chapter 8 optimization of power system...

97

CHAPTER 8

OPTIMIZATION OF POWER SYSTEM USING

L-INDEX APPROACH

8.1 INTRODUCTION

The optimal rating and location of FACTS devices are obtained to

achieve minimizing the real power loss, voltage profile improvement, voltage

stability enhancement and minimizing the total cost. The voltage stability

assessment is analyzed using L-index (Thukaram et al 2000, Durairaj et al

2005 and Vaisakh et al 2008) approach based on Bacterial Foraging

Algorithm. L-index gives scalar number (0 to 1) to each load bus of the

system. Highest value of L-Index of the load bus will be considered as critical

load bus. Among the different indices for voltage stability and voltage

collapse prediction, the L-index gives fairly consistent results (Durairaj et al

2005). This work uses minimization of L-index of the system as one of the

objective of the optimization problem. The Bacterial Foraging based L-index

is calculated in each step after performing Newton-Raphson (N-R) load flow

study. The proposed algorithm has been tested on 6-bus, IEEE 14-bus and

IEEE 30-bus reliability test systems. A load flow program written in

MATLAB using Bacterial Foraging technique was used to compute power

flow. For practical and economic considerations, the number of SVC units is

limited not exceeding three (Ishak et al 2004) TCSC and UPFC units are

limited to one at a time. (Garng Huang et al 2002 and Venkataramu et al

2006).

98

8.2 RESULTS AND DISCUSSION

The program for the Bacterial Foraging Optimization Algorithm

used in this study are written in Matlab 7.0 on Pentium IV, 3GHz, 512 MB

RAM processor and used to perform the optimization routines with 6-bus,

IEEE 14-bus and IEEE 30-bus systems.

The 6-bus system consists of 3 generator buses (Bus 1 is slack bus,

2 and 3 are PV buses), 3 load buses and 11 lines. The line parameters and

loads are taken from Wood et al (1984).

IEEE 14-bus test system, consists of 5 generator buses (bus 1 is

slack bus 2,3,6 and 8 are PV buses), 9 load buses and 20 lines in which 3 lines

(4-7, 4-9 and 5-6) are with tap changing transformers. The line parameters

and loads are taken from Pai (2006).

IEEE 30-bus system consists of 6 generator buses, 24 load buses

and 41 transmission lines in which 4 lines are with tap changing transformer.

The transmission line parameters of this system and the base loads are taken

from Pai (2006). Case-I (base case) is for light loads whose loads and initial

real power generations are same as in the case of Subbaraj and Rajnarayanan

(2009). Case-II (critical case) is for heavy loads whose loads and initial power

generations are twice as those of case-I. In both the cases, the base MVA is

taken 100.

Based on highest L-index values, bus 5 of the 6-bus system, bus 14

of the IEEE 14-bus system and bus 30 of the IEEE 30-bus system are

identified as critical load buses.

In 6 bus system, SVC is placed at bus 5, TCSC is placed in between

buses 2 and 5, and UPFC is placed in between buses 2 and 5 to perform the

99

test for the base and critical cases. L-index and voltage magnitudes of 6-bus

system without and with FACTS devices for base and critical cases are

summarized in Tables 8.1 to 8.4.

Table 8.1 shows the L-index values of the 6-bus system without and

with placement of FACTS devices for base case. When SVC is placed at bus

5, the L-index value is reduced from 0.0665 to 0.0463. When TCSC is placed

in between buses 2 and 5, the L-index value is reduced from 0.0665 to 0.0447

at load bus 5. When UPFC is placed in between buses 2 and 5, the L-index

value is reduced from 0.0665 to 0.0374 at load bus 5. Table 8.2 shows the

voltage magnitudes of the 6-bus system without and with placement of

FACTS devices for base case. The voltage of the load bus 5 without FACTS

devices for base case is 0.9972. When SVC is placed at bus 5, the voltage of

load bus 5 gets improved to 1.0193. When TCSC is placed in between buses 2

and 5, the voltage of load bus 5 gets improved to 1.0208. When UPFC is

placed in between buses 2 and 5, the voltage of load bus 5 gets improved to

1.0240.

Table 8.1 L-Index Values of 6-bus system (Base case)

Load

Bus

No.

Without

FACTS

With

SVC

(at bus 5)

With

TCSC(between

buses 2-5)

With UPFC

(shunt at bus 5

series between

buses 2-5)

4 0.0632 0.0628 0.0628 0.0628

5 0.0665 0.0463 0.0447 0.0374

6 0.0553 0.0546 0.0546 0.0546

100

Table 8.2 Voltage Magnitudes of 6-bus system (Base case)

Load

Bus

No.

Without

FACTS

With SVC

(at bus 5)

With TCSC

(between buses

2-5)

With UPFC

(shunt at bus 5

series between

buses 2-5)

4 0.9953 1.0005 1.0005 1.0005

5 0.9972 1.0193 1.0208 1.0240

6 1.0104 1.0181 1.0181 1.0181

Table 8.3 shows the L-index values of the 6-bus system without and

with placement of FACTS devices for critical case. When SVC is placed at

bus 5, the L-index value is reduced from 0.1126 to 0.0814. When TCSC is

placed in between buses 2 and 5, the L-index value is reduced from 0.1126 to

0.0733 at load bus 5. When UPFC is placed in between buses 2 and 5, the L-

index value is reduced from 0.1126 to 0.0662 at load bus 5. Table 8.4 shows

the voltage magnitudes of the 6-bus system without and with placement of

FACTS devices for critical case. The voltage of the load bus 5 without

FACTS devices for critical case is 0.9461 and it is below the minimum value

of 0.9500. When SVC is placed at bus 5, the voltage of load bus 5 gets

improved to 0.9526. When TCSC is placed in between buses 2 and 5, the

voltage of load bus 5 gets improved to 0.9566. When UPFC is placed in

between buses 2 and 5, the voltage of load bus 5 gets improved to 0.9592.

Table 8.3 L-Index Values of 6-bus system (Critical case)

Load

Bus

No.

Without

FACTS

With SVC

(at bus 5)

With TCSC

(between

buses 2-5)

With UPFC

(shunt at bus 5 series

between buses 2-5)

4 0.1047 0.1045 0.1045 0.1045

5 0.1126 0.0814 0.0733 0.0662

6 0.0912 0.0909 0.0909 0.0909

101

Table 8.4 Voltage Magnitudes of 6-bus system (Critical case)

Load

Bus

No.

Without

FACTS

With SVC

(at bus 5)

With TCSC

(between

bus 2-5)

With UPFC


between buses 2-5)

4 0.9546 0.9550 0.9550 0.9550

5 0.9461 0.9526 0.9566 0.9592

6 0.9610 0.9614 0.9614 0.9614

To illustrate convergence of the algorithm, the relationship between

optimum compensation (Qc) is plotted against the total cost ($) as shown in

Figures 8.1 and 8.2 for 6-bus system (Base case and Critical case).

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 22.1

2.15

2.2

2.25

2.3

2.35

2.4

2.45

2.5x 10

4

x=Qc

z=

Loss+

Instc

ost

Nutrient concentration (valleys=food, peaks=noxious)

Figure 8.1 Total Cost ($) – Optimum Compensation (Qc) Curve for 6-

bus system with SVC at Bus 5 (Base case)

(p.u)

($)

102

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 22.48

2.5

2.52

2.54

2.56

2.58

2.6x 10

4

x=Qc

z=

Loss+

Instc

ost


Figure 8.2 Total Cost ($) - Optimum Compensation (Qc) Curve for 6-bus

system with SVC at Bus 5 (Critical case)

In IEEE 14- bus system, SVC is placed at bus 14, TCSC is placed in

between buses 9 and 14, and UPFC is placed in between buses 9 and 14 to

perform the test for the base and critical cases. L-index and voltage

magnitudes of IEEE 14-bus system without and with FACTS devices for base

and critical cases are summarized in Tables 8.5 to 8.8.

Table 8.5 shows the L-index values of the IEEE 14-bus system

without and with placement of FACTS devices for base case. When SVC is

placed at bus 14, the L-index value reduced from 0.0256 to 0.0193. When

TCSC is placed in between buses 9 and 14, the L-index value is reduced from

0.0256 to 0.0099 at load bus 14 and the L-index value is reduced from 0.0129

to 0.0077 at load bus 9. When UPFC is placed in between buses 9 and 14, the

L-index value is reduced from 0.0256 to 0.0083 at load bus 14 and the

L-index value is reduced from 0.0129 to 0.0065 at load bus 9.

x=Qc (p.u)

z=L

oss

+In

stco

st (

$)

103

Table 8.6 shows the voltage magnitudes of the IEEE 14-bus system

without and with placement of FACTS devices for base case. The voltage of

the load bus 14 without FACTS devices for base case is 1.0168. When SVC is

placed at bus 14, the voltage of load bus 14 gets improved to 1.0265. When

TCSC is placed in between buses 9 and 14, the voltage of load bus 14 gets

improved to 1.0355 and the voltage of load bus 9 gets improved from 1.0267

to 1.0402. When UPFC is placed in between buses 9 and 14, the voltage of

load bus 14 gets improved to 1.0379 and the voltage of load bus 9 gets

improved from 1.0267 to 1.0412.

Table 8.5 L-Index Values of IEEE 14-bus system (Base case)

Load

Bus

No.

Without

FACTS

With SVC

(at bus 14 )

With TCSC

(between

buses 9-14)

With UPFC

( shunt at bus 14

series between

buses 9-14)

4 0.0115 0.0115 0.0115 0.0115

5 0.0020 0.0020 0.0020 0.0020

7 0.0000 0.0000 0.0000 0.0000

9 0.0129 0.0127 0.0077 0.0065

10 0.0064 0.0062 0.0062 0.0062

11 0.0039 0.0038 0.0038 0.0038

12 0.0084 0.0084 0.0084 0.0084

13 0.0106 0.0106 0.0106 0.0106

14 0.0256 0.0193 0.0099 0.0083

104

Table 8.6 Voltage Magnitudes of IEEE 14-bus system (Base case)

Load

Bus

No.

Without

FACTS

With SVC

(at bus 14 )

With TCSC

(between buses

9-14)

With UPFC

( shunt at bus 14

series between

buses 9-14)

4 1.0239 1.0239 1.0239 1.0239

5 1.0329 1.0329 1.0329 1.0329

7 1.0438 1.0438 1.0438 1.0438

9 1.0267 1.0270 1.0402 1.0412

10 1.0268 1.0271 1.0271 1.0271

11 1.0446 1.0450 1.0450 1.0450

12 1.0529 1.0529 1.0529 1.0529

13 1.0461 1.0461 1.0461 1.0461

14 1.0168 1.0265 1.0355 1.0379


without and with placement of FACTS devices for critical case. When SVC is

placed at bus 14, the L-index value is reduced from 0.1098 to 0.0848. When

TCSC is placed in between buses 9 and 14, the L-index value is reduced from

0.1098 to 0.0762 at load bus 14 and the L-index value is reduced from 0.0245

to 0.0160 at load bus 9. When UPFC is placed in between buses 9 and 14, the

L-index value is reduced from 0.1098 to 0.0724 at load bus 14 and the L-

index value is reduced from 0.0245 to 0.0156 at load bus 9.

Table 8.8 shows the voltage magnitudes of the IEEE 14-bus system

without and with placement of FACTS devices for critical case. The voltage

of the load bus 14 without FACTS devices for critical case is 0.9470 and it is

105

below the minimum value of 0.9500. When SVC is placed at bus 14, the

voltage of load bus 14 gets improved to 0.9502. When TCSC is placed in

between buses 9 and 14, the voltage of load bus 14 gets improved to 0.9521

and the voltage of load bus 9 gets improved from 1.0034 to 1.0220. When

UPFC is placed in between buses 9 and 14, the voltage of load bus 14 gets

improved to 0.9528 and the voltage of load bus 9 get improved from 1.0034

to 1.0228.



Figures 8.3 and 8.4 for IEEE 14-bus system (Base case and Critical case).

Table 8.7 L-Index Values of IEEE 14-bus system (Critical case)

Load

Bus

No.

Without

FACTS

With SVC

(at bus 14)

With TCSC

(between

buses 9-14)

With UPFC

( shunt at bus 14

series between

buses 9-14)

4 0.0246 0.0244 0.0244 0.0243

5 0.0042 0.0042 0.0042 0.0042

7 0.0000 0.0000 0.0000 0.0000

9 0.0245 0.0242 0.0160 0.0156

10 0.0168 0.0168 0.0168 0.0168

11 0.0073 0.0070 0.0070 0.0070

12 0.0118 0.0118 0.0118 0.0118

13 0.0206 0.0206 0.0206 0.0206

14 0.1098 0.0848 0.0762 0.0724

106

Table 8.8 Voltage Magnitudes of IEEE 14-bus system (Critical case)

Load

Bus

No.

Without

FACTS

With SVC

(at bus 14)

With TCSC

(between buses

9-14)

With UPFC (shunt

at bus 14 series

between buses 9-14)

4 0.9898 0.9902 0.9902 0.9902

5 0.9976 0.9976 0.9976 0.9976

7 1.0228 1.0228 1.0228 1.0228

9 1.0034 1.0040 1.0220 1.0228

10 1.0043 1.0048 1.0048 1.0048

11 1.0312 1.0316 1.0316 1.0316

12 1.0394 1.0394 1.0394 1.0394

13 1.0314 1.0314 1.0314 1.0314

14 0.9470 0.9502 0.9521 0.9528

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 22.051

2.052

2.053

2.054

2.055

2.056

2.057

2.058x 10

5

x=Qc

z=Loss+In

stc

ost


Figure 8.3 Total Cost ($) - Optimum Compensation (Qc) Curve for IEEE

14-bus system with SVC at Bus 14 (Base case)

($)

x=Qc (p.u)

z=L

oss

+In

stco

st (

$)

107

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 24.349

4.3495

4.35

4.3505

4.351

4.3515

4.352

4.3525

4.353

4.3535x 10

5

x=Qc

z=Loss+In

stc

ost



14-bus system with SVC at Bus 14 (Critical case)

In IEEE 30- bus system, SVC placed at bus 30, TCSC placed in

between buses 29 and 30, and UPFC placed in between buses 29 and 30 to

perform the test for the base and critical cases. L-index and voltage

magnitudes of IEEE 30-bus system without and with FACTS devices for base

and critical cases are summarized in Tables 8.9 to 8.12.


without and with placement of FACTS devices for base case. When SVC is


TCSC is placed in between buses 29 and 30, the L-index value is reduced

from 0.0340 to 0.0152 at load bus 30 and the L-index value is reduced from

0.0066 to 0.0038 at load bus 29. When UPFC is placed in between buses 29

and 30, the L-index value is reduced from 0.0340 to 0.0147 at load bus 30 and

the L-index value is reduced from 0.0066 to 0.0033 at load bus 29.

Table 8.10 shows the voltage magnitudes of the IEEE 30-bus

system without and with placement of FACTS devices for base case. The

x=Qc (p.u)

z=L

oss

+In

stco

st (

$)

108

voltage of the load bus 30 without FACTS devices for base case is 0.9614.

When SVC is placed at bus 30, the voltage of load bus 30 gets improved to

0.9701. When TCSC is placed in between buses 29 and 30, the voltage of

load bus 30 gets improved to 0.9732 and the voltage of load bus 29 gets

improved from 0.9708 to 0.9764. When UPFC is placed in between buses 29

and 30, the voltage of load bus 30 gets improved to 0.9751 and the voltage of

load bus 29 gets improved from 0.9708 to 0.9773.

Table 8.9 L-Index Values of IEEE 30-bus system (Base case)

Load Bus

No.

Without

FACTS

With SVC

(at bus 30)

With TCSC

(between buses

29-30)

With UPFC


between buses 29-30)

3 0.0009 0.0008 0.0008 0.0008

4 0.0013 0.0011 0.0011 0.0011

6 0.0000 0.0000 0.0000 0.0000

7 0.0129 0.0127 0.0127 0.0127

9 0.0000 0.0000 0.0000 0.0000

10 0.0013 0.0012 0.0012 0.0012

12 0.0050 0.0049 0.0049 0.0049

14 0.0092 0.0091 0.0091 0.0091

15 0.0045 0.0045 0.0045 0.0045

16 0.0040 0.0040 0.0040 0.0040

17 0.0063 0.0062 0.0062 0.0062

18 0.0030 0.0027 0.0027 0.0027

19 0.0051 0.0049 0.0049 0.0049

20 0.0013 0.0013 0.0013 0.0013

21 0.0036 0.0036 0.0036 0.0036

22 0.0000 0.0000 0.0000 0.0000

23 0.0046 0.0045 0.0045 0.0045

24 0.0107 0.0107 0.0107 0.0107

25 0.0000 0.0000 0.0000 0.0000

26 0.0206 0.0202 0.0202 0.0202

27 0.0000 0.0000 0.0000 0.0000

28 0.0000 0.0000 0.0000 0.0000

29 0.0066 0.0066 0.0038 0.0033

30 0.0340 0.0329 0.0152 0.0147

109

Table 8.10 Voltage Magnitudes of IEEE 30-bus system (Base case)

Load

Bus

No.

Without

FACTS

With SVC

(at bus 30)

With TCSC

(between buses

29-30)

With UPFC (shunt

at bus 30 series

between buses

29-30)

3 1.0230 1.0232 1.0232 1.0232

4 1.0190 1.0196 1.0196 1.0196

6 1.0182 1.0190 1.0190 1.0190

7 1.0049 1.0052 1.0052 1.0052

9 1.0334 1.0334 1.0334 1.0334

10 1.0128 1.0131 1.0131 1.0131

12 1.0346 1.0348 1.0348 1.0348

14 1.0170 1.0173 1.0173 1.0173

15 1.0117 1.0117 1.0117 1.0117

16 1.0185 1.0185 1.0185 1.0185

17 1.0094 1.0096 1.0096 1.0096

18 0.9998 1.0001 1.0001 1.0001

19 0.9960 0.9965 0.9965 0.9965

20 0.9993 0.9993 0.9993 0.9993

21 1.0004 1.0004 1.0004 1.0004

22 1.0006 1.0006 1.0006 1.0006

23 0.9968 0.9972 0.9972 0.9972

24 0.9852 0.9852 0.9852 0.9852

25 0.9850 0.9850 0.9850 0.9850

26 0.9669 0.9672 0.9672 0.9672

27 0.9938 0.9938 0.9938 0.9938

28 1.0151 1.0151 1.0151 1.0151

29 0.9708 0.9708 0.9764 0.9773

30 0.9614 0.9701 0.9732 0.9751

110


without and with placement of FACTS devices for critical case. When SVC is


TCSC is placed in between buses 29 and 30, the L-index value is reduced

from 0.0610 to 0.0357 at load bus 30 and the L-index value is reduced from

0.0149 to 0.0075 at load bus 29. When UPFC is placed in between buses 29

and 30, the L-index value is reduced from 0.0610 to 0.0349 at load bus 30 and

the L-index value is reduced from 0.0149 to 0.0073 at load bus 29.

Table 8.12 shows the voltage magnitudes of the IEEE 30-bus

system without and with placement of FACTS devices for critical case. The

voltage of the load bus 30 without FACTS devices for critical case is 0.9428

and it is below the minimum value of 0.9500. When SVC is placed at bus 30,

the voltage of load bus 30 gets improved to 0.9604. When TCSC is placed in

between buses 29 and 30, the voltage of load bus 30 gets improved to 0.9616

and the voltage of load bus 29 gets improved from 0.9608 to 0.9662. When

UPFC is placed in between buses 29 and 30, the voltage of load bus 30 gets

improved to 0.9622 and the voltage of load bus 29 gets improved from 0.9608

to 0.9668.

111

Table 8.11 L-Index Values of IEEE 30-bus system (Critical case)

Load

Bus

No.

Without

FACTS

With SVC

(at bus 30)

With TCSC

(between

buses 29-30)

With UPFC( shunt at

bus 30 series between

buses 29-30)

3 0.0018 0.0018 0.0018 0.0018

4 0.0028 0.0026 0.0026 0.0026

6 0.0000 0.0000 0.0000 0.0000

7 0.0305 0.0305 0.0305 0.0305

9 0.0000 0.0000 0.0000 0.0000

10 0.0042 0.0041 0.0041 0.0041

12 0.0142 0.0140 0.0140 0.0140

14 0.0313 0.0312 0.0312 0.0312

15 0.0154 0.0152 0.0152 0.0152

16 0.0123 0.0120 0.0120 0.0120

17 0.0186 0.0186 0.0186 0.0186

18 0.0104 0.0103 0.0103 0.0103

19 0.0173 0.0170 0.0170 0.0170

20 0.0045 0.0043 0.0043 0.0043

21 0.0098 0.0098 0.0098 0.0098

22 0.0000 0.0000 0.0000 0.0000

23 0.0100 0.0100 0.0100 0.0100

24 0.0215 0.0212 0.0212 0.0212

25 0.0000 0.0000 0.0000 0.0000

26 0.0405 0.0403 0.0403 0.0403

27 0.0000 0.0000 0.0000 0.0000

28 0.0000 0.0000 0.0000 0.0000

29 0.0149 0.0149 0.0075 0.0073

30 0.0610 0.0401 0.0357 0.0349

112

Table 8.12 Voltage Magnitudes of IEEE 30-bus system (Critical case)

Load

Bus

No.

Without

FACTS

With SVC

(at bus 30)

With TCSC

(between

buses 29-30)

With UPFC (shunt at

bus 30 series between

buses 29-30)

3 0.9714 0.9714 0.9714 0.9714

4 0.9684 0.9688 0.9688 0.9688

6 0.9863 0.9863 0.9863 0.9863

7 0.9662 0.9662 0.9662 0.9662

9 0.9898 0.9898 0.9898 0.9898

10 0.9553 0.9556 0.9556 0.9556

12 0.9810 0.9814 0.9814 0.9814

14 0.9542 0.9544 0.9544 0.9544

15 0.9770 0.9772 0.9772 0.9772

16 0.9580 0.9582 0.9582 0.9582

17 0.9581 0.9581 0.9581 0.9581

18 0.9541 0.9544 0.9544 0.9544

19 0.9583 0.9589 0.9589 0.9589

20 0.9502 0.9506 0.9506 0.9506

21 0.9501 0.9507 0.9507 0.9507

22 0.9504 0.9504 0.9504 0.9504

23 0.9508 0.9508 0.9508 0.9508

24 0.9589 0.9594 0.9594 0.9594

25 0.9581 0.9581 0.9581 0.9581

26 0.9514 0.9518 0.9518 0.9518

27 0.9504 0.9504 0.9504 0.9504

28 0.9818 0.9818 0.9818 0.9818

29 0.9608 0.9608 0.9662 0.9668

30 0.9428 0.9604 0.9616 0.9622



Figures 8.5 and 8.6 for IEEE 30-bus system (Base case and Critical case).

113

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 22.736

2.737

2.738

2.739

2.74

2.741

2.742x 10

5

x=Qc

z=Loss+In

stc

ost



30-bus system with SVC at Bus 30 (Base case)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 24.5385

4.539

4.5395

4.54

4.5405

4.541x 10

5

x=Qc

z=Loss+In

stc

ost


Figure 8.6 Total Cost ($) - Optimum Compensation (Qc) Curve for 30-

bus system with SVC at Bus 30 (Critical case)

x=Qc (p.u)

z=L

oss

+In

stco

st (

$)

x=Qc (p.u)

z=L

oss

+In

stco

st (

$)

114

The compensation for the installation of reactive power injections

and line reactance are identified with the help of proposed algorithm and the

optimum compensation values are listed in Table 8.13. The total cost was

calculated for different durations of application of load. Hence the increase in

cost was noticed for higher durations as in Table 8.13 even though the

percentage compensation is lesser for test systems.

Table 8.13 Total Cost ($) and Optimum Compensation (p.u)

Optimum

Compensation (p.u)Total Cost ($)

Test

System

Types

of

FACTS

Devices

Bus

No/LineBase case

Critical

case

Base

case

Critical

case

SVC 5 0.6031 0.6215 21110 24860

TCSC 2-5 -0.1482 -0.1680 23066 296246-Bus

System UPFC 2-5 -0.0312

& 0.5030

-0.0405&

0.5135

23124 46659

SVC 14 0.6247 0.6527 205170 434980

TCSC 9-14 -0.1402 -0.1578 95147 155488IEEE14-BusSystem UPFC 9-14 -0.03346

& 0.5147-0.0352

& 0.5214

102600 153110

SVC 30 0.6468 0.6491 273660 453890

TCSC 29-30 -0.2405 -0.2610 558400 378150IEEE

30-BusSystem UPFC 29-30 -0.0520

& 0.5012-0.0662&0.5164

294000 513520

Table 8.14 gives the real power loss values and computational time

for the proposed three test systems. In IEEE 14-bus system, Bacterial

Foraging Algorithm obtained 3.53% loss reduction, whereas the Evolutionary

Programming obtained 1.19% loss reduction and Self Adaptive Real coded

115

Genetic Algorithm obtained 2.19% loss reduction. In IEEE 30-bus system,

Bacterial Foraging Algorithm obtained 0.59% loss reduction compared with

base value. For IEEE 14-bus and IEEE 30-bus systems, the Bacterial

Foraging Algorithm gives minimum loss with lesser computational time

compared with the value reported in Subbaraj and Rajnarayanan (2009) for

the same test systems (By Referring to Table 8.14). Similar results are

obtained when TCSC and UPFC are placed between weakest load buses.

Table 8.15 summarizes the performance comparison of FACTS devices

(referring Tables 8.13 and 8.14). The significant advantages of self-

commutated compensators make them interesting alternative to improve

compensation characteristics and also increase the performance of AC power

systems.

Table 8.14 Real Power Loss and Computational Time

6 Bus IEEE-14 Bus IEEE-30 Bus

Algorithm Particulars Base

case

Critical

case

Base

case

Critical

case

Base

case

Critical

case

Real PowerLoss(MW)

-- -- 13.35 60.44 16.39 77.925EvolutionaryProgramming(EP Subbaraj andRajnarayanan (2009)

ComputationalTime (sec)

-- -- 72 78 103 118

Real PowerLoss (MW)

-- -- 13.22 59.49 16.09 76.25Self-Adaptive RealCoded GeneticAlgorithm (SARGASubbaraj andRajnarayanan (2009)


-- -- 54 66 87 101

Real PowerLoss (MW)

4.54 21.89 13.19 58.42 10.14 74.72Bacterial ForagingOptimizationAlgorithm (BFOA)for SVC


14 22 38 52 68 85

Real PowerLoss (MW)

4.47 21.66 13.16 58.34 10.12 74.64Bacterial ForagingOptimizationAlgorithm (BFOA)for TCSC


18 26 42 58 79 92

Real PowerLoss (MW)

4.32 20.83 13.05 58.08 10.10 74.41Bacterial ForagingOptimizationAlgorithm (BFOA)for UPFC


21 30 51 66 86 98

116

Table 8.15 Performance Comparison of FACTS Devices

FACTS DevicesParticulars

SVC TCSC UPFC

Voltage Profile Improvement (pu) Good Very Good Excellent

Loss Minimization (MW) Low Moderate High

Total Cost Minimization ($) Excellent Very Good Good

Computational Time (Sec) Low Moderate High

Figures 8.7 to 8.10 show the comparison of L – index values and

voltage magnitudes in 6-bus system without and with placement of FACTS

devices.

1 2 3 4 5 60

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Bus Number

L-i

nd

ex

L-INDEX VALUES FOR 6-BUS SYSTEM(BASE CASE)

without FACTS

SVC at bus 5

TCSC at line 2-5

UPFC at line 2-5

Figure 8.7 L-Index Values for 6-bus system (Base case)

117

1 2 3 4 5 60.99

1

1.01

1.02

1.03

1.04

1.05

1.06

1.07

Bus Number

Voltage M

agnitude(p

.u.)

VOLTAGES VALUES FOR 6-BUS SYSTEM(BASE CASE)

without FACTS

SVC at bus 5

TCSC at line 2-5

UPFC at line 2-5

Figure 8.8 Voltage Magnitudes for 6-bus system (Base case)

1 2 3 4 5 60

0.02

0.04

0.06

0.08

0.1

0.12

Bus Number

L-i

nd

ex

L-INDEX VALUES FOR 6-BUS SYSTEM(CRITICAL CASE)

without FACTS

SVC at bus 5

TCSC at line 2-5

UPFC at line 2-5

Figure 8.9 L-Index Values for 6-bus system (Critical case)

118

1 2 3 4 5 60.94

0.96

0.98

1

1.02

1.04

1.06

Bus Number

Voltage M

agnitude(p

.u.)

VOLTAGES VALUES FOR 6-BUS SYSTEM(CRITICAL CASE)

without FACTS

SVC at bus 5

TCSC at line 2-5

UPFC at line 2-5

Figure 8.10 Voltage Magnitudes for 6-bus system (Critical case)


voltage magnitudes in IEEE 14-bus system without and with placement of

FACTS devices.

1 2 3 4 5 6 7 8 9 10 11 12 13 140

0.005

0.01

0.015

0.02

0.025

0.03

Bus Number

L-index

L-INDEX VALUES FOR IEEE 14-BUS SYSTEM(BASE CASE)

without FACTS

SVC at bus 14

TCSC at line 9-14

UPFC at line 9-14

Figure 8.11 L-Index Values for IEEE 14-bus system (Base case )

119

1 2 3 4 5 6 7 8 9 10 11 12 13 141.01

1.02

1.03

1.04

1.05

1.06

1.07

1.08

Bus Number

Vo

ltag

e M

ag

nitu

de(p

.u)

VOLTAGE MAGNITUDES FOR IEEE 14-BUS SYSTEM(BASE CASE)

without FACTS

SVC at bus 14

TCSC at line 9-14

UPFC at line 9-14

Figure 8.12 Voltage Magnitudes for IEEE 14-bus system (Base case)

1 2 3 4 5 6 7 8 9 10 11 12 13 140

0.02

0.04

0.06

0.08

0.1

0.12

Bus Number

L-index

L-INDEX VALUES FOR IEEE 14-BUS SYSTEM(CRITICAL CASE)

without FACTS

SVC at bus 14

TCSC at line 9-14

UPFC at line 9-14

Figure 8.13 L-Index Values for IEEE 14-bus system (Critical case)

120

1 2 3 4 5 6 7 8 9 10 11 12 13 140.94

0.96

0.98

1

1.02

1.04

1.06

Bus Number

Vo

lta

ge

Ma

gn

itu

de

(p.u

)

VOLTAGE MAGNITUDES FOR IEEE 14-BUS SYSTEM(CRITICAL CASE)

without FACTS

SVC at bus 14

TCSC at line 9-14

UPFC at line 9-14

Figure 8.14 Voltage Magnitudes for IEEE 14-bus system (Critical case)


voltage magnitudes in IEEE 30-bus system without and with placement of

FACTS devices. From the results for all the three test systems, it is found that

TCSC produced better results in comparison with SVC. UPFC produced best

result in comparison with SVC and TCSC.

121

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 300

0.005

0.01

0.015

0.02

0.025

0.03

0.035

Bus Number

L-index

L-INDEX VALUES FOR IEEE30-BUS SYSTEM(BASE CASE)

without FACTS

SVC at bus 30

TCSC at line 29-30

UPFC at line 29-30

Figure 8.15 L-Index Values for IEEE 30-bus system (Base case)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 300.95

0.96

0.97

0.98

0.99

1

1.01

1.02

1.03

1.04

1.05

Bus Number

Volt

age M

agnit

ude

(p.u

)

VOLTAGE MAGNITUDES FOR IEEE 30-BUS SYSTEM(BASE CASE)

without FACTS

SVC at bus 30

TCSC at line 29-30

UPFC at line 29-30

Figure 8.16 Voltage Magnitudes for IEEE 30-bus system (Base case)

122

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 300

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Bus Number

L-in

de

x

L-INDEX VALUES FOR IEEE 30-BUS SYSTEM(CRITICAL CASE)

without FACTS

SVC at bus 30

TCSC at line 29-30

UPFC at line 29-30

Figure 8.17 L-Index Values for IEEE 30-bus system (Critical case)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 300.94

0.96

0.98

1

1.02

1.04

1.06

Bus Number

Voltage M

agnitude(p

.u)

VOLTAGE MAGNITUDES FOR IEEE 30-BUS SYSTEM(CRITICAL CASE)

without FACTS

SVC at bus 30

TCSC at line 29-30

UPFC at line 29-30

Figure 8.18 Voltage Magnitudes for IEEE 30-bus system (Critical case)

123

Table 8.16 shows the results comparison between FVSI and L-

index. Based on the test results, it is found that L-index gives high loss

reduction with less computational time.

Table 8.16 Results Comparison between FVSI and L-index

IEEE-14 Bus

FVSI

IEEE-14 Bus

L-indexAlgorithm Particulars

Base

case

Critical

case

Base

Case

Critical

case

Real Power

Loss(MW)13.35 58.68 13.19 58.42

Bacterial Foraging

Optimization

Algorithm (BFOA)

for SVC

Computational

Time(sec)

42 58 38 52

Real Power

Loss(MW)13.28 58.46 13.16 58.34

Bacterial Foraging

Optimization

Algorithm (BFOA)

for TCSC

Computational

Time(sec)46 60 42 58

Real Power

Loss(MW)13.20 58.12 13.05 58.08

Bacterial Foraging

Optimization

Algorithm (BFOA)

for UPFC

Computational

Time(sec)57 68 51 66

124

8.3 CONCLUSION

L-index values, voltage profile at each bus and power loss of

the systems without FACTS devices are calculated by

developing Newton-Raphson load flow algorithm to 6-bus,

IEEE 14-bus and IEEE 30-bus test systems.

Based on L-index values, the vulnerable load bus is identified

for the placement of FACTS devices.

SVC, TCSC and UPFC are placed accordingly and achieved

the multi-objectives of minimization of real power loss, L-

index, improvement of voltage profile, minimization of total

cost and enhancement of voltage stability.

From the results, it is concluded that the systems perform

better when the FACTS devices are connected. Results show

that Bacterial Foraging Algorithm can be used to optimize the

power system for practical and large scale applications.

chapter 8 optimization of power system...

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