ABSTRACT
This project
describes an approach for determining the most suitable locations for
installing FACTS devices and finding their optimal settings for congestion
management.
Congestion
management means the activities of the transmission system operator to relieve
transmission constraints in competitive electricity market. Congestion occurs
when the transmission network is unable to accommodate all of the desired
transactions due to violation of the system operating limits. Congestion can be
removed by using FACTS devices.
CHAPTER 1
1.
INTRODUCTION
Power systems are
commonly planned and operated such that the system should remain secure under
all conditions. In recent years, with the deregulation of the electricity
market, the traditional concepts and practices of power systems are changed.
This led to the introduction of Flexible AC Transmission System (FACTS)
devices. These devices are able to modify voltage, phase angle, impedance and
the power flows at particular points in power systems. FACTS devices controls
the power flow in the network, reduces the flow in heavily loaded lines thereby
resulting in an increase loadability, low system losses, improved stability and
security of network and reduced cost of production.
Power exchanges in
a deregulated system must be under controlled in order to avoid line
overloading known as congestion. Therefore the full capacity of the
transmission lines may not be used. This congestion is reduced to use the full
capacity of the network. Removing congestion in normal and contingency condition
in a power system without reducing the stability and security margin can be
achieved through fast power control by FACTS devices in a transmission system. Their
main function is to maximize the power flow. In the proposed work, a nontraditional optimization
technique, Particle Swarm Optimization (PSO) algorithm is used to optimize the
parameters of FACTS devices in a power system. The various parameters taken
into consideration are the location and settings of FACTS devices in
transmission lines. The simulation is performed on IEEE30 bus power system
with more than one TCSC, modelled for steady state studies.
CHAPTER
2
2. FACTS DEVICES IN AC
POWER SYSTEM
2.1
FACTS CONTROLLERS TO A.C POWER SYSTEMS
To achieve both
operational reliability and financial profitability, it has become clear that
more efficient utilization and control of the existing transmission system
infrastructure is required. Power electronics based equipment, or Flexible AC
Transmission Systems (FACTS), provide proven technical solutions to address
these new operating challenges being presented today. FACTS technologies allow
for improved transmission system operation with minimal infrastructure
investment, environmental impact, and implementation time compared to the
construction of new transmission lines. Traditional solutions to upgrading the
electrical transmission system infrastructure have been primarily in the form
of new transmission lines, substation, and associated equipment. However, as
experiences have proven over the past decade or more, the process to permit,
site, and construct new transmission line has become extremely difficult,
expensive, timeconsuming, and controversial. FACTS technologies provide
advanced solutions as costeffective alternatives to new transmission line
construction.
2.1.1 AC Power
Power is defined as the rate of flow of energy past a given point. In
alternating current circuits, energy storage elements such as inductance and
capacitance may result in periodic reversals of the direction of energy flow.
The portion of power flow that averaged over a complete cycle of the AC
waveform, results in net transfer of energy in one direction is known as real
power. On the other hand, the portion of power flow due to stored energy, which
returns to the source in each cycle, is known as reactive power.
2.1.2 Real, Reactive and Apparent Power
Consider a simple alternating current (AC) circuit consisting of a source
and a load, where both the current and voltage are sinusoidal. If the load is
purely resistive, the two quantities reverse their polarity at the same time,
the direction of energy flow does not reverse, and only real power flows. If
the load is purely reactive, then the voltage and current are 90 degrees out of
phase and there is no net power flow. This energy flowing backwards and
forwards is known as reactive power. A practical load will have resistive,
inductive, and capacitive parts, and so both real and reactive power will flow
to the load.
If a capacitor and an inductor are placed in parallel, then the currents
flowing through the inductor and the capacitor tend to cancel out rather than
adding. Conventionally, capacitors are considered to generate reactive power
and inductors to consume it. This is the fundamental mechanism for controlling
the power factor in electric power transmission; capacitors (or inductors) are
inserted in a circuit to partially cancel reactive power of the load.
The apparent power is the product of voltage and current. Apparent power is
handy for sizing of equipment or wiring. However, adding the apparent power for
two loads will not accurately give the total apparent power unless they have
the same displacement between current and voltage (the same power factor).
Engineers use the following terms to describe energy flow in a system (and
assign each of them a different unit to differentiate between them):
·
Real power (P) 
unit: watt (W)
·
Reactive power (Q)  unit: voltamperes
reactive (var)
·
Complex power (S)  unit: voltampere
(VA)
·
Apparent Power (S) , that is, the
absolute value of Complex power S  unit: voltampere (VA)
In the diagram 3.1, P is
the real power, Q is the
reactive power (in this case positive), S
is the complex power and the length of S
is the apparent power.
Reactive power does not transfer energy, so it is represented as the
imaginary basis. Real power moves energy, so it is the real basis.
Figure 3.1 The apparent power is the
vector sum of real and reactive power
The unit for all forms of power is the watt (symbol: W), but this unit is
generally reserved for real power. Apparent power is conventionally expressed
in voltamperes (VA) since it is
the product of rms voltage and rms current. The unit for reactive power is
expressed as "Var", which stands for voltamperes reactive. Since
reactive power flow transfers no net energy to the load, it is sometimes called
"wattles" power.
Understanding the relationship between these three quantities lies at the
heart of understanding power engineering. The mathematical relationship among
them can be represented by vectors or expressed using complex numbers,
S = P +
jQ
The complex
value S is referred to as the complex power.
Table 2.1 Active and Reactive power
Instantaneous
power p=


P=


Instantaneous
active power

Instantaneous
reactive power

Average
active power
P=VI
cos
Called
simply active power

Average
reactive power
=0
Ignored
usually

Maximum
instantaneous active power
VI
cos
ignored
usually as is the same
quality
as P.

Maximum
instantaneous reactive power
Q=VI
sin
called
simply reactive power

2.1.3 Reactive power
Reactive power is
essential to move active power through the transmission and distribution system
to the customer. While active power is the
energy supplied, reactive power provides the important function of regulating
voltage.
Reactive power is
used to provide the voltage levels necessary for active power to do useful
work.
The sources of
Reactive power:
·
Synchronous
Generators
·
Synchronous
Compensators
·
Capacitive
and Inductive Compensators
·
Overhead
Lines and Underground Cables
Reactive power (vars) is required to maintain the
voltage to deliver active power (watts) through transmission lines. Motor loads
and other loads require reactive power to convert the flow of electrons into
useful work. When there is not enough reactive power, the voltage sags down and
it is not possible to push the power demanded by loads through the lines.
2.1.4
Reactive power Vs system voltage
Voltage drop
between two nodes 1 and 2, at voltages V_{1} and V_{2} respectively,
connected by a short transmission line of impedance R + j X is
(RP_{2} +XP_{2})/V_{2}
where P_{2},
Q_{2} is the real and reactive power at node V_{2}. For most
power networks X>> R and the voltage drop determines Q. If V1 is in phase
advance of V_{2}, then the power P flows from node1 to node2. If V_{1}
>V_{2}, then reactive power is transferred from node1 to node 2. If
by varying the excitation of generators at nodes 1 & 2 V_{2} is
made >V_{1}, then the direction of Q will be reversed from node 2 to
node1. Hence P can be sent from node 1 to node2 or from node 2 to node1 by
suitably adjusting the amount of steam (or water0 admitted to the turbine and Q
can be sent in either direction by adjusting the voltage magnitudes. These two
operations are approximately independent of each other if X>>R.
Figure 3.2 Voltage
collapse phenomenon
2.1.5
Complex power flow
Consider
two ideal voltage sources connected by a line of impedance
Z=R + jX as shown in figure 3.3 below
Figure 3.3 Two
interconnected voltage sources
Let the phasor voltage be
V_{1 = }V_{1}
_{1 }and V_{2}
=V_{2}
_{2.}For the assumed direction of current
 V_{1 }
_{1}   V_{2} _{ }
_{2}
 Z

=
_{1 }

_{2} 
The complex power S_{12} is given by _{ }
S_{12} = V_{1}
I^{*}_{12}
=
Î´_{1 }[
Î³ –Î´_{1} 
Î³ –Î´_{2}]
=
Î³ 
Î³ +Î´_{1} – Î´_{2}
Thus, the real and reactive powers at the sending end
are
Power system
transmission lines have small resistance compared to the reactance. Assuming R = 0 (i.e., Z = X
90^{0}), the above equations become
Since R = 0, there are no transmission line losses and
the real power sent equals the real power received.
2.1.6
Power system control
When discussing
the creation, movement, and utilisation of electrical power, it can be
separated into three areas,
·
Generation
·
Transmission
·
Distribution
The three main
variables that can be directly controlled in the power system to impact its
performance are:
·
Voltage
·
Angle, Î´ and
·
Impedance
2.2
FACTS DEVICES
Some of the FACTS
controllers used for power system control are,
Table
2.2 Types of FACTS Devices
Type

Parameter Controlled

FACTS
Devices

Series
Controllers

Series

TCSC,
SSSC, TCPST

Shunt
controllers

Shunt

SVC,
STATCOM

Combined
SeriesShunt
Controllers

Series

UPFC

·
STATCOM  Static
Synchronous Compensator
·
SVC  Static Var Compensator
·
TCSC  Thyristor Controlled Series Compensator
·
TCPST  Thyristor Controlled Phase Shifting
Transformer
·
UPFC  Unified Power Flow Controller
·
SSSC  Static Synchronous Series Compensator
Each of the above
mentioned (and similar) controllers impact voltage, impedance, and/or angle
(and power).
A STATCOM operated
as a shuntconnected static var compensator whose capacitive or inductive
output current can be controlled independent of the AC system voltage. A SVC is
a shunt connected static var generator or absorber whose output is adjusted to
exchange capacitive or inductive current so as to maintain specified bus
voltage. A SSSC can be operated without an external electric energy source as a
series compensator whose output voltage is in quadrature with 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.
UPFC is a
combination of STATCOM and SVC which are coupled via a common DC link. It is
able to control the transmission line voltage, impedance and angle or,
alternatively, the real and reactive power flow in the line. TCSC is a
capacitive reactance compensator which consists of a series capacitor bank
shunted by a thyristorcontrolled reactor in order to provide a smoothly
variable series capacitive reactance thereby controlling the impedance of
transmission line.
TCPST is a phase
shifting transformer adjusted by thyristor switches to provide a rapidly
variable phase angle. Super Conducting Magnetic Energy Storage (SMES) is a
super conducting electromagnetic energy storage device containing electronic
converters that rapidly injects and/or absorbs real and /or reactive power and
dynamically controls power flow in an AC system.
2.2.1
Thyristor Controlled Series Capacitor (TCSC)
Basically, the
TCSC is comprised of a capacitor in series with a transmission line in parallel
with a TCR (a pair of antiparallel thyristor’s in series with a reactor).
Figure 3.4 shows the basic circuit of a TCSC.
2.2.2.
Operation of TCSC
Figure 3.4 Thyristor Controlled Series
Capacitor (TCSC)
The device can operate in three different
modes:
i.
Bypassed
mode
In this mode the thyristor’s are
triggered to full conductance, the module behaves approximately like a parallel
arrangement of the capacitor and the inductor. If the reactive impedance of the
inductor is lower than the reactive impedance of the capacitor, the current
through the device is inductive.
ii.
Blocked
mode
The thyristor are blocked and the current through the reactor gets zero
and the arrangement acts just like a fixed capacitor.
iii.
Vernier
mode
The thyristor’s conduction is controlled by a gate signal and therefore
the TCSC has a controllable reactance in both the inductive and capacitive
regions. This last case is of interest here. The thyristor firing angles (Î±)
can vary from 90 until a maximum inductive value in an inductive operating
range, and from 180 until a minimum capacitive value in a capacitive operating
range. The maximum value of inductive impedance and the minimum value of
capacitive impedance should be set up in the design of the device to prevent a
parallel resonance between the capacitor and the TCR at the fundamental
frequency.
2.2.3
Benefits of utilizing FACTS devices
The benefits of
utilizing FACTS devices in electrical transmission systems can be summarized as
follows:
·
Better utilization of
existing transmission system assets
·
Increased System Security
·
Increased transmission
system reliability and availability
·
Increased quality of
supply for sensitive industries
·
Environmental benefits
CHAPTER 3
3. CONGESTION
MANAGEMENT
3.1
DEFINITION OF CONGESTION
In a market, when
the producers and consumers of electric energy desire to produce and consume in
amounts that would cause the transmission system to operate at or beyond one or
more transfer limits, the system is said to be congested. Congestion is defined
as the violation of one or more constraints in the network that are imposed to
reflect the physical limitation of component facilities and that need to be
satisfied so as to ensure reliability of power system. In this project an
analytical framework to solve problem arising in transmission congestion
management is considered.
3.2
CAUSES FOR CONGESTION
Congestion occurs whenever the preferred generation or demand pattern
of various market player requires the
provision of transmission services beyond the capability of the transmission
system to provide. When the constraints on the transmission networks are taken
into account, the constrained transfer capabilities of the network may be
unable to accomodate the preferred unconstrained market schedule without
violating one or more constraints.
Therefore, congestion results from
insufficient transfer capabilities to simultaneously transfer electricity
between the various buying and selling entities.
Congestion introduces unavoidable
losses in market efficiently so that not all benefits foreseen in the
restructuring of electric power industry can be fully realised. Congestion is a
major obstacle to vibrant competitive electricity markets. Congestion should be
managed.
3.3 CONGESTION
MANAGEMENT
Congestion management means the
activities of the transmission system operator to relieve transmission
constraints in competitive electricity market.
Congestion
management is about controlling the transmission system so that transfer limits
are observed.
Effective
management of the congestion is a critically important contributor to the
smooth functioning of competitive electricity market through its key role of
minimizing the impacts of congestion. Congestion is managed through optimal
location of FACTS device.
CHAPTER
4
4. PARTICLE SWARM OPTIMIZATION
4.1 Overview of PSO
Population based,
cooperative and competitive stochastic search algorithms have been very popular
in the recent year’s arena of computational intelligence. Particle Swarm
Optimization (PSO) is motivated from the simulation of social behaviour. It is a robust stochastic optimization technique based
on the movement and intelligence of swarms.
It was developed in 1995 by James Kennedy (socialpsychologist) and
Russell Eberhart (electrical engineer).It uses a number of agents (particles)
that constitute a swarm moving around in the search space looking for the best
solution. Each particle is treated as a point in a Ndimensional space which
adjusts its “flying” according to its own flying experience as well as the
flying experience of other particles. Thus
it applies the concept of social
interaction to problem solving and so it is now applied
for solving electrical engineering related problems.
4.2 pbest value and gbest value
Each particle keeps track of its coordinates in the solution space which
are associated with the best solution (fitness) that has achieved so far by
that particle. This value is called personal best, pbest.
Another best value that is tracked by the PSO is the best value obtained
so far by any particle in the neighborhood of that particle. This value is
called gbest.
The basic concept of PSO lies in accelerating each particle toward its
pbest and the gbest locations, with a random weighted acceleration at each time
step as shown in Figure 3.5
V^{k}

S^{k}

V^{k+1}

S^{k+1}

V_{pbest}

V_{gbest}

y

x

Figure 3.5 Concept of modification of a
searching point by PSO
S^{k }:
current searching point
S^{k+1 }:^{ }modified searching point
V^{k} : Current velocity
V^{k+1 } :
modified velocity
V_{pbest }:
velocity based on pbest
V_{gbest }:
velocity based on gbest
Each particle tries to modify its position using the following information:
·
The
current positions,
·
The
current velocities,
·
The
distance between the current position and pbest,
·
The
distance between the current position and the gbest.
Start

Initialize
particles with random position and velocity vectors

Stop:
giving gbest, optimal solution.

For
each particle’s position (p) evaluate fitness

If
fitness (p) better than fitness (pbest) then pbest=p

Set
best of pBest as gBest

Update particles velocity and
position

Comparison with other evolutionary computation
techniques
Figure 3.6 Flowchart for
PSO Algorithm
4.3
Advantage of PSO
·
Unlike
in genetic algorithms, evolutionary programming and evolutionary strategies,
in PSO, there is no selection operation
·
All
particles in PSO are kept as members of the population through the course of
the run
·
PSO
is the only algorithm that does not implement the survival of the fittest.
·
No
crossover operation in PSO
4.4
Applications of PSO
The application of PSO helps in solving many of the Power system
problems. They are:
·
FACTS
device location and design
·
Economic
dispatch
·
Unit
Commitment
·
Generation
planning
·
Maintenance
Scheduling
·
Capacitor
placement
CHAPTER
5
5. POWER FLOW EQUATION
The
equation of power flow relates the power transfer between two buses and the
electrical data of the system. The electrical data comprises the receiving and
sending bus voltages, the power angle between the two buses and the series
impedance and natural capacitance of the transmission line connecting the two
buses. We consider the PI model for a transmission line (figure 3.7) and we
express the reactive power at the two ends as a function of the voltages Vs and VR and the
characteristic of the line (R, X_{L},
& X_{C}).
Figure 3.7 Transmission
line connecting two voltage buses
Using
the phasor representation, (bar symbol above the respective quantity) we have
for the voltages,
and
for the currents,
The
complex power for each end can be calculated by multiplying the voltage with
the complex conjugate of the corresponding current. As we are interested to
evaluate the reactive power Q (according with our definition the
amplitude of the
instantaneous reactive power), we take the complex part of the complex powers
which are
Considering
a small resistance comparative with the inductance (R<<L), the above
equation can be simplified. This assumption does not affect the results as the reactive power is stored,
absorbed or produced by the reactive part of the network (inductance or
capacitance). The simplified equations for the reactive power at the two end
are then
So
far the standard procedure followed by textbooks to introduce the power flow
equations was followed. As Q_{R} and Qs are not equal, the reactive power
loss is introduced as the
difference of the two expressions
The
reactive power loss is explained to be the reactive power produced or absorbed
by the line, depending on its sign. Accordingly, for a piece of electric network, the reactive power injected at one
end will be the reactive power at the other end plus the reactive power
produced or absorbed by the network element.
This
unanimously accepted interpretation of reactive power loss contradicts the
previous unanimously accepted interpretation that the reactive energy is
neither consumed nor produced but oscillates among different part of the
electric network. Here we would like to remind the reader that in fact not the
power is lost, neither the power is flowing but rather the energy.
The
confusion lies on the fact that the same term reactive power is used for the amplitude of the
instantaneous reactive power and for the average of reactive power, two completely
different concepts. The same confusion is avoided for the active power, as the amplitude of the
instantaneous active power and the average of active power happen to be the same.
The confusion is removed by
interpreting the two facts as following
1.
The average of reactive power is zero, is interpreted as the
energy is flowing for half a cycle in one direction and for the second half a
cycle, the same amount of energy is flowing in the opposite direction.
Therefore it is impossible to have a gain or loss of reactive energy (power).
2.The “loss of reactive power” should be seen
as a loss in the amplitude of
the instantaneous reactive power that in fact is not a loss in real
power.
5.1 Line flows
_{
}
Figure 3.8 Transmission line model for
calculating line flows
Consider the line connecting the 2
buses ‘i’&’j’ .The line currents are,
Iij=Il+Ii0;
Iji=Il+Ij0;
The complex powers are,
Sij=Vi*conj(Iij);
Sji=Vj*conj(Iji);
CHAPTER
6
6. PROBLEM
FORMULATION
In this project,
more than one TCSC’s are considered to maximize the power flow and reduce the
congestion.
Each
potential solution for the optimization problem is considered as a particle in
PSO. Initially the particles are randomly generated. All particles in PSO are
kept as members of the population through the course of the run. It is the
velocity of the particle, which is updated according to its own previous best
solution of its companions. The particles fly with the updated velocities .Thus
the PSO optimization problem is used to find the optimal settings of FACTS
devices with the objective of maximizing the power flow.
6.1
Optimal Placement of TCSC
The essential idea of the proposed TCSC
placement approach is to determine a branch, which has maximum power flow. Initially,
the TCSC is placed in every branch of the IEEE 30bus system and the power
flows are calculated. Then, the maximum difference in line power flows are
arranged in descending order for different locations of the TCSC. Optimal
location and number of TCSC’s are obtained for the branches based upon the maximum
power flow through lines.
6.2
Optimal settings of TCSC
FACTS devices constrains:
The FACTS device
limit is given by,
0.7
X_{L}<X_{TCSC}<0.2X_{L}
Where,
X_{L} original line reactance in pu
X_{TCSC}reactance added to the line where TCSC
is placed in pu
6.3
Proposed method of PSO implementation
In PSO, particles
fly in the search space with a velocity dynamically adjusted according to its
own flying experience and its own flying experience and its companies flying
experience. The position of each agent is represented in XY plane with
position (S_{x}, S_{y}),
V_{x} (velocity along Yaxis). Modification of the agent position is
realized by the position and velocity information.
Bird flocking
optimizes a certain objective function. Each agent knows its best value so far,
called ‘P_{best}’, which contains the information on position and
velocity. This information is the analogy of personal experience of each agent.
Moreover, each agent knows the best value so far, in the group ‘G_{best}’
among ‘P_{best}’. This information is the analogy of knowledge, how the
other neighbouring agents have performed. Each agent tires to modify its
position by considering current positions (S_{x},S_{y}), current
velocities (V_{x},V_{y}), the individual intelligence(P_{best}),
and the group intelligence (G_{best}).
The following
equations are utilized, in computing the position and velocities, in the XY
plane:
Where,
V_{id} : Particle velocity
X_{id} : current particle solution
P_{id} : Pbest
P_{gd} : Gbest
rand : random number between(0, 1)
C_{1} and
C_{2} : learning factors,
c1min=c2min=0.5; c1max=c2max=2.5
C_{1}=c1 max((c1 maxc1 min)/iter max)*iter
C_{2}=c2 min+ ((c2 maxc2min)/iter max)*iter
W is
weighting factor given by,
Where,
W max  initial
weight (taken as 0.9);
W min  final
weight (taken as 0.1)
iter 
current iteration number
iter max  maximum iterations
The minimum and maximum velocity is kept between 0.2
and +0.2.
6.4
PSO Algorithm for Congestion management
Step
1: Each particle is initialized with
random position and velocity
vectors.
Step
2: The initial population of individuals
is created by satisfying the FACTS device’s constraints.
Step
3: For each individual in the
population, the fitness function is evaluated.
Step
4: The velocity is updated by equation (2.5)
and new population is created by equation (2.6).
Step
5: For each individual in the
population, the fitness function is evaluated by using the updated velocity.
Step
6: Initial and updated fitness values
are combined and the better individuals are passed to the next iteration.
Step
7: If maximum iteration number is reached, then go to next step else go to step
3.
Step 8: Print the
best individual’s settings and loss value.