Mr. Dr. Hanno Stagge at RWTH-Aachen for their help, guidance, patience
and encouragement, without which, this thesis would not be possible to finish.
I would also like to thank my examiner at ETH-Zürich Prof. Dr. Göran Andersson for
offering me the opportunity to explore the challenging and promising topic of the VSC-
HVDC technology.
A special thanks to my examiner at RWTH-Aachen Univ.-Prof. Dr. Rik W. De Doncker for
his support to my research project.
Last but not the least; I want to thank my girlfriend Eva Yin for her love and support.
Jin Shuai
Zürich, Swizterland
August 2012
xiii
1
Chapter1
Introduction 1.1 Background
Miesbach–Munich Power Transmission in Germany was the first power transmission
system in the world over a long distance. The first transmission of electrical energy
started with direct current around 1880s. At that time the voltage level was limited to
some hundred volts, higher DC voltage cannot be generated due to the limitation of
semiconductor technology; in addition, high transmission voltage is needed for a long
distance power transmission in order to lower the transmission losses over the
overhead line due its ohmic characteristics [1].
In the late 1880s alternating current had first developed in Europe thanks to the work
of Nikola Tesla. In order to limit the transmission losses within an acceptable value, a
new and simple machine called transformer which can step up and step down voltage
was invented in 1886 [1]. After the utilization of transformer in transmission system, AC
technology was used world widely in the aspect of power transmission due to its
overwhelming advantages over DC system in these days.
The situation had not been changed until the 1930s in which high voltage DC became
possible with the development of high power electronic devices such as mercury arc
rectifier. DC power transmission system with high voltage DC which is called High
Voltage Direct Circuit (HVDC) was emerged. Finally, starting in the 1970s, high power
semiconductor devices like power thyristors, Insulated Gate Bipolar Transistor (IGBT),
Integrated Gate Commutated Thyristors (IGCT) and so on advance the development of
new technology like Current Source Converter (CSC) HVDC and Voltage Source based
Converter (VSC) HVDC [2].
1.2 Current Source Converter HVDC
1.2.1 Configurations of Current Source Converter HVDC
The CSC HVDC is also named as classical HVDC. The invention of mercury arc rectifiers
in the 1930s made this technology possible. In 1941, the first commercial HVDC system
was built in Berlin in Germany with +-200kV and 150 A by Siemens [3]. Since then,
several HVDC systems had been established with mercury arc valves and later on
replaced by thyristor valves. With respect to different operational requirement and
design, HVDC systems can be categorized into three different configurations.
Monopole system
Bipolar system
Back to back system
2
Monopole system
The Figure 1-1 (a) and (b) demonstrate the simplified equivalent circuit of Monopole
transmission system with ground return path and metallic return path respectively.
The technology with a return path through ground electrodes is particularly for a very
long sea cable transmission, however, in other cases, a metallic return path is used due
to the existing infrastructure or environmental constrains.
(a) (b)
Figure 1-1 (a) Monopolar Long-Distance Transmissions with ground return path [3] (b) Monopolar Long-Distance Transmissions with metallic return path [3] Bipolar system
When a higher transmission capacity or transmission voltage is needed the
configuration in Figure 1-2 (a) and (b) are the options. They are combination of two
poles. In such a structure a common low voltage return path only carries a small
current in normal operation due to unbalance, Figure 1-2 (b) will face function problem
when there is pole outage. However, Figure 1-2 (a) can be used to transfer part of the
full power even during maintenance or fault of one pole as be shown in Figure 1-2 (c)
and (d). In general, more than 50% of the transmission capacity can still be used, the
percentage depends on the actual overload capacity of the remaining pole. Comparing
with the monopolar line, bipolar solution is more cost effective because of only one
common return path.
(a) (b)
(c) (d)
Figure 1-2
(a) Bipolar Transmissions system with ground return [3]
(b) Bipolar Transmissions system without electrodes [3]
(c) In monopolar metallic return operation due to pole failure [3]
(d) In monopolar metallic return operation due to converter failure [3]
3
Different topology structures are utilized to satisfy different operational requirement
and enviromental contraint [3].
Back-to-back Converters
Back-to-back Converters are wildly used for power transmission between two adjacent
asynchronous AC systems to achieve a defined power flow, and its rectifier and inverter
are located in the same station as be shown in Figure 1-3 [3].
Figure 1-3 Back-to-back converter [3]
1.2.2 Application of Classic HVDC
Since the first HVDC transmission system was introduced in 1941. This techonolgy is
widely used due to many advantages including the interconnection of asynchronous
networks, economic benefits, long-distance bulk power delivery and environmental
benefits. In the big background of fast growth in offshore wind farms and other
renewable power stations, HVDC system will lead to a new power grid in the future [4].
With the benefits describled above, HVDC technology is very popluar in booming
economies due their huge electricity demand in some economic fast growing area. In
2006, Power Grid Cooperation of Indian decided to increase the transmission capacity
in Southeast of Indian from 2000MW to 2500MW at the rating of ±500kV. This project
is now online. This upgrade project made the power system more efficient and the
maximum use of the system’s overhead capacity [5].In 2007, the China Southern Power
Grid Company began to construct a ±800kV HVDC system between Yunnan province
and Guangdong province in South of China with the capacity of 5000MW. This is the
world's first ±800kV DC transmission project [5].
4
Table 1-1 shows the HVDC project around the world during 2000-2010.
HVDC SUPPLIER YEAR
COMMISSIONED
POWER
RATING
(MW)
DC
VOLTAGE
(kV)
LOCATION
ABB 2000 600 ±450 SWEDEN-
POLAND
ABB 2000 3 x 60 ±80 AUSTRALIA
HITACHI 2000 1400 ±250 JAPAN
ABB 2000 1100 ±70 ARGENTINA-
BRAZIL
ABB 2002 2000 ±70 ARGENTINA-
BRAZIL
GEC ALSTHOM 2000 70 20 URUGUAY-
BRAZIL
PIRELLI/ABB 2001 500 400 GREECE-ITALY
SIEMENS 2001 1800 ±500 CHINA
HITACHI/TOSHIBA 2001 300 125 JAPAN
SIEMENS 2001 300 ±300 THAILAND-
MALAYSIA
ABB 2002 330 ±150 U.S.A
ABB 2002 200 ±150 AUSTRALIA
GEC ALSTHOM 2002 500 205 INDIA
ABB 2003 2 x 100 ±13 U.S.A.
SIEMENS 2003 2000 ±500 INDIA
ABB/SIEMENS 2003 3000 ±500 CHINA
ABB 2004 3000 ±500 CHINA
SIEMENS 2004 3000 ±500 CHINA
SIEMENS 2007 3000 ±500 CHINA
ABB 2004 2x40 ±60 NORWAY
SIEMENS 2004 3100 ±400 U.S.A.
SIEMENS 2005 210 ±64 U.S.A.
SIEMENS 2006 500 400 AUSTRALIA
ABB 2006 3000 ±500 CHINA
SIEMENS 2007 660 500 U.S.A.
AREVA 2008 250 ±17.4 CANADA
SIEMENS 2009 2500 500 INDIA
ABB 2009 2x625 315 CANADA
AREVA 2009 3 x 600 3 x 222 SAUDI ARABIA
ABB 2009 300 350 SOUTH AFRICA
SIEMENS 2010 5000 ±800 CHINA
Table 1-1 HVDC projects list around the world during 2000-2010[14]
1.3 Advantages & Disadvantages
1.3.1 Advantages of HVDC
In comparions with High Voltage Alternating Current (HVAC) transmission
line, HVDC transmission line can save aroud 1/3 steel-core aluminium in
total to transmit the same amount of power, because HVDC overhead line
only requires two conductors to transmit the power comparing to three
conductors for HVAC transmssion line. Furthermore, simpler and smaller
tower can be used to carry the transmission lines [6].
5
A very long marine cable can not be used with HVDC due to the capacitive
characteristics of cables, thereby HVDC is the only solution to transmit
power to island in which case overhead line is not possible. Besides, with
the same insulation thickness and cross section, the transmission capacity
for DC cable is significantly higher than that of AC. Similarly like overhead
DC line, for HVDC, only one cable is required for monopole and two cables
for bipolar but three cables are needed for AC system due to three-phase
transmission.
Back-to-back HVDC links can be used to interconnnect two AC systems with
different operational frequencies without increasing the short-circuit
current level for both connected AC system.
Because of the fast reaction of power electronic devices, active and reactive
power can be controlled rapidly, HVDC systems can be used to improve the
stability and safety of AC systems.
HVDC transmission system has lower losses because of the fewer
conductors and suffering no skin effect.
Better solution to connect renewable energy source such as wind farm to
AC system due to its fast power control.
1.3.2 Disadvantages of HVDC
Cost
As can be seen from Figure 1-4, power electronics devices and converter
transformers are the most expensive part for HVDC transmission system
Sepcially, converter stations are much more expensive than that of the HVAC
stations.
Figure 1-4 Cost structure [7]
Cost Structure
Freight isurance
Converter trasformers
Power electronics
Civil works buildings
Engineering
Erection commissioning
Other equipment
Control
AC filters
6
Harmonics
In modern HVDC systems, 12-pulse-converter as be shown in Figure1-11 is
normally used which lead to high harmonics to the connected AC systems.
Power quality is impacted by these harmonics, the harmonics are recognized as
one of the biggest problems in HVDC systems, it leads to big filter banks and
higher costs [4].
Figure 1-5 A 12-pulse converter for HVDC
1.4 VSC-HVDC
1.4.1 Components of VSC-HVDC system
The recent development of the modern semiconductor devices such as the IGBT and
IGCT made a new generation of power electric converters possible. These devices,
unlike the conventional thyristors which have no intrinsic turn-off ability, are of the
fully controlled type. A typical VSC-HVDC system, shown in Figure 1-6, is structured by
transformers, AC filters, phase reactors, converters, DC capacitors and DC cable.
Figure 1-6 A VSC HVDC back-to-back system [8]
Transformers
Transformer is used to connect converter and AC system, the most significant function
of it is to adjust the voltage level of AC system to certain level that suitable for the
converter.
AC filters
AC filters are normally functions as AC harmonics filters and reactive power
compensators. The harmonics cause by IGBTs switching operation emitted into the AC
system must be mitigated to prevent other equipment in the system from malfunction.
7
Phase reactors
Phase reactors have two functions in the system. On one hand, they are used for
controlling the active and reactive power flow by regulating currents through them,
one the other hand they are also used to reduce the high frequency harmonic content
of the AC currents which are caused by switching.
DC capacitors
Capacitors are used to maintain the voltage level and keep the power balance during
transients. The size of these capacitors depends on the desired operating DC voltage.
Converters
Figure 1-7 indicates one of widely used VSC topology in the industry. It contains six
IGBTs in total, with two IGBTs stack on each leg. Besides, a diode is connected in anti-
parallel connection to each IGBT in order to allow bidirectional current flow.
Figure 1-7 A bi-polar two level PWM converter [9]
Assume the reactance of phase reactor is and it is lossless, and only one phase is
taken into account to express the power flow. The calculations of active and reactive
power are expressed in equation1-1 and 1-2 respectively.
(1-1)
(1-2)
Observations from these two equations:
The active power flow between the AC system and the VSC is determined by the
phase angle . When , active power flows into the AC system
otherwise flows out of AC system from the VSC.
The reactive power flow direction is determined by couple of parameters
; the contribution of phase angle is relatively small,
therefore, the main factors are the amplitude of the AC system voltage and
the fundamental part of VSC output voltage . When , the reactive
power flows into the AC system, while the VSC absorbs reactive
power from the AC system.
1.4.2 Control Strategy of VSC-HVDC
By using VSC-HVDC the reactive power, the active power, the AC voltage, the DC
Voltage and the frequency can be controlled. The controllability of VSC-HVDC is out the
8
scope of this thesis; however, considering the importance of the control strategy, it is
necessary to explain the principle of it. As described in last section, the VSC-HVDC can
control the active and reactive power independently. Both inverter and rectifier can
control the reactive power independently or by the required AC voltage separately. The
active power can be controlled by the DC voltage, the variation of frequency at the AC
side or set manually [10]. As be shown in Figure 1-8, both rectifier and inverter can
choose between AC voltage controller and reactive controller, a reference value for the
controller can be generated by each of these controllers.
Figure 1-8 Overall control structure of the VSC-HVDC [10]
It is easy to understand that there is no possibility for all controllers to be used at the
same time. In different operation conditions different kinds of control strategies are
employed.
In this thesis the controllability will not be explained in detail because of its complexity
and it is out the scope of this work.
1.4.3 VSC-HVDC vs. Classical HVDC
The VSC-HVDC has several main advantages over the Classical HVDC:
VSC-HVDC can independently control the active and reactive power. The
reactive capabilities can be used to control the AC network voltage and
enhanced power quality of AC system [10].
It can lower the risk of commutation failures. The commutation failures is
catastrophic sometime, as the VSC-HVDC uses self-commutating
semiconductor devices, it is no longer necessary to present a sufficiently high
AC voltage [10].
The VSC-HVDC is a better option to creating a DC grid with a number of
converters because of its constant voltage in the grid.
Due to the fast response of the VSC, VSC-HVDC is the best option to connect the
fluctuating renewable energy such as off-shore wind power farm.
9
The VSC-HVDC technology also has some disadvantages comparing to Classic HVDC.
VSC-HVDC technology is more expensive than Classic HVDC, due to the higher
cost of the converter stations.
VSC-HVDC system has higher converter losses than Classic HVDC because of
the higher switching frequency.
Classical HVDC has higher converter rating than VSC-HVDC technology up to
today because of IGBT has a lower capacity that of the thyristor.
1.4.4 Applications of VSC-HVDC
VSC-HVDC technology is utilising the state of the art semiconductors IGBT, and PWM is
also employed to create the desired voltage waveform, phase angle and magnitude,
which in turn can offer a wide range of applications:
Underwater power connection
VSC-HVDC is a sound option for underground power transmission, especially
underwater cables, the reactive power produced by an AC submarine cable
would take up the entire current-carrying capacity of the conductor above a
certain distance because of capacitive property of AC cable.
City center power distribution
VSC-HVDC is considered as the only alternative to increase capacity over short
distances due to the increasing difficulties in obtaining permission to build new
power lines notably in urban area.
Connecting onshore wind farms and offshore wind farms
By using self-commutated device IGBTs, the VSC converter can connect to very
weak systems like wind farms [11] due to its fast and independent active and
reactive power control .
Connecting asynchronous power system
The power quality will be improved as the VSC-HVDC terminals can control
reactive power in each station in excess of the active power transfer between
stations.
Providing shore power supplies to offshore oil & gas platforms
VSC-HVDC package is flexible to move and easy to set up.
In year 1999, the first commercial VSC-HVDC line with capacity rating of 50MW at
voltage level of 80kV was put into operation. These two 70km undergroud cables are
located between the southern part of Gotland with a Wind farm and the load center in
the city Visby due to difficulties to get permits to build an additional overhead
transmission line [12]. The following table shows some VSC-HVDC projects in the world:
10
Project In service Power DC voltage Distance Application
GOTLAND
Sweden 1999 50MW 80kV 70km
Wind
Undergrounding
DIRECLINK
Australia 2000 3x60MW 80kV 65km Undergrounding
CROSS SOUND
USA 2002 330MW 150kV 40km Grid reliability
VALLHALL
Norway 2005 2x41MW 60kV 67km Offshore
Nord E.ON 1
Germany 2009 400MW 150kV 203km Offshore wind
Table 1-2 Projects lists of VSC-HVDC
11
Chapter2 Optimal Placement of VSC-HVDC link to reduce Power Flow Contingencies 2.1 Introduction
On 28th September 2003, a cascading outage of transmission and generation facilities
in Italy resulted in a blackout of almost the whole country; it was the largest blackout in
Italy, affected more than 50 million people [13].
What caused the blackout? A report comes from Italy’s electricity supplier stated that a
power line transfers power from Switzerland to Italy has been tripped due to a tree
flashover. And the circuit breaker refused to reclose the line because of big phase angle
difference across the line due to heavy power flow into Italy. On the border side, two
400kV power lines between France and Italy tripped because of sudden increased
power demand from these two lines. Only in a couple of seconds, the power deficit in
Italy was so big that Italian power grid began to lose synchronism with the rest of
Europe. Finally, the frequency in Italy fall, with a shortage of more than 6000MW
power, and then the whole country’s power grid collapsed. This accident has given out
a warning that overloaded transmission lines cause the cascading outages, which in
further forces the system to collapse [13]. Base on this reality, an algorithm to mitigate
power flow contingencies is demonstrated in this chapter.
2.1.1 Causes of Power Flow Contingencies
Power systems should be well designed and properly operated so that only one outage
or few outages could not result in blackout [14]. In real operation of power grid, there is
high possibility of power flow contingencies due to different kinds of reasons. For the
purpose of solving this issue, the main causes of the power flow contingencies in the
AC transmission system are necessary to be specified. There are several reasons that
cause power flow contingencies in power system:
Line tripping in load centre may lead to overload on other lines in this area.
The improper operation of the power system during the maintenance of
transmission line will lead to power flow contingencies.
High loads in a weak transmission systems
2.1.2 Possible Solutions
Those power flow contingencies can be handled temporarily by the remedial actions
from system operators to alleviate line overloads. With respect to the cause analysis on
12
transmission line in power system, three main counter measures are analysed and
conducted so as that the safety and stability of power system can obtain.
Rescheduling of generators
Tap changing of transformers
Static Var Compensator (SVC)
The measures mentioned above are the most practiced method to alleviate overload
situation, nevertheless, these approaches mentioned above can not able to eliminate
the problem from the root. For this reason, a necessity of new and innovative solution
is becoming significant.
In the first chapter, the advantages of VSC-HVDC have been already demonstrated.
VSC-HVDC technology can greatly enhance the reliability and transfer capability of the
power systems, and the fast power run-back and instant power reversal can be used if
the transfer capability of the interconnected power systems is constrained by power
flow contingencies [15]. For a bulk power grid, it should be able remain stable and be
capable of withstanding a wide range of disturbances. For this reason, it is very
important that the system be well structured so that the possible power flow
contingencies do not cause worse situation such as cascading outages. A common
method in power system is the N-1 criterion which expresses the capability of the
power system to lose a power system equipment without resulting in a contingency
elsewhere. The VSC-HVDC technology has the advantage of being capable of changing
the active and reactive power instantly and independently. It behaves like an ideal
power generator with flexible working point and without inertia to the grid [15]. Base
on the benefits of this technology, there is no doubt that VSC-HVDC can alleviate
power flow contingencies in a bulk system, however, this solution raised another
problem which is a hot topic in power system research, that is where should the VSC-
HVDC links be installed in order to reduce power flow contingencies in a meshed AC
grid. In section 2.2, a new algorithm is proposed, which can solve the problem. The
validity and effectiveness of this new algorithm is supported by simulation results on
IEEE14 and IEEE118 bus system which are derived from Matpower 4.1 [16].
2.2 Algorithm
The proposed algorithm is deduced from the concept of Composite Security Index (CSI)
given in reference [17]. Composite Security Index is widely applied to select and rank
critical contingency in order to safeguard the system against major outages and
blackouts. It consists of Bus Voltage Security Index (BVSI) and Line Power Security Index
(LPSI) which are based on the concept of Hyper-ellipse inscribed within the Hyper-box
[17]. In this concept, each CSI corresponds to a certain contingency such as outage of
generating unit, transmission lines or buses. The value of CSI indicates the severity of
the corresponding contingency, the higher the index value the more severe the
corresponding contingency is.
, the system is in secure state and there is neither buses nor lines
violation cause by the contingency.
13
, the system is in unsecure state and there is either buses or lines
violation due to corresponding contingency.
More details about this concept can be found in paper [17]. All the CSI with respect to certain possible contingency in a given power system can be calculated, and the most severe one can be specified easily just by comparing the CSI. The contingency with high CSI should be carefully observed while it causes violations to buses or transmission lines in the system severely. Proper control actions such as installing a VSC-HVDC line around the location of this contingency line can be applied to enhance the stability of the power system. The concept mentioned above can specify and rank critical contingencies effectively, however, such method is not able to point out the optimal placement for VSC-HVDC line. As previously described, the basic theory of this concept provides a significant clue to the development of the new algorithm. In this section, the optimal starting terminal and ending terminal of VSC-HVDC link can be identified by solving the Bus Sensitivity Index (BSI) of each bus in a given system, the higher the BSI of one bus the more likely of the bus to be the starting terminal of the HVDC line, reversely, the bus with lowest BSI is the optimal ending terminal for the HVDC line. The validity and effectiveness of this algorithm is tested in two systems IEEE14 and IEEE118. BSI is a function of three factors: Bus Load Rate (BLR), Distribution of generation and
load centers (DGLC) and Generating cost (GC). The following couple of pages give the
mathematical calculation and theoretical explanations of the algorithm.
Calculation of factor 1: Bus Load Rate (BLR).
Step 1 Read system data of the testing system.
Step 2 Set only one transmission line l (l = 1, 2,…, nl) in outage, nl is the
amount of transmission lines in a given system.
Step 3 Calculate the power flow of the system based on step 2.
Step 4 Calculate the Sensitivity Index of Bus k (k = 1, 2,,…, nb) base on step and
then go back to step 2 until line outage i (i = 1,2,…,nl)
Step 5 Calculate Load Rate of Bus k based on Overall Line Contingencies
In the following, an example AC system consists of two generators, three buses and
four transmission lines is shown, the green arrows show the power flow direction, this
system is used to explain the Concept of Bus Load Rate which determine the optimal
placement for VSC-HVDC.
Figure 2-1 Example AC system
14
In order to simplify the situation, only symmetric line outages are considered to this
concept, the reasons of doing so are that:
Asymmetric faults are very difficult to analyse especially in a meshed power
grid with a large number of buses and generators even though the most of the
overhead line fault in transmission system belongs to this type
The most severe fault in transmission system is three-phase fault which
belongs to symmetric type.
A thorough understanding of symmetric faults is a good beginning of analysing
asymmetric faults.
In the following Figure 2-2, two generators are connected to Bus1 and load is in Bus3,
and power flows from Bus1 to Bus3 via Bus2.
Figure 2-2 Example system used to clarify BLR
The red value is the load rate of transmission line in a certain operation condition,
which is calculated as
(2-1)
15
Only steady state is considered for the power flow contingency issue. As be shown in
the example system, the outage line is isolated from the system by circuit breakers in
each contingency case. Four steps are needed to calculate the Load Rate of Bus k (K = 1, 2,
3…, nb) based on contingency i (i = 1, 2, 3…, nl)
1. Find out all transmission lines which are connecting to Bus k (K = 1, 2, 3…, nb),
the Load Rate of Bus k is only related to the load rate and power flow direction
of its connecting lines.
2. Figure out power flow direction of transmission lines which are connecting to
Bus k, name lines through which power flows out of BusK as OUT Lines, and line
flows power into Bus k as IN Lines
3. Load Rate of Bus k according to contingency i is calculated as following
equation2-2:
∑
∑
(2-2)
4. Load Rate of Bus k on Overall Line Contingencies (OLC) is calculated as
∑(
)
(2-3)
Overall Line Contingencies consist of outage of l4 in Contingency b, outage of l3 in
Contingency c, outage of l1 in Contingency d, and outage of l2 in Contingency e in this
example system. Table 2-1 shows the result of Bus Load Rate for each bus based on the
example system: According to Equation 2-3, Bus1 and Bus2 are defined as starting
terminal and Bus3 is the ending terminal for HVDC line.
Bus1 Bus2 Bus3
BLR on Contingency a 0.7+0.8=1.5 1.5-0.7-0.8=0 -1.5
BLR on Contingency b 0.7+0.8=1.5 1.5-0.7-0.8=0 -1.5
BLR on Contingency c 1.5 1.1+0.9-1.5=0.5 -1.1-0.9=-2.0
BLR on Contingency d 1.5 1.1+0.9-1.5=0.5 -1.1-0.9=-2.0
BLR on Overall Line
Contingency 6.0 1.0 -7.0
Table 2-1 Bus Sensitivity Index for each bus based on the example system
Calculation of Factor2: Distribution of Generation and Load Center (DGLC):
Step 6 This factor is associated with the topology structure of the whole power
system, which can be interpreted to the net power of each bus which
equals to the difference of generating capacity and load consummation
16
as be shown in equation 2-4, this factor is constant to each bus.
if then make ( )
(2-4)
The transmission operators always want to run the system both safely and cost
effectively at the same, even this is not the situation in most cases. Therefore, besides
operating factor BLR and configuration factor DGLC, the economical aspect should also
be introduced to the algorithm.
Calculation of Factor 3: Generating cost (GC)
Step 7 The GC of each bus can be calculated by equation 2-5, in which f(p) is the
generating cost per unit active power, and are the cost
coefficient which are constant.
if then make ( )
(2-5)
Step 1 to step 7 give the way to solve these three factors which can determine the
optimal placement, the following equation explains the contribution of each factors to
the decision of optimal placement .
Bus Sensitivity Index (BSI):
(2-6)
To any system the bus with highest positive Sensitivity Index is defined as the optimal
starting terminal of VSC-HVDC link and the bus with the lowest negative Sensitivity
Index is considered as the optimal ending terminal for this HVDC line. x, y and z are the
contribution factors, if x=y=z=1, the factor has the relationship with BLR in
Figure 2-3 (a), the other two factors are directly proportional to which
determines the optimal placement, as be shown in Figure 2-3 (b) and (c).
Figure 2-3 (a),(b) and (c) The relationship of these three factors with Bus Sensitivity Index
17
In Figure 2-4, the flow chart of the algorithm is demonstrated.
Figure 2-4 Flow Chart of the Algorithm
2.3 Simulation Results
The testing systems IEEE14 and IEEE118 are derived from Matpower 4.1, which is an open
sourcing package of MATLAB M-files for solving power flow and optimal power flow
problem.
2.3.1 Simulation Results on IEEE14
Basic introduction of IEEE14 bus system
IEEE14 bus system has 14 buses, 21 transmission lines and 3 Var Compensators
connecting to Bus3, Bus6 and Bus8 which only generate reactive power. In this system
the biggest and cheapest generator is located in Bus1 which is circled out in red and the
load centre is circled out in blue, In order to verify the algorithm’s validity, six
overloaded lines are set manually in order to test the performance of the algorithm, as
be shown in Figure 2-5, the green arrows represent the power flow direction. The
18
column on the left side displays the load rate in every transmission lines, where the
overloaded lines are bigger than 1.
Figure 2-5 Power flow of IEEE14 system in normal operation
Simulation results on IEEE14
The algorithm has been tested on IEEE14 by setting x=y=z=0. Table 2-2 (a) shows the
simulation results by the proposed algorithm explained in section 2.2, Bus1 has the
highest Sensitivity Index with 72.7 in contrast to the lowest Sensitivity index in Bus3
with BSI equals to -40.15, therefore optimal placement from bus 1 to bus 3 for a VSC-
HVDC line can be identified, the other possible placements such as Bus1 to Bus9, Bus1
to Bus14, Bus1 to Bus9 and Bus1 to Bus10 are also displayed in the table.
(a) (b)
Table 2-2 (a) Simulation result for the first VSC-HVDC line by Algorithm
(b) Simulation result for the second VSC-HVDC line by Algorithm
A VSC-HVDC is installed in the optimal placement from Bus1 to Bus3 in the IEEE14
system in order to reduce the overloaded lines. After installing the VSC-HVDC line, the
19
amount of overloaded transmission lines is reduced to 1 from 6 in Figure 2-6 without
VSC-HVDC line. The power transmission through the VSC-HVDC line is calculated as
77MW by optimal power flow with fixed generating capacity for all generators except
for the one on slack bus. The VSC-HVDC line parameters show in Table A-1 in Appendix
A.
Figure 2-6 Power flow of IEEE14 system after installing VSC-HVDC line from Bus1 to Bus3
The VSC-HVDC line is capable of reducing the power flow contingencies dramatically;
however, only one VSC-HVDC line is not sufficient to eliminate all overloaded lines,
which means a second line should be taken in to account. For this reason the algorithm
has been executed again to the IEEE14 with one VSC-HVDC line from Bus1 to Bus3,
where an equivalent treatment to the first VSC-HVDC line has been executed in Figure
2-7. In this equivalent treatment the VSC-HVDC line is replaced by a generator G at
ending terminal Bus3 and a load at starting terminal Bus1, and the size of the
equivalent generator and load equal to the real power flow through the HVDC line [18].
Figure 2-7 Equivalent treatment to the first VSC-HVDC line
The optimal placement for the second VSC-HVDC line from Bus1 to Bus9 is calculated
by the algorithm, and the other possibility such as bus2 to bus9, Bus1 to Bus14 and bus1
to bus4 are also shown in Table 2-2 (b).
20
Adding the second VSC-HVDC line either in the calculated placement from Bus1 to Bus9
or can eliminate the power flow contingencies, the power flow situations after
installing the second VSC-HVDC line are shown in Figure 2-8, from which a conclusion
can be made that the proposed algorithm is capable of determining the optimal
placement for VSC-HVDC line to reduce power flow contingencies in AC system
effectively.
Figure 2-8 Power flow of IEEE14 system after installing VSC-HVDC lines from Bus1 to Bus
and Bus1 to Bus9
Verification of the algorithm In order to evaluate the effectiveness and validity of the proposed algorithm a verifying method is introduced in this section. The verifying method is executed by implementing the VSC-HVDC line randomly between any two buses and the optimal placement can be deduced by comparing the amount of overloaded lines, the situation with the minimum amount of overloaded lines with respect to the optimal placement for VSC-HVDC line. Table 2-3 (a) and (b) provide part of the simulation results from verifying method,
where the optimal placement and other candidates for the first and second VSC-HVDC
lines have been pointed out, in addition, the economical optimisation of the whole
system is also achieved by installing VSC-HVDC lines in the identified optimal
placements where with the biggest and cheapest generating unit. The complete
simulation results by the verifying method is exhibited by Table A-3 and A-4 in
Appendix A
21
(a) (b)
Table 2-3 (a) Part of Simulation result for the first VSC-HVDC line by verifying method
(b) Part of Simulation result for the second VSC-HVDC line by verifying method
By comparing the simulation results of proposed algorithm and the verifying method
as shown in Table 2-4, the accuracy and effectiveness of the developed algorithm can
be determined although they do not agree with each completely. The algorithm is also
implemented on big system IEEE 118 in next section
Optimal
placement Algorithm Verifying method
First line Bus1 to Bus3 Bus1 to Bus3
Other candidates
Bus1 to Bus9,
Bus1 to Bus14,
Bus1 to Bus4…
Bus1 to Bus4,
Bus1 to Bus9,
Bus1 to Bus14…
Second line Bus1 to Bus9 Bus1 to Bus9
Other candidates
Bus2to Bus9,
Bus1 to Bus4,
Bus1 to Bus3…
Bus2 to Bus9,
Bus1 to Bus4,
Bus1 to Bus6…
Table 2-4 Simulation results comparison of the developed algorithm and verifying
method
2.3.2 Simulation Results on IEEE118
Basic introduction of IEEE118 As shown in Figure 2-9, IEEE118 system has 118 buses 187 transmission lines and 57
generators, the generator centres are circled out by red lines and the load centres are in
blue areas, green arrows indicate the power flow. According to power flow calculation,
there is almost no power exchange between the left part and right part of the system.
Bear the same reason as what have done to IEEE14 system, several line capacities are
set manually so that overloaded line exists in normal operation
22
Figure 2-9 Generation centre, load centre and power flow of the IEEE118 bus system
Zoom into the overloaded area in the upper left of IEEE118 system, as shown in Figure 2-
11, where 6 red lines are overloaded and green arrows indicate power flow direction.
Table 2-5 (a) and (b) show only a part of the load rates of transmission lines in this area
before and after installing of HVDC line, the whole load rates of transmission lines can
be read in Table A-5 and TableA-6 in Appendix A.
Figure 2-10 Overloaded area of the IEEE118 bus system
23
(a) (b)
Table 2-5
(a) A part of load rates of transmission lines in overloaded area without VSC-HVDC line
(b) A part of load rates of transmission lines in overloaded area with VSC-HVDC line from
Bus10 to Bus1
Simulation results on IEEE118
Table 2-6 shows part of the likely terminals in IEEE118 system in descending order for
starting terminals and ascending order for ending terminals, among which Bus 10 has
the highest sensitivity index at 182 in contrast to smallest index in Bus 1 at -124;
therefore, the optimal placement for VSC-HVDC is from Bus 10 to Bus 1. The complete
simulation results are in table A-7 in Appendix A.
Table 2-6 The simulation results by the proposed Algorithm
After installing the VSC-HVDC line with parameters is shown as in Table A-2 in
Appendix A in the calculated optimal placement, the 7 overloaded lines are eliminated
by the VSC-HVDC line with 82MW power flow from Bus10 to Bus1, which is shown as in
Figure 2-12, and Table 2-7 shows how much the VSC-HVDC line alleviated the power
flow contingencies in IEEE118 system.
24
Figure 2-11 Overloaded area of the IEEE118 bus system with VSC-HVDC
Verification of the algorithm
Like what has done in last section, verification on the proposed algorithm is necessary
so that the functionality of it can be judged. Similar to the verifying method on IEEE14
system, VSC-HVDC line is randomly placed in any two buses and the optimal placement
is identified by comparing the amount of overloaded lines.
Table 2-7 Part of the simulation results from verifying method
Table 2-7 shows part of the related simulation results from verifying method, the
placements with smallest amount of overloaded lines are from Bus10 to Bus1 , the same
as the proposed algorithm.
2.4 Conclusion
The effectiveness and accuracy of the proposed algorithm explained in section 2.2 can
be proved by the verifying method mentioned in section 2.2, the simulation results of
these two method are consistent with each other. The proposed algorithm can not only
utilized successfully in small system but can also spread to much more complex system
like IEEE118, according to the excellent performance of the algorithm on testing system
IEEE14 and IEEE118, a reasonable prediction can be made that the proposed algorithm is
capable of applying to more complicated power system with thousand buses in real life.
In addition, the economical optimization of the whole system is also achieved by the
proposed algorithm.
25
Chapter3 Optimal Placement of VSC-HVDC link to reduce Inter-area Oscillations 3.1 Introduction
With the development of new technologies such as power electronics in nowadays,
more and more loads, generators and other control equipments are added, which
stepped up the complexity and nonlinearity of power systems. These result in many
instability issues such as voltage, phase angle and frequency related problem which
can lead to partial or complete blackout of the system. The importance of these
problems should be never overlooked, even though they seldom cause eventually
blackout and collapse individually.
To maintain synchronism is challenging for complex power system when it subjected
to large disturbances such as loss of tie lines, large load increase, and loss of generators,
because some machines tend to speed up while some others slow down so as to adjust
to post disturbance operation. There is a high possibility for some generating units lose
synchronism with the grid if no control mechanism exists in the system to keep
electrical speed within the safe speed constraint. For this reason, fast exciter or
Automatic Voltage Regulators (AVR) can be introduced in the system as the
countermeasures to eliminate this phenomenon. However, the fast AVR is only able to
give the “coarse adjustment” to limit the electrical speed of generating units and not
capable of maintaining synchronism by controlling the first swing [19]. Therefore,
Power System Stabilizer (PSS) or VSC-HVDC can be used to offer “fine adjustment” to
damp out power oscillations that are also known as electromechanical or low
frequency oscillations.
Oscillations mode are inherent characteristics of power system, it could lead to partial
or full blackout of the system without proper control as it happened in many practical
power systems. There are several different categories of oscillation modes in power
system:
Intra-plant mode oscillations
The Intra-plant mode oscillation happens among machines in the same power
generation site at 2.0 to 3.0 Hz which depends on the generating unit capacity and
connecting reactance, the rest of the system is not affected.
Torsional mode oscillations
This mode is also called high frequency oscillation which is related to turbine generator shaft system in the frequency range of 10-46 Hz. The oscillation is normally caused by a multi-stage turbine generator and its connecting series compensated line [20]. Low Frequency Oscillation (LFO)
Low frequency oscillations are machines rotor angle oscillations in frequency range
from 0.1 -2.0 Hz
26
The root cause of electrical power oscillations are the unbalance between power
demand and available power at a period of time. In the earliest era of power system
development, the power oscillations are almost non observable because generators are
closely connected to loads, but nowadays, large demand of power to the farthest end of
the system that forces to transmit huge power through a long transmission line, which
results an increasing power oscillations. The phenomenon involves mechanical
oscillation of the rotor phase angle with respective to a rotating frame. Increasing and
decreasing phase angle with a low frequency will be reflected in power transferred
from a synchronous machine as phase angle is strong coupled to power transferred.
The LFO can be classified as local and inter-area mode [21].
Local plant mode oscillations
In this oscillation mode, only one machine swings against the rest of the system in the
frequency range of 1.0 to 2.0 Hz depending on output power and the impedance
connecting to the machine. The affection of this oscillation is localized to the generator
and the connection line, the rest of system maintains unaffected.
Inter-area mode oscillations
This oscillation is normally observed in the scope of the whole system, a large number
of generators are involved. Those involved machines belong to different coherent
groups; generators within a group swing synchronously, oscillated against each other
at 1 Hz or less among these groups [22].
In this chapter inter-area mode oscillations are studied due to its far-ranging influence
to the whole system. This oscillation can also lead to large-scale system disturbances if
cascading outages of transmission lines occur due to oscillatory power swings, like the
black out in Western North America on August 10, 1996, [23]. This accident is caused by
insufficient damping in the system. In the linear model the oscillation is described as a
sinusoid with an exponential decay. The time constant of this exponential decay is a
measure of damping. Even a minor disturbance may excite an expanding oscillation
when damping is negative [24]. The damping of inter-area oscillation is respect to
system characteristics such as grid structure and the operation situation. Hence a full
understanding of the problem would help in identifying countermeasures to handle it.
An advanced benefit of HVDC that has not been widely used is power oscillation
damping (POD) [25]. It is easy to control power flow through line rapidly with fast
acting power electronics such as the IGBT, IGCT and thyristor within the converter
stations. The possibility of implementing HVDC system with POD controllers to damp
inter-area electromechanical oscillations has been demonstrated in paper [25]. The
future power systems are expected to employ large numbers of HVDC lines due to
worldwide interest in large renewable generation sources specially after announcing of
quit nuclear power in Germany. In addition, agreement for new HVAC overhead
transmission lines is becoming increasingly difficult to get because of its bad
performance in long distance and undersea power transmission.
The low frequency oscillation is mainly caused by either high-gain exciters or heavy
power transfers across weak connections. Damping of power system oscillation has
always been a significant consideration for the stable operation of power systems. In
order to increase damping of the system and control power flow in weak connections,
27
an algorithm with the objective to find out the weak connections in an AC grid where
VSC-HVDC line can be installed to reduce inter-area oscillation is developed.
3.2 Algorthim
3.2.1 Concept of slow coherency
In a meshed AC system, the weak connections are normally located in the interface
among the out-of-step generator groups and they are determined by its topology
structure and real-time operating state. In this chapter, an algorithm based on the slow
coherency theory studied the sensitivity of line parameters to slow mode eigenvaules.
The weak connections can be identified by comparing sensitivity values, the higher the
value the more likely the transmission line to be the weak connection [26].
Slow coherency is originally used for developing of dynamic equivalents for transient
stability studies [27]. In paper [28], [20] and [21] some algorithms like time domain
approach, frequency domain approach and electrical distance method have been
developed to specify the slow coherent generator groups. Two hypotheses have been
made in these methods:
The grouping of slow coherent generators is not sensitive to the severity of
disturbances.
The inter-area oscillation modes among slow coherent groups are independent
of the complexity of generating unit model.
The first assumption is based on the Practical observation experience that the slow
coherency groups of the generators are not radically changed when the clearing time
of a certain disturbance is raised. The second assumption is based on the fact that the
basic network property such as inter-area modes does not change significantly when
different generator model are used [27].
Slow coherency theory is normally utilized to identify the theoretically weak connection
in a power system. Paper [20] concludes that the weakest connection in an
aggregated power system appears among the slow coherent generator groups. In fact,
slow coherency is a physical evidence of a weak connection, which is a network
characteristic [27] . The classical second order generator electromechanical model is
accurate enough to identify the weak connection. In many large power systems, there
always exists some groups with the characteristic that the machines inside one group
tend to swing synchronously, and weak connection normally locates among these
groups.
Generally speaking, the slow coherency theory based grouping method has the
following obvious advantage: The coherent groups of generators based on slow
coherency theory do not impact by varying the size of disturbance and complexity of
system model. Papers [29] and [30] introduced a power system analysis method which
based on singular perturbation and multi-time-scale theory. Even though the method
28
could not discern the weak connection of the system, it provides a meaningful clue:
connections among coherent groups influenced by slow mode eigenvalues significantly,
and lines within groups are not sensitive to slow mode eigenvalues. Based on this
reality, a weak connection identification algorithm based on the sensitivity of line
parameters to slow mode eigenvalues is demonstrated in this chapter. The basic idea is
to identify the cluster oscillation related slow mode eigenvalues and then calculate the
sensitivity of each line parameters with respect to the slow mode eigenvalues, the line
with the highest sensitivity is considered as the weakest connection in the system [26].
The weak connection is chose as the optimal placement to install VSC-HVDC line so as
to reduce the inter-area oscillations by proper action such as fast power flow control.
Two simplified power system model are utilized without any negative influence to the
simulation result in this chapter
Classical second order generator mode without damping
Constant impedance load mode
3.2.2 Analytical expression
The flow chart of the algorithm can be seen from Figure 3-1
Figure 3-1 Flow chart of the algorithm
The algorithm consists of several steps:
Step 1
Input power system parameters such as the resistance, reactance, conductance and
susceptance of transmission line, transformer ratio and dynamic parameters of
generators etc.
29
Step 2
Base on step 1 the linearized dynamic mode ̈ can be formed, matrix A is the
key component in this equation, ̈ manifests the second order differentiation of
power angle deviation of generators. The way of calculating matrix A is shown in the
following:
Under the circumstances of applying second order generator mode and constant
impedance load mode, the electromechanical oscillation mode of the power system
can be expressed as [26]:
{
(
)
(3-1)
[ ] Power angle vector of generators
{ } Inertial time constant of generators
[ ] Constant vector of mechanical input power
[ ] Column vector of electrical output power
[ ]
Excitation electromotive force of generator
[
]
Transient reactance of generator
[ ]
Terminal voltage of generator
[ ]
Terminal voltage angle of generator
Number of generators in the system
Norton equivalent input current of generators
The excitation electromotive force and its power angle can be calculated by following
equation:
(3-2)
(
) is the Norton equivalent input current of the generator
bus as be shown in Figure 3-2 , and can be calculated from power flow
calculation and is the power generated by generator:
Figure 3-2 Norton equivalent input current of generator
30
represents the equivalent input current vector of all buses,
and are the real and imaginary part of the equivalent input current and
only those elements corresponding to generator buses are non-zero.
T is a n x ng dimension matrix, the row k (k = 1…, n; n is the number of bus) is
responding to the Bus k: if there is no generator connecting to Bus k then all elements
in row k are zero; if Bus k with generator i (i =1….,ng; ng is the number of generator)
connected to it then only element and other elements in this row are zero.
Bus admittance matrix
Bus admittance matrix of power system is which including the
equivalent admittance of load, Y, G and B are n x n dimension matrix.
Buses voltage vector
expresses the buses voltage vector , and are the real and
imaginary part the voltage vector respectively:
[ ]
[ ]
(3-3)
[ ] is the voltage angle vector of bus and n is the number of bus
Make [
]
then [
] [
] is linearized as [26]:
[
] [
] [
] (3-4)
, and are the deviations of and separately,
{ }
{ }
(3-5)
{ } { }
{ } { }
(3-6)
Make [
] and [
] , then equation 3-4 can be expressed
as [
] . Linearize equation 3-1 at the equilibrium of the
electromechanical oscillation mode of the system:
31
[
] (3-7)
, and are the deviations of and separately, make
[
]
[
]
(3-8)
Substitute and into equation B-9:
[
] [
] [
] [
] (3-9)
Substitute [
], and [
] to equation 3-7, the matrix A
of a power system can be calculated by the following equation 3-9 [26]
(3-10)
Step 4
Eigenvalues of matrix A can be calculated in ascending order { } is the
number of generators, { √ √ √ } represent the potential oscillation
modes of the system [26], √ , from which the damping coefficient is
calculated as
√ and the frequency of oscillation in Hertz is
. Figure 3-3
gives relationship between eigenvalue and stability of the system.
Figure 3-3 Eigenvalue and stability of system
In general, is very close to zero which means represents zero oscillation mode. The
slow mode eigenvalues { } (r is the number of slow mode eigenvalue)
are the r smallest eigenvalues. Therefore, the slow mode can be expressed as [26]:
(3-11)
32
Step 5
Calculate the sensitivities of each transmission line to slow mode
eigenvalues . The sensitivity consists of two factors [26]:
The sensitivity of line susceptance b with respect to slow mode eigenvalues
(3-12)
The sensitivity of line conductance g with respect to slow mode eigenvalues
(3-13)
( ) and are the left and right eigenvector of slow mode , , ,
and are structure matrix, M is a 1 x nb dimension vector; If a transmission line L is connected from Bus i to Bus j, then M (i) = 1, M (j) = -1, the other elements are zero
[
] [
] (3-14)
[
] [
] (3-15)
For a transmission line, the resistance r and reactance x vary in proportion to the line
distance, therefore, conductance g and susceptance b of line are varied in
proportionality factor of -r/x due to
, which conclude to sensitivity
of Line l to slow mode eigenvalues [26]:
∑
(3-16)
By employing the method mentioned above, the weak connection in system can be
specified by comparing the absolute value of sensitivities, the weakest connection
corresponding to highest absolute sensitivity value. The weak connection is defined as
the optimal placement for VSC-HVDC line to reduce the inter-area oscillation in an AC
system. The effectiveness and validity of this algorithm is verified in Kundur second
order system and IEEE Two Area RTS-24 system in next section.
3.3 Simulation results
3.3.1 Simulation results on Kundur second order system
The testing system in Figure 3-4 is derived from [31] , this system has two similar areas
which are connected by a weak connection Bus7 to Bus8 and Bus8 to Bus9. Four
generators with generating parameters in Table 3-1 , and the dynamic data and line
parameters are shown in table Table A-9in Appendix A.
33
Figure 3-4 Kundur second order system [31]
Table 3-1 Generating parameters
Operation case one
In the first operation case, assume that the load in Bus 7 and Bus 9 equal to each other
with 1367MW, and there is almost no power transmission between two areas, and the
local generators can fulfil the load demand in both areas.
The proposed algorithm is employed to this operation case, table 3-2 shows the
simulation result. It can be seen obviously that transmission lines from Bus 7 to Bus 8
and Bus 9 to Bus 8 are specified as the weak connections due to their high sensitivity
to slow mode eingenvalues. This result is consistent with the reality what has already
been given, which means the algorithm demonstrated in section 3.2 is capable of
identifying weak connection in a given AC networks effectively. The weak connection is
considered as the optimal placement for VSC-HVDC line to reduce the inter-area
oscillations. Big power flow through weak tie is one of the significant causes to inter-
area mode oscillations.
Table 3-2 Simulation results on operation case one
Operation case two
In the second operation case, assume that the load in both Bus 7 and Bus 9 are 967MW
and in is 1767MW, unbalanced power between two areas occurs, 400MW power is
transmitted from area 1 to area 2.
34
Apply The proposed algorithm to the this operation case, the simulation results in Table
3-3 verified the effectiveness of the algorithm, in this unbalanced case, sensitivity of
lines from Bus9 to bus8 and Bus7 to Bus8 are higher than the first operation case due
to the extra 400MW power flow between these lines, which can conclude that the
algorithm can also reflect the power distribution among the system, especially in weak
connections.
Table 3-3 Simulation results on operation case two
Eigenvalue analysis
In this chapter, the eigenvalue of a linearized power system model can be expressed as
√ , from which the damping coefficient is calculated as
√ and the
frequency of oscillation in Hertz is
,
From right eigenvector and left eigenvectors of eigenvalues, the participation
factor P (ng x ng dimension matrix, ng is the number of eigenvalues) can be deduced by
, it is a measure of the relative participation of one generator’s state in ith
mode and can be used in identifying problematic machines for placement for PSS in
large power system [32]. Figure 3-6 shows the participation factor of four generators
rotor speed in Kundur testing system with respect to four oscillation modes. The higher
the participation factor of one generator to a certain mode, the more the generator
participate in this mode.
(a)
35
(b)
Figure 3-5 (a) and (b) Participation factor of Kundur second order system
Mode 1 and mode 2 with G1, G2, G3 and G4 participated and oscillation frequency at
0.038 Hz and 0.098Hz are inter-area oscillations, and mode 3 and mode 4 are
considered as local area oscillation modes due to their local machines swing against
each other, as been shown in Figure 3-6 and Table 3-4.
Mode Eigenvalues frequency (Hz) Damping Ratio Oscillation mode
1 -0.056 0.038 0 Inter-area
2 -0.376 0.098 0 Inter-area
3 -0.443 0.106 0 Local mode in area 1
4 -0.460 0.110 0 Local mode in area 2
Table 3-4 Oscillation modes in kundur second order system
3.3.2 Simulation result on IEEE Two Area RTS-24 system
Testing the algorithm on the small Kundur second order system successfully does not
mean it could be expanded to big systems. For this reason, in this section the algorithm
is implemented in IEEE Two Area RTS-24 system to verify its effectiveness for big
networks. The testing system is connected by two RTS-24 systems through three weak
tie lines: Bus7 to Bus27, Bus13 to Bus39 and Bus23 to Bus41. The system’s parameters
refer to paper [33].
G 1 0.2026 0.2261 0.5755 -0.0041
G 2 0.2891 0.2571 0.4771 -0.0233
G 3 0.2258 0.1424 0.008 0.6238
G 4 0.2258 0.3745 -0.0606 0.4036
Mode 1 Mode 2 Mode 3 Mode 4
Participation factor
36
Figure 3-6 IEEE Two Area RTS-24 system [33]
Table 3-5 shows the part of simulation result on IEEE Two Area RTS-24 system, in
descending order, where Bus23 to Bus41 and Bus13 to Bus39 are specified as the
weakest connection in the whole testing system with sensitivity value at 60e-5 and
46e-5 respectively, Bus7 to Bus27 in the third place with relatively lower sensitivity 16e-5
than the first two lines due to its low power transmission around at 12MW. The
simulation result is consistent with the expected outcome. And the complete data refer
to Table A-8 in Appendix A
Table 3-5 Part of simulation result on IEEE Two Area RTS-24 system
From To
Sensitivity on
slow mode 1
(10 x -5)
Sensitivity on
slow mode 2
(10 x -5)
Sensitivity on
slow mode 3
(10 x -5)
Sensitivity on
slow mode 4
(10 x -5)
Total
Sensitivity
(10 x -5)
23 41 1.80 1.80 3.50 60.00 60.00
13 39 5.80 5.80 3.00 37.00 46.00
7 27 2.50 2.50 1.70 13.00 16.00
13 23 1.90 1.90 0.34 9.90 13.00
1 3 3.10 3.10 0.61 6.70 12.00
14 16 1.30 1.30 4.90 18.00 11.00
36 47 9.80 9.80 5.20 0.12 11.00
3 24 0.21 0.21 0.15 10.00 10.00
12 23 2.90 2.90 0.38 3.90 9.00
37 47 7.90 7.90 4.10 0.35 8.60
25 27 3.00 3.00 0.16 1.10 6.80
45 46 3.90 3.90 1.20 0.09 6.00
8 9 0.34 0.34 0.01 5.20 5.90
3 9 0.38 0.38 1.30 5.90 5.30
15 24 0.16 0.16 0.03 4.70 4.80
11 14 0.08 0.08 2.00 2.60 4.50
37
3.4 Conclusion
Inter-area oscillations are a part of the systematic property of interconnected power
systems. Large-scale power systems with weak connections transmitting large power
tend to exhibit such modes of oscillations. As mentioned in the introduction, these
oscillations are caused by swing among coherent groups. This phenomenon may due to
small disturbances such as varying in loads or may happen as an aftermath of large
disturbances. Low frequency inter-area oscillations (LFIO) are most likely to be the type
of instability especially in interconnected power systems.
Network configuration, generator excitation systems and load characteristics affect the
mode properties of LFIO and stability of inter-area modes interconnected systems. In
addition, the natural frequency and damping of inter-area mode oscillations depend on
the weakness of inter-area ties and the power transmitted through them [31].
Attention has to be paid that the effects resulting from small disturbances might not
be instantaneously recognized, however, over a period time; they may become severe
and furthermore cause collapse of the system.
In this chapter, an algorithm derived from [26] with the function of specify weak
connections in AC power system is tested on Kundur second order system and IEEE Two
Area RTS-24 system, the simulation result shows its effectiveness and validity.
In Kundur second order system transmission lines from Bus7 to Bus8 and Bus8 to Bus9
with highest sensitivity to slow mode eigenvalues are identified as weak connections.
And in IEEE Two Area RTS-24 system the three additional tie line are calculated as the
weak connections by the proposed algorithm.
38
Chapter4
Conclusions and Future Work This chapter draws conclusions and presents some suggestions for further work.
4.1 Conclusions
The interest on research of VSC-HVDC has been growing after the world’s first VSC-
HVDC installation into Gotland, Sweden, 1997. The recent developments in
semiconductors and control equipment have made VSC-HVDC feasible. Due to the use
of VSC technology and PWM the VSC-HVDC has a number of potential advantages as
compared with classical HVDC, such as short circuit current reduction, rapid and
independent control of active and reactive power, etc. With those advantages VSC-
HVDC will likely be widely used in future transmission and distribution systems. In this
thesis, two different algorithms with the objectives to reduce power flow contingencies
and inter-area oscillations in AC power system are demonstrated.
In chapter 1, some basic structure of classic HVDC systems and their applications are
indicated . The advantages and disadvantages of HVAC, classic HVDC and VSC-HVDC
have been demonstrated. In addition, the application of VSC-HVDC are introduced.
Chapter 2 studies the causes and possible solutions of power flow contingencies; an
algorithm is developed to identify the optimal placement for VSC-HVDC line in order to
reduce the power flow contingencies of an AC grid. This algorithm has been tested on
IEEE14 and IEEE118 bus systems, and its effectiveness and validity have been evaluated
by the verifying method. In addition, the economical optimization of these testing
systems is achieved as well by installing the VSC-HVDC line in the optimal placement
calculated by the proposed algorithm.
Chapter 3 describes different oscillation modes and their causes in power system, and
an algorithm is developed to specify optimal placement for VSC-HVDC line in order to
reduce the inter-area oscillation in a given AC grid The algorithm is tested on Kundur
second order system and IEEE Two Area RTS-24 system, the weak connections in testing
system are specified by this algorithm and the oscillation modes is analysed in Kundur
second order system.
4.2 Future Work
As previously mentioned, modern HVDC systems can transfer up to three times more
power across the same wires and pylons as conventional AC systems, in addition, the
VSC-HVDC has lower short circuit current reduction and more rapid and independent
control of active and reactive power. With those advantages VSC-HVDC will likely be
widely used in future transmission and distribution systems. To further evaluate the
pros and cons of VSC technology for industrial power systems, more research can be
involved in the future work:
39
The two algorithms introduced in chapter 2 and chapter 3 are far from perfect due to
the knowledge and time limit of the author. However, this does not impact of the
meaning of the work has been done by the author. In order to optimize the algorithm,
some valuable works still need to be considered in the future.
Control scheme of VSC-HVDC in both algorithm
The control strategy as the key part of VSC technology is out the scope of this
thesis due to its complexity
Consideration of asymmetric line contingency
The asymmetric line outage can be considered in the future work in order to
accurate the algorithm in chapter 2
Increase the function of algorithm
Algorithm with function of finding out optimal placement for VSC-HVDC line to
connect renewable energies and asynchronous networks
Combine the two algorithms to one
Combine the two algorithms to one so as to find out the optimal placement
which can reduce power flow contingencies and inter-area oscillations at the
same time
40
Appendix A Table A - 1 Parameters of VSC-HVDC line in IEEE14
Reactance Phase Reactor R(p.u.) 0
Reactance Phase Reactor X(p.u.) 0.1643
Reactance Transformer R(p.u.) 0
Reactance Transformer X(p.u.) 0.113
Shunt Filter(Mvar) 15.15
Tap 0
Shift 0
AC Converter Voltage(kV) 230
Base MVA Converter 100
P Rectifier(MW) -15.34
P Inverter(MW) 15.34
Q Rectifier(MW) -0.17
Q Inverter(MW) 0.8
P max(MW) 100
P min(MW) -100
Q max(MW) 15
Q max(MW) -15
Udc nominal(pole-groud)kV 80
Udc Rectifier(p.u.) 1.1
Udc Inverter(p.u.) 1.1
Cable Resistance(p.u.) 0.05
41
Table A - 2 Parameters of VSC-HVDC line in IEEE118
R1 (p.u.) 0
X1 (p.u.) 0.1643
R2 (p.u.) 0
X2 (p.u.) 0.1643
Shunt Filter 1 (Mvar in p.u.) -0.1515
Shunt Filter 2 (Mvar in p.u.) -0.1515
n1 (p.u.) 1
n2 (p.u.) 1
Rdc (p.u.) 0.05
a1 (AC system p.u.) 11.033e-3*30/100
b1 (AC system p.u.) 3.464e-3*30/100
c1 (AC system p.u.) 4.400e-3*30/100
a2 (AC system p.u.) 11.033e-3*30/100
b2 (AC system p.u.) 3.464e-3*30/100
c2 (AC system p.u.) 6.667e-3*30/100
Converter 1 P setpoint (AC system p.u.) 1
Converter 1 Q setpoint (AC system p.u.) -0.0016
Udc setpoint (DC system p.u.) 1.0932829
Converter 2 Q setpoint (AC system p.u.) -0.0403
Uac setpoint converter 1 1
Uac setpoint converter 2 1
Converters Pmin (MW) -100
Converters Pmax (MW) 100
Converters Qmin (Mvar) -15
Converters Qmax (Mvar) 15
Udc min (DC system p.u.) 0.9
Udc max (DC system p.u.) 1.1
Converter 1 control 0
Converter 2 control 0
42
Table A - 3 Simulation Results of after installing first HVDC line on IEEE14 by verifying
method
From To
Generatio
n Cost
$/hour
Amount
of
Overloade
d lines
1 3 7982 2
1 4 8002 2
1 9 8015 2
1 14 8033 2
1 6 8048 3
1 7 8009 3
1 10 8032 3
1 11 8056 3
1 12 8072 3
1 13 8042 3
1 5 8033 4
1 8 8011 4
2 9 8067 4
1 2 8099 5
2 3 8038 5
2 4 8061 5
2 6 8092 5
2 7 8065 5
2 8 8066 5
2 10 8074 5
2 13 8102 5
5 7 8109 5
5 8 8111 5
5 9 8107 5
5 10 8107 5
5 11 8111 5
5 13 8107 5
5 14 8099 5
2 5 8084 6
2 11 8088 6
2 12 8095 6
2 14 8067 6
3 5 8101 6
4 5 8108 6
4 14 8108 6
5 12 8111 6
6 7 8115 6
6 9 8113 6
6 10 8113 6
6 14 8105 6
3 4 8111 7
3 6 8108 7
3 7 8113 7
3 8 8117 7
3 9 8111 7
3 10 8114 7
3 11 8115 7
3 12 8118 7
3 13 8117 7
3 14 8116 7
4 6 8112 7
4 7 8114 7
4 8 8117 7
4 9 8112 7
4 10 8112 7
4 11 8114 7
4 12 8115 7
4 13 8113 7
5 6 8113 7
6 8 8118 7
6 11 8116 7
6 12 8116 7
6 13 8111 7
7 8 8118 7
7 9 8115 7
7 10 8114 7
7 11 8116 7
7 12 8117 7
7 13 8115 7
7 14 8110 7
8 9 8116 7
8 10 8117 7
8 11 8119 7
8 12 8121 7
8 13 8118 7
8 14 8112 7
9 10 8113 7
9 11 8114 7
9 12 8115 7
9 13 8113 7
9 14 8109 7
12 14 8114 7
13 14 8114 7
11 14 8111 7
10 11 8115 7
12 13 8118 7
11 12 8118 7
10 12 8115 7
11 13 8115 7
10 13 8114 7
10 14 8111 7
43
Table A - 4 Simulation Results after installing second HVDC line on IEEE14 by Verifying method
From To
Generation
Cost
$/hour
Amount of
Overloaded
lines
1 9 8012 0
2 9 8042 0
1 4 8003 1
1 6 8035 1
1 7 8008 1
1 11 8041 1
1 12 8049 1
1 13 8027 1
1 14 8020 1
2 4 8038 1
2 6 8060 1
2 7 8041 1
2 8 8042 1
2 10 8047 1
2 11 8058 1
2 12 8063 1
2 13 8048 1
2 14 8039 1
3 7 8078 1
3 8 8080 1
3 9 8076 1
3 10 8076 1
3 11 8079 1
3 13 8075 1
3 14 8068 1
4 14 8073 1
5 7 8077 1
5 9 8075 1
5 10 8074 1
5 13 8073 1
5 14 8066 1
6 14 8071 1
1 2 8073 2
1 3 8032 2
1 8 8010 2
1 10 8024 2
2 3 8062 2
2 5 8052 2
3 4 8112 2
3 5 8079 2
3 6 8082 2
3 12 8080 2
4 5 8076 2
4 7 8080 2
4 8 8082 2
4 9 8079 2
4 10 8078 2
4 11 8080 2
4 12 8080 2
4 13 8078 2
5 6 8079 2
5 8 8079 2
5 11 8077 2
5 12 8077 2
6 7 8081 2
6 8 8084 2
6 9 8079 2
6 10 8079 2
6 11 8081 2
6 12 8081 2
6 13 8076 2
7 8 8083 2
7 9 8080 2
7 10 8080 2
7 11 8082 2
7 12 8082 2
7 13 8080 2
7 14 8075 2
8 9 8082 2
8 10 8082 2
8 11 8084 2
8 12 8085 2
8 13 8083 2
8 14 8077 2
9 10 8079 2
9 11 8080 2
9 12 8080 2
9 13 8079 2
9 14 8074 2
12 14 8080 2
13 14 8080 2
11 14 8077 2
10 11 8081 2
10 12 8081 2
12 13 8083 2
11 12 8083 2
10 14 8076 2
11 13 8081 2
10 13 8079 2
1 5 8022 3
4 6 8079 3
44
Table A - 5 Line load rate of IEEE118 before installing VSC-HVDC line
From Bus To Bus Load Rate
1 2 0.691
1 3 1.21
2 12 1.09
3 5 1.18
3 12 0.579
4 5 0.712
4 11 0.665
5 6 0.667
5 11 0.672
6 7 0.663
7 12 0.732
8 9 1.12
8 5 1.02
8 30 0.772
9 10 1.12
11 12 0.711
11 13 0.683
12 14 0.641
12 16 0.459
12 117 0.66
13 15 0.338
14 15 0.461
15 17 0.664
15 19 0.791
15 33 0.444
16 17 0.656
17 18 0.677
17 31 0.754
17 113 0.313
18 19 0.785
19 20 0.467
19 34 0.554
20 21 0.588
21 22 0.636
22 23 0.656
23 24 0.6
23 25 0.689
23 32 0.644
24 70 0.551
24 72 0.73
25 27 0.671
26 25 0.576
26 30 0.653
27 28 0.656
27 32 0.638
27 115 0.671
28 29 0.64
29 31 0.693
30 17 0.688
30 38 0.665
31 32 0.684
32 113 0.648
32 114 0.571
33 37 0.861
34 36 0.68
34 37 0.772
34 43 0.261
35 36 0.709
35 37 0.71
37 39 0.47
37 40 0.445
38 37 0.614
38 65 0.573
39 40 0.38
40 41 0.278
40 42 0.632
41 42 0.905
42 49 0.492
42 49 0.492
43 44 0.581
44 45 0.597
45 46 0.645
45 49 0.657
46 47 0.628
46 48 0.724
47 49 0.978
47 69 0.615
48 49 0.65
49 50 0.655
49 51 0.657
49 54 0.634
49 54 0.634
49 66 0.475
49 66 0.475
49 69 0.599
50 57 0.627
51 52 0.65
51 58 0.583
52 53 0.613
53 54 0.581
54 55 0.748
54 56 0.756
54 59 0.418
55 56 0.88
55 59 0.441
56 57 0.601
56 58 0.363
56 59 0.42
56 59 0.42
59 60 0.56
59 61 0.581
60 61 0.669
60 62 0.406
61 62 0.874
62 66 0.6
62 67 0.579
63 59 0.649
63 64 0.647
64 61 0.222
64 65 0.627
65 66 0.399
65 68 0.613
66 67 0.624
68 69 0.783
68 81 0.752
68 116 0.7
69 70 0.635
69 75 0.649
69 77 0.539
70 71 0.698
70 74 0.723
70 75 0.596
71 72 0.533
71 73 0.789
74 75 0.668
75 77 0.75
75 118 0.685
76 77 0.729
76 118 0.913
77 78 0.783
77 80 0.455
77 80 0.455
77 80 0.455
77 82 0.641
78 79 0.447
79 80 0.515
80 96 0.742
80 97 0.698
80 98 0.551
80 99 0.562
81 80 0.402
82 83 0.497
82 96 0.702
83 84 0.529
83 85 0.53
84 85 0.534
85 86 0.7
85 88 0.533
85 89 0.573
86 87 0.682
88 89 0.601
89 90 0.383
89 90 0.383
89 92 0.352
89 92 0.352
90 91 0.415
91 92 0.409
92 93 0.829
92 94 0.859
92 100 0.877
92 102 0.8
93 94 0.902
94 95 0.763
94 96 0.796
94 100 0.782
95 96 0.905
96 97 0.824
98 100 0.635
99 100 0.942
100 101 0.965
100 103 0.686
100 104 0.671
100 106 0.672
101 102 0.834
103 104 0.738
103 105 0.711
103 110 0.678
104 105 0.656
105 106 0.473
105 107 0.649
105 108 0.725
106 107 0.664
108 109 0.734
109 110 0.807
110 111 0.664
110 112 0.719
114 115 0.235
45
Table A - 6 Line load rate of IEEE118 after installing VSC-HVDC from Bus10 to Bus 1
From Bus To Bus Load Rate
1 2 0.969
1 3 0.89
2 12 0.8101
3 5 0.723
3 12 0.6294
4 5 0.6556
4 11 0.5805
5 6 0.5937
5 11 0.5926
6 7 0.4811
7 12 0.3258
8 9 0.9449
8 5 0.8559
8 30 0.6959
9 10 0.9432
11 12 0.4667
11 13 0.73
12 14 0.8059
12 16 0.6965
12 117 0.6604
13 15 0.5213
14 15 0.6668
15 17 0.6419
15 19 0.8293
15 33 0.5283
16 17 0.4465
17 18 0.6711
17 31 0.7648
17 113 0.3065
18 19 0.7712
19 20 0.4448
19 34 0.5484
20 21 0.5761
21 22 0.6275
22 23 0.6486
23 24 0.6126
23 25 0.6872
23 32 0.6397
24 70 0.5295
24 72 0.7287
25 27 0.6681
26 25 0.5694
26 30 0.6561
27 28 0.6517
27 32 0.6292
27 115 0.6681
28 29 0.631
29 31 0.7004
30 17 0.6633
30 38 0.6594
31 32 0.6768
32 113 0.6365
32 114 0.5761
33 37 0.8127
34 36 0.6818
34 37 0.768
34 43 0.2626
35 36 0.7129
35 37 0.7088
37 39 0.4719
37 40 0.4471
38 37 0.6102
38 65 0.5699
39 40 0.383
40 41 0.2815
40 42 0.6226
41 42 0.8975
42 49 0.4907
42 49 0.4907
43 44 0.5722
44 45 0.592
45 46 0.6422
45 49 0.6547
46 47 0.6262
46 48 0.7225
47 49 0.9798
47 69 0.6123
48 49 0.6496
49 50 0.6554
49 51 0.6571
49 54 0.6345
49 54 0.6345
49 66 0.4746
49 66 0.4746
49 69 0.596
50 57 0.6274
51 52 0.6505
51 58 0.5832
52 53 0.613
53 54 0.5811
54 55 0.749
54 56 0.7565
54 59 0.4175
55 56 0.8806
55 59 0.4405
56 57 0.6017
56 58 0.3636
56 59 0.42
56 59 0.42
59 60 0.5597
59 61 0.5804
60 61 0.6691
60 62 0.4058
61 62 0.8732
62 66 0.6
62 67 0.5787
63 59 0.649
63 64 0.6464
64 61 0.2218
64 65 0.6272
65 66 0.3988
65 68 0.6245
66 67 0.6246
68 69 0.7784
68 81 0.7498
68 116 0.7002
69 70 0.632
69 75 0.6478
69 77 0.5363
70 71 0.6856
70 74 0.726
70 75 0.5921
71 72 0.5149
71 73 0.7889
74 75 0.6659
75 77 0.749
75 118 0.6852
76 77 0.7285
76 118 0.9144
77 78 0.7825
77 80 0.4552
77 80 0.4552
77 80 0.4552
77 82 0.6409
78 79 0.447
79 80 0.5153
80 96 0.7425
80 97 0.6978
80 98 0.5509
80 99 0.5623
81 80 0.4018
82 83 0.4972
82 96 0.703
83 84 0.529
83 85 0.5295
84 85 0.5343
85 86 0.7003
85 88 0.533
85 89 0.5725
86 87 0.6824
88 89 0.6009
89 90 0.3827
89 90 0.3827
89 92 0.3521
89 92 0.3521
90 91 0.4147
91 92 0.4094
92 93 0.829
92 94 0.8587
92 100 0.8774
92 102 0.8004
93 94 0.902
94 95 0.7631
94 96 0.7964
94 100 0.782
95 96 0.9054
96 97 0.8245
98 100 0.6351
99 100 0.9416
100 101 0.9647
100 103 0.686
100 104 0.6709
100 106 0.6722
101 102 0.834
103 104 0.7379
103 105 0.7108
103 110 0.6777
104 105 0.6558
105 106 0.4734
105 107 0.6486
105 108 0.7247
106 107 0.6643
108 109 0.7337
109 110 0.8074
110 111 0.6644
110 112 0.7194
114 115 0.2506
46
Table A - 7 Simulation Results of IEEE118 by the proposed algorithm
Bus Bus Sensitivity
Index
Terminal
10 182.11 starting
69 70.19 starting
89 38.96 starting
26 38.86 starting
80 37.04 starting
65 36.11 starting
12 21.18 starting
61 15.59 starting
8 8.78 starting
111 5.09 starting
42 4.83 starting
92 3.98 starting
56 3.96 starting
66 3.61 starting
49 2.3 starting
87 2.28 starting
15 2.13 starting
54 1.69 starting
77 1.34 starting
25 0.96 starting
118 0.46 starting
70 0.36 starting
18 0.27 starting
5 0.23 starting
27 0.12 starting
101 0.12 starting
97 0.08 starting
106 0.08 starting
81 0.04 starting
95 0.04 starting
103 0.04 starting
11 0.03 starting
48 0.03 starting
7 0.02 starting
93 0.02 starting
85 0.01 starting
109 0.01 starting
17 0 starting
24 0 starting
32 0 starting
35 0 starting
37 0 starting
63 0 starting
91 0 starting
102 0 starting
108 0 starting
1 -124.13 ending
116 -41.53 ending
76 -31.39 ending
55 -22.92 ending
74 -21.35 ending
107 -12.57 ending
19 -12.24 ending
99 -9.88 ending
36 -9.28 ending
78 -9.26 ending
112 -9.15 ending
90 -9.13 ending
82 -8.71 ending
62 -5.03 ending
41 -4.99 ending
98 -4.11 ending
3 -3.92 ending
33 -3.65 ending
29 -3.64 ending
86 -3.54 ending
53 -3.02 ending
117 -3 ending
16 -2.77 ending
100 -2.24 ending
34 -1.9 ending
13 -1.83 ending
40 -1.67 ending
115 -1.62 ending
59 -1.47 ending
73 -1.44 ending
2 -1.1 ending
43 -1.1 ending
47 -0.59 ending
114 -0.31 ending
96 -0.29 ending
113 -0.21 ending
72 -0.2 ending
58 -0.19 ending
14 -0.18 ending
104 -0.13 ending
94 -0.11 ending
20 -0.09 ending
79 -0.09 ending
39 -0.08 ending
45 -0.08 ending
88 -0.08 ending
4 -0.04 ending
105 -0.04 ending
31 -0.03 ending
67 -0.02 ending
110 -0.02 ending
21 -0.01 ending
46 -0.01 ending
51 -0.01 ending
52 -0.01 ending
64 -0.01 ending
75 -0.01 ending
83 -0.01 ending
6 0 ending
9 0 ending
22 0 ending
23 0 ending
28 0 ending
30 0 ending
38 0 ending
44 0 ending
50 0 ending
57 0 ending
60 0 ending
68 0 ending
71 0 ending
84 0 ending
47
Table A - 8 Simulation Results of IEEE Two Area RTS-24 system
From To
Sensitivity on
slow mode 1 (10 x -5)
Sensitivity on
slow mode 2 (10 x -5)
Sensitivity on
slow mode 3 (10 x -5)
Sensitivity on
slow mode 4 (10 x -5)
Total
Sensitivity (10 x -5)
23 41 1.80 1.80 3.50 60.00 60.00
13 39 5.80 5.80 3.00 37.00 46.00
7 27 2.50 2.50 1.70 13.00 16.00
13 23 1.90 1.90 0.34 9.90 13.00
1 3 3.10 3.10 0.61 6.70 12.00
14 16 1.30 1.30 4.90 18.00 11.00
36 47 9.80 9.80 5.20 0.12 11.00
3 24 0.21 0.21 0.15 10.00 10.00
12 23 2.90 2.90 0.38 3.90 9.00
37 47 7.90 7.90 4.10 0.35 8.60
25 27 3.00 3.00 0.16 1.10 6.80
45 46 3.90 3.90 1.20 0.09 6.00
8 9 0.34 0.34 0.01 5.20 5.90
3 9 0.38 0.38 1.30 5.90 5.30
15 24 0.16 0.16 0.03 4.70 4.80
11 14 0.08 0.08 2.00 2.60 4.50
16 19 0.35 0.35 0.05 3.50 4.10
8 10 0.32 0.32 0.10 3.40 3.90
11 13 0.48 0.48 1.40 2.00 3.60
27 48 2.30 2.30 0.94 0.02 3.60
17 22 3.30 3.30 0.98 9.00 3.40
27 33 0.62 0.62 0.02 3.10 3.40
32 33 1.00 1.00 0.44 1.50 3.20
19 20 0.42 0.42 0.09 2.30 3.00
19 20 0.42 0.42 0.09 2.30 3.00
41 46 3.30 3.30 0.29 0.31 3.00
29 34 1.80 1.80 0.25 0.02 2.80
33 36 2.10 2.10 1.30 0.38 2.70
16 17 0.10 0.10 0.85 3.70 2.60
40 41 0.26 0.26 0.13 2.70 2.60
28 33 1.60 1.60 0.29 0.13 2.50
26 30 3.10 3.10 0.72 0.45 2.40
32 34 1.20 1.20 0.45 0.54 2.10
38 40 7.60 7.60 3.10 0.03 2.00
4 9 1.50 1.50 0.81 0.44 1.80
34 36 2.10 2.10 1.00 0.25 1.80
39 48 1.20 1.20 0.49 0.00 1.80
21 22 3.00 3.00 0.18 4.20 1.70
40 43 0.86 0.86 0.84 1.50 1.70
43 44 0.85 0.85 0.79 1.20 1.60
43 44 0.85 0.85 0.79 1.20 1.60
5 10 1.70 1.70 1.10 0.77 1.50
15 16 0.39 0.39 0.99 1.70 1.30
7 8 0.32 0.32 0.01 1.60 1.10
9 12 0.71 0.71 0.02 0.18 1.10
12 13 0.05 0.05 0.10 1.10 1.10
26 28 1.30 1.30 0.34 0.37 1.10
35 37 1.80 1.80 1.50 0.81 0.96
17 18 0.08 0.08 0.13 1.20 0.92
25 29 1.10 1.10 0.24 0.15 0.92
15 21 0.29 0.29 0.17 0.14 0.85
15 21 0.29 0.29 0.17 0.14 0.85
20 23 0.13 0.13 0.04 0.59 0.80
20 23 0.13 0.13 0.04 0.59 0.80
10 12 0.65 0.65 0.11 0.34 0.77
33 35 0.90 0.90 0.29 0.07 0.74
34 35 0.75 0.75 0.36 0.05 0.64
10 11 0.27 0.27 0.06 0.01 0.58
39 45 0.75 0.75 0.07 0.44 0.56
39 45 0.75 0.75 0.07 0.44 0.56
41 42 0.38 0.38 0.22 0.26 0.56
44 47 0.26 0.26 0.24 0.36 0.48
48
44 47 0.26 0.26 0.24 0.36 0.48
30 34 0.19 0.19 0.02 0.05 0.28
18 21 0.02 0.02 0.01 0.24 0.27
18 21 0.02 0.02 0.01 0.24 0.27
2 4 1.30 1.30 1.00 1.40 0.24
9 11 0.35 0.35 0.30 0.19 0.19
35 38 0.94 0.94 0.11 0.97 0.18
39 40 0.84 0.84 0.49 0.02 0.14
6 10 0.20 0.20 0.13 0.15 0.13
31 32 1.00 1.00 0.71 0.71 0.13
1 5 1.00 1.00 0.91 1.00 0.05
36 37 0.04 0.04 0.03 0.02 0.02
42 45 0.11 0.11 0.04 0.16 0.02
42 45 0.11 0.11 0.04 0.16 0.02
2 6 2.80 2.80 2.50 3.00 0.01
25 26 0.00 0.00 0.00 0.01 0.01
1 2 0.00 0.00 0.00 0.00 0.00
Table A - 9 Dynamic data of generators and line parameters for Kundur system
49
Reference
[1] "Development of direct current technology," [Online]. Available:
http://www.deutsches-museum.de/en/exhibitions/energy/electric-
power/direct-current/. [Accessed 07 08 2012].
[2] “High-voltage direct current,” wikipedia, [Online]. Available:
http://en.wikipedia.org/wiki/High-voltage_direct_current. [Accessed 07 08 2012].
[3] Siemens AG, “High Voltage Direct Current Transmission-Proven Technology for
Power Exchange,” Erlangen Germany.
[4] Hualei Wang, M.A. Redfern, “The advantages and disadvantages of using HVDC
to interconnect AC networks,” in UPEC, 2010 31st Aug - 3rd Sept 2010.
[5] Jochen Kreusel, Dietmar Retzmann, “Integrated AC/DC Transmission Systems,”
ABB, Siemens, Germany, 2008.
[6] Schmidt, G., Fiegl, B. and Kolbeck.S., “HVDC transmission and the environment,”
Power Engineering Journal, p. 209–210, October 1996.
[7] ANDERSEN, B.R., “HVDC transmission-opportunities and challenges,” in The 8th
IEE International Conference, March 2006.
[8] Mohan N., Undeland T. M., Robbins W. P., Power electronics: converters,
applications and design, New York: Wiley, 1995.
[9] Tang, Guosheng, “Damping subsynchronous reosonance oscillations using a
VSC-HVDC back-to-back system,” University of Saskatchewan, Saskatoon,
Saskatchewan, 07.2006 .
[10] Du CuiQing, “VSC-HVDC for Industrial Power Systems,” Chalmers unversity of
technology, Goeteborg, Sweden, 2007.
[11] “Development and Application of Self- Commutated Converters in Power
Systems,” in IEEE Winter Meeting, Singapore, 01.2000.
[12] “Gotland: the first commercial HVDC Light project,” ABB, [Online]. Available:
http://www.abb.de/industries/ap/db0003db004333/a34c41e0fe23b18cc125774a
0033abbe.aspx. [Accessed 20 08 2012].
[13] A. Berizz, “The Italian 2003 blackout”.
[14] Ian Dobson, Benjamin A., “Number and propagation of line outages in cascading
events in electric power transmission systems”.
[15] Lidong Zhang, Lennart Harnefors, Pablo Rey, “Power System Reliability and
Transfer Capability Improvement by VSC- HVDC,” Power Technologies ABB,
50
Sweden.
[16] Ray D. Zimmerman, Carlos E. Murillo-Sánchez and Deqiang (David) Gan ,
“Matpower-A MATLAB Power System Simulation Package,” [Online]. Available:
http://www.pserc.cornell.edu/matpower/. [Accessed 20 08 2012].
[17] Nara K., Tanaka K., Shoults R. R., Chen M. S., Van Olinda, “On-line contingency
selection for voltage security analysis,” IEEE Trans. Power Apparat. Syst., Vols. PAS-
104, pp. 847 - 856, April 1985.
[18] Tan Xiaoya, “HVDC-VSC Model for Matpower,” EEH – Power Systems Laboratory,
Zurich, 2012.
[19] K. Prasertwong, N. Mithulananthan, D. Thakur, “Understanding low frequency
oscillation in power systems,” Power and Energy System Group, School of
Information Technology and Electrical Engineering, The University of
Queenslanda, St. Lucia Campus, Brisbane, Qld 4072, Australia.
[20] Padiyar K.R., Analysis of Subsynchronous Resonance in Power Systems, USA:
Kluwer Academic Publishers, 1999.
[21] Pal B.C., “Robust Damping Control of Inter-area Oscillations in Power System
with Super-conducting Magnetic Energy Storage Devices.,” Imperial College of
Science Technology and Medicine, 1999.
[22] Yuwa Chompoobutrgool, Luigi Vanfretti, Mehrdad Ghandhari, “Survey on Power
System Stabilizers Control and their Prospective Applications for Power System
Damping using Synchrophasor-Based Wide-Area Systems.,” KTH Royal Institute
of Technology, Stockholm.
[23] Dmitry N. Kosterev, Carson W. Tylor, William A., “Model Validation for the August
10.1996 WSCC System Outage,” IEEE Transactions on Power Systems, vol. 14, pp.
967-979, August 1999.
[24] Samuelsson Olof, “Power System Damping Structural Aspects of Controlling
Active Power,” Department of Industrial Electrical Engineering and Automation,
Lund Institute of Technology, 1997.
[25] Preece R., “Damping of Inter-are oscillations using WAMS based supplementary
controller installed at VSC based HVDC line,” in PowerTech, 2011 IEEE Trondheim,
19-23 June 2011.
[26] Ni Jingmin, Shen Chen, Li Ying, Tan Wei, “An on-line Weak-connection
identification method for controlled islanding of power system,” Proceedings of
the CSEE, 05.02.2011.
[27] Haibo You, Vijay Vittal, Xiaoming Wang, “Slow Coherency-Based Islanding,” IEEE
Transactions on power systems, vol. 19, February 2004.
51
[28] Chow, J. H., Time-Scale Modeling of Dynamic Networks with Applications to
Power Systems, New York: Springer-Verlag, 1982.
[29] Avramotic B, Kokotovic P. V., Winkelman J., “Area decomposition for
electromechanical models of power systems,” Automatica, vol. 16, pp. 637-648,
1980.
[30] Kokotovic P V, Avramovic B, Chow J H．, “Coherency based decomposition and
aggregation,” Automatica, vol. 18, pp. 47-56, 1982.
[31] P. Kundur, N. J. Balu, Power System Stability and Control, McGraw-Hill, 1993.
[32] Fang Liu, Ryuichi Yokoyama, Yicheng Zhou, Min Wu, “Study on Oscillation
Damping Effects of Power System Stabilizer with Eigenvalue Analysis Method for
the Stability of Power Systems”.
[33] Cliff Grigg, Peter Wong, Paul Allan, Murty Billinton, “The IEEE Reliability Test
System - 1996,” IEEE Transactions on Power System, vol. 14, August 1999.
[34] “Fault (power engineering),” wikipedia, [Online]. Available:
http://en.wikipedia.org/wiki/Fault_(power_engineering). [Accessed 08 08 2012].
[35] Paserba, J., “Analysis and control of power system oscillation,” CIGRE Special
Publication, 1996.
[36] Germond, R. Podmore, “Development of Dynamic Equivalents for Transient
Stability Studies,” System Control, Inc., 04.1977.
[37] R. Sunitha, R. Kumar Sreerama and Abraham T. Mathew, “Electric Power
Components and Systems. Department of Electrical Engineering,” National
Institute of Technology, Calicut, Kerala, India, 15.01.2011.
[38] “HVDC Light® Technical Background: CIGRE Compendium of HVDC Schemes
Throughout the World,” 2005.
[39] Khalil H. K., Nonlinear Systems, 3rd edition, Englewood Cliffs: Prentice-Hall, 2000.
[40] Siemens AG, “The Smart Way: HVDC PLUS – One Step Ahead,” 91058 Erlangen,
Germany, 2011.
