Master Thesis on “Development of Sensitivity Based Indices for Optimal Placement of UPFC to Minimize Load Curtailment Requirements” XR-EE-ES-2009:006 Thesis Examiner: Mehrdad Ghandhari Thesis Supervisor: Jai Govind Singh Submitted by: Hassan W. Qazi
Master Thesis
on
“Development of Sensitivity Based Indices for Optimal Placement of UPFC to Minimize Load
Curtailment Requirements” XR-EE-ES-2009:006
Thesis Examiner: Mehrdad Ghandhari
Thesis Supervisor: Jai Govind Singh
Submitted by: Hassan W. Qazi
i
Contents
1 Introduction 1
1.1 General 1
1.2 Flexible AC Transmission Systems (FACTS) 2
1.3 Different Models and Operating Challenges of Electricity Market 5
1.4 State of the Art 7
1.4.1 Load Curtailment 7
1.4.2 Optimal placement of FACTS controllers 8
1.6 Motivation 9
1.7 Thesis Organization 10
2 Load Curtailment Sensitivity Factors for Optimal Placement of UPFC 13
2.1 Introduction 13
2.2 System Modeling 14
2.2.1 Representation of Transmission Lines 14
2.2.2 Static Representation of UPFC 15
2.3 Proposed Methodology for Optimal Location of UPFC 19
2.3.1 Criterion for Optimal Location of UPFC 23
2.4 Problem Formulation to Minimize Load Curtailment Requirement 23
2.5 Simulation Results and Discussions 25
2.5.1 UPFC Placement in IEEE 14-bus System 25
2.5.2 UPFC Placement in IEEE 30-bus System 28
2.6 Conclusions 31
3 Load Curtailment Minimization by UPFC at Increased Load Condition 33
3.1 Introduction 33
3.2 Impact Assessment of Optimally Placed UPFC 34
3.3 System Studies 34
3.3.1 UPFC Placement in IEEE 14-bus System 34
3.3.2 UPFC Placement in IEEE 30-bus System 36
ii
3.4 Conclusions 39
4 Load Curtailment Minimization by UPFC Considering Electricity Market
Scenarios
41
4.1 Introduction 42
4.2 Modeling of Bilateral/Multilateral Contracts 42
4.3 Problem Formulation 42
4.4 System Studies 43
4.4.1 UPFC Placement in IEEE 14-bus System 43
4.4.2 UPFC Placement in IEEE 30-bus System 47
4.5 Conclusions 54
5 Conclusions 55
5.1 General 55
5.2 Summary of Significant Findings 56
5.3 Scope for Future Research 57
References 59
Appendices
A Data for the IEEE 14-bus System 62
B Data for the IEEE 30-bus System 65
1
Chapter 1
Introduction
1.1 General
Deregulated electric power industries have changed the way of operation, structure, ownership
and management of the utilities. The existing power transmission networks may not have been
able to accommodate all the new scenarios for electricity trades. The energy transaction in open
access environment may lead to unexpected amount and direction of power flow through some
transmission corridors, resulting in the need for some load to be dropped momentarily in order to
maintain the system security. It is further endangered by relative decline in transmission
expansion due to requirement of huge investment coupled with the problems in acquiring right-
of-way for the new transmission facilities and the concerns towards environment and cost. It may
not be ideal for the power generation company to drop some loads, which may cost them
penalties while the system operates near its operating limits in terms of security. Curtailment of
loads under contract, costs the power companies, a reduction in their regular tariffs. It is always
preferable to have minimum curtailment in the system at all as it is better for the system
reliability and fulfilling the contractual obligations; therefore, load curtailment reduction is an
important issue to be addressed in electricity markets.
With increasing demand and supply in the power systems, maintaining the security,
stability and reliability have become a challenging task, specifically in the emerging electricity
market scenario. The basic challenge in the evolving deregulated power system is to provide a
transmission network capable of delivering contracted power from suppliers to consumers over
large geographic area under market forces-controlled, and continuously varying patterns of
demand and supply. Flexible AC Transmission Systems (FACTS) are being popularly used by
utilities due to their capability to enhance power system static as well as dynamic performance.
The FACTS controllers utilize power electronics based technology and can provide
dynamic control on line power flows, bus voltages and thus enhance system stability and
security. These capabilities allow transmission system owners and operators to maximize asset
utilization and effectively execute additional bulk power transfers. The FACTS controllers have
been broadly developed on two different principles, one that alters the line series reactance or
bus shunt reactance or voltage phase difference across a line and utilizes conventional thyristor
2
switches for control. These include static VAR compensator (SVC), Thyristor Controlled Series
Compensator (TCSC) and Thyristor Controlled Phase Angled Regulator (TCPAR). The second
that controls the series injected voltage and/or shunt injected current employing voltage source
converters include Static Synchronous Compensator (STATCOM), Static Synchronous Series
Compensator (SSSC) and Unified Power Flow Controller (UPFC). The SVC and STATCOM are
the shunt compensators, whereas, TCSC and SSSC are the series compensators. The UPFC
combines both series and shunt compensators, and offers more versatile characteristics compared
to other controllers.
Amongst the two shunt controllers, the SVC has been popularly used due to its lesser cost
and ability to provide voltage support and enhance system dynamic performance. Using series
controllers such as TCSC, TCPAR, SSSC and UPFC, line flows can be altered in flexible and
controlled manner, allowing lines to be loaded close to their thermal limits without violating
other operating limits, and enhancing system stability and reducing the need for load curtailment.
However, these controllers are very expensive and, hence, their optimal location in the network
must be properly ascertained. In this work, a few new indices have been suggested for the
optimal placement of UPFC, utilizing static criteria. These indices have been verified with
increased load conditions and various kinds of market scenarios.
1.2 Flexible AC Transmission Systems (FACTS)
The FACTS initiative [1,2,3,4,5,6,7,8,10,11,15] was originally launched in 1980s to solve the
emerging problems faced due to restrictions on transmission line construction, and to facilitate
growing power export/import and wheeling transactions among utilities. The two basic
objectives behind development of FACTS technology; to increase power transfer capability of
transmission systems, and to keep power flow over designated routes, significantly increase the
utilization of existing (and new) transmission assets, and play a major role in facilitating
contractual power flow in electricity markets with minimal requirements for new transmission
lines.
Injecting series voltage phasor, with desirable voltage magnitude and phase angle in a
line can provide a powerful means of precisely controlling the active and reactive power flows,
by which system stability can be improved, system reliability can be enhanced while operating
and transmission investment cost can be reduced. It is possible to vary the impedance of specific
transmission line to force power flow along a desired “contract path” in the emerging power
systems, and to regulate the unwanted loop power flows and parallel power flows in the
interconnected system. Dynamic reactive power compensation and damping power system
oscillations can also be achieved using FACTS controllers. In general, FACTS controllers can be
divided into four categories based on their connection in the network:
3
Series controllers: The series controller can be switched impedance, such as capacitor, reactor
etc. or power electronics based variable source of main frequency, sub-synchronous and
harmonic frequencies to serve the desired need. In principle, all series controllers inject voltage
in series with the line. Even variable impedance, provided by some of the FACTS controllers,
multiplied by the current flow through it represents an injected series voltage in the line. TCSC is
one of the widely used series controllers. As long as the voltage is in phased quadrature with the
line current, the series controller only supplies or consumes variable reactive power. Any other
phase relationship will involve handling of real power as well. A typical connection in a line,
having series impedance is shown in Figure 1.1.
ijij jxr
Line
Series FACTS
controller
Figure 1.1: Static FACTS controller
Shunt Controllers: Similar to the series controllers, the shunt controllers, as shown in Figure
1.2, may also be variable impedance, variable sources, or a combination of these. In principle, all
shunt controllers inject current into the system at the point of connection. SVC and STATCOM
are the two most widely used shunt controllers. Even variable shunt impedance provided by
shunt controller, such as SVC, cause a variable current injection into the bus/line. As long as the
injected current is in phase quadrature with the bus voltage, the shunt controller only supplies or
consumes variable reactive power. Any other phase relationship will involve handling of real
power as well.
ijij jxrLine
Shunt FACTS
controller
Figure 1.2: Shunt FACTS controller
4
Combined Series-Series Controllers: This could be a combination of multiple series
controllers, which are controlled in a coordinated manner, in a multi-line transmission system.
Alternatively, it could be a unified controller, in which series controllers provide independent
series reactive compensation for each line but also transfer real power among the lines via the
power link. The real power transfer capability of the unified series-series controller, referred to
as Interline Power Flow Controller (IPFC) , makes it possible to balance both the real and
reactive power flow in the lines and, thereby, maximize the utilization of the transmission
system. Note that the term “unified” here means that the DC terminals of al controller converters
as show in the Figure 1.3 are connected together for real power transfer.
ijij jxrLine -1
ijij jxrLine -2
DC-link
FACTS controller
FACTS controller
Figure 1.3: Combined series-series FACTS controller
Combined Series-Shunt Controllers: This could be a combination of separate shunt and series
controllers, which are controlled in a coordinated or unified manner. Unified Power Flow
Controller (UPFC) is one of the series shunt controllers. In principle, combined shunt and series
controllers inject current into the system with the shunt part of the controller and voltage in the
line with the series part of the controller. However, when the shunt and series controllers are
unified, there can be a real power exchange between the series and shunt controllers via a DC
link as shown in Figure 1.4.
5
ijij jxr
Line
DC-link
Shunt FACTS
controller
Series FACTS controller
Figure 1.4: Combined series-shunt FACTS controller
1.3 Different Models and Operating Challenges of Electricity
Market
In different regions of the world, the electricity industry is changing the its previous shape and
transforming from vertically integrated utilities to the competitive industry, in which market
forces drive the price of electricity through increased competition. The reasons for restructuring
have been different across various regions and countries. An independent operational control of
transmission grid in a restructured power industry would provide open access to all market
participants and facilitate a competitive market at wholesale and retail levels. However, the
independent operation of the grid requires an independent entity known as System Operator
(SO). Management of power market settlement is carried out either by a separate entity known as
“Market Administration”, or the system operator itself.
Several market structures and transactions exist to achieve a competitive electricity
environment. Based on the types of transactions, three basic market models are outlined below
[16, 30, 31, 32, 33]:
Pool model: In this model, a centralized market place clears the market. Electric power
sellers/buyers submit bids including the amount of power along with the price that they are
willing to trade in the market. Under this model, one single entity, the Pool Company (PoolCo),
may purchase the power from the competing generators in the open market and sell it at a single
market clearing price to the retailers/or consumers, In this market, low cost generators would
especially be rewarded. The trading takes place one day ahead on hourly or half-hourly basis in
6
Power Exchange (PX). When only generating companies submit bids in the PX, it is known as
„Single auction model‟. In the „Double auction model‟, both the generators/suppliers and the
buyers submit the bids. The buyers‟ bids include their demand and willingness to pay the price.
Bilateral Contract Model: In this market model, the transactions may take place directly
between buying and selling entities [16]. These transactions defined for a particular time interval
of the day and its value may be time varying. It may be either firm or non-firm and can be a short
term or long term transaction [23]. The bilateral contract model may include different kinds of
transactions as given below [20, 21]:
Bilateral Transaction: A bilateral transaction is made directly between a seller and a buyer
without any third party intervention.
Multilateral Transaction: A multilateral transaction is a trade arranged by energy brokers and
involves more than two parties. Multilateral transactions are the extensions of bilateral
transactions and may take place between a group of sellers and a group of buyers at different
nodes.
Ancillary Service Transactions: The SO may directly enter into transactions with some
Generating Companies (GENCOs) in order to provide essential ancillary services for the system
regulation. Ancillary services are required for power balancing or regulating power requirement,
frequency control, voltage/ reactive power control, reserve requirement, black start capability
etc.
Hybrid Model: The hybrid model combines various features of the previous two models [43]. In
the hybrid model, a customer is allowed to negotiate a power supply agreement directly with the
suppliers or choose to accept the power from the pool market. In this model, PoolCo will serve
all participants (buyers and sellers), who choose not to sign bilateral contracts. However,
allowing customer to negotiate power purchase agreements with suppliers would offer a true
customer choice and an impetus of creation of wide variety of service and the pricing options to
meet individual customer needs.
In order to operate the competitive market efficiently, while ensuring the reliability of a
power system, the SO and the market administrator must establish sound rules for energy and
ancillary service trading in a fair and non-discriminatory manner.
7
Pool
Generation Company-1
Generation Company-2
Distribution Companies
Dis Co.-1
Dis Co.-2
Dis Co.-3
Dis Co.-4
Dis Co.-5
Multilateral
Contract
Bilateral Contract
Generation Company-n
Dis Co.-n
Figure 1.5: Operation of a restructured market
1.4 State-of-the-Art:
1.4.1 Load Curtailment
Load curtailment can be defined as a coordinated set of control strategies that will result in
decrease of the electric power load in the system. It is one of the possible corrective actions that
aim at forcing the disturbed system to a new stable equilibrium state [18]. Load curtailment is
normally carried out in order for the system to stay in its stability limits. Utilities often offer
commercial and industrial building owners reduced rates for electricity in exchange for a
curtailed energy use at the request of the utility. This reduction in load is purchased as an
ancillary service as is suggested in [23]. Such requests usually are generated on the occurrence of
8
high loads such as a hot summer afternoon; the consumers can get lower rates by reducing their
consumption or switching to alternate sources of energy.
The main reasons for load curtailment are the following
Due to the occurrence of contingencies or congestions at various points in the system, if
at a certain time it is not possible for the system to be kept within the stability limits,
curtailing the load in order to avoid a total black out becomes inevitable. In such a
situation, the consumers that have a contract to curtail the loads are notified to meet a
certain load demand as per the contract, the utility has to pay for any amount of load thus
curtailed in this manner.
Utility rate structures provide all kinds of customers with fixed rates regardless of
generation costs. These utilities use most efficient (least costly) of their generation plants
in order to supply the bulk of the load, they operate the more expensive plants only when
the load increases. Since the energy to the consumer is supplied at a fixed cost it leaves a
negative impact on the utility‟s profit margins to use less efficient plants. The best option
at a certain cost level for the utility is; instead of bringing in a costly generator (may be a
coal generator with large start-up cost) is to pay the consumer instead to restrict his use of
electricity.
Both the utility and customer will incur costs to add controls and equipment in
customer‟s facility, both will also commit resources to track the operation of load curtailment
and they also have to give reports. Apart from that, curtailing the load is not a good sign for the
system reliability and customers, thus the load curtailment must be minimized. A global Particle
Swarm-Based-Simulated Annealing Optimization technique for under-voltage load shedding
problem has been used to tackle load curtailment [44]. Some schemes for load curtailment have
been developed using dynamic optimal power flow analysis, it is based on issue concerning the
selection of optimal interruptible load selection [10].
1.4.2 Optimal Placement of FACTS Controllers:
In case of a contingency or a steep load increment , line overload or low/high bus voltage
are likely to occur, some amount of load has to be curtailed in such a situation in order to
maintain the system security. In order to shed the least amount of load, re-dispatch of generation
using OPF is one solution. However, some lines may reach their capacity limits while there may
be others whose capacity is not completely used due to system topology. Directing the power in
such a way that the lightly loaded branches are also loaded to reduce the system load curtailment
is an option which can be achieved by making use of FACTS devices.
9
Series FACTS controllers, such as TCSC, TCPAR,SSSC , shunt FACTS controllers, such
as SVC, STATCOM and series-shunt FACTS controllers, such as UPFC , are capable of
effectively controlling the line power flows and bus voltage profile by dynamically adjusting the
line impedance, bus voltage magnitudes and phase angles of the lines, in which these are placed.
Among FACTS controllers, UPFC is more promising due to its ability to work as series and
shunt compensator together. TCSC and TCPAR are cheaper than voltage source converter based
compensators like SSSC and UPFC. However, the voltage source based converters are fast and
more flexible to control the power system parameters. These controllers are, however, very
expensive and hence, their optimal location in the network must be ascertained.
It is common to find optimal location for placement of FACTS controllers for various
purposes and there have been suggested several methods in [35,36,37,39,40], optimal location of
FACTS controllers for loadability enhancement has been presented. No significant work has
been done on finding the optimal location of FACTS controllers in order to minimize the load
curtailment requirement. Load curtailment has been worked upon with respect to other
parameters such as voltage stability margin, for example in [29], an evaluation of system load
curtailment has been carried out while incorporating voltage stability margin and it has been
concluded that the amount of load curtailment evaluated is observed to increase if more voltage
stability margin, from a possible collapse is required in a system.
In [26], the impacts of TCSC and SVC on load curtailment in a power system have been
examined. An OPF formulation has been developed to minimize the load curtailment, the
constraints being the system security constraints, real and reactive power generation of each
generator bus and the real and reactive loads at each load bus are taken as control variables.
Having included a TCSC in the system at random location, it has been observed that the real load
curtailment decreases when TCSC is placed in certain lines on randomly. Similarly when SVC is
placed in the system at random, it is shown that load curtailment in the system reduces. In this
work, a criterion for finding the optimal location of FACTS devices to reduce load curtailment
requirement, in power system, has been proposed.
1.6 Motivation:
Continuous change in power demand and supply patter, along with limited expansion of
transmission network, alters the power flow patterns in power system in such a way that some of
the corridors get over loaded. This raises serious challenges in operating the system in a secure
and reliable manner. The FACTS controllers are being increasingly used in the network to
address some of these challenges. Although FACTS controllers play an important role in
improving the power system operating performance these devices are costly and need to be
placed optimally in the power systems network.
10
For optimal location of FACTS controllers, several approaches, based on static criteria,
have been suggested in literature. These fall under three main categories. The first approach is
based on OPF formulation that minimizes the total cost and considers the number, location and
size of FACTS controllers as variables. The OPF, generally, has been formulated as mixed
integer optimization problem. The second approach first identifies a set of possible locations of
FACTS controllers based on some enumerative technique or analytical relationship. Then, it runs
load flow/continuation power flow, for each combination, to study their relative impact on
system performance and selects the best combination of FACTS controllers. These two
approaches, in general, involve exhaustive search, and hence require large computational time.
The third approach is based on utilizing a set of sensitivity factors, defined with respect to the
FACTS controller parameters, to decide its placement. This approach is computationally less
cumbersome and effective for large system.
In order to minimize the requirement of load curtailment, certain FACTS devices such as
SVC and TCSC have been placed randomly in the system in literature and their effect on the
reduction in load curtailment has been demonstrated. This approach is not very practical when it
comes to larger systems, therefore a sensitivity index has been developed based on variation in
load curtailment with respect to the change in FACTS parameters. A generalized sensitivity
index has been developed and its application has been demonstrated on a UPFC. The validity of
this index has been checked under increased load conditions as well as with different market
scenarios.
1.7 Thesis Organization
The work carried out, in this thesis, has been organized in five chapters. The present chapter
describes fundamental of FACTS controllers and a few energy market models and operating
challenges as well as load curtailment. It presents the relevant survey on the subject and sets
motivation behind present work.
Chapter 2 proposes a set of load curtailment sensitivity indices for optimal placement of UPFC.
The optimal power flow problem has been formulated having included the FACTS controller at
one of the locations. Analysis has been carried out on two IEEE test systems (one 14-bus and
another 30-bus). The obtained results have been presented under normal conditions and
conclusions have been drawn.
In chapter 3, the effectiveness of the criteria has been checked at increased load condition. This
is simulated by increasing the active and reactive power load on each bus
11
, and the optimal power flow problem has been run again and observed the impact of FACTS
controllers on minimization of load curtailment. The whole analysis is carried out on the same
two IEEE test systems as used in chapter 2.
Chapter 4 have been considered the different kinds of market scenarios, which include a
combination of pool and one bilateral contract, a pool and a multilateral contract and pool, a
bilateral and a multilateral contracts. The optimal power flow problem has been used to see the
effect of optimally placed FACTS device in the system for the above described market models.
In chapter 5, summary of the main findings of this work is presented and some suggestions for
future research in this area have been given
12
13
Chapter 2
Load Curtailment Sensitivity Factors for Optimal
Placement of UPFC
2.1 Introduction
Modern electric power system is very complex and undergoes unforeseen rapid changes in terms
of demand/generation patterns and trading activities that hinder the system stability. For
example, a steep rise in load or a certain critical line/equipment outage can cause line overload or
undesirable voltage profile and such events can push the system towards instability and possibly
even a black out. In order to cope with such situations, it is common practice to purchase the
rights of asking for a reduction of load from certain customers [23]. However, being critically
loaded is not an ideal situation for the power system. Load curtailment is the collection of control
strategies employed to reduce the electric power loading in the system and main aim is to push
the disturbed system towards a new equilibrium state as described in [18]. Load curtailment may
be required even when some lines reach their capacity limits but others still have not utilized
their capacity completely, such a scenario can occur due to system topology. The power flows
are rerouted in such a way so that the system transmission capability is completely utilized.
FACTS controllers could be a suitable alternative over erection of new transmission line,
in order to redirect power from certain corridors, because it is not easy to build more
transmission lines due to issues like environmental as well as the need to acquire the right of way
clearances. Due to high costs of FACTS devices, their proper location in the system must be
ascertained before placement such that, maximum benefit can be obtained along with specified
purpose.
In literatures, there are few work reported for the use of FACTS devices in order to
reduce the system load curtailment but no one suggested any proper method to optimally place
FACTS devices in the system. The authors in [26] have been demonstrated the use of TCSC &
SVC for reduction in the total system load curtailment. From suggested method in [26], the
FACTS devices have been placed in the system by hit and trial basis and their location has been
validated through OPF problem formulation. It is however important to lay out a criteria for the
14
placement of FACTS devices, due to high costs, which can indicate the optimal location for the
FACTS device.
A new method has been proposed, in this chapter, in terms of sensitivity factors for the
optimal location of UPFC to minimize the system load curtailment requirement, to maintain the
system security, and called as the Load Curtailment Sensitivity Factors (LCSF). The load
curtailment sensitivity factors can be described as the change in total load curtailment with
respect to the change in UPFC parameters. In this work, UPFC has been considered for the study
to minimize the load curtailment as it is most versatile device in FACTS family. The main
motivation of finding such a sensitivity coefficient is to determine the best location for the UPFC
in a system for this purpose.
In this chapter, brief overviews of system modeling including the transmission line and
UPFC‟s static power injection model have been used for the investigation of the effectiveness of
the proposed method. Results have been obtained on IEEE 14-bus, IEEE 30-bus systems and
discussed the suitability of the proposed.
2.2 System Modeling
It is necessary to model the complex real life power system with a set of equations that can
describe the behavior of a system to a satisfactory level of exactness. The modeling of
transmission line as well as the representation of UPFC under static conditions can be described
as under.
2.2.1 Representation of transmission lines
A simple transmission line, connected between bus-i and bus-j with the line admittance
gij+jbij=1/( rij+jxij), can be represented by its lumped π equivalent parameters as shown in Figure
2.1. Let complex voltages at bus-i and bus-j be Vi δi and Vj δj, respectively. The real (Pij) and
reactive (Qij) power flows from bus-i to bus-j can be written as
(2.1)
(2.2)
where, = - .
Similarly, the real (Pji) and reactive (Qji) power flows from bus-j to bus-i can be expressed as
15
(2.3)
(2.4)
where Bsh is full line charging impedance.
ijijij jbgy
2/shjB 2/shjBBus-i
Bus-j
jV iV
ji
Figure 2.1 Static model of a transmission line
2.2.2 Static representation of UPFC
The Unified Power Flow Controller (UPFC) [8,11,12,13,19] can be viewed as a combination of
Static Synchronous Compensator (STATCOM) and a Static Synchronous Series Compensator
(SSSC). Both compensators are coupled via a DC link, which allows bidirectional flow of real
power between the series output terminals of the SSSC and the shunt output terminal of the
STATCOM. A simple circuit model of UPFC is shown in Figure 2.2
STATCOM
DC Link
SSSC
Line
Figure 2.2: A simple model of UPFC
16
The UPFC consists of a shunt (exciting) & series (booster) transformers. Both the transformers
are connected by two Gate-Turn-Off (GTO) converters and a DC circuit having a capacitor. The
shunt converter is primarily used to provide the real power demand of the series converter via a
common DC link terminal from the AC power system. Shunt converter can also generate and
absorb reactive power at its AC terminal. Therefore with proper control it can also act as an
independent advanced static VAR compensator providing reactive power compensation for the
line and thus executing indirect voltage regulation at the input terminal of the UPFC. A series
converter is used to generate voltage source at fundamental frequency with variable amplitude
(0≤Vs≤ Vsmax
) and phase angle (0≤ s ≤π), which are added to the AC transmission line by series
connected boosting transformer. The converter output voltage, injected in series with the line,
can be used for direct voltage control, series compensation, phase shifter and their combinations.
This voltage source can internally generate or absorb all the reactive power required by different
type of controls applied and transfers active power at its DC terminal.
Presently there are two reported UPFC installations in the world one in Inez substation of
American Electric Power (AEP) system [14], USA, and the other in France. The UPFC, in AEP,
increases the line flow by about 125MW, while simultaneously regulating area voltage.
UPFC is the new generation of power system FACTS control family, which can play a
major role in solving technical issues of open power market [22, 25, 27, 28]. Most of the FACTS
devices are generally installed in substations for convenient operation and maintenance.
Therefore, the line shunt impedance (Bsh) on sending end of the line should be represented on the
right side of the FACTS device. To simplify the problem formulation, the shunt impedance has
been moved to the left hand side of the UPFC, as shown in Figure 2.3. In practice, this
approximation has little effect on computing accuracy.
The conventional UPFC consisting of two converters capable of simultaneously
controlling three power system quantities, i.e. the bus voltage at substation, real and reactive
power flows in a line connected to the substation. The component (IT) of the shunt current is in
phase with the voltage at bus-i and current component (Iq) is taken as zero, in this work. The
equivalent circuit of the UPFC placed in line-k connected between bus-i & bus-j having series
impedance gij+jbij=1/( rij+jxij) , is shown in Figure 2.3 and its control vector diagram is shown in
Figure 2.4. UPFC has three controllable parameters viz., the inserted voltage magnitude (Vs) and
the phase angle ( s) and the magnitude of the quadrature current (Iq) [43].
17
Bus-p
Bus-k
Bus-j
2/shjB 2/shjB
iI
TIqI
Bus-i
ijij jbg
'
iI
'
iViVjV
s sV
Figure 2.3: Equivalent circuit diagram of UPFC
(2.5)
, (2.6)
(2.7)
18
iV
'
iV sV
max
sV
s
TI
iI
qI
'
iIqI
jV
Figure 2.4: Vector diagram of UPFC control action
The power injection at bus-i can be written as
(2.8)
where, Iip is the line current from bus-i to bus-p and Iish is the complex shunt current due to line
charging and „*‟ shows the complex conjugate.
The UPFC can be represented by power injection model as shown in Figure 2.5. The
injected complex powers, due to UPFC, are at bus-i, and at
bus-j, and can be expressed as
(2.9)
(2.10)
where, is the complex power injection without UPFC in a line.
From equation (2.9), the real and reactive power injection at bus- i can be derived as
(2.11)
19
(2.12)
The injected active (Piu) and reactive (Qiu) power at bus-i will be
(2.13)
(2.14)
Similarly, the real (Pju) and reactive (Qju) power injections at bus-j can be derived as
(2.15)
(2.16)
ijijij jbgy
iuSjuS
Bus-i Bus-j
Line
Figure 2.5: Power injection model of UPFC
2.3 Proposed Methodology for Optimal Location of UPFC
Total load curtailment requirement in a system and the active and reactive power balance on
every node are the basic equations which are used to derive the criteria for the placement of
UPFC, the load curtailment in a system is written as
(2.17)
where , Sireq denotes the total apparent power demand on a particular bus whereas Siavl is the
complex power available on that particular bus. The apparent power can be given as
(2.18)
20
(2.19)
(2.20)
where , Gij and Bij are the real and imaginary elements of Y-bus matrix. Piu and Qiu are the
active and reactive powers injected from the FACTS device into the bus-i, given in equation
(2.13 & 2.14)
Equation (2.17), in the presence of a FATCS device, can be a function of bus voltage magnitude
(V) voltage angle (δ) and injected FACTS parameter (X) and given as
(2.21)
From Taylor‟s expansion, equation (2.21) can be written as
(2.22)
where, matrices H and W have the following values
, represents injected FACTS parameter, Nl is the total number
of lines in the system.
When using UPFC as the FACTS device
, i , j are the end buses of line ‘l’
The dimensions of matrix [H] are 1 (2nb-2) as the derivatives corresponding to slack bus are not
included in the above matrices.
While using UPFC, equation (2.22) becomes
21
(2.22a)
where,
Similarly for UPFC angle
(2.22b)
where,
The dimensions for and are .
The power balance equation at each node can be written as
(2.23)
(2.24)
The power balance equations, at steady state, can be expressed as a function of bus voltage ,
bus angle (δ) and FACTS parameter and are written for each node as
(2.25)
(2.26)
From Taylor‟s expansion of equations (2.25) & (2.26)
(2.27)
In equation (2.27), the change in loads is assumed to be met by the slack bus generator and can
be written as
(2.28)
22
The dimension of matrix is and for matrix , dimension is
For UPFC, equation (2.28) can be written as
, where (2.28a)
And
, where (2.28b)
Substituting equation (2.28a) into (2.22a) and equation (2.28b) into (2.22b)
(2.29)
(2.30)
Therefore,
(2.31)
(2.32)
The sensitivity factors are derived as change in load curtailment with respect to change in
FACTS parameters.
23
Equation (2.31) describes the sensitivity factor corresponding to injected voltage magnitude
having angle of injection as zero, while equation (2.32) gives the sensitivity factor corresponding
to the voltage angle injection while keeping the injected voltage as constant.
The index calculated from equation (2.31) is the Load Curtailment Sensitivity Factor,
and the index calculated from equation (2.32) is the Load Curtailment Sensitivity
Factor .
2.3.1 Criterion for Optimal Location of UPFC
The following criteria have been used for optimal placement of UPFC.
The branches having transformers have not been considered for the UPFC placement.
The branches having generators at both the end buses have not been considered for
the UPFC placement, in this work.
The line having the highest absolute load curtailment sensitivity factor
with respect to UPFC angle is considered the best location for UPFC, followed by
other lines having less values of .
When two or more lines are having similar sensitivity factors , then the line
having the highest magnitude, with negative sign, of load curtailment sensitivity
factor with respect to UPFC voltage is considered as the best location for
UPFC placement.
2.4 Problem Formulation to Minimize the Required Load
Curtailment Requirement
The effectiveness of the proposed approach, for optimal placement of UPFC, has been
verified in terms of its impact on reducing total required load curtailment in the system. It has
been assumed that power factors at all load buses are remains constant while minimizing the
system load curtailment. The problem to determine the minimum required system load
curtailment has been formulated as an OPF problem which is given below.
Minimize 1
bN
lireq li
i
LC P P
Subject to the following constraints:
24
a) Equality constraints: Power balance equations corresponding to both the real and the
reactive powers, as defined in equations (2.23) and (2.24), must be satisfied. In order
to keep the load power factor as constant it is assumed that when a certain amount of
real load has been curtailed at one bus, the corresponding reactive load at that bus will
also be curtailed and this condition can be represented mathematically as
(2.33)
, is the real power demand at bus-i;
, is the actual real power supply at bus-i;
, is the reactive power demand at bus-i;
, is the actual reactive power supply at bus-i;
b) Inequality constraints: These include the operating limits on various power system
variables and the parameters of UPFC as given below
(2.34)
(2.35)
(2.36)
; (2.37)
Equation (2.34) represents the limits on reactive power generations. The limits on the bus voltage
magnitude and angle are given by equations (2.35) and (2.36) respectively. Equation (2.37)
represents the limits on UPFC ( ) parameters. The shunt current „ ‟ has been taken zero in
this work, as it has no significant impact on real power control because it is in quadrature of
sending end bus voltage.
The above OPF problem involves a non linear objective function and a set of nonlinear
equality and inequality constraints. This problem can be solved by any nonlinear optimization
technique. In this work, GAMS/SNOPT solver library [34] has been used for solving the OPF
problem.
25
2.5 Simulation Results and Discussions
The proposed sensitivity approach for optimal placement of UPFC has been tested on IEEE 14-
bus system and IEEE 30-bus systems. The details of these systems are given in appendix-A and
B, respectively.
2.5.1 UPFC placement in IEEE 14-bus system
The sensitivity factors , as derived in equations (2.31), have been obtained and given in
Table 2.1. The top 10 locations, in their order, have been given in column 2 based on sensitivity
factors which are given in 4th
column.
Table 2.1: Rank orders based on sensitivity factor (14-bus system)
Rank order
Line no. Buses i-j Proposed sensitivity factors
1 08 01-02 -0.9601
2 04 01-08 -0.4509
3 01 08-03 -0.3458
4 11 02-09 -0.3230
5 02 09-06 -0.3172
6 12 06-07 -0.3165
7 09 02-04 -0.3096
8 05 02-08 -0.2485
9 03 09-07 -0.1887
10 16 03-13 -0.1271
The optimal locations, based on sensitivity factor with respect to UPFC angle , as given
in equation (2.32), have been obtained and top 10 locations are shown in Table 2.2.
26
Table 2.2: Rank orders based on sensitivity factor ) (14-bus system)
Rank order
Line no. Buses i-j Proposed sensitivity factors )
1 08 01-02 1.1340
2 09 02-04 0.5564
3 07 09-08 0.5384
4 04 01-08 0.5187
5 11 02-09 0.4155
6 05 02-08 0.2913
7 06 09-04 0.2327
8 01 08-03 0.2008
9 02 09-06 0.1833
10 12 06-07 0.1568
The values of minimum load curtailment obtained through OPF solution by placing UPFC in
each line, taken one at a time are given in Table 2.3.
Table 2.3: Sensitivity factor and load curtailment in 14-bus system
Rank order
Line no.
Buses i-j
Sensitivity factors
OPF results by varying only
(pu) (pu)
1 04 01-08 -0.4509 0.51348 0.100
2 11 02-09 -0.3230 0.61533 0.100
3 12 06-07 -0.3165 0.64265 0.041
4 05 02-08 -0.2485 0.60572 0.100
5 16 03-13 -0.1271 0.64307 0.015
For an IEEE 14-bus system, using UPFC voltage based sensitivity factor , the
best location for the placement of UPFC is found as line-04, followed by branches 11,12,5 and
16. Load curtailment value in the absence of a UPFC is 0.643281 pu. The maximum
voltage injected by UPFC is set as 0.100 pu. The maximum and minimum limits of bus
voltage magnitude are 1.04 and 0.96 pu, respectively. The minimum value of load curtailment as
obtained by placing UPFC in line-4 is 0.51348 pu. The results, given in Table 2.3, have been also
shown through bar chart in Figure 2.6.
27
Figure 2.6: Variation of load curtailment with rank order for (14-bus system)
Table 2.4: Sensitivity factor ) and load curtailment in 14-bus system
Rank order Line no. Buses i-j Sensitivity factors ) OPF results by varying &
(pu) (pu) (rad)
1 07 09-08 0.5384 0.50203 0.100 1.570
2 04 01-08 0.5187 0.29462 0.100 1.197
3 11 02-09 0.4155 0.48350 0.100 1.291
4 05 02-08 0.2913 0.52682 0.100 1.267
5 06 09-04 0.2327 0.59214 0.100 1.212
The value of load curtailment have been obtained and given in Table 2.4 for the case
when varying both the injected voltage magnitude (Vs) from 0 to 0.1 pu and phase angle ( s)
from –π to π. The best location as calculated from the sensitivity factor is line-07 and required
load curtailment is found to be 0.50203 pu. The second best location, based on sensitivity factor,
is line-04 and the value of required load curtailment is 0.29462 pu. This is due to the non
linearity of the system. The branches not fulfilling the criteria, laid out in section 2.3.1, have
been excluded. The results, given in Table 2.4, have been also shown through bar chart in Figure
2.7.
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
Without
UPFC
UPFC in
line 04
UPFC in
line 11
UPFC in
line 12
UPFC in
line 5
UPFC in
line 16
Lo
ad c
urt
ailm
ent
(pu)
28
Figure 2.7: Variation of load curtailment with rank order for ) (14-bus system)
2.5.2 UPFC placement in IEEE 30-bus system
The sensitivity factors as derived in equations (2.31) and (2.32) are calculated for all the lines
and shown in Tables 2.5 and 2.6, respectively. The optimal locations found for required
minimum load curtailment in the system using these equations are given as under. The line most
suitable for the placement of UPFC has been assigned rank 1; similarly later ranks/orders
demonstrate the position to be less suitable for the placement of a UPFC. The top 10 ranks orders
only, based on sensitivity factor with respect to UPFC injected voltage magnitude and
phase angle ) have been given in Tables 2.5 and 2.6, respectively.
Table 2.5: Optimal locations based on sensitivity factor (30-bus system)
Rank order Line no. Buses i-j Proposed sensitivity factors
1 11 01-02 -0.7108
2 12 01-27 -0.3536
3 06 02-13 -0.2288
4 33 27-11 -0.2283
5 05 02-05 -0.2187
6 07 11-13 -0.2080
7 01 13-07 -0.1746
8 14 02-11 -0.1711
9 03 11-09 -0.1615
10 13 07-08 -0.1329
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
Without
UPFC
UPFC in
line 07
UPFC in
line 04
UPFC in
line 11
UPFC in
line 05
UPFC in
line 06
Lo
ad c
urt
aim
ent
(pu)
29
Table 2.6: Optimal locations based on sensitivity factor ) (30-bus system)
Rank order Line no. Buses i-j Proposed sensitivity factors )
1 11 01-02 0.3390
2 05 02-05 0.2562
3 33 27-11 0.2285
4 12 01-27 0.2337
5 07 11-13 0.1540
6 01 13-07 0.1364
7 03 11-09 0.1048
8 41 07-04 0.1045
9 06 02-13 0.0626
10 02 13-08 0.0572
The values of required minimum load curtailment obtained through OPF solution by placing
UPFC in each line, selected one at a time, are given in Table 2.7.
Table 2.7: Sensitivity factor and load curtailment in 30-bus system
Rank
order Line no. Buses i-j
Sensitivity
factors
OPF results by varying only
(pu) (pu)
1 12 01-27 -0.3536 0.01371 0.100
2 06 02-13 -0.2288 0.11386 0.100
3 33 27-11 -0.2283 0.09693 0.057
4 07 11-13 -0.2080 0.13401 0.041
5 14 02-11 -0.1711 0.10584 0.100
The required minimum load curtailment is found to be 0.14161 pu at the base case without
any UPFC. The maximum and minimum voltage limits are 1.04 and 0.96 pu, respectively. Table
2.7, also shows that the smallest value of sensitivity factor is -0.3536 which
corresponds to line-12, followed by line-6, 22, 7 and 14 respectively. The required load
curtailment decreases from 0.14161 pu to 0.01371 pu when UPFC is placed in the best location
(line-12). The last column gives the value of UPFC injected voltage. The maximum value of
UPFC injected voltage is set as 0.100 pu. Figure 2.8 demonstrates the results of Table
2.7.
30
Figure 2.8: Variation of load curtailment with rank order for (30-bus system)
Table 2.8: Sensitivity factor and load curtailment in 30-bus system
Rank
order
Line
no.
Buses i-j
Sensitivity factors
OPF results by varying &
(pu) (pu) (rad)
1 33 27-11 0.2285 0.00000 0.073 0.473
2 12 01-27 0.2337 0.00000 0.100 0.070
3 07 11-13 0.1540 0.00303 0.100 1.352
4 06 02-13 0.0626 0.03532 0.100 1.203
5 09 13-12 0.0563 0.10172 0.100 1.043
Similarly, Table 2.8 shows that the highest value of sensitivity factor ) is 0.2285 pu
which corresponds to line-33, followed by lines 12, 07, 06 and 09, respectively. The required
load curtailment decreased from 0.14161 pu to 0.0000 pu when UPFC is placed in the best
location i.e., line-33 while varying both the UPFC injected voltage magnitude as well as
UPFC phase angle . The maximum value of UPFC injected voltage magnitude is set
as 0.100 pu while phase angle can be varied between – and π. The branches not fulfilling
the criteria, laid out in section 2.3.1, have been excluded.
From Table 2.8 and Figure 2.9, it can be seen that the required load curtailment value is
zero for both the lines-33 and 12. A final placement may be decided based on meeting other
objectives such as power flow control, dynamic stability improvements, cost, availability of site
etc, which have not been considered in this work.
0
0,02
0,04
0,06
0,08
0,1
0,12
0,14
0,16
Without UPFC
UPFC in line 12
UPFC in line 06
UPFC in line 33
UPFC in line 07
UPFC in line 14
Lo
ad c
urt
ailm
ent
(pu)
31
Figure 2.9 Variation of load curtailment with rank order for ) (30 bus system)
2.6 Conclusions
A new set of AC power flow based indices has been developed, in terms of change in system
load curtailment with respect to change in UPFC series controller parameters, for the optimal
placement of UPFC. Two kinds of sensitivity factors have been defined with respect to the series
injected voltage magnitude and phase angle parameters of UPFC. The optimal location of UPFC
has been decided based on the calculated indices. A steady state power injection model of UPFC
has been utilized in this work. An OPF formulation has been developed, with minimization of
required system load curtailment as an objective, to study the impact of the optimal UPFC
placement. Results obtained, on IEEE 14-bus and IEEE 30-bus systems, reveal the following.
1. With the optimal placement of UPFC at the location obtained based on the proposed
sensitivity factors, the required system load curtailment decreases in both the test
systems.
2. The rank order of the locations, obtained for the optimal placement of the UPFC, are
validated through OPF results in terms of the decrement in required system load
curtailment with the placement of UPFC. The high ranked lines for the UPFC placement
have resulted in a larger reduction in total system load curtailment in both the systems.
0
0,02
0,04
0,06
0,08
0,1
0,12
0,14
0,16
Without
UPFC
UPFC in
line 33
UPFC in
line 12
UPFC in
line 07
UPFC in
line 06
UPFC in
line 09
Lo
ad c
urt
ailm
ent
(p
u)
32
33
Chapter 3
Load Curtailment Minimization by UPFC at
Increased Load Condition
3.1 Introduction
In the deregulated power system, the loads and generations can change rapidly, causing certain
corridors to be loaded to their thermal limits. Once a small disturbance occurs in a part of the
system it can rapidly cascade triggering a chain of events that may eventually lead to a system
black out. In case, a line in the system has been overloaded or a contingency has occurred (loss
of a line, or loss of a large generator), the balance of load and generation in the system is
disturbed causing the some corridors to be overloaded.
In the previous chapter, a new method has been developed to ascertain the optimal
location of FACTS devices in the system so that the required net load curtailment of the system
is minimized. However, it is important to check if such a criterion remains valid in the condition
of system being overloaded. The location stipulated as most suitable, in order to minimize the
required load curtailment, in a system operating at normal conditions, should remain most
suitable even if there is a certain overload in the system, as it can not be avoided. It is therefore
important to investigate if the developed load curtailment sensitivity factors can accurately
predict the best location of FACTS devices to reduce the required load curtailment with the
system being overloaded.
In this chapter, an overview of the system response and the validity of Load Curtailment
Sensitivity Factors , ), as calculated in chapter 2, have been carried out to an
increment in system loading. It has been investigated that the optimal location obtained using
equations 2.31 and 2.32 still stayed valid under an increased system load (both active and
reactive). The results have been validated through the solution of OPF problem stipulated as in
section 2.4.
The analysis has been carried out, on IEEE 14-bus and IEEE 30-bus systems, to assessed
the impact of proposed methodology and followed by obtained results and the drawn
conclusions.
34
3.2 Impact Assessment of Optimally Placed UPFC
In order to evaluate the impact of optimal placement of UPFC in the system based on calculated
sensitivity factors it could be modify the load conditions of the system. The active as well as
reactive load in the system is increased by 30% at all buses in order to simulate a possible
overloading of the system. A criterion for finding the optimal location of a UPFC under normal
conditions; can also be able to predict the optimal location of UPFC under increased load, to a
fair degree of accuracy. The rank calculated from equations 2.31 and 2.32 are verified by running
an OPF simulation in GAMS.
3.3 System studies
The proposed sensitivity approach for optimal placement of UPFC has been tested on IEEE 14-
bus system and an IEEE 30-bus system. The details of these systems are given in appendix A and
B, respectively. The system base is 100 MVA.
3.3.1 UPFC placement in IEEE 14-bus system
The sensitivity factors, as derived in equations (2.31) and (2.32), have been calculated for 14-bus
system. The best location has been assigned rank order 1 and so on. The rank/order considering
sensitivity factor with respect to UPFC voltage have been obtained based on equation
2.31 and only top 10 rank/orders given in Table 3.1. The values of the required minimum load
curtailment obtained through OPF solution by placing UPFC in each line, selected one at a time,
and given in Table 3.1. Only top 5 locations have been shown in the table below. The lines
having transformers or having generators at both their end buses have been neglected, in
accordance with the criteria, for the placement of UPFC described earlier in section 2.3.1.
Table 3.1: Load curtailment at increased load conditions (14-bus system)
Rank order
Line no.
Buses i-j
Sensitivity factors
OPF results by varying only
(pu) (pu)
1 04 01-08 -0.4509 1.29351 0.100
2 11 02-09 -0.3230 1.39536 0.100
3 12 06-07 -0.3165 1.42269 0.041
4 05 02-08 -0.2485 1.38575 0.100
5 16 03-13 -0.1271 1.42311 0.015
For 14-bus system, using injected UPFC voltage based sensitivity factor , the best
location for the placement of UPFC is predicted as line-04, followed by lines-11, 12, 5 and 16.
35
The required load curtailment value in the absence of a UPFC is 1.42331 pu. The
maximum voltage injected by UPFC is set as 0.100 pu. The maximum and minimum
voltage limits are again set to 1.04 and 0.96 pu, respectively. The minimum value of required
load curtailment as obtained by placing UPFC in line-4 is 1.29351 pu.
Figure 3.1: Required load curtailments at increased load for obtained locations based on
LCSFVs
factors (14-bus system)
The locations considering sensitivity factor with respect to injected UPFC voltage phase angle
has been calculated based on equation 2.31 and top 10 rank/orders are given in Table
3.2. The values for required load curtailment, sensitivity index, injected UPFC voltage
magnitude and phase angle for the first 5 locations have been given in Table 3.2.
Table 3.2: Sensitivity factor ) and required load curtailment at increased load (14-
bus system)
Rank order
Line no.
Buses i-j
Sensitivity factors )
OPF results by varying &
(pu) (pu) (rad)
1 07 09-08 0.5384 1.28207 0.100 1.570
2 04 01-08 0.5187 1.07465 0.100 1.197
3 11 02-09 0.4155 1.26354 0.100 1.291
4 05 02-08 0.2913 1.30686 0.100 1.267
5 06 09-04 0.2327 1.37217 0.100 1.212
1,22
1,24
1,26
1,28
1,3
1,32
1,34
1,36
1,38
1,4
1,42
1,44
Without
UPFC
UPFC in
line 04
UPFC in
line 11
UPFC in
line 12
UPFC in
line 05
UPFC in
line 16
Lo
ad c
urt
ailm
ent
(pu)
36
The value of required load curtailment, when varying both from 0 to 0.1 pu and from –π to
π, for the best location is 1.28207 pu. The best location is found to be line-07 followed by line-04
and the value of load curtailment when UPFC is placed in line-04 is 1.07465 pu. This is due to
the non linearity of the system. The value of sensitivity factor ) for line-04 is 0.5187 pu.
Figure 3.2: Required load curtailments at increased load for obtained locations based on
LCSFs factors (14-bus system)
3.3.2 UPFC Placement in IEEE 30-bus System
The sensitivity factors, with respect to injected UPFC voltage magnitude , have been
calculated and top 10 locations only given in Table 3.3 for the 30-bus system. The values of
minimum required load curtailment obtained through OPF solution by placing UPFC in each
line, selected one at a time and have also been given in 5th
column of Table 3.3.
Table 3.3: Required load curtailment at increased load condition (30-bus system)
Rank order
Line no.
Buses i-j
Sensitivity factors
OPF results by varying only
LC (pu) Vs (pu)
1 12 01-27 -0.3536 0.86361 0.100
2 06 02-13 -0.2288 0.96376 0.100
3 33 27-11 -0.2283 0.94680 0.057
4 07 11-13 -0.2080 0.98391 0.041
5 14 02-11 -0.1711 0.95574 0.100
0
0,2
0,4
0,6
0,8
1
1,2
1,4
1,6
Without
UPFC
UPFC in
line 04
UPFC in
line 11
UPFC in
line 12
UPFC in
line 05
UPFC in
line 16
Lo
ad c
urt
ailm
ent
(pu)
37
The required minimum load curtailment is found to be 0.99680 pu at the base case without any
UPFC. The maximum and minimum voltage limits are 1.04 and 0.96 pu, respectively. Table 3.3,
also shows that the smallest value of sensitivity factor is -0.3536 pu which corresponds
to line-12, followed by lines-6, 22, 7 and 14. The required load curtailment decreased from
0.99680 to 0.86361 pu when UPFC is placed at the location (line-12). The last column gives the
value of UPFC injected voltage magnitude. The maximum value of UPFC injected voltage
is set as 0.100 pu. The Figure 3.3 demonstrates the obtained results in Table 3.3.
Figure 3.3: Variation of load curtailment with rank order for (30 bus system)
(Increased load condition)
The obtained locations considering sensitivity factor with respect to UPFC angle, has
been given in Table 2.6. The values for load curtailment, sensitivity index, UPFC voltage and
UPFC angle for the first 5 locations are given in Table 3.4.
0,78
0,8
0,82
0,84
0,86
0,88
0,9
0,92
0,94
0,96
0,98
1
Without
UPFC
UPFC in
line 12
UPFC in
line 06
UPFC in
line 33
UPFC in
line 07
UPFC in
line 14
Lo
ad c
urt
ailm
ent
(pu)
38
Table 3.4: Sensitivity factor ) and load curtailment in 30-bus system
(Increased load condition)
Rank
order
Line
no.
Buses i-
j
Sensitivity
factors )
OPF results by varying &
(pu) (pu) (rad)
1 33 27-11 0.2337 0.84990 0.073 0.469
2 12 01-27 0.2285 0.84990 0.100 0.081
3 07 11-13 0.1540 0.85293 0.100 1.352
4 06 02-13 0.0626 0.88522 0.100 1.203
5 09 13-12 0.0563 0.95162 0.100 1.043
The minimum load curtailment is found to be 0.9960 pu at the base case without any UPFC. The
maximum and minimum voltage limits are 1.04 and 0.96 pu respectively. Table 3.4 also shows
that the highest value of sensitivity factor ) is 0.2337 pu which corresponds to line-33,
followed by lines-12, 07, 06 and 09 respectively. The load curtailment decreases from 0.9960 pu
to 0.84990 pu when UPFC is placed in the best location (line-33) and UPFC voltage
as well as UPFC angle are varied. The maximum value of UPFC injected voltage
is set as 0.100 pu and the angle can be varied between – and π. The branches not
fulfilling the criteria laid out in section 2.3.1 have been excluded.
Figure 3.4: Variation of load curtailment with rank order for ) (30 bus system)
(Increased load condition)
0,75
0,8
0,85
0,9
0,95
1
Without
UPFC
UPFC in
line 33
UPFC in
line 12
UPFC in
line 07
UPFC in
line 06
UPFC in
line 09
Lo
ad c
urt
ailm
ent
(pu)
39
3.4 Conclusions
The criteria for optimal placement of UPFC in a system to minimize load curtailment based on
load curtailment sensitivity factors ( ), has been employed to calculate the best
location, under an increased load condition. The active and reactive load on each bus has been
increased by 30%, results have been obtained for top 5 rank/orders using OPF formulation in
GAMS, and the following conclusion is drawn. However, location is decided based on normal
loading condition but it is checked for increased load condition as well.
Criteria for placement of UPFC using sensitivity factors predicts the best location for UPFC
placement in a system to minimize load curtailment accurately even under increased load
conditions. The position of UPFC does not have to be altered in case of increased loading on the
buses.
40
41
Chapter 4
Load Curtailment Minimization by UPFC Considering
Electricity Market Scenarios
4.1 Introduction
In the present electricity markets, consumers have the option of choosing their power suppliers;
therefore depending upon the numbers of contracted customers, a seller node has the obligation
to supply power to either a single or many customers, thus the load at such buses can not be
curtailed below a certain amount. A generation node can have a contract of supplying power to
one load bus, or it can be under the obligation to supply several buses along with the pool
depending on the type of contract. A modeling of today‟s power system is incomplete without
the inclusion of contracts between different nodes. In real power system, there can be several
generation nodes with the contract of supplying electricity to several load buses.
These contracts and market scenarios become particularly interested when considered in
context with the system load curtailment. A generator bus having the contract to supply a load
bus means that the generator bus can not curtail the contracted power beyond the amount
specified in the contract, this result in making the system constraints stiffer.
In the previous chapter, the proposed load curtailment sensitivity factors was checked for
validity in case of a increased load condition, it is imperative to the various scenarios prevalent
in the electricity market in order to investigate the effectiveness of such a methodology. It can be
interesting to see the effect of optimally placed FACTS devices in the presence of various market
models when certain restrictions are imposed on load curtailment amount.
In this chapter effectiveness of the UPFC, optimally placed based on load curtailment
sensitivity factors , ), has been investigated. Three kinds of market scenarios
have been considered and the impact of UPFC on load curtailment has been estimated. In this
work, modeling of various contracts is presented followed by problem formulation and results
analysis have been carried out on IEEE 14-bus & IEEE 30-bus systems.
42
4.2 Modeling of Bilateral/Multilateral Contracts
The conceptual model of bilateral dispatch is that sellers and buyers enter into transactions where
the quantities traded and the associated prices are at the discretion of these parties and not a
matter of SO. These transactions are then brought to the SO with the request that transmission
facilities of the contractual amount of the power transfer be provided. If there is no static or
dynamic security violation, the SO simply dispatches all the requested transactions and charges
for the transmission usage.
In a practical system, not all the sellers have bilateral contract with buyers and vice-versa.
Mathematically, each bilateral transaction between a seller at bus-i and power purchaser at bus-j
satisfies the following power balance relationship:
(4.1)
The bilateral concept can be generalized to a multilateral case, where the seller, for example a
generation company, may inject power at one node and the buyers draw load at several nodes
and vice-versa. Unlike pool dispatch there will be a transaction power balance in that the
aggregate injection equals the aggregate draw off for each contractual transaction. The
contracted demands of the buyers are shared by the generators in a proportion already decided.
Mathematically, a multilateral contract-k involving more than one supplier and/or one consumer
can be expressed as
(4.2)
where, and stand for the power injections into the seller bus-i and the power taken out
at the buyer bus-j, respectively. is the total number of contracts.
4.3 Problem Formulation
In order to simulate various market conditions of bilateral and multilateral contracts, constraints
expressed by equation (4.1 & 4.2) have been included in OPF problem formulation. The load bus
having a contract of a certain minimum amount of power , must get at least that amount, and the
load can not be curtailed beyond it similarly, the generation node, having the contract must
produce at least the amount stated in the contract and the transmission losses. These conditions
have been included in GAMS program, and the minimum load curtailment requirement for the
system has been thereafter calculated. Initially single bilateral contract has been considered,
43
followed by a multilateral contract and both the bilateral and multilateral contracts
simultaneously.
4.4 System Studies
The effect of optimally placed UPFC presented in chapter 2, for load curtailment minimization
in the presence of various market scenarios has been illustrated on IEEE 14-bus and IEEE 30-bus
systems. The detailed data for these systems have been given in Appendix-A and B and system
base is 100 MVA. The results obtained on two systems are given below.
4.4.1 UPFC placement in IEEE 14-bus system
a) Single bilateral contract:
In this scenario, one bilateral contract between bus-1 as generator and bus-2 as a load bus is
considered. The contracted amount of power is 18 MW; therefore, bus-1 must at least produce 18
MW while the load at bus-2 can not be curtailed below 18 MW. In the presence of these
constraints, the value of load curtailment requirement in the absence of any UPFC is
65.7180MW.
Table 4.1: Values of required load curtailment in 14-bus system (Single bilateral contract)
Rank order
Line no.
Buses i-j
Sensitivity factors
OPF results by varying only
(pu) (pu)
1 04 01-08 -0.4509 0.52777 0.100
2 11 02-09 -0.3230 0.62867 0.100
3 12 06-07 -0.3165 0.65654 0.036
4 05 02-08 -0.2485 0.61846 0.100
5 16 03-13 -0.1271 0.65697 0.015
The optimally located UPFC in chapter 2, have been used here for this scenario as well. It is
visible that the load curtailment, for some of the locations with UPFC, has increased due to
stiffer constraints while for some other locations it has stayed almost the same as before.
The values for required load curtailment for different placements of UPFC in the system
according to angle based sensitivity factor ), varying both the UPFC angle and UPFC
44
voltage magnitude are calculated with the inclusion of a single bilateral contract along with the
pool model and results are given in Table 4.2.
Table 4.2: Sensitivity factor ) and load curtailment in 14-bus system
(Single bilateral contract)
Rank order
Line no.
Buses i-j
Sensitivity factors )
OPF results by varying &
(pu) (pu) (rad)
1 07 09-08 0.5384 0.50203 0.100 1.570
2 04 01-08 0.5187 0.29973 0.100 1.201
3 11 02-09 0.4155 0.49559 0.100 1.264
4 05 02-08 0.2913 0.53967 0.100 1.288
5 06 09-04 0.2327 0.60457 0.100 1.237
b) Single multilateral contract:
A single multilateral contract has been considered in this case, where generator bus-1 has an
obligation to supply at least 18 MW to the bus-2 and 94 MW to the bus-4. The load at bus-2 can
not be curtailed beyond 18 MW while the load at bus-4 can not be curtailed beyond 94 MW.
Bus-1 must produce at least 112 MW in order to satisfy its obligations. The value of load
curtailment for these constraints in the absence of UPFC is 0.74777 pu. The required load
curtailments with UPFC, at the obtained locations based on found sensitivity factors in
chapter 2, have been given in Table 4.3. From Table 4.3, line-04 is found to be most suitable
location for minimization of required load curtailment.
Table 4.3: Sensitivity factor and load curtailment in 14-bus system
(Single multilateral contract)
Rank order
Line no.
Buses i-j
Sensitivity factors
OPF results by varying only
(pu) (pu)
1 04 01-08 -0.4509 0.60515 0.100
2 11 02-09 -0.3230 0.71554 0.100
3 12 06-07 -0.3165 0.74728 0.012
4 05 02-08 -0.2485 0.70213 0.100
5 16 03-13 -0.1271 0.74767 0.009
45
Similar to the scenario with a single bilateral contract, with the stiffness in the conditions
increased further, by limiting load curtailment at 2 nodes instead of one, the total system load
curtailment, after UPFC placement, at certain buses remains the same, while it increases in other
cases. It is evident from the obtained results that the proposed placement is also effective with
having included different market models.
The values of load curtailment for different placements of UPFC in the system according
to angle based load curtailment sensitivity factor ) , varying both the UPFC angle and
UPFC voltage are calculated with the inclusion of a single multilateral contract along with the
pool model and obtained results are given in Table 4.4. From Table 4.4, UPFC also working
effectively as reduced the load curtailment requirements in these market model.
Table 4.4: Sensitivity factor ) and load curtailment in 14-bus system
(Single multilateral contract)
Rank order
Line no.
Buses i-j
Sensitivity factors )
OPF results by varying &
(pu) (pu) (rad)
1 07 09-08 0.5384 0.55704 0.100 1.270
2 04 01-08 0.5187 0.33929 0.100 1.207
3 11 02-09 0.4155 0.56025 0.100 1.273
4 05 02-08 0.2913 0.61072 0.100 1.287
5 06 09-04 0.2327 0.68790 0.100 1.144
c) Bilateral & Multilateral contract:
In this scenario, it has been consider that there is a multilateral as well as a bilateral contract in
the market along with the pool model. The bilateral contract is between buses-2 and 14, the
contracted load is 14.9 MW, and therefore generator bus-2 must produce at least 14.9 MW along
with the losses to satisfy the contract. The multilateral contract is that bus-1 has an obligation to
supply at least 18 MW to bus-2 and 94 MW to bus-4. The load at bus-2 can not be curtailed
beyond 18 MW while the load at bus-4 can not be curtailed beyond 94 MW. Bus-1 must produce
at least 112 MW in order to satisfy its obligations. In the presence of both a single bilateral and a
multilateral contract, the system constraints have become stiffer; the minimum load curtailment
requirement in the system, in the absence of a UPFC is 0.74918 pu. The required minimum load
curtailments are given in the Table 4.5 for the corresponding locations.
46
Table 4.5: Sensitivity factor and load curtailment in 14-bus system
(Bilateral & multilateral contract)
Rank order
Line no.
Buses i-j
Sensitivity factors
OPF results by varying only
(pu) (pu)
1 04 01-08 -0.4509 0.60559 0.100
2 11 02-09 -0.3230 0.71602 0.100
3 12 06-07 -0.3165 0.74824 0.006
4 05 02-08 -0.2485 0.70267 0.100
5 16 03-13 -0.1271 0.74914 0.001
The values of load curtailment calculated for placements of UPFC at different locations
in the system according to angle based load curtailment sensitivity factor ) , varying
both the UPFC angle and UPFC voltage are calculated with the inclusion of a single multilateral
contract, a single bilateral contract along with the pool model, obtained results are given in Table
4.6.
Table 4.6: Sensitivity factor ) and load curtailment in 14-bus system
(Bilateral & multilateral contract)
Rank order
Line no.
Buses i-j
Sensitivity factors )
OPF results by varying &
(pu) (pu) (rad)
1 07 09-08 0.5384 0.55757 0.100 1.270
2 04 01-08 0.5187 0.33929 0.100 1.207
3 11 02-09 0.4155 0.56057 0.100 1.273
4 05 02-08 0.2913 0.61107 0.100 1.287
5 06 09-04 0.2327 0.68857 0.100 1.139
It has been the case with two previous market scenarios, the load curtailment for some
buses increases while it stays the same for some other buses. Since after the inclusion of both
multilateral and bilateral contracts the system becomes stiffer, the minimum load curtailment
must increase for the system, as load can not be curtailed on particular contracted buses. From
Tables 4.5 and 4.6, the minimum required load curtailment reduced due to having an UPFC in
the system in existence of different market models. Therefore, it has been seen from these results
that UPFC working well under different market scenarios as well.
47
4.4.2 UPFC placement in IEEE 30-bus system
The three market structures comprising taken for study are
Pool model and one bilateral contract
Pool model and one multilateral contract
Pool model, a multilateral contract and a bilateral contract
a) Single bilateral contract:
In this scenario, one bilateral contract between bus-1 as generator and bus-2 as a load bus is
considered. The amount of power in the contract is 19 MW; therefore, bus-1 must at least
produce 19 MW while the load at bus-2 can not be curtailed below 19 MW. In the presence of
these constraints in the system, the optimally placed UPFC reduced the load curtailment
requirement. The value of load curtailment for these constraints in the absence of any UPFC is
14.9550 MW.
Table 4.7: Sensitivity factor and load curtailment in 30-bus system
(Single bilateral contract)
Rank order
Line no.
Buses i-j
Sensitivity factors
OPF results by varying only
(pu) (rad)
1 12 01-27 -0.3536 0.01371 0.100
2 06 02-13 -0.2288 0.11609 0.100
3 33 27-11 -0.2283 0.09884 0.057
4 07 11-13 -0.2080 0.13717 0.041
5 14 02-11 -0.1711 0.10584 0.100
It can be observed that at certain locations, UPFC handles the excess power required to minimize
load curtailment, due to increased stiffness in the system, while by placing UPFC at certain other
locations, the load curtailment requirement of the system increases. The load curtailment by
UPFC in line-12 stays the same as before (pool model only); and it is 1.3710MW.
48
Table 4.8: Sensitivity factor ) and load curtailment in 30-bus system
(Single bilateral contract)
Rank order Line no. Buses i-j
Sensitivity factors )
OPF results by varying &
(pu) (pu) (rad)
1 33 27-11 0.2337 0.00000 0.074 0.445
2 12 01-27 0.2285 0.00000 0.100 0.069
3 07 11-13 0.1540 0.00303 0.100 1.352
4 06 02-13 0.0626 0.03553 0.100 1.202
5 09 13-12 0.0563 0.10364 0.100 1.059
From Tables 4.7 & 4.8, again found that the UPFC is effective and minimized to zero
load curtailment requirement for few top locations while considering the different market
models.
b) Single multilateral contract:
A single multilateral contract has been considered in this case, where generator bus-1 has an
obligation to supply at least 19 MW to bus-2 and 94 MW to bus-5. The load at bus-2 can not be
curtailed beyond 19 MW while the load at bus-5 can not be curtailed beyond 94 MW. Bus-1
must produce at least 113 MW in order to satisfy its obligations. In the presence of these
constraints in the system, the optimally placed UPFC reduced the load curtailment requirement.
The value of load curtailment for these cases in the absence of any UPFC is 15.9330MW.It is
evident, from OPF results given in Tables 4.9 & 4.10, that the optimally placed UPFC is also
effective for these types of market models.
Table 4.9: Sensitivity factor and load curtailment in 30-bus system
(Single multilateral contract)
Rank order Line no. Buses i-j Sensitivity factors OPF results by varying only
(pu) (pu)
1 12 01-27 -0.3536 0.01371 0.100
2 06 02-13 -0.2288 0.12327 0.100
3 33 27-11 -0.2283 0.10477 0.057
4 07 11-13 -0.2080 0.13717 0.041
5 14 02-11 -0.1711 0.11432 0.100
49
Table 4.10: Sensitivity factor ) and load curtailment in 30-bus system
(Single multilateral contract)
Rank order Line no. Buses i-j Sensitivity factors ) OPF results by varying &
(pu) (pu) (rad)
1 33 27-11 0.2337 0.00000 0.056 0.771
2 12 01-27 0.2285 0.00000 0.100 0.076
3 07 11-13 0.1540 0.00303 0.100 1.352
4 06 02-13 0.0626 0.03623 0.100 1.202
5 09 13-12 0.0563 0.11021 0.100 1.052
c) Bilateral & multilateral contracts:
It has been considered that there is a multilateral contract as well as a bilateral contract along
with the pool model in this case study. The bilateral contract is between buses-2 and 12, the load
at bus-12 is 21.7 MW, while the contracted load is 19 MW, therefore generator bus-2 must
produce at least 19 MW along with the losses to satisfy the contract. The multilateral contract is
that bus-1 has an obligation to supply at least 19 MW to bus-2 and 94 MW to bus-5. The load at
bus-2 can not be curtailed beyond 19 MW while the load at bus-5 can not be curtailed beyond 94
MW. Bus-1 must produce at least 113 MW in order to satisfy its obligations. In the presence of
both a single bilateral and a multilateral contract, the system constraints have become stiffer; the
minimum load curtailment requirement in the system, in the absence of a UPFC for this scenario
is 17.1280MW.
Table 4.11: Sensitivity factor and load curtailment in 30-bus system
(Multilateral & bilateral Contract)
Rank order
Line no.
Buses i-j
Sensitivity factors
OPF results by varying only
(pu) (pu)
1 12 01-27 -0.3536 0.01371 0.100
2 06 02-13 -0.2288 0.13102 0.100
3 33 27-11 -0.2283 0.11106 0.058
4 07 11-13 -0.2080 0.15524 0.045
5 14 02-11 -0.1711 0.12151 0.100
50
Table 4.12: Sensitivity factor ) and load curtailment in 30-bus system
(Multilateral & bilateral contract)
Rank order
Line no.
Buses i-j
Sensitivity factors )
OPF results by varying &
(pu) (pu) (rad)
1 33 27-11 0.2337 0.00000 0.055 0.757
2 12 01-27 0.2285 0.00000 0.100 0.080
3 07 11-13 0.1540 0.00303 0.100 1.352
4 06 02-13 0.0626 0.03695 0.100 1.202
5 09 13-12 0.0563 0.11693 0.100 1.039
It is the case with two previous market scenarios, the load curtailment requirement for
some buses increases while it stays the same for some other buses. Since the inclusion of both
multilateral and bilateral contracts the system becomes stiffer, the minimum load curtailment
requirement must increase for the system, as load can not be curtailed on particular contracted
buses and all results corresponding to these cases have been given in the Tables 4.11 & 4.12.
From obtained results, it is cleared again that the optimally placed UPFC is effectively reduced
the load curtailment requirement in these market scenarios as well.
The effectiveness of the optimally placed UPFC, based on proposed methodology, has
been shown graphically in Figures 4.1 to 4.6. Figure 4.1 and 4.2, show the variation in system
load curtailment during different market scenarios for 14-bus and a 30-bus system respectively
when there is no UPFC in the system.
Similarly, when UPFC is placed according to the developed criteria, the value of load
curtailment decreases for all the scenarios, the load curtailment values in the lines predicted to be
optimal and have been shown in Figures 4.3 & 4.5 for a 14-bus and Figures 4.4 & 4.6 for a 30-
bus System, by placing UPFC in the system.
51
Figure 4.1: Load curtailments without UPFC using different market models
(14-bus system)
Figure 4.2: Load curtailments without UPFC using different market models
(30-bus system)
0,560,580,6
0,620,640,660,680,7
0,720,740,76
Pool modelPool &
Bilateral
model
Pool
&Multilateral
model
Pool,Bilateral
&
Multilateral
model
Lo
ad c
urt
ailm
ent
(pu)
00,020,040,060,080,1
0,12
0,14
0,16
0,18
Pool modelPool &
Bilateral
model
Pool
&Multilateral
model
Pool,Bilateral
&
Multilateral
model
Lo
ad c
urt
ailm
ent
(pu)
52
Figure 4.3: Load curtailment for top rank voltage based orders in market
scenarios (14-bus system)
Figure 4.4: Load curtailment for top rank voltage based orders in market
scenarios (30-bus system)
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
1 2 3 4 5
Lo
ad c
urt
ailm
ent
(pu)
Pool model Pool & Bileteral
Pool & Multilateral Pool,Bilateral & Multilateral
0
0,02
0,04
0,06
0,08
0,1
0,12
0,14
0,16
0,18
1 2 3 4 5
Lo
ad c
urt
ailm
ent
(pu)
Pool Model Pool & Bilateral
Pool & Multilateral Pool,bilateral & Multilateral
53
Figure 4.5: Load curtailment for top rank voltage based ) orders in market
scenarios (14-bus system)
Figure: 4.6 Load curtailment for top rank voltage based ) orders in market
scenarios (30-bus system)
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
1 2 3 4 5
Lo
ad c
urt
ailm
ent
(pu)
Pool model Pool & Bilateral
Pool & Multilateral Pool,Multilateral & Bilateral
0
0,02
0,04
0,06
0,08
0,1
0,12
0,14
1 2 3 4 5
Lo
ad c
urt
ailm
ent
(pu)
Pool Model Pool & Bilateral
Pool & Multilateral Pool,Bilateral & Multilateral
54
4.5 Conclusions
As the initial analysis was carried out considering only the pool model in chapter-2, but the
scope has been extended to the combinations of pool with bilateral, pool with multilateral and
pool, multilateral and bilateral market scenarios, in this chapter. The effectiveness of the
optimally placed UPFC, based on using load curtailment sensitivity factors ),
has been investigated in all these market scenarios and the following conclusions have been
drawn:
1) Without UPFC, the load curtailment requirement in a system increases as we make the
constraints stiffer, increasing the number of bilateral & multilateral contracts between
generator and load buses results in stiffer constraints.
2) When the optimally located UPFC is considered with the various market scenarios are
considered, the load curtailment requirement decreases, but the value consistently
increases in proportion with stiffer constraints for most cases, apart from the cases when
UPFC can cater for the bindings as per the contract. The UPFC is still effective in the
studied market scenarios.
55
Chapter 5
Conclusions
5.1 General
Secure, stable and reliable operation of the power system has become a serious challenge,
specifically in the emerging electricity market scenario. Continuous growth in power demand
and supply pattern, along with limited expansion of transmission network, changes the power
flow patterns in the power system in such a way that some of the transmission corridors get over
loaded. The Flexible AC Transmission Systems (FACTS) controllers are being increasingly used
in the network to address some of these challenges. The FACTS controllers have been used for
power flow control, voltage control and stability enhancement, Amongst shunt type FACTS
controllers, Static VAR Compensator (SVC) has been popularly used due to its lesser cost and
ability to provide voltage support and enhance system dynamic performance, The Unified Power
Flow Controller (UPFC) combines both series and shunt compensators and offers more versatile
characteristics as compared to other controllers. Using the series FACTS controller, line flows
can be altered in flexible and controlled manner, allowing lines to be loaded close to their
thermal limits, and reducing load curtailment. However, these controllers are very expensive and
hence, their optimal locations in the network must be properly ascertained.
Reducing load curtailment in a system has been considered as an important operating
challenge in electricity markets. Various load curtailment schemes are utilized in order to find
the priority for the loads to be disconnected, FACTS have been considered in order to redirect
power flows and thus play a part in reducing total system load curtailment. As mentioned earlier
the optimal location of FACTS devices is very important due to their cost. FACTS controllers
have been placed in some works, on a hit and trial basis, generating an optimal power flow
programs to determine their optimal location in the grid, however, such approaches are very
calculation intensive. A need has been identified to develop a sensitivity based suitable approach
for the identification and then placement of FACTS devices.
The aim of this chapter is to elaborate the major findings of this work and to deliver few
suggestions for further research work in this research area.
56
5.2 Summary of Significant Findings
Chapter 2, of this thesis work, has proposed a new sensitivity index, in terms of change in system
load curtailment with respect to change in UPFC parameters, for the optimal placement of UPFC
to minimized the required load curtailment. Two sensitivity factors, for UPFC series controller,
have been defined, one with respect to series injected voltage magnitude and the other with
respect to injected voltage phase angle. An OPF formulation considering the minimization of
load curtailment requirement as an objective has been developed to study the impact of optimal
placement of UPFC. Results have been obtained on IEEE 14-bus and IEEE 30-bus systems and
provide the following main conclusions:
1) Optimal locations for UPFC placement in a line has been obtained for the minimization
of system load curtailment requirements.
2) The locations, obtained from the proposed factors for the optimal placement of UPFC,
are verified through OPF results in terms of reduction in system load curtailment
requirement after the placement of UPFC. The locations ranked high for the UPFC
placement have resulted in greater reduction in system load curtailment requirement for
both the systems.
3) The optimally placed UPFC, based on the proposed sensitivity factors is also
significantly effective under increased load conditions. The system load curtailment
requirement gets reduced significantly with UPFC even when the load on each bus is
increased by 30 percent.
4) Considering various market scenarios, same optimally placed UPFC offering the
minimum load curtailment requirement in the system when the constraints get stiffer as
the types and number increases. For various market models, the optimally placed UPFC
is still effective.
57
5.3 Scope for Future Research
Further research in this area can be done in the following ways.
In this thesis, optimal placement of UPFC‟s only series controller has been studies. This
can be extended for the placement of some other types of FACTS series controllers, such
as TCSC, TCPAR & SSSC.
Such criteria can be extended to various shunt devices such as SVC, STATCOM.
Economic aspects such as FACTS device cost can be compared with the price to be paid
for load curtailment while considering load curtailment which can result into a new
formulation.
Various models for the loads in the system can be taken into account.
Only static criteria have been used, in this thesis, for the optimal placement of FACTS
controllers. A set of hybrid indices can be developed using both static and dynamic
criteria.
Besides static analysis, dynamic performance should also be checked.
For solution of OPF a SNOPT solver in GAMS has been used. Some of the evolutionary
methods such as GA, Particle Swarm Optimization (PSO) and other Artificial
Intelligence (AI) based methods, can be tried out.
58
59
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63
Appendix A
Data for the IEEE 14-bus System
IEEE 14-bus system is shown in Figure. A.1.The system data (at 100 MVA base) is taken from
[44] and the buses are renumbered. The bus data and the line data are given in the Tables B.1 and
A.2, respectively.
Figure A.1: Single line diagram of the IEEE 14 bus system
G
G
G
G
G
1
2
3
4
5 6 7 8
9
10
11
12 13 14
64
Table A.1: Bus data (pu)
Bus
no.
Vm PG PL QL PGmin PGmax QGmin QGmax Bsh
(external
shunt)
1 1.060 0.00 0.000 0.000 0.50 2.00 -0.45 1.00 0.00
2 1.045 0.40 0.217 0.127 0.20 1.00 -0.40 0.50 0.00
3 1.070 0.10 0.112 0.075 0.20 1.00 -0.06 0.24 0.00
4 1.010 0.00 0.942 0.190 0.00 0.00 0.00 0.40 0.00
5 1.090 0.00 0.000 0.000 0.00 0.00 -0.06 0.24 0.00
6 1.000 0.00 0.000 0.000 0.00 0.00 0.00 0.00 0.00
7 1.000 0.00 0.295 0.166 0.00 0.00 0.00 0.00 0.19
8 1.000 0.00 0.076 0.016 0.00 0.00 0.00 0.00 0.00
9 1.000 0.00 0.478 -0.039 0.00 0.00 0.00 0.00 0.00
10 1.000 0.00 0.090 0.058 0.00 0.00 0.00 0.00 0.00
11 1.000 0.00 0.035 0.018 0.00 0.00 0.00 0.00 0.00
12 1.000 0.00 0.061 0.016 0.00 0.00 0.00 0.00 0.00
13 1.000 0.00 0.135 0.058 0.00 0.00 0.00 0.00 0.00
14 1.000 0.00 0.149 0.050 0.00 0.00 0.00 0.00 0.00
Table A.2: Line data (pu)
Line no. From To R X Bsh
(full charging)
Tap
1 08 03 0.00000 0.25202 0.00000 0.962
2 09 06 0.00000 0.20912 0.00000 0.978
3 09 07 0.00000 0.55618 0.00000 0.969
4 01 08 0.05403 0.22304 0.04920 1.000
5 02 08 0.05695 0.17388 0.03400 1.000
6 04 09 0.06701 0.17103 0.03460 1.000
7 09 08 0.01335 0.04211 0.01280 1.000
8 01 02 0.01938 0.05917 0.05280 1.000
9 02 04 0.04699 0.19797 0.04380 1.000
10 06 05 0.00000 0.17615 0.00000 1.000
11 02 09 0.05811 0.17632 0.03740 1.000
12 06 07 0.00000 0.11001 0.00000 1.000
13 07 10 0.03181 0.08450 0.00000 1.000
14 03 11 0.09498 0.19890 0.00000 1.000
15 03 12 0.12291 0.25581 0.00000 1.000
16 03 13 0.06615 0.13027 0.00000 1.000
65
17 07 14 0.12711 0.27038 0.00000 1.000
18 10 11 0.08205 0.19207 0.00000 1.000
19 12 13 0.22092 0.19988 0.00000 1.000
20 13 14 0.17093 0.34802 0.00000 1.000
66
Figure B.1: Single line diagram of the IEEE 30-bus system
Appendix B
Data for the IEEE 30-bus System The Figure B.1 is shown for IEEE 30-bus system and simplified representation of the 132 and 33
kV [44] transmission system, having 3 generators, 3 synchronous condensers and 24 load buses.
The bus data, assumed cost coefficients of the generators and line data are shown in the Tables
B.1, B.2 and B.3, respectively (at 100 MVA base)
67
Table B.1: Bus data (pu)
Bus
no.
Bus
voltage
Bus
angle PG QG PD QD
Shunt
suceptance
QGmax QGmin
1 1.0600 0.00 2.3862 -0.1599 0.0000 0.0000 0.000 4.5000 -1.0000
2 1.0443 -5.03 0.4000 0.5000 0.2170 0.1270 0.000 0.5000 -0.4000
3 1.0100 -9.81 0.2000 0.1960 0.0000 0.3000 0.000 0.4000 -0.1000
4 1.0820 -18.37 0.0000 0.2277 0.3000 0.0000 0.000 0.2400 -0.0600
5 1.0100 -13.53 0.0000 0.3580 0.9420 0.1900 0.000 0.4000 -0.4000
6 1.0710 -15.01 0.0000 0.1942 0.0010 0.0000 0.000 0.2400 -0.0600
7 1.0398 -15.19 0 0 0.0000 0.0000 0.000 0 0
8 1.0242 -16.11 0 0 0.0580 0.0200 0.000 0 0
9 1.0456 -15.00 0 0 0.1100 0.0750 0.000 0 0
10 1.0790 -15.54 0 0 0.0000 0.0000 0.190 0 0
11 1.0147 -8.78 0 0 0.0760 0.0160 0.000 0 0
12 1.0029 -12.07 0 0 0.2280 0.1000 0.000 0 0
13 1.0104 -10.14 0 0 0.0000 0.0000 0.000 0 0
14 1.0310 -15.94 0 0 0.0620 0.0160 0.000 0 0
15 1.0265 -16.07 0 0 0.0820 0.0250 0.000 0 0
16 1.0291 -15.74 0 0 0.0350 0.0180 0.000 0 0
17 1.0202 -16.21 0 0 0.0900 0.0580 0.000 0 0
18 1.0133 -16.80 0 0 0.0320 0.0090 0.000 0 0
19 1.0087 -17.04 0 0 0.0950 0.0340 0.000 0 0
20 1.0118 -16.86 0 0 0.0220 0.0070 0.000 0 0
21 1.0152 -16.52 0 0 0.1750 0.1120 0.000 0 0
22 1.0169 -16.49 0 0 0.0000 0.0000 0.000 0 0
23 1.0205 -16.51 0 0 0.0320 0.0160 0.000 0 0
24 1.0208 -16.75 0 0 0.0870 0.0670 0.043 0 0
25 1.0517 -16.16 0 0 0.0000 0.0000 0.000 0 0
26 1.0346 -16.55 0 0 0.0350 0.0230 0.000 0 0
27 1.0231 -7.28 0 0 0.0240 0.0120 0.000 0 0
28 1.0119 -10.75 0 0 0.0000 0.0000 0.000 0 0
29 1.0603 -16.64 0 0 0.0240 0.0090 0.000 0 0
30 1.0495 -17.43 0 0 0.1060 0.0190 0.000 0 0
68
Table B.2: Line data (pu.)
From
bus
To
bus Resistance Reactance
Line
charging Tapping
Line flows
Pij Qij Pji Qji
13 7 0.0000 0.2080 0.0000 0.978 0.4551 -0.0132 -0.4551 0.0536
13 8 0.0000 0.5560 0.0000 0.969 0.1999 0.0451 -0.1999 -0.0236
11 9 0.0000 0.2560 0.0000 0.962 0.4668 0.0630 -0.4668 -0.0119
28 10 0.0000 0.3960 0.0000 0.968 0.2374 -0.0789 -0.2374 0.1016
2 5 0.0472 0.1983 0.0418 1 0.7986 0.0264 -0.7709 0.0459
2 13 0.0581 0.1763 0.0374 1 0.5477 0.0239 -0.5316 -0.0146
11 13 0.0119 0.0414 0.0090 1 0.5713 -0.0573 -0.5675 0.0613
5 12 0.0460 0.1160 0.0204 1 -0.1711 0.1221 0.1732 -0.1375
13 12 0.0267 0.0820 0.0170 1 0.4055 -0.0414 -0.4012 0.0375
13 3 0.0120 0.0420 0.0090 1 -0.1258 0.0411 0.1260 -0.0495
1 2 0.0192 0.0575 0.0528 1 1.6263 -0.2097 -1.5805 0.2882
1 27 0.0452 0.1852 0.0408 1 0.7599 0.0498 -0.7365 0.0020
7 8 0.0000 0.1100 0.0000 1 0.1551 0.1488 -0.1551 -0.1441
2 11 0.0570 0.1737 0.0368 1 0.4172 0.0345 -0.4080 -0.0453
9 14 0.1231 0.2559 0.0000 1 0.0798 0.0219 -0.0790 -0.0203
9 15 0.0662 0.1304 0.0000 1 0.1850 0.0606 -0.1827 -0.0561
9 16 0.0945 0.1987 0.0000 1 0.0910 0.0440 -0.0901 -0.0421
14 15 0.2210 0.1997 0.0000 1 0.0170 0.0043 -0.0169 -0.0043
16 17 0.0824 0.1923 0.0000 1 0.0551 0.0241 -0.0548 -0.0234
15 18 0.1070 0.2185 0.0000 1 0.0733 0.0264 -0.0727 -0.0251
18 19 0.0639 0.1292 0.0000 1 0.0407 0.0161 -0.0405 -0.0159
19 20 0.0340 0.0680 0.0000 1 -0.0545 -0.0181 0.0546 0.0184
8 20 0.0936 0.2090 0.0000 1 0.0772 0.0267 -0.0766 -0.0254
8 17 0.0324 0.0845 0.0000 1 0.0352 0.0348 -0.0352 -0.0346
8 21 0.0348 0.0749 0.0000 1 0.1281 0.0638 -0.1274 -0.0623
8 22 0.0727 0.1499 0.0000 1 0.0565 0.0226 -0.0563 -0.0220
21 22 0.0116 0.0236 0.0000 1 -0.0476 -0.0497 0.0476 0.0498
15 23 0.1000 0.2020 0.0000 1 0.0443 0.0090 -0.0442 -0.0086
22 24 0.1150 0.1790 0.0000 1 0.0087 -0.0278 -0.0086 0.0279
23 24 0.1320 0.2700 0.0000 1 0.0122 -0.0074 -0.0121 0.0074
24 25 0.1885 0.3292 0.0000 1 -0.0663 -0.0575 0.0677 0.0599
25 10 0.1093 0.2087 0.0000 1 -0.1031 -0.0836 0.1049 0.0869
27 11 0.0132 0.0379 0.0084 1 0.7125 -0.0140 -0.7061 0.0237
10 29 0.2198 0.4153 0.0000 1 0.0618 0.0164 -0.0610 -0.0150
10 30 0.3202 0.6027 0.0000 1 0.0708 0.0163 -0.0693 -0.0136
29 30 0.2399 0.4533 0.0000 1 0.0370 0.0060 -0.0367 -0.0054
69
3 28 0.0636 0.2000 0.0428 1 0.0740 -0.0545 -0.0736 0.0120
13 28 0.0169 0.0599 0.0130 1 0.1643 -0.0783 -0.1638 0.0669
25 26 0.2544 0.3800 0.0000 1 0.0354 0.0236 -0.0350 -0.0230
9 6 0.0000 0.1400 0.0000 1 0.0010 -0.1896 -0.0010 0.1942
7 4 0.0000 0.2080 0.0000 1 0.3000 -0.2025 -0.3000 0.2277