Master Thesis on “Development of Sensitivity Based Indices ...610179/FULLTEXT01.pdf · Optimal...

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


2.6 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



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



4.5 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)


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.


Rank

order Line no. Buses i-j

Sensitivity

factors


(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)


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.


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


(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 )


(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


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



Rank

order

Line

no.

Buses i-

j

Sensitivity

factors )


(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)


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.


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


(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.


(Single bilateral contract)

Rank order

Line no.

Buses i-j



(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.


(Single multilateral contract)

Rank order

Line no.

Buses i-j

Sensitivity factors


(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.



Rank order

Line no.

Buses i-j



(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


(Bilateral & multilateral contract)

Rank order

Line no.

Buses i-j

Sensitivity factors


(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.


(Bilateral & multilateral contract)

Rank order

Line no.

Buses i-j



(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


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.



Rank order

Line no.

Buses i-j

Sensitivity factors


(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



Rank order Line no. Buses i-j



(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.



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



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.


(Multilateral & bilateral Contract)

Rank order

Line no.

Buses i-j

Sensitivity factors


(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


(Multilateral & bilateral contract)

Rank order

Line no.

Buses i-j



(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


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


Figure: 4.6 Load curtailment for top rank voltage based ) orders in market


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

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