Hypothetical Study For Selection Of Optimal Location Of Multiple FACTS Devices Under Contingent...

8/13/2019 Hypothetical Study For Selection Of Optimal Location Of Multiple FACTS Devices Under Contingent Condition Using

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Electrical and Electronics Engineering: An International Journal (ELELIJ) Vol 2, No 4, November 2013

71

Hypothetical Study For Selection Of OptimalLocation Of Multiple FACTS Devices Under

Contingent Condition Using Different ObjectiveFunctions

B.P. Saoji1and A.P. Vaidya

2

1Smt. Indira Gandhi College of Engineering, Mumbai University, Navi Mumbai, India

2Walchand College of Engineering, Shivaji University, Sangli, India

ABSTRACT

Improvement in the system's reactive power handling capacity incorporating FACTS devices is a remedy

for prevention of voltage instability and hence voltage collapse. FACTS devices are very costly and need tobe placed optimally. In this study dynamic programming approach based on Bellmans principle of

optimality was used to solve multi objective optimization problem to find unique optimal location of single

and multiple FACTS devices under normal and single line outage contingent condition. Power system

loadability enhancement is considered as an individual objective function evaluated under normal and

single line contingent condition. Then reduced active power loss and minimum voltage deviation for

enhanced loadability was evaluated for which unique location of FACTS devices is calculated. The

operational and load constraints are considered for optimal procedure. Static Var Compensator (SVC) and

Thyristor Controlled Series Capacitor (TCSC) are used to achieve the objectives. Simulation is performed

on IEEE 30 Bus system to test the effectiveness of the proposed method.

KEYWORDS:

SVC, TCSC, Power System Loadability, Power loss, Voltage Deviation, Line contingency.

1. INTRODUCTION

Voltage instability and hence voltage collapse is a major concern in the power system over

several years as incidences are recorded worldwide [1][2]. Voltage stability is defined as theability of system to supply load and maintain voltage level of all load bus in range of standard in

both normal and abnormal conditions. The power systems which are having shortage of reactive

power due to fault or heavy load on it, experiences a voltage collapse [3]. So reserve of reactive

power source is necessary for the stable operation of power system. The voltage collapse points

are also known as maximum loadability points (MLP). The loadability margin of a system isdefined as the amount of power that the system can supply before it undergoes voltage collapse.

Therefore to prevent voltage collapse several studies point out that the use of FACTs devices

stabilize an unstable power system to move the system into a stable voltage operatingpoint[4][5][6].

A system is said to be voltage secure, if it has sufficient loading margin under N-1 contingency

which implies that the system should be able to remain in a security condition under all important

first contingencies.


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Due to the inherent limits of AC power transmission system it restricts the power transmission.

This restriction is overcome worldwide restructuring the electric utilities together with

semiconductor switches such as thyristor. Modern technologically advanced voltage sourceconverters based FACTS controllers, are made possible due to rapid progress in high powersemiconductors switching devices [7][8][9].

Today power systems are being forced to operate close to the transmission system thermal and

stability limit. Certain constraints such as cost, limit the expansion of transmission networks.Utilities try to maximize the utilization of the existing transmission asset that may sometime leadsto insecure operation of power system.

Controlling the power flow in the network helps in reducing the flows in heavily loaded lines,

resulting in increased system loadability, reduced power loss, improved stable operation of powersystem and hence increases reliability of the system.

Flexible Alternating Current Transmission Systems (FACTS) devices have been proposed to be

effective for controlling power flow and regulating bus voltage in electrical power systems,

leading to an increased transfer capability, low system losses and improved stability under

contingency situations, up to their thermal limits without degrading the system security [10 - 11].In the coming year the demand of power consumption is expected to increase more than double in

developing and transition countries where as, in developed countries it is expected to increase by35-40%. There is challenge to meet the demand of customers uninterrupted reliable power supply

with quality. One way is to use the existing equipments up to their maximum capacity. FACTS

devices increase the thermal capacity of transmission line and the reliability of the system.

In [12] optimal no. of FACTS devices and their level of compensation for cost of installation andloadability were calculated. Study presented in [13] finds optimum type, location, and capacity of

FACTS devices in a power system using a multi-objective optimization function. Thyristorcontrolled series compensator (TCSC) and static var compensator (SVC) were utilized to achieve

objectives: active power loss reduction, reduction in installation cost. A strategy for placementand sizing of shunt FACTS controller using Fuzzy logic and Real Coded Genetic Algorithm was

proposed. A fuzzy performance index based on distance to saddle node bifurcation, voltageprofile and capacity of shunt FACTS controller was calculated [14].

Optimal location and size of FACTS devices to reduce the active power loss in transmission line,

to minimize the voltage deviation and to minimize the installation cost considering it as multi-

objective function solved by different approaches such as multi objective GA, Modified ArtificialImmune Network Algorithm (MAINetA), Multi-Objective Particle Swarm Optimization

(MOPSO), Fuzzy based GA approach. In most of these studies any two individual functions are

considered together as multi objective function [15 - 19].

In all the previous work in these area different locations of FACTS devices were obtained under

normal and contingent situation, often using more than two devices. However with our approachsame locations were obtained under normal as well as contingent situation by using only two

FACTS devices.

Proposed study presented in this paper uses Dynamic Programming approach based on Bellmansprinciple of optimality to find single optimal location of FACTS devices for multi-objective

function under normal and single line outage contingent condition. Initially optimal location and

size of FACTS devices for enhancement in loadability as an individual function was calculatedand then for this enhanced loadability reduction in power loss and minimization of voltage


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deviation was calculated considering both as an individual objective function. The operational

and load constraint are considered.

This paper is organised as follows section II describes in brief FACTS devices. In section IIIindividual problem formulation is described in detail. Section IV gives information aboutdynamic programming. Results and discussion of a case study is presented in section V.

Conclusion is summarised in section VI.

2. FACTS DEVICES MODELLING

2.1 Static VAr Compensator

A static VAR compensator (SVC) is an electrical device for providing fast-acting reactive power

compensation on high voltage transmission networks and it can contribute to improve the voltageprofiles in the transient state and therefore, in improving the quality performances of the electric

services. A SVC is one of FACTS controllers, which can control one or more variables in a powersystem.

A Static VAr Compensator is capable of both generating and absorbing variable reactive power

continuously as opposed to discrete values of fixed and switched shunt capacitors or reactors.Further improved system steady state performance can be obtained from SVC applications. With

continuously variable reactive power supply, the voltage at the SVC bus may be maintainedsmoothly over a wide range of active power transfers or system loading conditions. This entails

the reduction of network losses and provision of adequate power quality to the electric energy

end-users.

Figure 1- Model of SVC

From figure 1 the current drawn by SVC is given by equation as

KVSVCjB

SVCI = (1)

Reactive power drawn by SVC that is the same as injected power to bus k is given as2KVSVC

BKQCVCSQ == (2)

2.2 Thyristor Controlled Series capacitor (TCSC)

TCSC is series type FACTS device which provide series capacitive reactance compensation. Thecharacteristics for TCSCs consist of capacitive and inductive region; it can increase or decrease

the transmission line reactance. These devices can cause increasing the transmission powercapacity of lines, static voltage security margin enhancement, voltage profile improvement, and

decreasing power loss. The TCSC is modelled as series compensation is shown in fig.2

Figure 2 - Model of TCSC


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The real and reactive power injected at buses i and j with TCSC connected between buses i and j

and line having impedance of Zij= (rij+ jxij) and jxcare in series expressed as

]ij

sinij

cos[j

Vi

V-2i

Vci

P ijBijGijG += (3)

]ijcosijsin[jViV-2

iV

c

iQ ijBijGijB = (4)

]ijsinijcos[jViV-2i

Vci

P ijBijGijG = (5)

]ijcosijsin[jViV-2i

Vci

Q ijBijGijB = (6)

Where

)2

)(2

)(22

(

)2(

c

cc

xijxijrijxijr

ijxxijrx

ijG++

= and)

2)(

2)(

22(

)22

(

cxijxijrijxijr

ijx

cx

ijx

ijrcx

ijB++

+

=

(7)

jijiij ==

3. PROBLEM FORMULATION

This paper focuses on the optimal location and level of compensation of FACTS devices. This

paper indentifies three objective function viz. Power system loadability, power loss intransmission lineand voltage deviation. Problem formulation now boils down to maximization of

power system loadability, minimization of power loss and voltage deviation.

3.1 Power System Loadability

Maximum Loading Point (MLP) is the value of loading factor at the critical point or loadabilitymargin of a system is defined as the amount of power that the system can supply before it

undergoes voltage collapse. The P V curve is shown in fig.3

Figure 3 - P V curve

The loads on power system increases gradually from initial point to the voltage collapse point i.e.up to MLP. At every load level system state is calculated until the maximum or critical conditionis reached. In order to assess and enhance voltage security conditions, is then evaluated using

Dynamic Programming. The P- V curve is shown in figure 3.

f = max() (8)where is the maximum loadability factor.


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3.2 Active Power Loss

The aim is to minimize total active power loss

ijcosij)]Yjicos(jVi2V2jV

2i

[VL

P += (9)

in transmission line.

where Viand i are the magnitude and angle of voltage at bus i, respectively and Yijand ijarethe magnitude and angle of the admittance of the line between bus i to busj.

3.3 Voltage Deviation

To have an improved voltage regulation (profile), the voltage deviation at each load bus must bemade as small as possible. The voltage deviation to be minimized is as follows:

2)refKVKV

K

(VD = (10)

where Vkis the voltage magnitude at load bus k and Vref kis the nominal or reference voltage atbus k.

All the three objective functions are subject to the following constraints

Active power balance in the network

0PP),V(P digii =+ (i = 1, 2,, NB) (11)

1. Reactive power balance in the network0QQ),V(Q digii =+ (i =NV +1, NV +2, , NB (12)

2. Security related constraints called as soft constraintsa. Limits on real power generation.

maxmin

giP

giP

giP (i = 1, 2,..., NG) (13)

b. Limits on voltage magnitudemax

ii

min

i VVV (NV +1, NV+2,..., NB) (14)

c. Limits voltage anglesmax

ii

min

i (i = 2, 3, , NB) (15)

3. Functional constrain which is a function of control variablea. Limits on reactive power

max

gigi

min

gi QQQ (i=1, 2,,NG) (16)

Line flow limitsmaxmin

fff PPP

(f = 1,, Noele) (17)

The active power and reactive power flow on lines can be applied as follows,The real power flow equation is

=

+=

NB

1i

jiijjiijjii ))sin(B)cos(G(VV),V(P (18)


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++++

+=+====

NB

NVi

qi

NB

NVi

i

NB

i

pi

NB

i

i

NG

i

gi VP1

2

1

2

1

2

2

2

1

2 )()()()()(

and optimality conditions. If condition is not satisfied then GOTO step 6 else GOTO step8.

8. Modify the variables ,Pgi= Pgi+ Pgi (i=1, 2 NG)i=i+i (i=1, 2 NB)

pi=pi+pi (i=1, 2 NB)

Vi= Vi+ VI (i=NV+1, NV+2, NB)

qi=qi+qi (i=NV+1,NV+2,., NB)9. Check the limits. If any limit of a variable is violated, then impose or remove power flow

equation of a penalty for inequality. Add or remove derivatives for penalty or equation

change and GOTO step 4 to update the solution.10.Calculate the objective function.11.Stop.


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5. DYNAMIC PROGRAMMING METHOD

Dynamic programming is an approach to solve the optimization problem in which the problem is

broken down into number of sub problems called stages. These sub problems are then solved

sequentially until the original problem finally is solved. The methods used for solving a sub

problem are calculus, linear programming etc. or whichever is suitable for given problem

structure. The solution of the Dynamic programming problem is based upon Bellmans principleof optimality. Consider a system whose state may change in every phase Di for a given decision.

The number of phases Di (i =0,1,.,n) may be finite or numerable infinite. A certain sequencesof decision from D0 to Dn are defined as a policy and a sequence of decision belonging to a

policy is defined sub- policy. If a function with values related to the changes in state isassigned, and it is required to optimize that function, the following statement holds:

An optimal policy has the property that whatever the initial state and initial decisions are, theremaining decision must continue an optimal policy with regard to state resulting from the first

decision.

By applying this principle, the objective function can be optimized.

6. CASE STUDY

The proposed study is carried out on IEEE 30 Bus system.

Figure 4 Single line diagram IEEE 30 Bus System

The proposed study is divided into two parts as Study A Normal operation of system

Study B Line outage, contingent condition

6.1 Study A Normal Operation

As the load on each bus increases gradually and approaches Maximum Loading Point (MLP), thesupply and demand increases leading to rapid increase in real and reactive power loss


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consequently system tends to more towards voltage instability and may lead to voltage collapse.

The only way to save the system from voltage collapse is to reduce the reactive power load or

supply additional reactive power prior to reaching the point of voltage collapse for the stableoperation of power system.

Initially all load buses and all transmission line except transformer connected line are candidatefor optimal location of SVC and TCSC respectively. In this study there are 979 candidate

locations for SVC and TCSC under normal operation. This is obtained by connecting SVC or

TCSC individually at a bus and SVC plus TCSC together at all possible candidate locations.Starting from base load, the load is increase gradually till the voltage collapse point is reached,

with SVC and TCSC size varied from -1 to 1 and -0.8 to 0.8 respectively to maximize the systemloadability. For this objective function actual active power loss and voltage deviation is

calculated.

The enhanced loadability with SVC connected to 24 possible combinations is shown in Table1.

Table1 Enhanced Loadability with SVC at bus No. 24

Bus No. Loadability BusNo. Loadability BusNo. Loadability

3 1.559595 15 1.553628 23 1.553235

4 1.556555 16 1.552434 24 1.554534

6 1.556039 17 1.553290 25 1.552676

7 1.552410 18 1.552735 26 1.551287

9 1.553073 19 1.552865 27 1.552272

10 1.553906 20 1.552817 28 1.553828

12 1.552846 21 1.554272 29 1.551227

14 1.551707 22 1.554191 30 1.551290

From this Table1 the first maximum five enhanced loadability conditions are considered for

further study which is shown in Table (2).

Out of these five conditions, for a given loadability the minimum active power loss was

calculated one by one for all five locations.

Thereafter for a given loadability the minimum voltage deviation was calculated one by one forall five locations.

Similar procedure was repeated for TCSC and SVC and TCSC combined together.

The results are shown in Table 2, 3 and 4. All values in tables are in pu.


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Table 2 - SVC Result Under Normal Condition

Table 3 - TCSC Result Under Normal Condition

Obj. Fun

Tr.

Line

No.

LoadabilityPower

Loss

Voltage

Deviationxc

Enhancementof Loadability

1 1.561819 0.1057 0.3868 -0.0115

2 1.583568 0.1122 0.3921 -0.0622

4 1.568081 0.1068 0.3786 -0.0303

7 1.558326 0.1031 0.3625 -0.0331

14 1.548886 0.0994 0.3325 -0.0374

Minimizationof PowerLoss

1 1.561819 0.0909 0.2755 -0.0115

2 1.583568 0.0969 0.2744 -0.05414 1.568081 0.0924 0.2758 -0.0303

7 1.558326 0.0896 0.2756 -0.0331

14 1.548886 0.0860 0.2823 -0.0880

Minimization

of Voltagedeviation

1 1.561819 0.0909 0.2755 -0.0115

2 1.583568 0.0969 0.2744 -0.0541

4 1.568081 0.0924 0.2758 -0.0303

7 1.558326 0.0896 0.2756 -0.0331

14 1.548886 0.0917 0.2350 -0.0880


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Table 4 - SVC and TCSC Result Under Normal Condition

6.2 Study B Single Line Outage Contingent Condition

In proposed studies optimal placement and sizing of multiple FACTS devices under single line

outage condition are simulated one by one to determine the severity of the contingency.

During simulation it was observed that Line No. 36 outage is the most sever contingency. Thisoutage reduces the loadability drastically to 1.352856 and from voltage profile it is observed that

14 buses violate the voltage stability margin as shown in fig5.

Figure 5 - Voltage profile under Line No.36 contingent w/o Compensation.

To obtain the location of FACTS devices optimally under line no. 36 outage, the same procedure

was adopted as that of normal operation.

For loadability as an objective function actual active power loss and voltage deviation was

calculated.

45

55

65

75

85

95

105

115

1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930

VoltageinKV

Internal Bus no.

Normal Operation w/o Compensatation Line No.36 Outage w/o Compensatation


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Minimization of active power loss as an objective function with enhanced loadability under line

no. 36 contingent was calculated.

Minimization of voltage deviation as an objective function with enhanced loadability under lineno. 36 contingent was calculated

The results are shown Figure 6, 7 and 8. All values in table are in pu.

Figure 6 Enhanced Loadability under line no. 36 contingent with compensation.

Figure 7 - Minimized Power Loss under line no. 36 contingent with compensation.

Figure 8 - Minimized Voltage Deviation under line no. 36 contingent with compensation.

1.3

1.4

1.5

1.6

24, 2, 9-14 25, 14, 10-227, 31, 24-229, 33, 25-430, 35, 26-2

Loadabilityinpu

Internal Bus and Tr. Line No.

Only SVC Only TCSC SVC and TCSC togather

0

0.1

0.2

24, 2, 9-14 25, 14, 10-227, 31, 24-229, 33, 25-430, 35, 26-2

ActivePowerLossinpu

Internal Bus and Tr. Line No.


0

0.5

1

24, 2, 9-14 25, 14, 10-227, 31, 24-229, 33, 25-430, 35, 26-2

VoltageDeviationinpu

Internal Bus and Tr.Line No.



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Table 5 - SVC and TCSC Compensation Table under line no. 36 contingent

Obj Fun Bus No. Tr. Line No Qsvc xc

Enhanced

Loadability

9 14 -0.5359 -0.0705

10 2 -0.5505 -0.0443

24 2 -0.4043 -0.043925 4 -0.2630 -0.0303

26 2 -0.2115 -0.0771

Minimized

Power Loss

9 14 -0.7917 -0.2634

10 2 -0.6974 -0.2634

24 2 -0.2948 -0.2634

25 4 -0.2946 -0.0303

26 2 -0.1235 -0.0880

Minimized

Voltage

Deviation

9 14 -0.7917 -0.2634

10 2 -0.6974 -0.2634

24 2 -0.6419 -0.0347

25 4 -0.2946 -0.0303

26 2 -0.1235 -0.088

Result from figure 6,7,8 and 9and 10 clearly indicate that SVC at Bus No.24 and TCSC at Tr.Line No. 2 are the optimum location for individual FACTS location as well as composite (SVC

and TCSC used together) FACTS location. With this combination loadability is enhanced up to

1.564448pu, also it reduces power loss to 0.1304pu and minimizes the voltage deviation up to

0.4740pu for obj. function of enhanced loadability for minimization of Power Loss.

Figure 9 voltage Profile under normal condition for various Obj. Function

85

90

95

100

105

110

115

1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930

VoltageinKV

Internal Bus No.

Enhanced Loadability w/o compensation

Enhanced Loadbility with compensation

Enhanced Loadability with Power loss with compensatation


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Figure 7 - voltage Profile under line no. 36 contingent for various Obj. Function

Table 6 Line Flow under Line No. 36 contingent for different Objective Functions

Line

NoELWC ELC ELPLC ELVDC

Line

NoELWC ELC ELPLC ELVDC

1 0.8402 0.9943 0.7258 0.7529 22 0.0950 0.1032 0.1050 0.1043

2 0.4127 0.4706 0.2429 0.2666 23 0.0483 0.0495 0.0514 0.0507

3 0.2448 0.2856 0.1777 0.1912 24 0.0886 0.1088 0.1067 0.1073

4 0.3739 0.5536 0.7708 0.7392 25 0.1233 0.1492 0.1466 0.1472

5 0.3355 0.4896 0.4459 0.4549 26 0.0423 0.0817 0.0785 0.0810

6 0.2908 0.3643 0.2767 0.2893 27 0.4334 0.3957 0.3937 0.3880

7 0.2073 0.3502 0.4485 0.4356 28 0.2372 0.2108 0.2085 0.2059

8 0.1214 0.0980 0.1015 0.0588 29 0.1371 0.1420 0.1265 0.1374

9 0.2596 0.3593 0.3973 0.4037 30 0.2457 0.2056 0.2035 0.201610 0.0855 0.0379 0.0381 0.0380 31 0.3639 0.3197 0.3050 0.3103

11 0.1758 0.1817 0.1690 0.1711 32 0.1838 0.1531 0.1488 0.1504

12 0.2175 0.2053 0.2003 0.1984 33 0.3538 0.3546 0.3390 0.3390

13 0.5788 0.5978 0.6032 0.5955 34 0.0601 0.0684 0.0680 0.0680

14 0.7488 0.7402 0.7359 0.7272 35 0.2308 0.2429 0.2363 0.2363

15 0.3137 0.3621 0.3604 0.3595 36 0.0000 0.0000 0.0000 0.0000

16 0.6076 0.6101 0.6157 0.6073 37 0.0973 0.1065 0.1048 0.1048

17 0.1516 0.1543 0.1546 0.1530 38 0.1114 0.1215 0.1194 0.1194

18 0.4102 0.4038 0.4041 0.3995 39 0.0537 0.0604 0.0599 0.0599

19 0.1633 0.1591 0.1623 0.1597 40 0.0276 0.0335 0.0350 0.0345

20 0.0612 0.0510 0.0513 0.0502 41 0.0339 0.0236 0.0285 0.0278

21 0.1050 0.0939 0.0972 0.0949

ELWC - Enhanced Loadability without compensation.ELC - Enhanced Loadability with compensation.

ELPLC - Enhanced Loadability with Power Loss with compensation.ELVDC - Enhanced Loadability with Voltage Deviation with compensation

Voltagein

KV

Internal Bus No.

Enhanced Loadability w/o compensation

Enhanced Loadability with compensatation

Enhanced Loadability with Power Loss with compensatation

Enhanced Loadability with VD with compensatation


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From Table 3 it was observed that, line loading under objective function of enhanced loadability

with minimization of Power Loss, relieves by 10.39% and 41.15% of line no 1 and 2 respectively.

Line flow through line no. 4 and 7 increases by almost double to minimize the power loss.

All observations clearly indicate that SVC at Bus No.24 and TCSC at Tr. Line No. 2 with level of

compensation -0.6419pu and -0.0347pu respectively under normal condition and -0.2948pu and -0.2634pu respectively under contingent condition is optimum location.

6. CONCLUSION

In this paper, first enhancement of power system loadability was calculated as an individual

objective function under normal and single line contingent condition and then minimization ofpower loss and minimization of voltage deviation for enhanced loadability was calculated.

Optimal location and level of compensation of FACTS devices for this objective function was

calculated. This strategy is validated successfully on IEEE 30 bus system giving optimal locationand level of compensation to enhance the power system loadability with reduced loss and

minimized voltage deviation. The results are very much promising.

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Volume 30, Issue 10, December 2008, Pages 563-568

AUTHORS

Biographical notes: B.P.Saoji received his Bachelor degree in Electrical Power System from AmravatiUniversity in 1989 and Masters degree in Electrical Engineering from Gujarat University, India in 1992.

He is currently working as an Assistant Professor in Electrical Engineering at Smt. Indira Gandhi College

of Engineering, Navi Mumbai, India. He is currently a Ph.D. student at Amravati University, Maharashtra,

India since 2010.

A. P. Vaidya obtained his Bachelors degree in Electrical Engineering in 1983 and Masters degree in

Electrical Power Systems in 1993. He completed his doctoral degree from Indian Institute of Science,

Bangalore in High Voltage Engineering in the year 2005. He is presently working as Professor, in Electrical

Engineering, at Walchand College of Engineering, Sangli, Maharashtra (India). His areas of interest are

Power System Analysis, Protection Systems, Microprocessor Applications and High Voltage Engineering.

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