International Journal of Scientific & Engineering Research, Volume 3, Issue 5, May-2012 1

ISSN 2229-5518

Reactive Power Optimization and Voltage Stability Limit Improvement with TCSC Device through DE algorithm under Most Credible

Contingency Condition

S.Sakthivel, Dr.D.Mary, S.Ramya

Abstract - Modern power systems are at risks of voltage instability problems due to highly stressed operating conditions caused by increased load d e- mand and economical and/or environmental constraints in construction of new transmission lines. This paper proposes a Differential Evolution (DE) algo- rithm based optimal reactive power flow control task incorporating only one type of FACTS device under contingency condition. DE is efficient in explor a- tion through the search space of the problem and easy to implement. Optimal settings of control variables of generator voltages, transf ormer tap settings and location and parameter setting of thyristor controlled series capacitor (TCSC) is considered for optimal solution for rea ctive power flow control and the resultant reactive power reserves. Coordinated control of TCSC parameter and control parameters of reactive power dispatch is taken. The effec- tiveness of the proposed work is tested on IEEE-30 Bus test system under most critical line outage contingency condition.

Index Terms— FACTS devices, TCSC, Reactive Power optimization, Differ ential Evolution, Contingency Condition, Voltage Stability.

—————————— ——————————

1 INTRODUCTION

Present day power system networks are forced to be oper- ated much closer to stability limits due to the increased de- mand for electric power than ever before. In such a stressed condition, the system may enter into voltage instability prob- lem and it has been found responsible for many system block outs in many countries across the world [1]. Voltage instability is primarily caused by insufficient reactive power support un- der stressed conditions.
In the emerging scenario of deregulation of power sys-
tem networks, the optimum generation bidders are chosen
based on real power cost characteristics and it results in reac- tive power shortage and hence the loss of voltage stability of the system. Transmission open access in a deregulated envi- ronment might result in congestion [2]-[3] and the consequent line outage and voltage instability. Possibility of voltage insta- bility is more in a system under contingencies like line outage than in the system under normal condition. Voltage stability analysis including contingency constraints is necessary for ensuring the security of a power system. Various methods have been reported [4]-[5] to assess voltage stability of power systems to find the possible ways to improve the voltage sta- bility limit.

Asst Prof, Dept of Electrical and Electronics Engineering

V.R.S. College of Engineering and Technology, Villupuram, TN, India

E-mail:sithansakthi@gmail.com
Prof, Dept of Electrical and Electronics Engineering Government College of Engineering, Bargur, TN, India E-mail:dmary.1008@yahoo.com

UG Student, Dept of Electrical and Electronics Engineering

V.R.S. College of Engineering and Technology, Villupuram, TN, India

E-mail-ramyabhakiaraj@ymail.in
A power system needs to be with sufficient reactive re- serves to meet the increased reactive power demand under heavily loaded conditions and to avoid voltage instability problems. Reactive reserve of generators can be managed by optimizing reactive power dispatch. Generator bus voltages and transformer tap settings are the control parameters in the optimization of reactive power. The amount of reactive power reserves at the generating stations is a measure of degree of voltage stability. Several papers [6]-[7] are published on reac- tive power reserve management with the perspective of ensur- ing voltage stability by providing adequate amount of reactive power reserves.
Evolutionary algorithms (EAs) like Genetic Algorithm (GA), Differential (DE) and Particle Swarm Optimization (PSO) [8]-[9] are widely exploited during last two decades in the field of engineering optimization. They are computational- ly efficient in finding global best solution for optimization problems and will not easily trap into local minima. Such in- telligent algorithms are used for optimal reactive power dis- patch is considered in [10]-[13]. K.Vaisakh in his work [14] has adopted the easy to implement and most efficient evolutio- nary algorithm, the DE for reactive power and voltage control to improve system stability.
The modern power systems are facing increased power
flow due to increasing demand and are difficult to control. The rapid development of fast acting and self commutated power electronics converters, well known as FACTS control- lers, introduced in 1988 by Hingorani [15] are useful in taking fast control actions to ensure security of power systems. FACTS devices are capable of controlling the voltage angle,

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voltage magnitude [16] at selected buses and/or line imped- ance of transmission lines. TCSC is a series connected FACTS device inserted in transmission lines to vary its reactance and thereby reduces the reactive losses and increases the transmis- sion capacity. But the conventional power flow methods are to be modified to take into account the effects of FACTS devices. Lu et.al [17] presented a procedure to optimally place TCSCs in a power system to improve static security. TCSC has been proved to be efficient in improving stability of a power system

3. MODEL OF TCSC

TCSC is a series compensation component which consists of a series capacitor bank shunted by thyristor controlled reac- tor. The basic idea behind power flow control with the TCSC is to decrease or increase the overall lines effective series trans- mission impedance, by adding a capacitive or inductive reac- tance correspondingly. The TCSC is modeled as variable reac- tance, where the equivalent reactance of line Xij is defined as:
[18]-[21].

X 0.8X X

0.2X 1

Most of the works [22]-[23] on voltage stability limit im-
provement takes the system in normal condition and it is not sufficient since voltage instability is usually triggered by faults like line outages. Therefore it would be more meaningful to consider a system under contingency condition for voltage stability limit improvement. Recently, few works [24]-[25] have been done on voltage stability improvement under contingen- cy condition.
The proposed algorithm for optimal reactive power flow control achieves the goal by setting suitable values for genera- tor terminal voltages, transformer tap settings and reactance of TCSCs. This work proposes a coordinated control of all para- meters of reactive power control and the system is considered under line outage condition to make this work more meaning- ful with regard to voltage stability limit improvement. The optimal location of TCSCs is done based on different factors

ij Line TCSC Line

where, Xline is the transmission line reactance, and XTCSC is the TCSC reactance. The level of the applied compensation of the TCSC usually varies between 20% inductive and 80% capaci- tive (1).

4. STATIC VOLTAGE STABILITY INDEX (SVSI)


Controlling of decision variables and location of TCSC are done based on the performance using the voltage stability in- dex of each line for the same operating conditions. The SVSI technique is applied as the tool to indicate the optimal values of control parameters for voltage stability limit improvement. The concept of SVSI is demonstrated through a simple 2 bus system [26] and the mathematical expression for SVSI is as follows:
such as loss reduction, voltage stability enhancement and reac-

2 R2

X 2 P2 Q2

tive power generation reduction. The cost of FACTS devices

SVSI

ij ij j j

2

are high and therefore care must be taken while selecting their

ij V 2

2 X Q

position and number of devices. With a view to reduce the cost of FACTS devices only, the low cost TCSC alone is consi- dered but the results obtained are encouraging one.

2. REACTIVE POWER RESERVES

The different reactive power sources of a power system are synchronous generators and shunt capacitors. During a disturbance or contingency the real power demand does not change considerably but reactive power demand increases dramatically. This is due to increased voltage decay with in- creasing line losses and reduced reactive power generation from line charging effects. Sufficient reactive power reserve should be made available to supply the increased reactive power demand and hence improve the voltage stability limit.
The reactive power reserve of a generator is how much
more reactive power that it can generate and it can be deter- mined from its capacity curves [1].Simply speaking, the reac- tive power reserve is the ability of the generators to support bus voltages under increased load condition or system distur- bances. The reserves of reactive sources can be considered as a measure of the degree of voltage stability.

i ij j

Where i is the sending end bus and j the receiving end bus of the line i-j, Rji and Xji are resistance and reactance of the line, Pj and Q j are the receiving end real and reactive powers. SVSI takes values between 0 and 1. 1 represents the voltage instabil- ity condition while 0, the no load condition. The value of SVSI should be kept well below 1 to ensure the power system under voltage stability condition.

5. DIFFERENTIAL EVOLUTION ALGORITHM (DE)

Differential evolution (DE) is a population based evolu- tionary algorithm [8], capable of handling non-differentiable, nonlinear and multi-modal objectives functions. DE generates new offspring by forming a trial vector of each parent indi- vidual of the population. The population is improved itera- tively, by three basic operations namely mutation, crossover and selection. A brief description of different steps of DE algo- rithm is given below.

5.1. Initialization

The population is initialized by randomly generating in- dividuals within the boundary constraints

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X 0 X min

rand X max

X min 3

THE PSEUDO CODE OF THE DE ALGORITHM:

ij j j j

i=1,2,3<<.NP; j=1,2,3<<.D
where ‚rand ‛ function generates random values uniformly in the interval (0, 1);NP is the size of the population;D is the number of decision variables. Xjmin and Xjmax are the lower and
For i=1 to NP For j=1 to D

0 min max min

upper bound of the jth decision variable, respectively.

5.2. Mutation

As a step of generating offspring, the operations of “Mu-

Xij X j

End

rand X j X j

tation” are applied. “Mutation” occupies quite an important role in the reproduction cycle. The mutation operation creates mutant vectors Vik by perturbing a randomly selected vector Xak with the difference of two other randomly selected vectors Xbk and Xck at the kth iteration as per the following equation:
Calculate f X 0
End
Repeat until the stopping criterion is not met

V k X k

F X k

X k ; i

1, 2, 3.....NP 4

i a b c

Xak, Xbk and Xck are randomly chosen vectors at the Kth iteration
For i=1to NP

k k k k

and a≠b≠c≠i and are selected anew for each parent vector.F is Vi
the scaling constant that controls the amount of perturbation

X a F X b

X c ; i

1, 2, 3.....NP

in the mutation process and improve convergence.

5.3. Crossover

For j=1 to D

k

Crossover represents a typical case of a ‚genes‛ ex- U k

Vij ,

if rand CR or j q

change. The trial one inherits genes with some probability. The
parent vector is mixed with the mutated vector to create a trial
vector, according to the following equation:

ij k

ij

End

Otherwise

k k ij

ij k ij

if rand CR or j q

Otherwise

5 Calculate

f U k

U k ,

if f U k

f X k ; i

1, 2, 3.....NP

k 1

Where i=1,2,3<<<<<NP;j=1,2,3<<<<..D. Xij k , Vij k Uij k i

i i i

k

are the jth individual of target vector, mutant vector, and trial vector at kth iteration, respectively. q is a randomly chosen in- dex in the range (1,D) that guarantees that the trial vector gets
End

X i ,

otherwise

at least one parameter from the mutant vector. CR is the cross over constant that lies between 0 and 1.

5.4. Selection

Selection procedure is used among the set of trial vector and the updated target vector to choose the best one. Selection is realized by comparing the fitness function values of target vector and trial vector. Selection operation is performed as per the following equation:

6. THE STEP BY IMPLEMENTATION OF DE FOR REACTIVE POWER CONTROL

6.1. Representing an individual:

Each individual in the population is defined as a vector containing the values of control parameters including the size of TCSC.
Individual is defined as (Vg1, Vg2<<.. Vgn ,t1, t2 <<.XTCSC )

6.2. Number of individuals:

There is a trade-off between the number of individuals

U k ,

if f U k

f X k ;i

1, 2, 3.....NP
and the number of iterations of the population and each indi-

X k 1

i i i

6 vidual fitness value has to be evaluated using a power flow

i X k ,

i

otherwise

solution at each iteration, thus the number of individuals should not be large because computational effort could in- crease dramatically. Individuals of 5,10 and 20 are chosen as an appropriate population sizes.

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6.3. Feasible region Definition:

There are several constraints in this problem regarding the characteristics of the power system and the desired voltage

Qgen

N PV

k 1

Qk gen 10

profile. Each of these constraints represents a limit in the search space. Therefore the DE algorithm has to be pro-
grammed so that the individual can only move over the feasi-

N PQ

k 1

lim

k k

Vlim max min 11

ble region. For instance, the network in Fig. 1 has 4 transmis-
sion lines with tap changer transformer. These lines are not
considered for locating TCSC, leaving 37 other possible loca-
tions for the TCSC. In terms of the algorithm, each time that an individual’s new position includes a line with tap setting transformer, the position is changed to the geographically closest line (line without transformer). Finally, in order to limit the sizes of the TCSC units, the restrictions of level of compen- sation is applied to the individuals.

6.4. Optimal Parameter Values:

Table.1. Optimal values of DE parameters

Parameter Optimal value


Number of individuals 10


Cross over constant 0.5

Vk Vk

N L

SVSI SVSI k 12

k 1

where Ploss is the total system real power loss; Qloss is the total reactive power loss; Qgen is the total reactive power generated by generators; the third term in the objective function is the normalized violation of load bus (also known as ‘PQ bus’) voltage, Vi; the fourth term is the sum of SVSI of all lines; NL is the number of transmission lines; NPQ and NPV are the num- ber of load buses and generator buses respectively; λ1 and λ2 are the penalty coefficient and are set to 500.
Subject to
Equality constraints

NB

Scaling constant 0.2

No of iterations 25

PGi

PD i

ViVjYij X

j 1

TCSC

cos

ij j i

0 13

6.5. Integer DE:

For this particular application, the position of individuals

QGi

QD i

NB

ViVjYij X

j 1

TCSC

sin

ij j i

0 14

is determined by an integer number (line number). Therefore
the individuals’ movement is approximated to the nearest in- teger numbers. Additionally, the location number must not be

X min

Inequality constraints

X X max 15

a line with tap setting transformer. If the location is line with
tap setting transformer, then the individual component re-

TCSC TCSC TCSC

garding position is changed to the geographically closest line

V min

V V max ; i N 16

without a tap setting transformer.

i i i PQ

6.6. Fitness function

S Smax ;

k N 17

The goal of optimal reactive power planning is to minim- ize the reactive power generation and reactive power loss by optimal positioning of TCSC and its corresponding parame-

k k L

ters. Hence, the objective function can be expressed as:

Qmin

Q Qmax ; i N 18

F min

Ploss

Qloss

Qgen

1Vlim 2 SVSI 7

Gi Gi Gi PV

The terms in the objective function are:

N L

7. SIMULATION RESULTS AND DISCUSSIONS

P G V 2 V 2

2V V

cos 8

The optimal reactive power flow control is formulated

loss k i j i j i j

k 1

N L

with the primary objective of minimization of reactive power generation and secondary objective of minimization of real

Qloss

Qk loss k 1

9 power loss subject to voltage limit and reactive power limit

constraints. The effectiveness of proposed approach has been
illustrated using the medium size IEEE 30 bus test system [27].

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Figure.1. One line diagram of IEEE 30 Bus System
The system has 6 generator buses, 24 load buses and 41 transmission lines. Transmission lines 6-9, 6-10, 4-12, and 28-
27 are with tap changer transformers and therefore are not
suitable for positioning of TCSC. Only the remaining 37 lines are considered as candidate locations for positioning of TCSC.
Reactive power flow in the system is optimized by con-
trolling the parameters of generator bus voltages, tap settings of transformers and reactance of TCSCs. These control para- meters are varied within their respective limits and the limits are given in table 2.
Table. 2. Limits of control parameters
ages for consideration of voltage stability improvement. All the possible line outages of the system are considered one each at a time. The line, whose outage leaves the system with de- creased voltage level, increased reactive power generation and line loss is identified as the most critical line. The step by step procedure for contingency ranking [28]-[29] is given below.

Step1: Read the system data.

Step2: Run the load flow program considering only one

line outage and calculate the total reactive power genera- tion and total line losses.

Step3: The reactive power generation and losses correspond-

ing to all the lines of the system are arranged in descending order.

Step4: The most critical line is identified as the line, whose outage results in the highest value of reactive power genera- tion and losses (highly stressed condition).

Line outage contingency screening and ranking, carried out on the test system is shown in table 3. The line outage is ranked according to the severity and severity is taken on the basis of increased reactive power generation and real power losses. It is clear from the table that outage of line 2-5 is the most critical line outage and this condition is considered for voltage stability improvement.
Table. 3. Contingency Ranking in IEEE 30 bus system
Reactive power optimization is considered under two dif- ferent operating conditions of the system. The first case is the most critical line outage contingency condition without FACTS devices and the second case is the same contingency condition with TCSC devices.
Voltage instability is usually initiated by faults like line
outages. As such, voltage stability improvement under contin- gency condition is more meaningful rather under normal con- dition of a power system. Line outage contingency screening and ranking is carried out first to identify the critical line out-
The system with 40% increased loading level is consi- dered as a stressed condition for reactive power flow control to improve the voltage stability limit. NR load flow is run sev-
eral times considering two TCSCs at two different lines and the reduction in real power loss and reactive power generation (objectives) are calculated. The best solution for minimization of the objectives is found by implementing the evolutionary based DE algorithm. The TCSC devices are located in the global best positions (Lines) to improve the voltage stability by controlling the reactive power flow through the transmission lines of the system. The reactive power flow control is achieved so that the total real power loss and reactive power generation are reduced.
The values of generator terminal voltages and tap set- tings are allowed to vary within their limits during the opti-

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mization process and the values shown in table 4 are the most
suitable ones for the objectives considered.
Table. 4. Optimal Values of Control Parameters
Table. 6. Reduction in Qgen, Qloss, Ploss and SVSI

Control

Buses Value

Variables

Without

With

TCSC TCSC

Pg1 1 298.024 250.239

Pg2 2 47.8820 45.0646

Pg5 5 36.6785 49.4068

Pg8 8 25.3832 34.4774

Pg11 11 12.4525 16.1434

Pg13 13 15.4662 30.6575

V1 1 1.0600 1.0600

V2 2 1.0291 1.0893

V5 5 0.9986 1.0764

V8 8 1.0839 1.0813

V11 11 1.0543 1.0063

V13 13 1.0150 1.0036

T1 6-9 0.9276 0.9106

T2 6-10 0.9488 0.9290

T3 4-12 1.0562 0.9645


T4 28-27 1.0009 0.9218
Two TCSCs are located, one in line 12-15 and other one in
9-11 and the line reactances are modified as given in table 5. It
is ensured that the locations of TSCSs are lines without tap
changer transformers. The TCSCs are helping the control pa- rameters in optimizing the reactive power dispatch.
Table. 5. Global best position of TCSC devices
after the installation of TCSC device and the resultant im- provement in voltage profile is illustrated in figure 2. It is clear from the figure that the voltage profile is improved considera- bly. In this case both the real power loss minimization and voltage profile improvement are better. A power system is with increased real power loss and decreased bus voltage magnitudes especially during disturbance/contingency condi- tion (under highly stressed condition).The much reduction in real power loss and increase in voltage magnitudes after the insertion of TCSC proves that FACTS devices are highly effi- cient in relieving a power network from stressed condition and improving voltage stability improvement.

Device

Number

Global

BestLoction


Line Reactance Old New

TCSC1 12-15 0.1304 0.1373

TCSC2 9-11 0.2080 0.1075

Coordinated control of generator bus voltages, tap set-
tings and reactance’s of TCSCs reduces the line losses and reactive power generation greatly. The values of reactive pow- er generation, reactive power loss and real power loss before and after TCSCs are compared in table 6. Reduction in reactive power generation is an indication that the system is relieved from the stressed condition. The amount of reactive power generation reduction can be seen as reactive power reserve and it may be used when the system needs it again in future. The voltage stability limit improvement is obvious from the reduction in the value of sum of SVSI after the TCSCs are lo- cated.
Figure. 2. Voltage profile improvement
Voltage stability improvement is assessed by observing the value of SVSI that is, the reduction in the value of SVSI is an indication that voltage stability limit is improved. SVSI val- ue of all the lines in the system before and after optimization is compared in fig 3. It is obvious from the chart that voltage stability limit is improved considerably in all the lines. The better improvement in voltage stability limit is due to the change in power flow through the lines caused by the inser- tion of TCSCs.

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reactive power generation can be used as reactive power re-
serve when the system needs it again. That is the system is left with reactive capability and thereby under voltage secured condition. The DE algorithm is efficient, easy to implement and gained popularity only during the last one decade. The settings of the DE parameters are shown to be optimal for this type of application. The algorithm is able to find the optimal solutions with a relatively small number of iterations and in- dividuals, therefore with a reasonable computational effort.
Figure. 3. Minimization of SVSI
Figure. 3. SVSI of lines before and after insertion of TCSC For quick understanding of the relief of the system from
stressed conditions and increased capability of reactive power reserves, the reduction in the three parameters are compared in fig 4.

Figure. 4. Reduction in Qgen, Ploss and Qloss

8. CONCLUSIONS

This work demonstrates the application of the DE algo- rithm to solve the problem of optimal reactive power control including the placement and sizing of TCSC device in a me- dium size power network for voltage stability limit improve- ment by controlling the reactive power flow and reducing the real power loss. This work proves that voltage stability limit improvement is more effective when it is done both by control of reactive power generation and reactive power flow control. Reactive power generation control is indicated by the control of generator bus voltages and reactive power flow by the con- trol of tap setter positions and reactance of TCSCs. It is clear from the simulation results that TCSC device is good at con- trolling the reactive power flow through different transmis- sion lines of the system by changing their reactance and it re- sults in reduced reactive power generation. The reduction in

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BIOGRAPHIES

Prof.S.Sakthivel received the Degree in Electrical and Elec- tronics Engineering and Master Degree in Power Systems Engineering in 1999 and

2002 respectively. He is doing the Ph.D.,
Degree in Electrical Engineering faculty from Anna University of Technology, Coimbatore, India. He is working as an assistant professor of Electrical and Elec- tronics Engineering at V.R.S.College of
Engineering and Technology, Villupuram, Tamil Nadu, India. His research areas of interest are Power System control, Opti- mization techniques, FACTS and voltage stability improve- ment.

Dr.D.Mary received the Ph.D. Degree from Bharathiyar Uni- versity,Tamil Nadu India in 2002. She is the Professor and Head of the Depart- ment of Electrical and Electronics Engi- neering, Government College of Engi- neering, Bargur Tamil Nadu,India. Power System Control and Instrumentation and Intelligent Techniques are some of her areas of interest. She has published more

than 50 technical papers in leading international ‘research
journals.

Mrs. S. Ramya is an undergraduate student in the Department of Electrical and Electronics Engineering at V.R.S. College of Engineering and Technology, Villupuram, Tamilnadu, In- dia. She is involved in optimization of power system operations.

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