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Real Power Spot Pricing using Unified Power Flow

Controller

Thesis submitted in partial ful fi llment of the requi rement for the Degree of

Master of Power Engineer ing f rom the Faculty of Engineeri ng &Technology, Jadavpur University in the year 2010

Submitted by

ARNAB BHADURI

Master of Power Engineering

Regn. No. 104350 of 2008-2009

Exam Roll No. M4POW10-09

Under the guidance of

Dr. Mousumi BasuDepartment of Power Engineering

Jadavpur University

Saltlake Campus

Kolkata-700098

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Department of Power engineering

Faculty of Engineering and Technology

Jadavpur University

The foregoing thesis, ent it led as Real power spot pricing using unified power f low

controlleris hereby approved by the committee of final examination for evaluation of

thesis as a creditable study of an engineering subject carried out and presented byArnab

Bhaduri (Regn. No.104350 of 2008-2009; Exam Roll No. M4POW10-09) in a manner

satisfactory t o warrant it s acceptance as a perquisite to the Degree of Master of Power

Engineering. I t is understood that by this approval, the undersigned do not necessarily

endorse or approve any statement made, opinion expressed or conclusion drawn therein,

but approve the thesis only for t he purpose for which it is submitted.

Committee of final examination for evaluation of thesis:

-----------------------------

-----------------------------

----------------------------

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Acknowledgement

The author remembers the with gratitude the constant guidance, suggestions and

encouragement forwarded by several respected persons and knows well that it is not

possible to express his indebt ness for all those valuable assistances by writing some

lines. Following conventions, he, therefore, acknowledges in this page, the assistance

rendered by all the concerened persons, as a token of his gratitude.

The author thankfully acknowledges the kind and persistent valuable suggestion, advice,

guidance, help and encouragement from Dr. Mousumi Basu without whom this thesis

would not have been a reality.

The author is thankful to the head of Power Engineering department for his kind

permission to carry out the project under Dr. Mousumi Basu.

The author is likely to convey his gratitude to all teachers in ME course in the Power

Engineering department of Jadavpur University for excellent teaching that helps to

complete the project smoothly.

The author would also like to express his sincere thanks to all his classmates specially

Mr. Sanjay Chauhan who came with some valuable suggestions to make this thesis

possible.

Finally, the author wishes his profound gratitude to his parents, family members for

providing constant encouragement throughout his thesis work.

Arnab Bhaduri

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Abstract_______________________________________

This thesis proposes real power spot price analysis using Unified Power Flow Controller.

Real power spot price is analyzed and compared with the base case to the case after

implementing the Unified Power Flow Controller. Optimal placement for Unified Power

Flow Controller by analyzing the sensitivity for the UPFC parameters is also done in this

thesis work. All the proposed methods and algorithms are tested on IEEE standard 30bus

system for verification.

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Contents_______________________________________

Subjects Page No.

Chapter 1: INTRODUCTION

1.1Introduction 1

1.2Motivation behind this work 2

1.3 Literature Survey 3

1.3Overview 4

Chapter 2: OPTIMAL POWER FLOW

2.1 Optimal power flow problem 5

2.2 Optimal power flow problem formulation 6

2.2.1 The objective function 6

2.2.2 The equality contstraints 6

2.2.3 The inequality constraints 7

2.2.3.1 Real power generation limit 8

2.2.3.2 Reactive power generation limit 8

2.2.3.3 Voltage limit 8

2.2.3.4 Line flow limit 9

2.2.3.5 UPFC parameters limit 9

2.3 Comparative study of different solution techniques for the OPF 9

2.3.1 Newtons Method 9

2.3.2 Gradient method 10

2.3.3 Lambda iteration method 10

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2.3.4 Linear Programming method 10

2.3.5 Interior poinr method 10

2.3.6 Genetic algorithm method 11

2.3.7 PSO method 11

Chapter 3: FLEXIBLE AC TRANSMISSION SYSTEM

3.1 About FACTS 12

3.2 Classification of FACTS 12

3.2.1 Shunt controller 13

3.2.1.1 Shunt controller 13

3.2.1.2 Types 14

3.2.2 Series Controller 16

3.2.2.1 Series compensation 16

3.2.2.2 Types 17

3.3.3 Combined shunt-series controller 21

3.3 Utility of FACTS 22

3.4 Maintenance of FACTS 22

Chapter 4: UNIFIED POWER FLOW CONTROLLER

4.1 About Unified power flow controller 23

4.2 Structures and operations of UPFC 24

4.3 Equivalent circuit of UPFC 25

4.4 Modeling of UPFC 27

4.5 Location of UPFC 30

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Chapter 5: GRADIENT METHOD

5.1 Problem formulation 35

5.2 Computational procedure 36

5.3 Inequality constraints on control variables 37

5.4 Inequality constraints on dependent variables 37

5.5 Lagrangian for solving OPF in gradient method 38

Chapter 6: SPOT PRICING

6.1 Introduction 39

6.2 Power pools 39

6.2.1 Advantages 40

6.2.2 Disadvantages 40

6.3 Spot price 41

6.4 Marginal cost 42

Chapter 7: RESULTS AND DISCUSSIONS

7.1 IEEE 30- bus test system 43

7.2 Tabulated results 43

7.3 Graphical results 49

Chapter 8: CONCLUSIONS

8.1 Conclusion 51

8.2 Future scope 51

References 52

Nomenclature 54

Appendix 55

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1

Chapter 1: INTRODUCTION

1.1 IntroductionElectrical engineering is an essential ingredient for the industrial and all-round

development of any country. It is a one of the most desirable form of energy, since it can

be generated centrally in bulk and transmitted economically over long distances. The

system which generates controls, transmits and finally distributes electrical energy to the

consumers is called an electrical power system. Electricity cannot be stored economically

and the electric utility need some control over the load or power demand at any time.

This system therefore should be capable of matching the output from the generators to thedemand at any time at the specified voltage and frequency.

The electrical power must be transmitted in steady-state mode under their normal

operating conditions. In accordance to this, three major problems encountered in steady-

state mode of operations are: 1) load flow problem, 2) optimal load dispatch problem and

3) systems control problem. The aim of power flow calculations is to determine the

steady-state operating characteristics of a power generation or transmission system for a

given set of bus-bar loads. Active power generations are specified according to economic

dispatching. In system operation and planning, the voltages and powers are kept within

certain limits. The power system networks of today are highly complicated consisting of

hundreds of buses and transmission links. Thus the load flow study involves extensive

calculations.

With increasing pace of power system restructuring, transmission systems are being

required to provide increased power transfer capability and at the same it is also required

to accommodate a much wider range of possible generation patterns. Power systems,

throughout the world, have been forced to operate in almost full capacities due to the

environmental and/or economical constraints to build new generation centers and

transmission lines. If the power flow limit exceeds a certain permissible limit the system

is said to be congested. There is an interest in better utilization of available power system

capacities by installing new devices such as flexible ac transmission system (FACTS).

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These devices are useful in modern power system operation to reduce the flows in

heavily loaded lines, resulting in increased load ability, low system loss, improved

stability of the network, reduced production cost, and fulfilled contractual requirement by

controlling the power flows in the network. If there is no congestion, the optimal location

of FACTS devices can be decided on the basis of real power flow performance index

( )PI has been used due to security and stability reasons. A definite methodology has

been used to locate the FACTS device (UPFC) for congestion management in the

deregulated power sector and in doing that a nonlinear optimization problem has been

formulated and evaluated by some certain power flow solution algorithm (Gradient

Method) with and without incorporating FACTS device (UPFC) to see the impact on

transmission real power spot pricing.

1.2 Motivation behind this work

In modern days deregulated power system environment major organizational and

structural changes has been observed. In view of this transmission pricing is an important

issue. For a participant of electric power system two things need to be fully examined,

firstly the relationship between competition requirements and the market structures and

secondly optimal operation of supply and demand in terms of social welfare. In this

respect many researchers used different methods for determining spot prices in

deregulated power systems. In competitive electricity markets, to supply deregulation, it

is important that both the producers and consumers reach an optimum goal so that both of

them get benefited. In this respect, spot price applications and participants bids must be

considered simultaneously in deregulated power market operations. FACTS device plays

an important role for improving the power pricing.

All these aspects related to deregulated electricity market and modern economic scenario

lead to this thesis work. In this work spot prices are calculated at different load buses

after formulating an optimal power flow problem. Moreover optimal placement of facts

device in a line of network also has been considered in this work to compare the spot

prices at different load buses for base case as well as with implementing the FACTS

device.

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1.3 Literature survey

In 1995 Gyugyi, Rietman, Edris, Schauder, Torgerson, Williams [1] show the unique

capability of a UPFC in multiple line compensation by controlling both the transmitted

real power power and, independently, the reactive power flows at the sending-end and the

receiving end of the transmission line.

In 1996, Jenn-Huei Jeffrey Kuan [2] in his thesis work described the necessary

optimization technique for economic operations in an open-accessed transmission grid

industry and suggested a suitable supply demand curve in order to achieve social welfare.

Also gradient method based optimization solution process has been derived in the thesispaper.

In 1998, Choi et al [3]presented a theory and simulation results of real-time pricing of

real and reactive powers that maximize social benefits.

In1998 Lima et al. [4] presented the dynamic aspects of pricing and its impact on long

term expansion planning of both generation and transmission.

The basic principle and operation are discussed by J.Y.Liu and Y.H. Song [5] in 1999

and by J.Y. Liu and Y.H. Song and P.A. Mehta [6] in the same year respectively.

In April 1999, Keri, Mehraban, Lombard, Elriachy, Edris [A1] analyze a set of equations

for a system including UPFC and an equivalent two bus network.

In 2000, Srivastava and Verma [7] utilize a location based pricing concepts and suggested

a nonlinear programming problem formulation to determine real and reactive power

prices.

In July,2001, K.S. Verma, S.N. Singh and H.O. Gupta [8] proposed a method for the

suitable location of unified power flow controller.

Same year in [9] and [10] also a suitable location of unified power flow controller had

been derived, with a static point of view. The optimal location is based on real power

flow performance index sensitivity with respect to control parameters of unified power

flow controller.

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In July, 2001, K.S. Verma, S.N. Singh and H.O. Gupta [11] introduced a steady-state

model of UPFC (unified power flow controller) power injection model which has been

introduced in the minimum price dispatch algorithm.

In 2006, K.S. Verma and H.O. Gupta [12] formulated a suitable method for finding the

real and reactive spot price incorporating UPFC at an optimal location after analyzing the

sensitivities with respect to the UPFC parameters.

In 2010, A.Urkmez [13] presents a new formula for determining spot price and a new

algorithm for economic dispatch in deregulated power systems.

1.4 Overview

Real power time spot prices are calculated in this thesis incorporating n unified power

flow controller (UPFC) and the results are used for a comparative study with the base

case, i.e without incorporating UPFC. While doing this optimal location of UPFC is also

calculated with the help of performance index sensitivity factors for the respective UPFC

parameters like voltage, phase angle etc. The optimal power flow problem has been

solved by gradient method for finding the respective Lagrange multipliers for the

Lagrangian function. In chapter 2 the OPF is formulated. Flexible AC Tranasmission

System (FACTS) is discussed in chapter 3. Chapter 4 describes the model, structures and

operations about UPFC and also some useful facts for finding the optimal location.

Chapter 5 describes the Gradient method for solving the OPF related to this problem

elaborately. Chapter 6 gives an idea of spot pricing. Chapter 7 concludes with a summary

and several improvements, which would aid in creating a more efficient pricing method.

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Chapter 2: OPTIMAL POWER FLOW

2.1 Optimal power flow problem

The computational procedure required to determine the steady-state operating

characteristics of a power system network is termed as Load Flow. The aim of power

flow calculations is to determine the steady-state operating characteristics of a power

generation or transmission system for a given set of bus bar loads. In the past two

decades, the problem of optimal power flow (OPF) has received much attention. It is of

current interest of many utilities, and it has been marked as one of the most operational

needs. The OPF problem solution aims to optimize a selected objective function, such as

fuel cost via optimal adjustment of the power system control variables, while at the same

time satisfying various equality and inequality constraints. The equality constraints are

the power flow equations, and the inequality constraints are the limits on control

variables and the operating limits of power system-dependent variables. The problem

control variables include the generator real powers, the generator bus voltages, the

transformer tap settings, and the reactive power of switch able VAR sources, while the

problem-dependent variables include the load bus voltages, the generator reactive

powers, and the line flows. Generally, the OPF problem is a large-scale, highly

constrained, nonlinear, no convex optimization problem.

Optimal Power Flow (OPF) has been extensively used in power systems at the generation

or transmission level to designate the problem of finding the optimal value for the control

variables (real and reactive power, voltage settings, batteries set points, etc.) when

minimizing the total operation cost, while respecting the technical constraints of the

network and equipments. In distribution systems, many approaches exist dedicated to the

optimization of the configuration and the optimization of the voltage profile through

batteries. In both cases the objective function seeks for losses reduction, but in separate

ways. The recent development of distribution systems has led to the presence of

distributed generation that introduces uncertainty in the previously mentioned problems,

but may contribute to voltage control and optimization. In the same cases, regional

dispatch of this unit is possible; tuning is possible to seek for optimal operating policies.

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An optimal load-flow solution gives the optimal active and reactive power dispatch for a

static power-system loading condition. Computationally, it is a very demanding nonlinear

programming problem, due to the large number of variables and in particular to the much

larger number and types of limit constraints which define the boundaries of technical

feasibility.

2.2 Optimal power flow problem formulation

2.2.1 The objective function

Generally it can be written as

min ( , , )F x u p (2.1)

Here the obejective function to be minimized is the difference of the operational cost for

the active power of pool generator to the pool load, which is given by,

( ) ( )G D

T i Pi j pj

i I j I

F C P B D

=

(2.2)

2.2.2 The equality constraints

Generally it can be written as

( , , ) 0h x u p = (2.3)

where

state vector V, , DV , D , qI

u control parameters giP , giQ

p fixed parameters diP , diQ

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The objective function motioned in eq _ is subjected to equality constraints og real and

reactive power balance equations. For all buses except buses i and j between which the

UPFC device is connected, as

1

[ cos( ) sin( )]Nb

l gl dl l m lm l m lm l m

m

P P P V V G B =

= = + (2.4)

1

[ sin( ) cos( )]Nb

l gl dl l m lm l m lm l m

m

Q Q Q V V G B =

= = for l=1,2,.. bN ;but l i , j (2.5)

For buses i and j only, the equality constraints can be written as

_

1

[ cos( ) sin( )]Nb

i gi di i m im i m im i m i s

m

P P P V V G B P =

= = + (2.6)

_

1

[ sin( ) cos( )]Nb

i gi di i m im i m im i m i s

m

Q Q Q V V G B Q =

= = (2.7)

_

1

[ cos( ) sin( )]Nb

j gj dj j m jm j m jm j m j s

m

P P P V V G B P =

= = + (2.8)

_

1

[ sin( ) cos( )]Nb

j gj dj j m jm j m jm j m j s

m

Q Q Q V V G B Q =

= = (2.9)

2.2.3 The inequality constraints

While solving the OPF problem with objective function and equality constraints it is

often observed that the variables used to exceed their limits. thats why an inequality

constraints for the respective variables are included in the OPF to keep the variables

within their specified predefined limits.

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In general the inequality constraints can be written as

( , , ) 0g x u p > (2.10)

where

state vector V, , DV , D , qI

u control parameters giP , giQ

p fixed parameters diP , diQ

2.2.3.1 Real power generation limit

This constitutes the upper and lower limits of real power llimit of generators

min maxgi gi giP P P , i =1, 2, 3.. g (2.11)

where mingiP and maxgiP are the minimum and maximum limits of real power

generation at bus- i respectively.

2.2.3.2 Reactive power generation limit

This constitutes the upper and lower limits of reactive power limit of generators

min maxgi gi giQ Q Q , i =1, 2, 3.. q (2.12)

where mingiQ and maxgiQ are the minimum and maximum limits of real power

generation at bus- i respectively.

2.2.3.3 Voltage Limit

This constitutes the uppermax

iV and lowermin

iV limits on the bus voltage magnitudemin maxi i iV V V i =1, 2, 3.. bN (2.13)

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2.2.3.4 Line flow limit

This constraint signifies the maximum power flow is a transmission line and are usually

based on thermal and dynamic stability considerations, If maxliP is the maximum active

power flow in line-i and liP is the active power flow at any time of that particular line,then this can be written as

maxli liP P i =1, 2, 3 lN (2.14)

2.2.3.5 UPFC parameter limits

If we include some FACTS device (UPFC in this case) in between bus- i and bus- j the

device has some inequality constraints due to its own parameters like voltage magnitude

( )DV and phase angle ( )D of the series voltage source of it. Along with these two limitsthe reactive power component of shunt current ( )qI should also be less than its rating.

Mathematically, it can be written as

( ) max0 D DV V (2.15)

( ) max0 D D (2.16)

and ( )min maxq q qI I I (2.17)

2.3 Comparative study of different solution techniques for the

optimal power flow

There are various methods for solving the optimal power flow problem. Some most

common methods are described below:

2.3.1 Newtons Method

This method is used to to speed up the convergence [14]. But at the same time handling

inequality constraints is very difficult in this method. Inequality constraints must be

handled by some additional means in terms of adding a constraint penalty function to

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the objective function. Furthermore the matrix equation for this method is extremely

sparse and requires special sparsity logic as the size of the Hessian matrix can be very

large.

2.3.2 Gradient Method

Gradient method is easy to compute. It requires only the first order derivative of the

Lagrangian function with respect to the state vector and control variables. It has the

difficulty in determining the step size because small step size will give slow convergence

whereas larger step size will make the system oscillatory. Is also has the problem for

solving with inequality constraints.

2.3.3 Lambda iteration method

[B] matrix is developed[14] to represent the losses of the system. Also beside this penalty

factors may be calculated outside by the power flow.

2.3.4 Linear Programming (LP) method

The difficulty of handling the inequality constraints is easily overcome in this method as

this method is very adaptive in handling inequality constraints [14], as long as the

problem to be solved is such that it can be linearized without loss of accuracy.

2.3.5 Interior Point (IP) method

It is comparatively a new solution algorithm [16] derived from the linear programming

problems that did not solve for the optimal solution by following a series of points that

were on the constrained boundary but, rather followed a path through the interior of the

constraints [15] directly toward the optimal solution on the constrained boundary. This

load flow solution technique is much faster than the conventional Linear programming

algorithm.

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2.3.6 Genetic Algorithm (GA) method

It is mainly used in large scale systems for solving the economic dispatch problem. It is a

new type of encoding method in which a set of chromosome [15] contains only an

encoding of the normalized system incremental costs. Genetic algorithm is integrated

with conventional OPF to select the best control parameters to minimize the total

generation fuel cost and keep the line flows within permissible limits. It is faster than

lambda iteration method in large systems.

2.3.7 Evolutionary Programming (EP) method

It is a genetic population based metaheuristic [15] optimization algorithm. In this method

fitness function converges smoothly without any oscillations.

2.3.8 Particle Swarm Optimization (PSO) method

This method is inspired by the social behavior and movement dynamics of insects, birds

and fish. It is very simple method to implement. It is derivative free. Another advantage

of this method is that it has very few algorithm parameters [17]. PSO is an efficient

global optimizer for continuous variable problems and can accommodate constraints by

using a penalty method.

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Chapter 3: FLEXIBLE AC TRANSMISSION SYSTEM

3.1 About FACTS

Most of the worlds electric power supply systems are widely interconnected for

economic reasons, to reduce the cost of electricity and to improve reliability of power

supply. The purpose of transmission network is to pool power plant and load centres in

order to minimize the total generation capacity and fuel cost. On the other hand, as the

power transfers grow, the power system becomes increasingly more complex to operate

and the system can become less secure due to the probability of major outages. As a

result full potential of transmission interconnection cannot be envisaged. In modern day,

greater demands on the transmission network and the most importantly the introduction

of deregulated environment, a tendency towards less security and reduced quality of

supply is evoked. A flexible alternating current transmission system (FACTS) is a

technology is essential to fulfill all these drawbacks mostly. It is a system composed of

static equipment used for the AC transmission of electric energy. It is meant to enhance

the controllability and increase the power transfer capability of the network. It is first

proposed by Dr. N. Hingorani.

3.2 Classification of FACTS

In broader sense FACTS controller can be classified into three categories:

1) Shunt controllers

2) Series controllers

3) Combined shunt-series controllers

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3.2.1 Shunt controller

3.2.1.1 Shunt compensation

Shunt controller provides the shunt compensation [18] of an AC network. As the name

suggests it is connected in shunt (or parallel) to the transmission line. It works as acontrollable current source. It may have variable impedance. It injects current into the

system at the point of connection. As long as the injected current is in phase quadrature

with the line voltage, the shunt controller only supplies or consumes variable reactive

power.

Shunt compensation is of two types

Shunt capacitive compensation

This method is used to improve the power factor. Whenever an inductive load is

connected to the transmission line, power factor lags because of lagging load current.

To compensate, a shunt capacitor is connected which draws current leading the

source voltage. The net result is improvement in power factor.

Fig. 3.1: Shunt compensation circuit and phasor diagram

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Shunt inductive compensation

This method is used either when charging the transmission line, or, when there is very

low load at the receiving end. Due to very low, or no load , very low current flows

through the transmission line. Shunt capacitance in the transmission line causes

voltage amplification (Ferranti Effect). The receiving end voltage may become

double the sending end voltage (generally in case of very long transmission lines). To

compensate, shunt inductors are connected across the transmission line.

3.2.1.2 Types of shunt controllers

i. Static synchronous compensator (STATCOM):It is previously known as static

condenser (STATCOM). It is a static synchronous generator operated as a shunt-

connected static var compensator whose capacitive or inductive output current can

be controlled independent of the ac system voltage. It is based on a power

electronics voltage-source converter and can act as either a source or sink of

reactive AC power to an electricity network. If connected to a source of power it

can also provide active AC power.

Fig. 3.2(a) Fig. 3.2(b)

Fig 3.2: STATCOM controller (a) voltage source converter based

(b) current source converter based

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ii. Static var compensator (SVC): It is a shunt connected static var generator or

absorber whose output is adjusted to exchange capacitive or inductive current so

as to maintain or control specific parameters of the power system.

Some most common types of SVCs are as follows:

a. Thyristor controlled reactor (TCR): It is connected in series with a

bidirectional thyristor valve[19]. The thyristor valve is phase-controlled.

Equivalent reactance is varied continuously. Its effective reactance is

varied in continuous manner by partial conduction control of the thyristor

valve.

Fig. 3.3: Thyristor controlled reactor

b. Thyristor-switched reactor (TSR): Same as TCR but thyristor is either in

zero- or full- conduction [19]. Equivalent reactance is varied in stepwise

manner. It,s effective reactance is varied in stepwise manner by full or

zero conduction operation of thyristor valve.

c. Thyristor-switched capacitor (TSC):A capacitor is connected in series with

a bidirectional thyristor valve [19]. Thyristor is either in zero- or full-

conduction. Equivalent reactance is varied in stepwise manner.

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Fig.3.4: Thyristor switched capacitor

d. Mechanically-switched capacitor (MSC): capacitor is switched by circuit-

breaker. It aims at compensating steady state reactive power. It is switched

only a few times a day.

iii. Static Var Generator or absorber (SVG):It is a static electrical device capable

of drawing controlled[19] capacitive and/or inductive current from an electrical

power system and thereby generating or absorbing reactive power.

iv. Thyristor Controlled Braking Resistor(TCBR): A shunt-connected thyristor-

switched resistor[19], which is controlled to aid stabilization of a power system or

to minimize power acceleration os a generating unit during a disturbance.

3.2.2 Series controller

3.2.2.1 Series compensation

In series compensation, the FACTS is connected in series with the power system. It

works as a controllable voltage source [18]. Series inductance occurs in long transmission

lines, and when a large current flow causes a large voltage drop. To compensate, series

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capacitors are connected. As long as the voltage is in phase quadrature with the line

current, the series controller only supplies or consumes variable reactive power.

Fig.3.5: Series compensation and its phasor diagram

3.2.2.2 Types of series controllers

i. Static synchronous series compensator(SSSC):It is a static synchronous generator

operated without an external electric energy source as a series compensator whose

output voltage is in quadrature with, and controllable independently of, the line

current for the purpose of increasing or decreasing the overall reactive voltage

drop across the line and thereby controlling the transmitted electric power [19].

SSSC is one of the most important FACTS controller. SSSC can be based onvoltage-source converter or a current source converter without an extra energy

source SSSC can only inject a variable voltage which is 90 degrees leading or

lagging the current.

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Fig. 3.6: Static synchronous series compensator

ii. Thyristor-controlled series capacitor (TCSC): It is a series capacitor bank is

shunted by a thyristor-controlled reactor in order to provide smoothly variable

series capacitive reactance [19]. It is based on the thyristors without gate turn-off

capability. TCSC may be a single, large unit, or may consist of several equal ordifferent sized smaller capacitors in order to achieve a superior performance.

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Fig. 3.7: Thyristor controlled series compensator

iii. Thyristor-controlled series reactor (TCSR): In this type of controller a series

reactor bank is shunted by a thyristor-controlled reactor[19]. Like TCSC, TCSR

may also be a single large unit or several smaller series units.

Fig 3.8: Thyristor controlled series reactor

iv. Interline power flow controller (IPFC): A combination of two or more static

synchronous series compensators (SSSC) which are coupled via a common dc

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link to take part in bidirectional flow of real power between[19] the ac terminals

of the SSSCs, and are controlled to provide independent reactive compensation

for the adjustment of real power flow in each line and maintain the desired

distribution of reactive power flow among the lines.

Fig.3.9: Interline power flow controller

v. Thyristor-switched series reactor (TSSR): A series reactor[19] bank is shunted by

a thyristor-switched reactor in order to provide a stepwise control of series

inductive reactance.

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Fig. 3.10 Thyristor-switched series reactor

3.2.3 Combined shunt-series controllers

This type of controllers mainly consist of both shunt and series type controllers. Most

important controller under this category is unified power flow controller (UPFC).

Types of combined shunt-series controllers

i. Unified power flow controller (UPFC): It is a combination of static synchronous

compensator (STATCOM-shunt type) and static series compensator (SSSC) [19].

This two controllers are coupled via a common dc-link to allow a bidirectional

flow of real power between the series and shunt output terminal of SSSC and

STATCOM reapectively. By injecting angularly unconstrained series voltage,

UPFC is able to control, selectively, the transmission line voltage, impedance and

phase angle or alternatively, the real and reactive power flow in the line. It also

independently helps to control the shunt reactive compensation.

Fig. 3.11: Unified power flow controller

There are some other types of controllers also which does not belong to these three

main categories mentioned above. Some of them are, Thyristor Control Voltage

Limiter (TCVL), Thyristor Controlled Voltage Regulator (TCVR) etc.

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3.3 Utility of FACTS

I. Improve power transmission capability.

II. Improved system stability and availability.

III. Improved power quality for sensitive industries.IV. Minimized environmental impact.

V. Minimized transmission losses.

3.4 Maintenance of FACTS

Compared to shunt capacitors, reactors and transformers, the maintenance of FACTS

devices are found to be lot easier. No special training or guideline is necessary to perform

a maintenance operation on FACTS devices. The amount of maintain ace ranges from150 to 250 man-hours per year and depends upon the size of the installation and local

ambient condition.

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Chapter 4: UNIFIED POWER FLOW CONTROLLER

4.1 About Unified Power Flow Controller

The Unified Power Flow Controller (UPFC) concept was first proposed by Gyugyi [22]

in 1991. Unified Power Flow controller is a novel real time power flow controlling

device. It provides full dynamic control of transmission parameters, voltage, line

impedance and phase angle by fulfilling multiple functions of power flow like reactive

shunt compensation, series compensation and phase shifting. In other words it can be said

that both the real and reactive power flow in a line is controlled independently by this

device. Thus by controlling the line power flow UPFC satisfies the load demand and

other operating conditions. With suitable electronic controls, the UPFC can cause the

series-injected voltage vector to vary rapidly and continuously in magnitude and/or phase

angle as desired. Thus it simultaneously controls the wide range of variation of active and

reactive power as well as also has the capability to transition rapidly from one such

achievable point to any other.

As the need for flexible and fast power flow controllers, such as the UPFC, is expected to

grow in the future due to the changes in the electricity markets, there is a corresponding

need for the reliable and realistic models of these controllers to investigate the impact of

them on the performance of the power system.

4.2 Structures and operations of UPFC

UPFC can be categorized under new generation of FACTS device which combines the

features of two old FACTS devices, the Static Synchronous Compensator (STATCOM)

and the Static Synchronous Series Compensator (SSSC). In practice these two devices are

two voltage source converters connected respectively in parallel with the transmissionline through a shunt connected transformer and in series with the transmission line

through a series connected transformer. The other terminals of both the converters are

connected to each other through a common dc link including a storage capacitor. This

type of arrangement functions as an ac-to-ac power converter in which the real power can

freely in either direction between the ac terminals of the two converters, and each

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converter can independently generate or absorb reactive power at its own output ac

terminal.

Fig.4.1: Equivalent circuit of

STATCOM

Fig. 4.2: Equivalent circuit of SSSC

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The shunt converter is primarily used to provide active power demand of the series

converter through the common dc link. Shunt converter can also provide independent

shunt reactive compensation for the line by generating or absorbing reactive power when

desired. The series converter provides the main function of the UPFC by injecting a

voltage by controllable magnitude and phase angle in series with the line via the insertion

transformer. The injected voltage acts essentially as a synchronous ac voltage source. The

transmission line current flows through this voltage source resulting in reactive and real

power exchange between it and the ac system. The reactive power exchanged at the ac

terminal of the series insertion transformer is generated internally by the converter. The

real power exchanged at the ac terminal is converted into dc power which appears at the

dc link as a positive or negative real power demand.

The basic function of shunt converter is to supply or absorb the real power demanded by

the series converter at the common dc link to support the real power exchange resulting

from the series voltage injection [19]. This dc link power demand of series converter is

converted back to ac by the shunt converter and coupled to the transmission line bus via a

shunt connected transformer. It is important to note that whereas there is a closed direct

path for the real power negotiated by the action of series voltage injection through shunt

and series converters back to the line, the corresponding reactive power exchanged is

supplied or absorbed locally by series converter and therefore does not have to be

transmitted by the line. Thus, shunt converter can be operated at a unity power factor or

be controlled to have a reactive power exchange with the line independent of the reactive

power exchanged by series converter. Most certainly there can be no reactive power flow

through the UPFC dc link.

4.3 Equivalent Circuit of UPFC [20]

As said earlier UPFC is a combination of both STATCOM and SSSC. It has both series

and shunt voltage sources as well as impedance. The equivalent circuit of STATCOM

and SSSC is shown in the Fig.4.1 and Fig. 4.2 respectively. In Fig.4.3 the equivalent

circuit of UPFC is shown.

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Fig. 4.3: Equivalent circuit of UPFC

The voltage vector of series converter is se se seV V = and for shunt converter it is

sh sh shV V = .Bus voltage vector of thi bus is i i iV V = and for thj it is j j jV V = .

Active power exchange between the two converters will be

* *Re( ) 0sh sh se jiPE V I V I= =

The bus voltage control constraint is 0specified

i iV V =

The two equivalent voltage injection binding constraint is as follows:

min maxse se seV V V

min maxsh sh shV V V

min maxse se se

min maxsh sh sh

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4.4 Modeling of UPFC [12]

The UPFC model is very helpful in understanding the impact of the UPFC on the power

system in the steady state. The injection model also can easily be incorporated in the

steady state power flow model. Since the series voltage source converter does the mainfunction of the UPFC, it is appropriate to discuss the modeling of a series voltage source

converter. To analyze the UPFC injection it is important to note that the series converter

is used to generate a voltage source at the fundamental frequency with variable amplitude

0 maxD DV V and phase angle 0 2D .

The equivalent circuit model of UPFC is shown in the fig 4.4. It has three parameters

namely inserted voltage magnitude and phase angle ( DV , D ) and the magnitude of the

reactive power component of shunt current qI . The device is connected between two

nodes i andj . The buses situated in these two nodes have voltage magnitudes of iVfor

thi bus and jV for the thj bus. The transmission line connected between these two buses

is l (say).The transmission line has an impedance ij ij ijz r jx= + where ijr is theresistance of the transmission line and ijx is the reactance of that line. The total line

charging B is equally divided in two parts between the transmission line and each part is

known as half line charging of transmission line.

Fig.4.4: Equivalent model of UPFC

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From the UPFC vector diagram the mathematical formulation from the above diagram

can be written as:

'

i i DV V V= + (4.1)( ) ( ) / 2q iArg I Arg V = (4.2)

Because of the voltage vector can be leading or lagging in nature with respect to the

series transformer current vector.

The voltage vector at bus i and the current vector for the shunt converter DI are in phase

so that,

( ) ( )D irg I Arg V = , (4.3)

where,

*'Re[ ]D i

D

i

V II

V= (4.4)

Now apparent power flows from bus i to bus j will be,

*'

* ' * ' *Re[ ]( /2 ) ( /2 )D i

ij ij ij i ij i D q i i i q iV I

S P jQ VI V jViB I I I V jVB I I Vi

= + = = + + + = + + + (4.5)

and apparent power flows from bus j to bus iwill be,

* *' *( / 2 )ji ji ji j ji j ji j j iS P jQ V I V I V jV B I = + = = = (4.6)

Separating the real part and imaginary part from both left and right hand side of the

equation_ and comparing, we get the active and reactive power flow of the line having

UPFC.

The active power flow from thi bus to thj bus for the line having UPFC is,

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2 2( ) ( ) 2 cos( )ij ij i D ij i D ij D iP real S V V g V V g = = + + (4.7)

[ cos( ) sin( )] ( cos sin )j D ij D j D j i j ij ij ij ijV V g bij V V g b + + (4.8)

The reactive power flow from thi bus to thj bus for the line having UPFC is,

2( ) ( / 2)ij ij i q i ijQ imag S V I V b B= = +

[ sin( ) ( / 2) cos( )]i D ij D i ij D iV V g b B + + (4.9)

The active power flow from thj bus to thi bus for the line having UPFC is,

2( ) [ cos( ) sin( )]ji ji j ij j D ij D ij D iP real S V g V V g j b = =

( sin cos )i j ij ij ij ijV V g b (4.10)

The reactive power flow from thj bus to thi bus for the line having UPFC is,

2( ) ( / 2) ( sin( ) cos( ))ji ji j ij j D ij D j ij D iQ imag S V b B V V g b = = + + +

(( sin cos )j ij ij ij ijV V g b + + (4.11)

Where, ij i j =

The injected equivalent circuit from the principle of basic circuit theory can be obtained

as given below:

Fig.4.5: Injection model of UPFC

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The injected active power at bus i , _i sP for the UPFC line l is,

2_ 2 cos( ) [ cos( ) sin( )]s D ij i D ij D i j D ij D j ij D jP V g VV g VV g b = + + (4.12)

The injected reactive power at bus i , _i sQ , for the UPFC line l is,

_ [ sin( ) ( / 2)cos( )]s i q i D ij D i ij D iQ V I V V g b B = + + + (4.13)

The injected active power at bus j , _j sP ,for the UPFC line l is,

_ [ cos( ) sin( )]j s j D ij D j ij D jP V V g b = (4.14)

The injected reactive power at bus , _j sQ ,for the UPFC line l is,

_ [ sin( ) sin( )]j s j D ij D j ij D jQ V V g b = + (4.15)

4.5 Location of UPFC[12]

4.5.1 Contingency Selection and Performance Index

For consistent service, power system must remain intact and be able to endure a wide

variety of disturbances. It should operate in normal and secured condition. Therefore, it is

important that the system to be designed and operated so that the more possible

contingencies can be sustained with no loss of load. Operating conditions of power

system can be determined if the network model and complex phasor voltages at every

system bus is known.If all the loads in the system can be supplied power without

violation of any operational constrains, then the system is in normal state. Examples of

these operational constrains include the limits on the transmission line flow, as well as

upper and lower (i.e. limits) on bus voltage magnitudes.

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It should be noted that, line or generation outage may cause flow or voltages to fall

outside limits. The contingency analyses (CA) are used to predict the effect of these

outages. The state estimators solutions are used to perform contingency analysis in

power systems.

We would like to get some measure as to how much a particular outage might affect the

power system. The idea of a performance index (PI) seems to fulfill this need. The

definition for the overload performance index is as follows:

max1

22

Nlm lk

lkm

w PPI n

n P=

= (4.16)

Where lkP is the real power flow and maxlkP is the rated capacity of line-k,n is the

exponent, and mw is a nonnegative weighting coefficient that may be used to reflect the

importance of the lines. lis the total number of lines in the network.

Various techniques have been tried to obtain the value of PIwhen a branch is taken out.

These calculations can be made exactly if n=1, that is, a table of PI values, one for

each line in the network can be calculated quite quickly. However when n=1, the PI

does not snap from near zero to near infinity as the branch exceeds its limit. Instead, it

rises as a quadratic function. A line that is just below its limit contributes to PIalmost

equal to one that is just below their limit. Thus the PIs ability to distinguish or detect

bad cases is limited when n=1.

Using the second order performance indices in contingency selection algorithm can be

suffered from the masking effects. The lack of discrimination, in which the performance

index for a case with many small violations may be comparable in value to the index for

a case with one huge violation, is called the masking effect. The masking effect can be

minimized by choosing higher values of n (>1). In this case it is taken as 2 and mw istaken as1.0 .

In a line of networks there are some lines which are found to be weaker than the other

lines in terms of line power flow and injected bus power. We have to include the device

in that weaker line (say l ) in between 2 buses (say i andj ) after calculating the

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sensitivities for each UPFC parameters. Sensitivity matrix helps to find the weakest line

among the network of lines. Performance index sensitivities factors are calculated by

partially differentiate the performance index with respect to each of the UPFC control

parameters ( DV , D , q ) and can be defined as

1

0

l

D VD

PIc

V =

=

(4.17)

2

0

l

D DD

PIc

V

=

=

(4.18)

3

0

l

q Iq

PIcI =

= (4.19)

where 1lc , 2lc and 3lc arePIsensitivity with respect to UPFC parameters l( DV , D

and q ) respectively connected between bus i and bus j . Using Equation_, we get

4

3

max1

1Nl

lkk lk

l lk l k

PI Pw PP R=

= (4.20)

The real power flow in line-k ( lkP ) can be represented in terms of real power injections

using dc power flow equations wheres is the slack or reference bus, as

1

_1

Nbkn n

nn slk

Nbkn n j sn

n s

S PP

S P P

=

=

=

+

(4.21)for k = l

for k l

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Where knS is the knthelement of matrix [ ]S that relates line flow with power injections

at the buses without UPFC, and bN is the number of buses in the system. _j sP ,

therefore, is the additional power flow, at bus-j , in the line containing UPFC, due to the

presence of the device.Using equation 4.20 and 4.21, the following relationship can be obtained

_ _

_ _ _

i s j ski kj

l llk

l i s j s j ski kj

l l l

P PS S

R RP

R P P PS S

R R R

+ = + +

(4.22)

where , ,l D D qR V I= .

Now if we put these three control parameters one by one in equation 4.22, we get the the

partial differentiation of lkP with respect to the UPFC control parameters.

The partial differentiation of _i sP and _j sP with respect to each control parameters can

be evaluated distinctly as follows

_

0

2 cos( ) [ cos( ) sin( )]D

i si ij D i ij D ij D j

D V

PV g Vj g j b

V

=

= + +

(4.23)

_

0

2 sin( ) ( sin cos )

D

i si ij j ij j ij j

D D

PV g Vj g b

V

=

= + + (4.24)

_

0

0i s

qIq

P

I =

= (4.25)

_

0

( cos sin )D

j sj ij j ij j

D V

PV g b

V

=

= + (4.26)

for k l

for k = l

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_

0

( sin cos )D

j sj ij j ij j

D

PV g b

V

=

= (4.27)

_

0

0j sq

Iq

PI =

= (4.28)

Thus the sensitivity factors can be obtained from equation 4.23 to 4.28. In this case

equation 4.25 and 4.28 the partial differentiation of injected bus power with qI gives

zero value. It suggests that the sensitivities are calculated for DV and D only.

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Chapter 5: GRADIENT METHOD

5.1 Problem formulation

The objective function is to be minimized the difference of the operational cost for the

active power of pool generator to the pool load.

The optimization problem can be restated as

min ( , , )F x u pu

(5.1)

Subject to equality constraints( , , ) 0g x u p = (5.2)

To solve the optimization problem, we define Lagrange functions as

( , , ) ( , , ) ( , , )TL x u p F x u p g x u p= + (5.3)

where is the vector of Lagrangian multipliers [21] of the same dimensionas ( , , )g x u p .

The necessary conditions to minimize the unconstrained Lagrangian function are

0

TL F g

x x x

= + = (5.4)

0

TL F g

u u u

= + = (5.5)

( , , ) 0L

g x u pu

= =

(5.6)

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Equations 5.4, 5.5 and 5.6 are nonlinear algebraic equations and can only be solved

iteratively. A simple yet efficient iteration scheme, that can be employed, is the steepest

descent method (also called the gradient method). The basic technique is to adjust the

control vector u, so as to move from one feasible solution point (a set of values of x

which satisfies eq.5.6 for given u andp ; it indeed the load flow solution) in the direction

of negative gradient to a new feasible set of solution with lower value of objective

function.

5.2 Computational Procedure [21]

1) Make an initial guess for u, the control variables.

2) Find a feasible load flow solution by Newton-Raphson iterative method. The

method improves the solution as follows:

1r rx x+ = + (5.7)

3) Where x is obtained by soling the set of linear equations given below:

( , ) ( , )r rg

x y x g x yx

= (5.8)

1

( , ) ( , )r rg

x x y g x yx

=

(5.9)

4) The end result of Step 2 is a feasible solution of x and the Jacobian matrix,

5) Solve eq 5.4 for

1F

x

=

(5.10)

6) Put the values of obtained from eq. 5.10 to eq. 5.5 and compute the gradient

TF g

L u u = + (5.11)

7) If L equals are within prescribed tolerance, the minimum has been reached.

Otherwise:

8) Find a new set of control variables

new old u u u= + where u L = (5.12)

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Here u is a step in negative direction of the gradient. The step size is adjusted by thepositive scalar .In this algorithm, the choice of is very critical. Too small a value of

guarantees the convergence, but slows down the rate of convergence. Too high a value

causes oscillations around the minimum.

5.3 Inequality constraints on control variables

Though in the previous discussion, the variables are assumed unconstrained, the

permissible values are, in fact, always constrained, i.e.

min maxu u u

e.g min maxgi gi giP P P These inequality constraints on control variables can be easily handled. If the correction

u in eq. 5.12 causes u to exceed one of the limits, u is set equal to the

corresponding limit, i.e.

max

min

i

i i

oldi i

u

newu u

u u

= +

After a control variables reaches any of the limits, its component in the gradient should

continue to be computer in lated iterations, as the variables may come within limits at

some later stage.

5.4 Inequality constraints on dependent variables

Often, the upper and lower limits on dependent variables are specified as:

min maxx x x e.g min maxi i iV V V

Such inequality constraints can be conveniently handles by the penalty function methods.

The objective function is augmented by penalties for inequality constraints violations.

If oldi iu u+ > maxiu

If oldi iu u+ < miniu

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This forces the solution to lay sufficiently close to the constraint limits, when these limits

are violated. In this problem all iV are within the specified limit. So that no penalty

function has been included.

5.5 Lagrangian for solving the OPF in gradient method

The objective function is

( ) ( )G D

T i Pi j pj

i I j I

F C P B D

=

(5.13)

The equality constraints for i thbus are

_

1

[ cos( ) sin( )]Nb

i i m im i m im i m i s

m

P V V G B P =

+

(5.14)

and _

1

[ sin( ) cos( )]Nb

i i m im i m im i m i s

m

Q V V G B Q =

(5.15)

Hence the Lagrange function will be

( , ) ( ) ( )G D

i Pi j pj

i I j I

L P Q C P B D

=

( ) _1

[ cos( ) sin( )]Nb

i i m im i m im i m i s

i Nb m

p P V V G B P

=

+ +

( ) _1

[ sin( ) cos( )]Nb

i i i m im i m im i m i s

i Nb m

q Q V V G B Q =

+

(5.16)

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where pi and qi are the Lagrange multipliers of respective equality

constraints. The Lagrange multiupliers for the real power equations of the load flow

are invariably positive; however, for reactive power, the multipliers can either be

positive or negative.

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Chapter 6: SPOT PRICING

6.2 Introduction

The spot price or spot rate of a commodity, a security or a currency is the price that

is quoted for immediate (spot) settlement (payment and delivery). Spot settlement is

normally one or two business days from trade date. Spot rates are estimated via the

bootstrapping method, which uses prices of the securities currently trading in

market, The result is the spot curve, which exists for each of the various classes of

securities.

In modern world transmission open access has become an important issue on

deregulated electrical sector [13]. In a generation marketplace, the agents will

maximize their individual revenues not taking into account the social welfare. So

there should be a valid coordination between the generation marketplace and the

centralized or deregulated transmission open access. In a competitive market

environment, no participant can absolutely control the power system operation.

That is the existing spot price cannot be changed by adjusting the bids which mostly

matches a single participants marginal cost. Therefore the minimum power system

operation cost and the maximum participant benefit are reached at the same time ina real competitive market.

6.2 Power pools

Interchange of power between systems can be economically advantageous.

However, when a system is interconnected with many neighbors, the process of

setting up one transaction at a time with each neighbor can become very time

consuming and will rarely result in the optimum production cost [14]. To overcomethis burden, several utilities may form a power pool which incorporates a central

dispatch office. The power pool is administered from a central location that has

responsibility for setting up interchange between members. The pool members take

certain responsibilities to the pool operating office in return for greater economies

in operation.

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6.2.1 Advantages of power pools

1) The certain advantages for centrally dispatched power pools are as follows:

2) Minimize operating costs (or maximize operating efficiency alternatively)

3) Perform a system-wide unit commitment.

4) Minimize the reserves being carried throughout the system.

5) Coordinate maintenance scheduling to minimize costs and maximize

reliability by sharing reserves during maintenance periods.

6) Maximize the benefits of emergency procedures.

6.2.2 Disadvantages of power pools

There are some disadvantages that should be included along with the advantages

like economic operation. Some of the disadvantageous factors are as follows:

1) The complexity of the pool agreement and the continuing costs of

supporting the interutility structure required to manage and administer thee

pool.

2) The operating and investment costs associated with the central dispatch

office and the needed communication and computation facilities.

3) The relinquishing of the right to engage in independent transactions outside

of the pool by the individual companies to the pool office and the

requirement that any outside transactions be priced on a split-saving basis

based on pool members costs.

4) The additional complexity that may result ion dealing with regularity

agencies if the pool operates in more than one state.

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6.3 Spot price

For decades, power factor penalties have been used in providing reactive power

pricing. It has been shown that the practice of power factor penalties is unable to

provide accurate price signals to customers. Spot pricing means that electricityprices to the customer follow as closely as technically practical the real cost of

electricity at the time that it is produced and supplied. Most findings in real-time

pricing of reactive power are closely related to those of active power pricing. Spot

prices as defined are change according to power production units and transmission

lines in the power system. If total power demand is higher than participants offer,

spot price will increase [13]. Conversely, if total power demand is lower than

participants offer, spot price will decrease. All electrical power producers want to

run their units in the most productive operating conditions in every period.

Fig.6.1: power production-bid price characteristics

!imax

!i2

!i0

!i1

!imin

Pimin PimaxPi0

Ti1 Ti2Ti

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As in Fig. 1, if the spot price for one participant is determined as optimum that

particular participant dose not want to buy or transact any power from other

participants. Participants will produce electrical energy for only their own

agreement. Participants only export power after fulfilling their own internal needs if

the spot price is higher than !i0 , the participant reduce its own local generation. As

shown in the graph with increase in power flow power cost increase too. Power

system must have extra supply for this lack of restriction of participants. If the

power systems have no extra supply, then spot price applications cannot apply

frequently.

6.4 Marginal cost

In purely economic point of view marginal cost can be defined as the cost of the

additional inputs needed to produce that output. More formally, the marginal cost is

the derivative of total production costs with respect to the level of output.

The prices for active powers at bus- i are actually the marginal cost associated with

the corresponding load flow equations when the OPF( with and without FACTS)

are solved as a nonlinear programming problem [12].

From the power system point of view, the active power marginal cost price at the

bus- i is defined by

i

di

PP

=

[total cost of providing electricity to all customers subject toConstraints]

i

i

d

LC

P

= =

where piC is the marginal cost price of active power at bus i and L is the

Lagrange function defined in eq.(5.16) for which the total cost to supply the

electrical energy for all consumers and subject to operation restrictions.

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Chapter 7: RESULTS AND DISCUSSIONS

7.1 IEEE 30-bus test system

The proposed method has been tested on a IEEE 30-bus system for the base case

(without UPFC) and with incorporating UPFC. The single line diagram of a 30 bus

system is given in figA.1 and 2. The prices bid by generators are given in table A.1,

where P is in megawatts and cents is a monetary unit. Bus data is given in table A.2

and line data is given in table A.3.

7.2 Tabulated results

Table 7.1 to 7.4 shows the test results after the proposed method is implemented on

MATLAB 7.8 for IEEE 30 bus system and the computation is performed on a

computer having 2.80 GHz, core 2 duo processor and 2 GB RAM.

Table 7.1: Sensitivity table matrix for c1l

and c2l

Line

nos.

ith

bus jth

bus c1l

(withrespect to VD)

c2l

(withrespect to !D)

1 1 2 0.105400553705582 -0.0133720592871952

2 1 3 0.00133199832472405 -0.000177325849024417

3 2 4 -7.07350277184786e-07 5.97848915732095e-08

4 3 4 -5.92411347915431e-06 5.30658325775049e-07

5 2 5 -2.64755442531785e-05 3.09421014094045e-06

6 2 6 0 0

7 4 6 0 0

8 5 7 -6.77830371534241e-07 7.66349639648712e-08

9 6 7 -0.00564853278969574 0.000683726222919481

10 6 8 -0.115285393796341 0.0121133089179766

11 6 9 0 0

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12 6 10 -0.000418200645620308 6.48355308725975e-05

13 9 11 0.00196413791901515 -7.02601044429364e-05

14 9 10 -0.00122302880608463 0.000225231891633056

15 4 12 -0.00024825225853467 3.97762834798397e-05

16 12 13 0.0864586908875991 -0.00692698291034724

17 12 14 -0.00082000115723229 0.000129868604021993

18 12 15 -0.0318824780904561 0.00526855828148936

19 12 16 -3.72830064390911e-05 5.44808465509381e-06

20 14 15 -1.01197858354723e-07 1.56359511392211e-08

21 16 17 -8.35586841618415e-06 1.23570331144695e-06

22 15 18 -.000102875012565942 1.71018303129115e-05

23 18 19 -2.11151486575580e-05 3.51021581055078e-06

24 19 20 -3.86353128575040e-06 3.51021581055078e-06

25 10 20 -0.000118208007108670 1.99877337651416e-05

26 10 17 -0.00407858966864019 0.000606189386310992

27 10 21 -0.451710876271081 0.0713922481669822

28 10 22 0 0

29 21 22 0 0

30 15 23 -4.92238355279217e-05 8.01072407001902e-06

31 22 24 -.000982100994548929 0.000164976633443186

32 23 24 -2.15948688895622e-06 3.55294032408022e-07

33 24 25 0 0

34 25 26 -4.93083082491196e-06 8.90526237374516e-07

35 25 27 0 0

36 28 27 0 0

37 27 29 -6.82699456110101e-05 1.37196248158477e-05

38 27 30 -0.00669484624381917 0.00150712030528960

39 29 30 -0.000272858780586663 5.83462425139716e-05

40 8 28 0 0

41 6 26 0 0

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Table 7.2:Optimum generation schedule

Parameter Base Case (without UPFC) UPFC in line 27

Generator 1 123.58+j4.03 124.64-j26.3Generator 2 55.26-j14.42 54.24-j10.32

Generator 3 41.07-j4.35 40.02-j2.39

Generator 4 12.78+j18.30 11.2+j29.26

Generator 5 16.82-j39.20 15.76+j37.08

Generator 6 16.89 -j23.14 15.85+j27.03

VD(p.u) ------ 0.5

!D(degree) ------ 5.72

Iq(p.u) ------ 0.005

Generation Cost (cents/h) 510.3976 499.8153

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Table 7.3:Voltage and phase angle computed without UPFC

Bus No. Voltage Magnitude (p.u) Phase angle (in degree)

1 1.0500 0

2 1.0338 -0.0388

3 1.0245 -0.0835

4 1.0181 -0.1000

5 1.0058 -0.1295

6 1.0140 -0.1192

7 1.0025 -0.1328

8 1.0230 -0.1272

9 1.0001 -0.1258

10 0.9728 -0.1844

11 1.0713 -0.0870

12 1.0040 -0.1690

13 1.0400 -0.1422

14 0.9807 -0.1868

15 0.9807 -0.1885

16 0.9831 -0.1806

17 0.9701 -0.1874

18 0.9650 -0.2008

19 0.9589 -0.2044

20 0.9616 -0.2005

21 0.9249 -0.1964

22 0.9643 -0.1890

23 0.9699 -0.1969

24 0.9643 -0.2014

25 0.9853 -0.2037

26 0.9671 -0.211627 1.0074 -0.1998

28 1.0090 -0.1283

29 0.9872 -0.2220

30 0.9755 -02379

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Table 7.4: Voltage and phase angle computed with UPFC

Bus no. Voltage( in p.u) Phase angle (in degree)

1 1.05 0

2 1.0338 -0.03832

3 1.027001 -0.08334

4 1.021119 -0.09985

5 1.0058 -0.12856

6 1.017826 -0.11925

7 1.004823 -0.13247

8 1.023 -0.12618

9 1.006625 -0.12577

10 0.992189 -0.18266

11 1.0813 -0.08754

12 1.009206 -0.16608

13 1.04 -0.1394

14 0.993342 -0.18394

15 0.987963 -0.18633

16 0.994389 -0.17826

17 0.987228 -0.1853418 0.976651 -0.19845

19 0.973254 -0.20197

20 0.977158 -0.19824

21 0.975972 -0.19974

22 0.977524 -0.19802

23 0.976794 -0.19638

24 0.970804 -0.20322

25 0.99087 -0.20431

26 0.972701 -0.21204

27 1.012264 -0.1997

28 1.012097 -0.12819

29 0.992186 -0.22165

30 0.980574 -0.23741

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7.3 Graphical results

The graph in fig. 7.1 and 7.2 shows the real power spot pricing tabulated with and

without UPFC for each load buses.

Fig. 7.1: Real power spot prices (cents/ MWhr) at load buses without UPFC

Real power spot price at load buses without UPFC

200202.5

205

207.5

210

212.5

215

217.5

220

222.5

225

227.5

230

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Bus number

Spotprices(cents/MWh)

Spot

prices

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Fig. 7.1: Real power spot prices (cents/MWhr) at load buses with UPFC

Real power spot prices at load buses with UPFC at line-27

200

202.5

205

207.5

210212.5

215

217.5

220

222.5

225

227.5

230

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Bus number

Spotprices(cents/MWh)

Spot

prices

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Chapter 8: CONCLUSION

8.1 ConclusionIn this paper real power spot price has been calculated with and without implementing the

FACTS device (UPFC). Here the OPF is solved in gradient method. Moreover a

sensitivity based approach has been used for finding a suitable location to place UPFC.

Test results obtained on test systems show that the new sensitivity factors could be

effectively used for placement in response to required objectives. The placement of a

UPFC in a particular line affects both the real power and reactive power prices. It can be

concluded that by incorporating UPFC in the OPF model, significant reduction occurs in

real power loss and generation cost.

8.2 Future Scope

Only real power pricing is dealt with in this paper. There are many approaches towards

the reactive power pricing has also been done in recent years and in future with

increasing demand of electric power and more competitive power market. The reactive

power pricing should play an important role beside real power pricing. By knowing the

bid price for the reactive power generation reactive power price can be determined after

formulating a corresponding OPF for the reactive power.

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REFERENCES

[1]L.Gyugyi, T.Rietman , A.Edris, C. D. Schauda . S.L.Williams, The unified powerflow controller: A new approach to power transmission control, IEEE Transactions onPower Delivery, Vol. 10, No. 2, April 1995.

[2] Jenn- Huei Jeffrey Kuan, Optimal power flow with price elastic demand, Thesis

report ,dept. of Master of Science in Electrical Engineering, Massachusetts Institute ofTechnology, August 1996.

[3] J. Y. Choi, S.-H. Rim, and J.-K. Park, Optimal real time pricing of real and reactive

powers,IEEE Trans. Power System., vol. 3, no. 4, pp., 12261231, Nov. 1998.

[4] J. W. Marangon Lima and E. J. de Oliveira, The long-term impact of transmission

pricing,IEEE Trans. Power Syst., vol. 13, no. 4, pp.15141520, Nov. 1998.

[5] J. Y. Liu and Y. H. Song, Comparison studies of unified power flow controller with

static var compensators and phase shifters, Elect. Mach. Power Syst., vol. 27, pp. 237251, 1999.

[6]J. Y. Liu, Y. H. Song, and P. A. Mehta, Strategies for handling UPFC constraints in

the steady state power flow and voltage control,IEEE Trans. Power Syst., vol. 15, no. 2,pp. 566571, May 2000.

[7]S. C. Srivastava and R. K. Verma, Impact of FACTS devices on transmission pricing

in a de-regulated electricity market, in Proc. IEEE Int. Conf. Electric UtilityDeregulation Restructuring Power Technologies, London, U.K., Apr. 2000, pp. 642648.

[8] K. S. Verma, S. N. Singh, and H. O. Gupta, Optimal location of UPFC for

congestion management,Elect. Power Syst. Res., vol. 58, no. 2, pp. 8996, Jul. 2001.

[9]-----, FACTS device location for enhancement of total transfer capability, in Proc.IEEE Power Eng. Soc.Winter Meeting, vol. 2, Columbus, OH, pp. 522527, Jan. 28Feb.

1 2001.[10]-----,Location of UPFC for power systems security in deregulated environment,

inProc. Int. Conf. EAIT-2001. Kharagpur , West Bengal, Dec. 2001, pp. 149154.

[11] S. N. Singh, K. S. Verma , and H. O. Gupta, Optimal power flow control in openpower market using unified power flow controller, in Proc. IEEE Power Eng. Soc.

Summer Meeting, vol. 3, Vancouver, BC, Canada, Jul. 1519, 2001, pp. 16981703.

[12] K.S. Verma and H.O.Gupta, Impact on real and reactive power pricing in openpower market using unified power flow controller, Trans. On power systems, vol. 21,

no. 1, February 2006.

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[13] Abdullah Urkmez, Determined spot price and economic dispatch in deregulatedpower systems, Mathematical and Computational Applications, Vol. 15, No. 1, pp. 25-

33, 2010.

[14] A. J. Wood and B. F. Wollenberg, Power Generation, Operation, and Control,

2nd edn. Wiley India (P) Ltd., New Delhi, 2007.

[15] K.S.Pandya, S.K.Joshi, A survey of optimal power flow methods, Journal of

Theoretical and Applied Information Technology.

[16] J.A. Momoh, J.Z. Zhu, Improved interior point method for OPF problem,IEEETransactions on Power Systems, Vol. 14, No. 3, August 1999.

[17] Jaco F. Schutte, The particles swarm optimization algorithm, EGM 6365 -

Structural Optimization, Fall 2005.

[18] www.wikipedia.com

[19] Hingorani N.G. and Gyugyi L., Understanding FACTS: concepts and technologyof flexible ac transmission systems.New York: IEEE Press; 1999.

[20] Xiao-Ping Zhang, Edmund Handschin, Transfer capability computation of powersystems with comprehensive modeling of FACTS controllers, 14thPSCC,Sevilla, Section 30.paper 2, page no. 1-4, 24-28 June, 2002.

[21] D. P. Kothari and J. S. Dhillon, Power System Optimization,Prentice Hall ofIndia Pvt. Ltd., New Delhi, 2006.

[22] L. Gyugyi, A unified power flow control concept for flexible AC transmissionsystems,Proc. Inst. Elect. Eng., pt. C, vol. 39, no. 4, pp. 323331, Jul. 1992.

[23]The IEEE 30bus test system available at:http://ee.washington.edu/research/pstca/pf30/pg_tca30bus.htm

http://www.wikipedia.com/http://ee.washington.edu/research/pstca/pf30/pg_tca30bus.htmhttp://ee.washington.edu/research/pstca/pf30/pg_tca30bus.htmhttp://www.wikipedia.com/

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NOMENCLATURE

iC Bid price of pool generator-i.

pi Active power of pool generator-i

jB Bid price of pool load-j

pj Active power of pool load-j

GI Set of pool generator buses

DI Set of pool load buses

DV Voltage magnitude of UPFC series controller

D Phase angle magnitude of UPFC series controller

qI Shunt current

gi Generated active power at bus-i

iQ Generated reactive power at bus-i

di Active power demand at bus-i

diQ Reactive power demand at bus-i

bN Total number of buseslN Total number of lines

qN Number of reactive power sources

iV Bus voltage magnitude at bus-i

i Phase angle at bus-i

mingiP Minimum active power generation limit at bus-i

maxgiP Maximum active power generation limit at bus-i

mingiQ Minimum reactive power generation limit at bus-i

maxgiQ Maximum reactive power generation limit at bus-i

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APPENDIX

Table A.1:Generator data

Bus no. Pgmin(MW) Pgmax(MW)b(cent/MW-

hr) c(cent/MW2-hr)

1 50 200 2 0.00375

2 20 80 1.75 0.0175

5 15 50 1 0.0625

8 10 35 3.25 0.00834

11 10 30 3 0.025

13 12 40 3 0.025

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Table A.2: IEEE 30 bus characteristics

BusNo.

Active powerdemand(MW)

Reactive powerdemand(MVAR)

Bus voltagemagnitude(in p.u)

Bus voltageangle

Yshunt

1 0 0 1.05 0 0

2 21.70 12.70 1.0338 0 0

3 2.40 1.20 1.0 0 0

4 7.60 1.60 1.1.00580 0 0

5 94.20 19.00 1.0 0 0

6 0 0 1.0 0 0

7 22.80 10.90 1.0230 0 0

8 30.00 30.00 1.0 0 09 0 0 1.0 0 0

10 11.9 2.00 1.0913 0 00

11 0 0 1.0883 0 0.19

12 11.2 7.50 1.10 0 0

13 0 0 1.0 0 0

14 6.20 1.60 1.0 0 0

15 8.20 2.50 1.0 0 0

16 3.50 1.80 1.0 0 0

17 9.00 5.80 1.0 0 0

18 3.20 0.90 1.0 0 0

19 9.50 3.40 1.0 0 0

20 2.20 0.70 1.0 0 0

21 34.3 11.20 1.0 0 0

22 0 0 1.0 0 0

23 3.20 1.60 1.0 0 0

24 8.70 6.70 1.0 0 0.04

25 0 0 1.0 0 0

26 3.50 2.30 1.0 0 0

27 0 0 1.0 0 0

28 0 0 1.0 0 0

29 2.40 0.90 1.0 0 0

30 10.60 1.90 1.0 0 0

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Fig. A1:Single line diagram of IEEE 30-bus system [23]

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