Page 1

Reduction of Transmission line Loss by Using

Interline Power Flow Controllers

S. Jangjit*, P. Kumkratug** and P. Laohachai***

*Kasetsart University Chalermphakiet Sakon Nakhon Province Campus,

Electrical and Computer Engineering, Sakon Nakhon, Thailand

Email: seesak.j@hotmail.com

**Kasetsart University Sriracha Campus, Electrical Engineering, Chonburi, Thailand

Email: PC475601@gmail.com

*** Kasetsart University Bangkhen Campus, Electrical Engineering, Bangkok, Thailand

Email: fengptl@ku.ac.th

Abstract-

transmission line loss by using Interline Power Flow Controller

(IPFC). The IPFC is a novel FACTS device which can control

power flow in power systems. The IPFC consists of multi-series

converters. The power flow through the line can be regulated by

controlling both magnitudes and angles of the series voltages

injected by an IPFC. This paper used differential evolution to

determine the control parameters on an IPFC. The proposed

method is tested on a sample multi-machine system.

This paper deals with improvement the

I.

INTRODUCTION

A variety factor, such as environmental legislation, rights

of way issues, capital investment, deregulation policies, etc.

constrain the construction of transmissions. Electric utilities

are now forced to operate their system in such a way that

makes better utilization of existing transmission facilities. A

number of Flexible AC Transmission System (FACTS)

controllers, based on the rapid development of power

electronics technology, have been proposed in recent years for

better utilization of existing transmission facilities [1]. One of

the consequences such a stressed system is the treat of

transmission line loss.

For many years, one of the major interests of power

utilities is the improvement of transmission. FACTS devices

are found to be very effective for improving the transmission

line loss [2]. An interline Power Flow Controller (IPFC) is a

novel FACTS device. It is the combination of two or more

SSSCs coupled via a common DC link. With this

configuration, IPFC has the capability to provide controllable

active power exchange between transmission lines [3]. To

reduce transmission line loss of power system, the IPFC is

needed to be carefully control.

The trial and error method of optimization solution is time

consuming. The differential evolution (DE) algorithm,

proposed by Stron and Price [4], is a powerful method to find

global optimizer. The successful applications of DE were

reported in [5, 6, and 7].

The outline of the paper is follows: In Section II, the

mathematical model is briefly derived. In Section III, The

control strategy of IPFC based on differential evolution is

discussed. The capability of IPFC to improve transmission

line loss is verified in Section IV.

II. MATHEMATICAL MODEL

The IPFC consists of multiple series voltage source

converters coupled through a common DC link as shown in

Figure. 1. The DC link provides a path to exchange active

power between series converters [8-11].

The power flow through the line can be regulated by

controlling both magnitudes and angles of the series voltage

injections. The converters have the capability of independently

generating or absorbing the reactive power. However, without

loss of transformer and converter, the overall active power

exchange between series converters is zero [8].

Figure 2 shows the equivalent circuit of Figure 1, where the

converters are represented by synchronous voltage sources

with associate transformer leakage reactance.

The complex power injected by series converter I can be

written as

P jQ

=+

S

11

()

sL

=−

VI

⎡

⎢

⎣

Here,

11

1/

s

bX

=

111sss

∗

1111

11

1

mmssnn

ss

s

VVV

V

jX

θθθ

θ

∗

∠−∠−∠

=∠

⎤

⎥

⎦

(1)

Figure 1. Configuration of IPFC.

Page 2

mm

V

θ∠

11nn

V

θ∠

1 s

jX

22nn

V

θ∠

11ss V

θ∠

22ss V

θ∠

2s

jX

1L I

2L I

Figure 2. Equivalent Circuits for IPFC.

The active (

series converter I are given by

[

11

Re

ss

P =

S

cos(90

ms

bV V

= −

+

and

[

11

Im

ss

Q =

S

sin(90

ms

bV V

= −

++

Similarly, the active (

injected by the series converter II are given by

[

22

Re

ss

P =

S

o

22

cos(90

ms

bV V

= −

+

and

[

22

Im

ss

Q =

S

o

22

sin(90

ms

bV V

= −

++

Here,

22

1/

s

bX

=

The complex power flow in direction

=+

S

1

()

mL

= V I

1sP ) and reactive (

1s

Q ) powers injected by the

]

o

111

o

11111

)

cos(90)

ms

snns

bV V

θ

θ−

θ

θ+

−+

(2)

]

o

111

θ−

2

1

o

111111

)

sin(90)

ms

ssnns

bV bV V

θθ

θ

−+

+

(3)

2sP ) and reactive (

2s

Q ) powers

]

2

o

22222

)

cos(90)

ms

snns

bV V

θ

θ−

θ

+θ

−+

(4)

]

2

2

2

o

222222

)

sin(90)

ms

−

ssnns

bVbV V

θθ

θθ

−+

+

(5)

1

mn

→

is

111 mn mnmn

P jQ

∗

1

jX

111

1

mmssnn

mm

s

VVV

V

θθθ

θ

∗

∠−∠−∠

=∠

⎡

⎢

⎣

⎤

⎥

⎦

(6)

The active power flow in direction

1

mn

→

is given by

o

1111

o

111

cos(90)

cos(90)

mnmssm

nmnm

P bV V

bV V

θ

θ−

θ

θ+

= −−+

−

(7)

and the reactive power flow in direction

2

111

mnmm

Q bV bV V

=−

−

With no active power loss between bus m and bus

can be written as

PP

= −

However the reactive power flow

1

mn

→

is written by

o

11

o

111

sin(90)

sin(90)

ssm

nmnm

bV V

θ

θ

θ

θ

−

+

+

−

(8)

1n , this

11 mn n m

(9)

1m

Q from bus

1n to bus

m is not equal to

→

is given by

QbV

=

−

Consider the power flow in direction

1 n m

Q

. The reactive power in direction

1nm

2

1

o

1111111

o

111

sin(90)

sin(90)

n mnnssn

nmmn

bV V

bV V

θ

θ

θ

θ

+−+

−+

(10)

2

mn

→

.The

complex power flow in direction

=+

S

(

mL

= V I

⎡

⎢

⎣

The active power flow in direction

cos(90

mnms

PbV V

= −

−

And the reactive power flow from bus m to bus

written by

2

2222

sin(90

mnmms

QbVbV V

=−

−−

It can be seen from (6) to (13) that the power flow of the

power system can be controlled by the series injected voltages

2

mn

→

is given by

222

)

mnmn mn

P jQ

1

∗

1122

1

mmssnn

m

s

VVV

jX

θθθ

∗

∠−∠−∠

=

⎤

⎥

⎦

n

V

(11)

2

m

→

is given by

o

2222

o

222

)

cos(90)

sm

nmnm

bV V

θ

θ−

θ

θ+

−+

(12)

2n is

o

2

o

222

)

sin(90)

sm

nmnm

bV V

θ

θ

θ

θ

−

+

+

(13)

Page 3

of converter I (

respectively. From the operating principle of IPFC mentioned

in Section 2, the reactive power injections from converter I

(

1s

Q ) and converter II (

2s

Q

without loss consideration on both converters and

transformers, the active power flow injection

to

2

to incorporate IPFC in power flow analysis using numerical

methods such as Gauss-Seidel, Newton-Raphson, and

Decouple method [12]. It can be seen from above equations

that an IPFC can control power flow. That indicates that the

IPFC can also control the transmission line loss.

When the line loss is the summation of line flows from bus

i to j (

ji

S ), these are given by

*

ij

i ij

S

V I

=

and

where

defined positive in the direction i to j .Similarly, the line

current

direction j to i . Then, the power loss in line i

summation of

ij

i ij

S

V I

=

and

S

be written as

Lij

S

=

This paper applies the DE to minimize the total

transmission line loss.

1sV ,

1 s θ

) and converter II (

2sV

,

2s θ

),

) are independent. However,

1sP is equal

sP . With the above mathematical models, it is not difficult

ijS ) and j to i (

*

ji

ji

j

S

V I

=

(14)

ijI is the line current, which measured at bus i and

ji I is measured at bus j and defined positive in the

j

−

is the

**

ji

ji

j

V I

=

from (14), that can

ijji

SS

+

(15)

III. DIFFERENTIAL EVOLUTION (DE)

The equation of total transmission line loss is written by

=∑

X

Here n is the number of line.

X is the control parameters

If the IPFC consists of k converters the X is

1

[ x x x

=

X

It may be mentioned here that the

parameter members. It must be regulated in the such way that

the net active power exchange between converter is zeros.

Thus the objective function is given by

⎛

=⎜

⎝

The step of DE to obtain the global optimization of (17)

can be summarized by following steps[13]:

1

( )( )X

n

Lij

i

JS

=

(16)

23121

] [

=

]T

sss

V V θ

2sθ is not controlled

2

1

min ( )J ( )

ϕ

n

Lij

i

S

ϕ

=

⎞

⎟

⎠

∑

(17)

a. Initialization

The first step is to initialize the candidate solution vectors

written by

{

GjGjGj

xx

,,,

,...,

=

X

Here n is number of populations

G is number of generations

D is number of control parameters

The equation of random candidate solution is given by

(

,0 minmax

(0,1).

x randx

Here

j

xxx

max0 , min

≤≤

b. Mutation

The DE applies mutation operation to produce mutant

vector (

,,, 2,

[, ,...,

j G j G j G

mmm

=

M

vector. The DE/rand/1,one of the mutation strategies, is given

by

(

jj

j G

r Gr G

F

MXXX

Here

Grj,

1

F is positive scaling factor

c. Crossover

The crossover operation is used for generating the trail

vector

,...,(

,,,GjGjGj

uuu

=

U

binomial equation of crossover operation is written by

( [0,1)

j Gi

i

j G

i

j G

x otherwise

⎪ ⎩

Here

CR is a constant crossover rate within the range [0,1).

irand is a random integer within the range [0,D]

randi is a random number with the range [0,1)

d. Selection

For the objective function values, the control parameters

are replaced by mutation vector and target vector. The next

generation of target vector (

, +

j

X

()

j G j G

U if f

≤

=⎧⎪⎨

⎪ ⎩

The above 3 steps are repeated until the objective function is

satisfied.

}

D

1

,j=1,….,n (18)

)

min

x

iiii

jx

=+−

i =1,…..,D (19)

iii

12

]

D

G

) associated with target

123

,

,,,

)

j

r G

=+−

i=1…n (20)

X

is target vectors

)

,

21D

jG

. The standard form of

,

,

,

( ))

i

rand

im if randCR or i

u

⎧

⎪

≤=

=⎨

(21)

1G

) is selected by

,,,

,1

,

()

j G

j G

j G

f

Xotherwise

+

UX

X

(22)

Page 4

IV. SIMULATION RESULTS IN MUTI-MACHINE POWER SYSTEM

The mathematical model of IPFC is tested on 2 generators

and 3 buses as shown in Figure 3. The details of the system

data and initial operating point are given in the Appendix. The

simulation results of power flow with and without IPFC are

summarized in Table I. It can be seen from the table that the

total active and reactive power loss of the system without

IPFC are 12,266.5 kW and 33,630.8 kVAR, respectively.

However, with IPFC (

1

0.1099 pu

0.1318 pu

,

2

109.73

= −

power loss decrease to 11,950.1 kW and 31,631.5 kVAR,

respectively. This indicates that IPFC can reduce power loss in

power systems.

sV =

,

o

1

96.50

sθ = −

, and

2sV =

o

sθ

) the total active and reactive

TABLE I

SIMULATION RESULTS

Transmission Line

Line

no.

Transmission Line

Loss without IPFC

Loss

with IPFC

Ploss

(kW)

561

7,315

4,073

11,950

Improvement

Ploss

(kW)

Qloss

(kVAR)

Qloss

(kVAR)

1,122

18,288

12,220

31,631

Ploss

(kW)

Qloss

(kVAR)

-163

-4,842

7,005

1,999

1

2

3

479

5,378

6,408

12,267

959 -82

13,447

19,22

33,631

-1,937

2,335

316 Tot

Figure 3. Sample System equipped with an IPFC

V. CONCLUSION

This pare applied the Interline Power Flow Controller to

decrease transmission line loss. The IPFC is modeled as a

multi-series voltage injection. The mathematical model

indicates that IPFC can control both active and reactive power

flows. This paper uses differential evolution to control IPFC

parameter for improving the transmission line loss. The

proposed method was tested on multi-machine system.

Simulation results indicate that IPFC can reduce total active

and reactive power losses

ACKNOWLEDGMENT

The authors gratefully acknowledge Faculty of Science and

Engineering of Kasetsart University, Chalermphakiet Sakon

Nakhon Province Campus for financial support.

APPENDIX

Bus data:

Bus1: Swing bus ,

Bus 2: Regulate bus , P2=200 MW, V2=1.04 pu

Bus 3: Load bus , PL3 = 0 pu, QL3 = 0 pu

Bus 4: Load bus , PL4 = 400 MW, QL4 = 250 MVAR

Line data impedance:

Power Transformer: reactance =0.02 pu

IPFC transformer: reactance =0.001 pu

Transmission line 1: resistance=0.02 pu, reactance = 0.04 pu

Transmission line 2: resistance=0.01 pu, reactance = 0.025 pu

Transmission line 3: resistance=0.01 pu, reactance = 0.03 pu

o

1

1.05 0 pu

∠=

V

REFERENCES

[1] S.Teerathana, A. Yokoyama, Y.Nakachi and M. Yasumatsu, “An Optimal

Power Flow Control Method of Power System by Interline Power Flow

Controller (IPFC)”, in Proc. the 7th Int. Power Engineering Conf., pp 1-

6

[2] N.G. Hingorani and L. Gyugyi, “Understanding FACTS: concepts and

technology of flexible ac transmission systems”, IEEE Press, NY, 1999.

[3] L. Gyugyi, K.K.Sen, C.D.Schauder, “The interline power flow controller

concept: A new approach to power flow management in transmission

line system”, IEEE Trans. on Power Delivery, Vol. 14, No. 3, 1999, pp.

1115-1123.

[4] R. Storn and K. V. Price, “Differential evolution-A simple and efficient

heuristic for global optimization over continuous Spaces,” J. Global

Optim., vol. 11, pp. 341–359, 1997.

[5] T. Rogalsky, R. W. Derksen, and S. Kocabiyik, “Differential evolution in

aerodynamic optimization,” in Proc. 46th Annu. Conf. ofCan. Aeronaut.

space Inst., Montreal, QC, Canada, May 1999, pp. 29–36.

[6] R. Joshi and A. C. Sanderson, “Minimal representation multisensory

fusion using differential evolution,” IEEE Trans. Syst. Man Cybern.

A,Syst. Humans, vol. 29, no. 1, pp. 63–76, Jan. 1999.

[7] R. Storn, “On the usage of differential evolution for function

optimization,” in Proc. Biennial Conf. North Amer. Fuzzy Inf. Process.

Soc.,Berkeley, CA, 1996, pp. 519–523.

[8] L. Gyugyi, K.K.Sen, C.D.Schauder, “The interline power flow controller

concept: A new approach to power flow management in transmission

line system”, IEEE Trans. on Power Delivery, Vol. 14, No. 3, 1999, pp.

1115-1123.

[9] S. Bhownick, B. Das and N. Kumar, “An Advanced IPFC Model to Reuse

Newton Power Flow Codes”, IEEE Trans. on Power System, Vol. 24,

No. 2, 2009, pp. 525-532.

[10] X.P. Zhang, “Modelling of the interline power flow controller and the

generalized unified power flow controller in Newton power flow”, IEE

Proc.-Gener. Transm. Distrib., Vol. 150, pp. 268-274, May 2003.

[11] R. Leon Vasquez-Arnez and L. Cera Zanetta, “A novel approach for

modeling the steady state VSC based multiline FACTS controllers and

their constrains”, IEEE Trans. on Power System, Vol. 23, No. 1, 2008,

pp. 457-464.

[12] S.Jangjit, P.Kumkratug and P.Laohachai, “Power Flow Control by Use of

Interline Power Flow Controllers”, Journal of Research in Engineering

and Technology, Vol. 6, No.4, 2009, pp.379-385,

[13] Qin, A.K.; Huang, V.L.; Suganthan, P.N.; “Differential Evolution

Algorithm With Strategy Adaptation for Global Numerical Optimization

Evolutionary Computation”, IEEE Transactions on Volume 13, Issue 2,

April 2009 Page(s):398 - 417