Congestion Management in Deregulated Power Systems using Series FACTS Controller

International Journal of Research in Advanced Technology - IJORAT Vol. 2, Issue 2, FEBRUARY 2016

All Rights Reserved © 2016 IJORAT 1

Congestion Management in Deregulated Power

Systems using Series FACTS Controller

K.Ganesan1, K.Pandiarajan

2, R.Sathishkumar

3

PG Scholar, Electrical and Electronics Engineering, Regional Office, Anna University, Madurai, India1.

The HOD, Electronics and Communication Engineering, Sasurie College of Engineering., Vijayamangalam, India2.

Faculty, Electrical and Electronics Engineering, Regional Office, Anna University, Madurai, India3.

Abstract: The extensive restructuring process in the electric power industry has led to more demanding and different

usage of transmission grids irrespective of the designed limits. This has resulted in unanticipated congestion interfaces in

the regional transmission network. The system is however is not capable of withstanding the rapidly changing demands of

the competitive markets. Thus an efficient and sensible way of dealing with the congestion has become vital to maintain

the system reliability. This paper investigates the prediction of the optimal location and size of the Thyristor-Controlled

Series Capacitor (TCSC) so as to alleviate the congestion in a deregulated environment. The location of TCSC is identified

with the help of priority list based on the locational marginal price (LMP) difference between the buses. As LMP can be

easily calculated from the security constrained optimal power flow, this method reduces the computational difficulties.

Also the PSO algorithm fixes the optimal size of the TCSC which relieves the congestion thereby reduces the LMP and the

overall generation cost. The effectiveness of the proposed approach is tested in 6 bus and 30 bus systems under MATLAB

environment.

Keywords: Deregulated power systems, Thyristor-controlled series capacitor, Locational marginal price, Particle swarm

optimization, Congestion management.

I. INTRODUCTION

The restructuring process of the power industry

starts with the separation of the transmission activities

from the generation activities. The subsequent step was to

introduce competition in generation activities, either

through the creation of power pools, provision for direct

bilateral transactions or bidding in the spot markets. On

the other hand, the transmission system having significant

economies of scale consequently had a tendency to

become a monopoly. Thus it was felt necessary to

introduce regulation in transmission so as to prevent it

from overcharging for its services and to manage the

congestion [1]. The condition where overloads in

transmission lines or transformers occur is called

congestion. Congestion could prevent system operators

from dispatching additional power from a specific

generator. Congestion may occur due to various reasons,

such as transmission line outages, generator outages,

changes in energy demand and uncoordinated transactions.

Congestion may result in preventing new contracts,

infeasibility in existing and new contracts, additional

outages and monopoly of prices in some regions of power

systems and damages to system components. Congestion

may be prevented by means of rights, reservations and

congestion pricing. Also, it can be corrected by applying

controls such as phase shifters, tap transformers, TCSC,

redispatch of generation and load curtailment [2].

Several congestion management methods have

been presented in the literature. In [3] the authors‟

proposed a demand side based congestion management

approach to manage transmission line congestion for a

pool market model. FACTS devices like SVC and TCSC

were used to manage the function from single line

congestion case to three line congestion cases. The authors

have proved congestion cost was less after connecting

FACTS devices rather than without connecting. LMP

difference and congestion rent contribution methodologies

for locating series FACTS devices to manage congestion

in deregulated electricity markets have been depicted in

[4]. These methods were compared with sensitivity factor

method. The results proved that the best location of TCSC

was identified by proposed methods. The status of

congestion after placing the TCSC was not addressed. In

[5] an alleviation of overloads by redispatch of generators

with minimum rescheduling cost has been proposed. The

optimal rescheduling of active powers of generators was

selected based on the generator sensitivity to the congested

line, utilizing fuzzy adaptive bacterial foraging (FABF)

algorithm. In [6] particle swarm optimization based social

welfare maximization and congestion management has

been presented. The congestions were managed by using

rescheduling of generators. The participation of generators

was selected using generator sensitivities to the power

flow on overloaded lines. In [7] the authors‟ proposed a

type of security-constrained OPF for minimizing total

generation costs using FACTS devices. In [8] fuzzy

inference based generator active power rescheduling for

managing network congestion under normal and

contingency conditions has been discussed. The network

congestions were managed using counter flow information

obtained from the tracing of network virtual flows due to

various sources. In [9] the authors‟ proposed an optimal

congestion management approach in a deregulated

http://ieeexplore.ieee.org/search/searchresult.jsp?searchWithin=p_Authors:.QT.Thukaram,%20S.S.D..QT.&newsearch=partialPref



electricity market using particle swarm optimization with

time-varying acceleration coefficients. Minimum

redispatch cost was taken as objective function. The re-

dispatched generators were selected based on values of

generator sensitivity. PSO-TVAC is used to determine the

minimum redispatch cost. In [10] min cut algorithm has

been used to select proper location of TCSC for secured

optimal power flow under normal and contingencies

operating condition. They proposed two-step approach.

First, the optimal location of the TCSC in the network

must be ascertained by min cut algorithm and then, the

optimal power flow with TCSC under normal and

contingencies operating condition was solved. Reactive

power loss reduction and real power flow performance

index methods for the optimal location of TCSC have

been used in [11]. In reactive power loss reduction

method, TCSC were placed in a line having the most

positive loss sensitivity index. In real power flow

performance index method, TCSC were placed in a line

having most negative sensitivity index. In [12] the

authors‟ presented a multi-objective framework for

congestion management where three competing objective

functions such as total operating cost, voltage and

transient stability margins were simultaneously optimized.

Optimal location and sizing of series FACTS devices on

the most congested branches were determined by a priority

list based on locational marginal prices. In [13], TCSC has

been used for congestion management in a power system.

Minimization of severity index was taken as objective

function. The optimal location of TCSC was done by

sensitivity analysis and sizing of TCSC by using genetic

algorithm. In [14], the authors‟ used SQP techniques to

find the optimal number and placement of FACTS devices

to manage the transmission congestion. An adaptive

bacterial foraging algorithm for transmission congestion

management has been depicted in [15]. Congestions were

managed by rescheduling of generators. In this paper,

LMP difference based optimal location and PSO based

optimal sizing of TCSC are presented.

Section 2 presents the optimization problem

formulation for congestion management. Section 3 and 4

presents overview of Particle Swarm Optimization (PSO)

and Thyristor-Controlled Series Capacitor (TCSC)

respectively. Optimal location and sizing of TCSC is

given in section 5. The results achieved by applying the

proposed method on 6 bus and 30 bus systems are

presented in section 6. Finally, conclusion is given in

Section 7.

II. PROBLEM FORMULATION

A. Objective Function

The objective of the proposed method is to minimize the

total generation cost. The problem is stated

mathematically as

i j

DjjGiiPP

PBPCMinDjGi

)()(,

(1)

where, PGi and PDj are the active powers of pool generator

i with bid price Ci and pool load j with offer price Bj

respectively.

B. Problem constraints

Generation/load balance Equation

DG N

j

LDj

N

i

Gi PPP

11

0 (2)

Generator constraints

max,min, GiGiGi PPP (3)

max,min, GiGiGi QQQ (4)

Bus voltage constraints

max,min, iii VVV (5)

Transmission line flow limits

max

ijij SS

(6)

TCSC reactance limit

max,min, TCSCiTCSCiTCSCi XXX (7)

The working range of TCSC is considered as follows.

lTCSCl XXX 2.08.0 (8)

where

TCSCX =TCSC reactance and lX =Reactance of the line

where TCSC is located.

III. OVERVIEW OF PARTICLE SWARM

OPTIMIZATION

PSO is a simple and efficient population-based

optimization method [16]. PSO simulates the behaviors of

bird flocking. 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, N dimensional space which adjusts its “flying”

according to its own flying experience as well as the flying

experience of other particles. 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 particle 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 global best (gbest).The

basic concept of modification of a searching point by PSO

is shown in figure1.

Figure 1: Concept of modification of a searching point

by PSO

where, pkix current searching point,

1pk

ix modified

searching point,

pkiv current velocity,

1pkiv modified velocity,

ip particle best position

and g

kp global best position.

Current

Motion

Influence

Particle

Memory

Influence

Swarm

Influence

pkix

1pkix

1pkiv

g

kp

ip

pkiv



PSO is initialized with a group of random

particles (solutions) and then searches for optima by

updating generations. In every iteration, each particle is

updated by two "best" values such as pbest and gbest.

After finding the two best values, the particle updates its

velocity and positions using the following Equations (9)

and (10).

)()(

)()(

)(2

)(1

)()1(

uii

uii

ui

ui

PgbestrandC

PpbestrandCVwV

(9)

)1()()1(

ui

ui

ui VPP (10)

where

The term )()()(u

ii Ppbestrand is called particle

memory influence.

The term )()()(u

ii Pgbestrand is called swarm

influence. )(u

iV is the velocity of thi particle at iteration u must lie

in the range.

max)(

min VVVu

i (11)

The parameter maxV determines the resolution, or

fitness, with which regions are to be searched between the

present position and the target position. If maxV is too

high, particles may fly past good solutions. If minV is too

small, particles may not explore sufficiently beyond local

solutions [17]. The constants 1C

and 2C pull each

particle towards pbest and gbest positions. The inertia

weight w is considered as an important parameter for the

convergence of the algorithm. A large inertia weight

facilitates exploration, i.e., searching newer areas, while a

small value tends to facilitate exploitation, i.e., a finer

searching of current search area. Thus, the choice of

inertia weight should be carefully made. Suitable selection

of inertia weight provides a balance between global and

local explorations, thus requiring less iteration on average

to find a sufficiently optimal solution. In general, the

inertia weight w is set according to the following

equation [18].

iteriter

wwww

max

minmaxmax (12)

where

maxw Maximum value of weighting factor,

minw Minimum value of weighting factor, w inertia

weighting factor, maxiter maximum number of

iterations and iter current number of iteration.

IV. THYRISTOR-CONTROLLED SERIES CAPACITOR

(TCSC)

Thyristor-controlled series capacitors (TCSC) are

connected in series with the lines. The effect of a TCSC on

the network can be seen as a controllable reactance

inserted in the related transmission line that compensates

for the inductive reactance of the line. This reduces the

transfer reactance between the buses to which the line is

connected. This leads to an increase in the maximum

power that can be transferred on that line in addition to a

reduction in the effective reactive power losses.

The series capacitors also contribute to an

improvement in the voltage profiles. Figure2 shows a

model of a transmission line with a TCSC connected

between buses i and j. The transmission line is represented

by its lumped π-equivalent parameters connected between

the two buses. During the steady state, the TCSC can be

considered as a static reactance -jXC. This controllable

reactance is directly used as the control variable to be

implemented in the power flow equation.

This controllable series line compensation can be

applied to achieve full utilization of transmission assets by

controlling the power flow in the lines, preventing loop

flows and with the use of fast controls, minimizing the

effect of system disturbances thereby reducing traditional

stability margin requirements.

The basic idea behind series capacitive

compensation is to decrease the overall effective series

transmission impedance (Xeff) from the sending end to the

receiving end. The power transmission over a single line is

characteristics by the equation

sinX

VVP RS (13)

The effective transmission impedance Xeff, with

the series capacitive compensation is given by

Ceff XXX (14)

or XkX eff )1( (15)

where k is degree of series compensation, i.e.

XXk C ; Its values range between 0 and 1

The series compensator is primarily applied to

solve power flow problems. These problems may be

related to the length of the line or the structure of the

transmission network. The electric length of the line can

be shortened to meet power transmission requirements by

fixed (percent) compensation of the line.

Figure 2: Model of a TCSC

Network structure related problems, which

typically result in power flow unbalance, as well as

parallel and loop power flows, may require controlled

series compensation, particularly if contingency or

planned network changes are anticipated.

Fixed or controlled series capacitive compensation

can also be used to minimize the end-voltage variation of

radial lines and prevent voltage collapse. Series

compensation, appropriately controlled to counteract

prevailing machine swings, can provide significant

transient stability improvement for post-fault systems and

can be highly effective in power oscillation damping.

R+jX

jBc jBc

-jXC Sij

Bus i Bus j

Sji



V. OPTIMAL LOCATION AND SIZING OF TCSC

A. Optimal location and sizing of TCSC using LMP

difference method

Locational Marginal Price (LMP) is the marginal

cost of supplying, at least cost, the next increment of

electric demand at a specific location (node) on the

electric power network, taking into account both supply

(generation/import) bids and demand (load/export) offers

and the physical aspects of the transmission system

including transmission and other operational constraints.

LMP (nodal price) at bus i can be determined using

the following equation

j

jijfirefi SFXL )()( Re

(16)

ii congestionlossrefi (17)

where

i Nodal price at bus i; ref Nodal price at the

reference bus; iloss Marginal cost of losses from ref.

bus to bus i; icogestion Marginal cost of transmission

congestion from reference bus to bus i; iL Marginal loss

factor at bus i (∂Ploss/∂Pi); j Shadow price of

constraint j and jiSF Shift factor for real load at bus i

on constraint j.

The step by step procedure of LMP difference method for

optimal location of TCSC is given below.

Step 1: Run the base case OPF to calculate the LMP at all

buses and the power flow across all line sections.

Step 2: Determine the absolute value of the LMP

difference for all buses and prioritize the values

in descending order of magnitude to form LMP

difference table.

Step 3: From the LMP difference table, place the TCSC

in the lines, which have high values of LMP

differences one by one.

Step 4: Using PSO algorithm, the size of TCSC are

optimized for the selected lines in step 3. The

detailed steps of PSO algorithm are given in

section 5.2.

Step 5: TCSC are placed one by one until the congestion

on the test systems is relieved.

Step 6: Determine the LMP values at all buses and total

generation cost.

B. Optimal sizing of TCSC based on particle swarm

optimization

The step by step procedure of PSO algorithm for

optimal sizing of TCSC is given below.

Step 1: Initialize the PSO parameters such as the particle

size (NP), number of generations or iterations (G),

and number of variables to be optimized, limits of

each variable in the particle, acceleration

constants and inertia weight (w). NP =20, G=100,

Cognitive Constant C1=2, Social Constant C2=2

and w = 0.9-0.4.

Step 2: An initial population is randomly generated

considering the variables to be optimized.

Step 3: For each particle in the population, run Newton

Raphson power flow under base case conditions

for the test systems and evaluate the objective

function using equation (1).

Step 4: Find particle best )( pbest and global

best )(gbest .

Step 5: Increase the iteration count.

Step 6: A new population is created by changing the

velocity, position of the particle.

Step 7: Evaluate the objective function values for each

new individual.

Step 8: Update pbest and gbest values by comparing

current fitness values with local best and global

best values.

Step 9: Update pbest and gbest .

Step 10: If stopping criteria is satisfied, then the best

individual is obtained, otherwise repeat the

procedure from step 5.

VI. SIMULATION RESULTS

The simulation studies are performed on computer

having 2.27 GHz Intel 5 processor with 2 GB of RAM in

MATLAB environment [19]. The following two cases are

considered for the study.

A. 6-Bus System under Base Case Condition

The objective function in this case is to

alleviate the congestion in the network under base case

conditions thereby minimizing the total generation cost.

Form the power flow results of 6 bus system under base

case before placing TCSC, it is observed that the line 2-4

gets congested and total generation cost of 3143.97 $/h.

The locational marginal price (LMP)

value of different buses is shown in Table I. The LMP

difference values between buses are calculated and the

priority list based on LMP differences is shown in Table

II.

TABLE I LMP VALUES OF THE BUSES

Bus Number LMP

($/MWhr) Bus Number

LMP ($/MWhr)

1 12.4922 4 15.6741

2 11.5646 5 12.9389

3 11.8766 6 12.2062

TABLE II PRIORITY LIST BASED ON LMP DIFFERENCES

From i-j LMP Difference

($/MWhr) From i-j

LMP Difference

($/MWhr)

2-4 4.1095 5-6 0.7327

1-4 3.1819 2-6 0.6416

4-5 2.7352 1-5 0.4467

2-5 1.3743 3-6 0.3295

3-5 1.0623 2-3 0.3120

1-2 0.9276



Line flow data and constraint status before and

after placing TCSC is shown in Table III. The generation

cost convergence characteristics for optimal sizing of

TCSC by PSO is shown in Figure3.

TABLE III LINE FLOW DATA AND CONSTRAINT STATUS

From

i-j

MVA limit

without TCSC with TCSC

P (MW)

Q (MVAR)

Status P

(MW) Q

(MVAR) Status

1-2 40 15.41 -9.58 -1.98 -1.21

1-4 60 33.95 22.50 34.69 32.63

1-5 40 27.86 12.80 17.29 14.41

2-3 40 0.29 -11.76 -0.93 -11.52

2-4 60 41.74 43.11 yes 44.12 32.33 relieved

2-5 30 17.35 14.93 19.43 13.71

2-6 90 25.03 12.67 24.76 12.51

3-5 70 23.18 21.57 26.29 19.53

3-6 80 47.50 59.90 49.89 58.99

4-5 20 3.21 -4.71 6.32 -2.91

5-6 40 -0.90 -9.03 -3.01 -7.91

The optimal values of reactance of TCSC using

PSO are shown in Table IV.

TABLE IV OPTIMAL REACTANCE VALUES OF TCSC

From i-j Reactance of TCSC

2-4 -0.0200

1-4 -0.1095

Form the power flow results of 6 bus system

under base case after placing TCSC, it is observed that the

congestion is relieved on line 2-4 also the total generation

cost is reduced to 3124.07 $/h.

0 10 20 30 40 50 60 70 80 90 1003225

3230

3235

3240

3245

Iteration Number

Gen

era

tio

n C

ost

($

/h)

Figure 3 Generation cost convergence characteristics for the optimal TCSC size (6 bus system)

B. 30-Bus System Under Base Case Condition

The objective function in this case is to alleviate the

congestion in the network under base case conditions thereby

minimizing the total generation cost. Form the power flow

results of 30 bus system under base case before placing TCSC,

it is observed that the lines 6-8 and 25-27 get congested and

total generation cost of 576.89 $/h.

The locational marginal price (LMP) value of different

buses is shown in Table V.

The LMP difference values between buses are

calculated and the priority list based on LMP differences is

shown in Table VI.

TABLE V LMP VALUES OF THE BUSES

Bus

Number

LMP

($/MWhr)

Bus

Number

LMP

($/MWhr)

Bus

Number

LMP

($/MWhr)

1 3.6617 11 3.8232 21 3.8540

2 3.6891 12 3.8100 22 3.8425

3 3.7542 13 3.8100 23 3.8133

4 3.7709 14 3.8677 24 3.8844



5 3.7444 15 3.8561 25 3.9320

6 3.7791 16 3.8488 26 3.9987

7 3.8008 17 3.8625 27 3.9157

8 5.3827 18 3.9112 28 4.1058

9 3.8232 19 3.9262 29 3.9664

10 3.8462 20 3.9100 30 4.0508

TABLE VI PRIORITY LIST BASED ON LMP DIFFERENCES

From i-j LMP Difference

($/MWhr) From i-j

LMP Difference ($/MWhr)

6-8 1.6037 15-23 0.0428

8-28 1.2769 22-24 0.0419

6-28 0.3267 4-12 0.0391

28-27 0.1901 12-16 0.0388

27-30 0.1351 1-2 0.0274

1-3 0.0925 9-10 0.0230

2-6 0.0900 6-7 0.0217

29-30 0.0844 3-4 0.0167

2-4 0.0818 25-27 0.0164

23-24 0.0711 10-17 0.0163

6-10 0.0671 19-20 0.0162

25-26 0.0666 18-19 0.0151

10-20 0.0638 16-17 0.0137

12-14 0.0577 14-15 0.0116

5-7 0.0565 21-22 0.0114

2-5 0.0553 4-6 0.0082

15-18 0.0551 10-21 0.0078

27-29 0.0507 10-22 0.0037

24-25 0.0476 12-13 0

12-15 0.0461 9-11 0

6-9 0.0441

The optimal values of reactance of TCSC using PSO

are shown in Table VII. Line flow data and constraint status

before and after placing TCSC is shown in Table VIII. The

generation cost convergence characteristics for optimal sizing

of TCSC by PSO is shown in Figure4.

TABLE VII OPTIMAL REACTANCE VALUES OF TCSC

From i-j Reactance of TCSC

6-8 -0.0080

8-28 -0.0903

Form the power flow results of 30 bus system under

base case after placing TCSC, it is observed that the

congestion is relieved on lines 6-8 and 25-27 also the total

generation cost is reduced to 574.51 $/h.

TABLE VIII LINE FLOW DATA AND CONSTRAINT STATUS

From

i-j

Line

limit

without TCSC with TCSC

P

(MW)

Q

(MVAR) Status

P

(MW)

Q

(MVAR) Status

1-2 130 21.04 -2.34 22.44 -3.82

1-3 130 20.50 -3.10 21.35 2.49

2-4 65 18.63 -5.85 20.01 1.89

3-4 130 17.88 -3.22 18.73 2.65

2-5 130 14.36 -0.69 15.19 3.01

2-6 65 21.66 -4.21 23.41 4.44

4-6 90 17.58 5.68 19.64 11.64

5-7 70 14.25 0.96 15.08 4.92

6-7 130 8.70 8.46 7.86 4.24

6-8 32 23.82 21.37 yes 20.96 22.22 relieved

6-9 65 7.27 -8.27 8.28 -3.20

6-10 32 4.15 -4.73 4.73 -1.83

9-11 65 0 0 0 0

9-10 65 7.27 -8.54 8.28 -3.35

4-12 65 11.06 -15.24 11.24 -7.31

12-13 65 -16.20 -34.01 -17.34 -25.36

12-14 32 4.68 2.08 4.89 2.14

12-15 32 6.07 3.18 6.84 3.55

12-16 32 5.31 5.04 5.65 4.42

14-15 16 -1.55 0.41 -1.34 0.48

16-17 16 1.76 3.14 2.10 2.53

15-18 16 7.20 3.75 7.26 3.19

18-19 16 3.93 2.70 4.0 2.16

19-20 32 -5.58 -0.73 -5.51 -1.26

10-20 32 7.85 1.58 7.78 2.11

10-17 32 7.27 2.73 6.92 3.34

10-21 32 -4.43 -11.56 -3.19 -7.10

10-22 32 -5.06 -8.39 -4.29 -5.75

21-22 32 -21.97 -22.87 -20.71 -18.34

15-23 16 -10.92 -2.72 -10.0 -1.74

22-24 16 -4.46 2.59 -2.03 4.60

23-24 16 2.03 2.39 3.51 3.54

24-25 16 -11.18 -1.75 -7.28 1.38

25-26 16 3.54 2.36 3.54 2.36

25-27 16 -14.96 -4.52 yes -10.92 -1.15 relieved

28-27 65 -11.45 -21.09 -8.37 -9,39

27-29 16 6.16 1.65 6.16 1.65



27-30 16 7.10 1.63 7.10 1.64

29-

30 16 3.68 0.60 3.68 0.60

8-28 32 -6.29 -9.07 -9.13 -8.06

6-28 32 -5.05 -14.50 0.85 -4.35

0 10 20 30 40 50 60 70 80 90 1000

0.5

1

1.5

2

2.5x 10

4

Iteration Number

Gen

era

tio

n C

ost

($

/h)

Figure 4 Generation cost convergence characteristics for the optimal TCSC size (30 bus system)

VII. CONCLUSION

In this paper we reviewed LMP difference based optimal

location and PSO based optimal sizing of series FACTS

controller, Thyristor-Controlled Series Capacitor (TCSC) for

congestion management in deregulated power systems. The

proposed methodologies have been tested and examined on 6

bus system and 30 bus system under base case conditions. In

case 1, the proposed method relieves the congestion on line

2-4 and total generation cost is reduced from 3143.97 $/h to

3124.07 $/h. In case 2, the proposed method relieves the

congestion occur on lines 6-8 and 25-27. The Total generation

cost is reduced from 576.89 $/h to 574.51 $/h. The result

shows that the proposed methodology is capable of managing

the transmission congestion with minimum generation cost.

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Congestion Management in Deregulated Power Systems using Series FACTS Controller

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