Master Thesis on “Development of Sensitivity Based Indices for Optimal Placement of UPFC to Minimize Load Curtailment Requirements”

(1)

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

(2)

i

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.

(5)

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.

(6)

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.

ij ij

jx

r

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. ij ij jx r Line Shunt FACTS controller

(7)

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.

ij ij

jx

r

Line -1

ij ij

jx

r

Line -2

DC-link

FACTS controller

Figure 1.3: Combined series-series FACTS controller

Combined Series-Shunt Controllers: This could be a combination of separate shunt and series

(8)

5 ij ij

jx

r

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

(9)

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.

(10)

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

(11)

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:

(12)

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:

(13)

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

(14)

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

(15)

(16)

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.

(17)

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, = - .

(18)

15

(2.3)

(2.4)

where Bsh is full line charging impedance.

ij ij ij

g

jb

y

2 / sh jB

jB

sh

/

2

Bus-i Bus-j j

V





i

V





j i

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

(19)

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.

j

V

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

(22)

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) ij ij ij

g

jb

y

iu

S

ju

S

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

(23)

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.

(24)

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

(25)

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)

(26)

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 b N lireq li i LC P P

(27)

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.

(28)

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 30-14-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

(29)

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

(30)

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

(31)

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

(32)

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

(33)

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.

(34)

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.

(35)

(36)

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.

(37)

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 30-14-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)

(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

(38)

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)

(39)

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

LCSF s 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)

(40)

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.

(41)

38

(Increased load condition)

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)

(42)

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.

(43)

(44)

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.

(45)

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

(46)

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

(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.

(47)

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)

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

(48)

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.

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:

(49)

46

(Bilateral & multilateral contract)

(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)

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

(50)

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.

(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

(51)

48

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.

(52)

49

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)

(53)

50

(Multilateral & bilateral contract)

Rank order Line no. Buses i-j _{Sensitivity factors} ₎

(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.

(54)

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

Master Thesis on “Development of Sensitivity Based Indices for Optimal Placement of UPFC to Minimize Load Curtailment Requirements”

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

Contents

Chapter 1

Introduction

1.1 General

1.2 Flexible AC Transmission Systems (FACTS)

jx

r

jx

r

Line -1

jx

r

Line -2

DC-link

FACTS controller

FACTS controller

jx

r

1.3 Different Models and Operating Challenges of Electricity

Market

1.4 State-of-the-Art:

1.4.1 Load Curtailment

1.4.2 Optimal Placement of FACTS Controllers:

1.6 Motivation:

1.7 Thesis Organization

Chapter 2

Load Curtailment Sensitivity Factors for Optimal

Placement of UPFC

2.1 Introduction

2.2 System Modeling

2.2.1 Representation of transmission lines

g

jb

y

jB

/

2

V





V





2.2.2 Static representation of UPFC

2

/

jB

jB

/

2

I

I

I

jb

g

I

V

V

V

V

V

V

V

I

I

I

I