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.

The FACTS device considered in this work is TCSC. In this project, Particle Swarm Optimization (PSO) algorithm is used for finding the optimal settings of installed FACTS device. The proposed approach used for locating and finding the optimal settings of FACTS devices reduces the congestion. A sample IEEE- 30 bus system is used to demonstrate the effectiveness of the proposed approach.


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 non-traditional 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 IEEE-30 bus power system with more than one TCSC, modelled for steady state studies.




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, time-consuming, and controversial. FACTS technologies provide advanced solutions as cost-effective 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: volt-amperes reactive (var)
·                 Complex power (S) - unit: volt-ampere (VA)
·                 Apparent Power (|S|) , that is, the absolute value of Complex power        S - unit: volt-ampere (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 volt-amperes (VA) since it is the product of rms voltage and rms current. The unit for reactive power is expressed as "Var", which stands for volt-amperes 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=
Instantaneous active power

Instantaneous reactive power
Average active power
P=VI cos
Called simply active power
Average reactive power
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 V1 and V2 respectively, connected by a short transmission line of impedance R + j X is
(RP2 +XP2)/V2

where P2, Q2 is the real and reactive power at node V2. For most power networks X>> R and the voltage drop determines Q. If V1 is in phase advance of V2, then the power P flows from node1 to node2. If V1 >V2, then reactive power is transferred from node1 to node 2. If by varying the excitation of generators at nodes 1 & 2 V2 is made >V1, 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 V1 = |V1| 1    and V2 =|V2| 2.For the assumed direction of current

                                     | V1 | 1 - | V2 | 2
                            I12  =    
                                              | Z |
                                 = 1 - -   2 -

The complex power S12 is given by  

                           S12 = V1 I*12

  = δ1 [ γ –δ1 - γ –δ2]
                                 = γ - γ +δ1 – δ2

Thus, the real and reactive powers at the sending end are

 P12 = cos γ -  sin (γ+δ12)                                             (2.1)
Q12 = sin γ -  sin (γ+δ1-δ2)                                              (2.2)

Power system transmission lines have small resistance compared to the reactance. Assuming R = 0 (i.e., Z = X 900), the above equations become

 P12 =  sin (δ1 – δ2)                                                                  (2.3)

Q12 =  [  -  cos (δ1 – δ2)]                                                   (2.4)
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, δ and
·       Impedance


Some of the FACTS controllers used for power system control are,

Table 2.2 Types of FACTS Devices

Parameter  Controlled
FACTS Devices
Series Controllers
Shunt controllers
Series  & Shunt

·       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 shunt-connected 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 thyristor-controlled 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 anti-parallel 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 (α) 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


                        3. CONGESTION MANAGEMENT


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.


      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.


          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.      


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 (social-psychologist) 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 N-dimensional 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








   Figure 3.5 Concept of modification of a searching point by PSO

           Sk        : current searching point
Sk+1     : modified searching point
Vk      : Current velocity
Vk+1   : modified velocity
Vpbest : velocity based on pbest
Vgbest : 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.


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
Text Box: Loop until max iterText Box: Loop until all particles exhaust

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



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, XL, &  XC).

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 QR  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,


The complex powers are,




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 30-bus 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 XL<XTCSC<-0.2XL           
XL- original line reactance in pu
XTCSC-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 X-Y plane with position   (Sx, Sy), Vx (velocity along Y-axis). 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 ‘Pbest’, 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 ‘Gbest’ among ‘Pbest’. 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 (Sx,Sy), current velocities (Vx,Vy), the individual intelligence(Pbest), and the group intelligence (Gbest).

The following equations are utilized, in computing the position and velocities, in the X-Y plane:

Vid=W x Vid + C1 x rand x (Pid-Xid) + C2 x rand x (Pgd-Xid)                  (2.5)
 Xid=Xid+Vid                                                                                           (2.6)                                                                                                                                          
Vid             : Particle velocity
Xid             : current particle solution
Pid              : Pbest
Pgd             : Gbest
rand          : random number between(0, 1)
C1 and C2 : learning factors,
c1min=c2min=0.5; c1max=c2max=2.5
C1=c1 max-((c1 max-c1 min)/iter max)*iter
C2=c2 min+ ((c2 max-c2min)/iter max)*iter

W is weighting factor given by,


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.