Optimization Study on TSF Based on Dynamic Modeling Combined with Genetic Algorithm for a Steel Mill

(1)

Optimization Study on TSF Based on Dynamic

Modeling Combined with Genetic Algorithm for a

Steel Mill

Wang Li-guo

1

, Li Linchun

1

, Lv Linlin

1

, Xu Dian-guo

1

Dept. of Electrical and Electronics Engineering, Harbin Institute of Technology, Harbin, China

Abstract— Considering the terrible harmonic

pollution and rapid variable reactive power due to the

furnaces of 35kV bus, the TSF（Thyristor Switched

Filters）has been studied in this paper. Due to superior

performance of TSF such as high voltage, big capacity and

fast response of compensating reactive power, it was

applied to suppress harmonic current and compensate

reactive power of secondary side of main transformer of a

steel mill of Heilongjiang Province in China. An

optimization method of TSF that combining dynamics

with GA (Genetic Algorithm) is proposed in this paper.

The work conditions of TSF were modeled and analyzed

by Thevenin and Norton theorem, respectively.

Considering the perturbation of impedance and frequency

of the 35kV power system, response of fundamental

current injected into every filter of TSF was analyzed

based on dynamics analyzing method. Expressions of

harmonic current injected into every filter of TSF were

given by character calculation. The results of numerical

analysis and measuring results show that, by TSF the

harmonic currents injected into power system accord with

Chinese national standard GB/T-14549-93 and its power

factor is increased to 0.95 from before 0.82. In fact,

proposed method can apply to suppress harmonics and

compensate reactive power of furnace of 35kV bus of the

steel mile.

Index Term— Thyristor Switched Filter; dynamics

modeling; parameter perturbation; harmonic current;

reactive power; GA (Genetic Algorithm)

I. INTRODUCTION

Comparing to Passive Power Filter (PPF), Thyristor

Switched Filters (TSF) can compensate dynamic reactive

power and prevent over compensation. Comparing to

Static Var Compensator (SVC) [1-2] and Static Var

Generator (SVG) [3], TSF has the advantages of high

voltage, fast compensating dynamic reactive power,

suppressing harmonic and eliminating voltage flicker

efficiently. Comparing to Hybrid Active Power Filter

(HAPF) [4,5], TSF has the advantage of lower cost and

better work effect. Therefore, the research on TSF has

great practical value on solving the problems of serious

harmonic pollution and dynamic compensation of

reactive power on electrical distribution network of high

voltage. It also has better effect on protecting power

system and corresponding electrical equipment [6,7].

The biggest advantage of TSF to PPF is that the

switch of PPF was substituted by thyristor of TSF. In

fact, TSF can switch tuning filter by thyristor

immediately and accurately according to require of

actual reactive power. Considering the resonance of the

reactance of power system with filter capacitor of TSF

due to the harmonic current, selecting a set of

appropriate parameters of TSF is one of the main

difficulties for designing TSF. Corresponding to the

basic coding rules Thyristor Switched Capacitor (TSC)

and PPF, TSF must be taken into consideration of both

difficulties [8]. Among performance criterion of TSF

such as stability, cost, voltage grade, filter effect,

compensation capacity, the stability must be first

considered due to the potential influence of resonance

between TSF and inductance of the power system.

Especially the perturbation of frequency and inductance

of power system must be considered in order to avoid

the resonance of TSF. In fact series and parallel

resonance between TSF and power system often decided

Manuscript received Jul. 25, 2010; revised Aug. 9, 2011

†

Corresponding Author: [email protected] Tel: +86-451-86413420, Fax: +86-451-86413420, Harbin

Institute of Tech.

*

(2)

by parameters of TSF. Fig.1 gives a resonance photo of

TSF with power system of 690V. It shows that the

thyristor and the capacitor of TSF are all burned-out due

to the resonance. Therefore, when design TSF, accurate

parameters that may be avoid resonance and ensure the

safety and stability of TSF must be considered [9-10].

Fig. 1. Resonance photo of TSF with power system

How to obtain optimization parameters of TSF

based on analyzing the performance, effect and cost is

the main study intention in this paper. A method of

optimization modeling TSF that combining dynamics

analysis with GA [11] is proposed, in order to suppress

harmonic current and compensate reactive power of the

DC furnace of a steel mill. Based on modeling

fundamental and harmonic current between power

system, DC furnace and TSF, the equations described

dynamic behavior of TSF has been derived. By the

dynamic modeling TSF the influence of perturbation of frequency and power system’s impedance on TSF has been analyzed. Moreover, in order to avoid resonance of

TSF with power system, parameters of TSF may be

optimized by GA based on optimization criterion of

stability and cost. Based on above discussing, a TSF that

consists of 3.th, 5.th, 7.th, 11.th, 13.th and high pass

filter which capacity is 6.82MVar is given. The practice

measuring data show that, the harmonic currents inject

into 35kV bus completely accord with Chinese national

standard GB/T-14549-93 and its power factor is

increased to 0.95 from 0.82. The actual measured

harmonic current of the 35kV distribution feeder verifies

the feasibility and validity of proposed method.

II. GENETIC ALGORITHM

Based on GA that was proposed by professor

Holland of Michigan state university, multi-objective

optimization of parameters of TSF was considered. It

superiority function consist of some terms discussed as

follows [11].

A. Filter effect and total harmonic distortion (THD)

The design principle of TSF is to filter the

harmonic current that feedback to the power system. By

TSF the harmonic current must be lower than Chinese

national standard GB/T-14549-93. THD of the current is

the first optimizing criterion when the multi objective

optimization method is applied to optimize the TSF. If

fundamental current and every order of harmonic current

was obtained the THD may be expressed as follows

.



3,5,7,11,13,23,25



2 25

1 1

      







i I I T

i hi

I (1a)

max T

T_I (1b)

There, variable T_I denotes the THD of studied

harmonic current. Variable I₁ denotes fundamental

current. Variable Ihi (i3,5,7,11,13,23,25) denote the

harmonic current that was induced by the load of

harmonic source such as power rectifier of DC furnace,

inverter of the motor with high capacity and etc.

Variable T_Im_ax is the standard value of THD that is

allowed by Chinese national standard GB/T-14549-93.

According to optimization criterion of GA TI that

describes the distortion degree of current must be

minimized.

B. Power factor

0 P

Q

Pmi n

Qmax

QC

1



2

 Qmin

Pmax S1

S2

Fig. 2. Vector analysis of reactive power compensation

Compensating fundamental reactive power is an

important function of TSF that including several single

tuning filters and a high passing filter. By the power

analyzer U900F the maximal and minimal reactive

power of the inductive load of a power system may be

(3)

min

Q respectively. In fig.2 variable P_max and P_min

correspond to maximal and minimal active power of

inductive load that satisfy following expression

1 _max _max

tag Q / P (2a)

2 _min _min

tag Q / P (2b)

Suppose TSF consists of 3.th, 5.th, 7.th, 11.th, 13.th

and high pass filter, according to multi objective

optimization method of GA, following expression must

be satisfied

max , 13 , 11 , 7 , 5 , 3

min Q Q Q

Q

h i

i  







(3)

There variable Q denotes the sum of

compensating capacity of total filter that one among it

may be denoted by variableQ_i



i3,5,7,11,13,h



. Trouble

of Eq.3 is that if above filter was switched a ccording to

reactive power only, the filter effect of TSF can’t be

considered. So filter capacity must be regarded as a

criterion of multi objective optimization of GA. Suppose

there are 3rd, 5th, 7th, 11th, 13th, 23rd and 25th harmonics

that may be denoted by I₃,I₅,I₇,I₁₁,I₁₃,I₂₃ and I₂₅

respectively, compensating capacity of every filter may

be described as follows









3 5 7 11 13 23 25

i i i

i , , , , , ,

Q I / i I / i Q



 

 _ _





 (4)

Based on above discussing a optimization strategy

of switching TSF was given which including following

two conclusions,

First, the filter with maximum compensating

capacity may be divided into several groups that with

same capacity in order to avoid overcompensation.

Second, in order to increase filter capacity of every

group, a capacitor of TSF may be instead of a group of

two series combined with two parallel connection of

capacitor.

Fig.3 Phase diagram of measured voltage and current

Fig.3 is the phase diagram of voltage and current

that measured by power analyzer. Angle of power factor

and degree of unbalancedness of three phases may be

analyzed by positive sequence, negative sequence and

zero sequence voltage and current. Fig.3 show that,

according to the multi objective optimization method of

GA, the power factor of studied power system must be

closed to 1.0, at least closed to 0.95.

C. The Lowest Cost of TSF

The cost of TSF is decided by the compensating

and filter capacity of TSF which was associated with

classification of voltage and capacity of capacitor.

Moreover, TSF may be described by a topology consists

of circuit breaker, thyristor, fuse, reactor and capacitor

and etc.. Except breaker, thyristor and fuse which rated

voltage and rated current were only calculated by above

topology model, the capacity of every reactor and

capacitor which parameters may be modified must be

considered, in order to decrease the cost of TSF.

According to multi objective optimization method

of GA, the cost of TSF was given by following

expression

h C h L h R i

i C i

LL PC P R PL PC

P

F



   

3,5,7,11,13

)

( (5)

ThereP_R,P_L and P_C denote the unit price of the

resistor, reactor and capacitor of TSF. Li(i3,5,7,11,13)

and Ci(i3,5,7,11,13) denote the reactor and capacitor of

ith single tuning filter respectively. R_h,L_handC_h denote

the resistor, reactor and capacitor of high pass filter of

TSF. Variable

F

that denotes the total cost of TSF must

be minimized by above multi objective optimization

method of GA.

III.STUDY BACKGROUND OF DCARC-FURNACE

In order to suppress harmonic current and

compensate reactive power, a harmonic current, power

factor, total harmonic distortion and etc. of 35kV bus of

a steel mill has been studied. The topology of

distribution power system is shown as Fig.4. Rating

capacity of main transformer 1# is 12.5MVA. The

voltage of primary side and secondary side is 35kV and

0.24kV respectively. Short-circuit impedance of main

transformer which connection type is Y/△ is 6.67%.

There is in-phase inverse parallel rectifier with rated

current 6kA in order to eliminate 5th and 7th harmonic

(4)

iA iA ’

i

35kV

ia id/2 ia ’

i

d

T2

id/2

AC DC

furnace

T3

furnace

240V

220V

12500kV A 6.67%

T1

Fig. 4. Schematic diagram of electric arc furnace

There are two DC electric arc-furnaces for rough

working and two AC arc-furnaces for precision working

in steel mill. Due to asymmetric triggering pulse of

inverse parallel rectifier there are 5th, 7th, 11th, 13th, 23rd

and 25th harmonic current in 35kV bus. Considering AC

arc-furnace with 5000kVA the 3rd harmonic current must

be analyzed.

As shown in Fig.4 primary side of transformer T₁

and T₂ was measured by a Power Quality Analyzer

U900F. Every harmonic current injected into 35kV

distribution feeder was shown as Tab.1. According to

Chinese national standard GB/T-14549-93 and base

short-circuit capacity of 35kV bus the harmonic

standard value was given that was shown by second row

of Tab.I.

Table I

Harmonic current injected into phase C of 35kV distribution feeder

（A）

order n harmonic

(A)

3 5 7 11 13 23 25

China

standard 18.0 18.0 13.2 8.4 7.0 4.1 3.8 95%

probability 20.3 32.0 36.6 20.5 15.2 4.5 3.9 Maximum

value 30 60 52 32 22 8.3 7.2

The Tab.I and Fig.5 - Fig.10 show that, the 3rd, 5th,

7th, 11th, 13th, 23rd and 25th harmonic currents were

greater than national standard of China. In particular

maximum values of 5th and 7th harmonic current are

especially terrible. Moreover, there are periodic

harmonic currents that were induced by work period of

arc furnace.

Fig.11 shows that the current THD of power system

is greater than 4% that permitted by Chinese national

standard. Fig.12 indicates that the power factor of this

power system is about 0.82.

Third harmonic without TSF

0 5 10 15 20 25 30 35

12:23:24 13:13:24 14:03:24 14:53:24 15:43:24 16:33:24 17:23:24 18:13:24 19:03:24 19:53:24 20:43:24 21:33:24 22:23:24 23:13:24 0:03:24 0:53:24 1:43:24 2:33:24 3:23:24 4:13:24 5:03:24 5:53:24 6:43:24 7:33:24 8:23:24 (A)

Fig. 5. 3rd harmonic inject into power system without TSF

Fifth harmonic without TSF

0 10 20 30 40 50 60 70

12:23:24 13:13:24 14:03:24 14:53:24 15:43:24 16:33:24 17:23:24 18:13:24 19:03:24 19:53:24 20:43:24 21:33:24 22:23:24 23:13:24 0:03:24 0:53:24 1:43:24 2:33:24 3:23:24 4:13:24 5:03:24 5:53:24 6:43:24 7:33:24 8:23:24 (A)

Fig. 6. 5th harmonic inject into power system without TSF

Seventh harmonic without TSF

0 10 20 30 40 50 60

12:23:24 13:13:24 14:03:24 14:53:24 15:43:24 16:33:24 17:23:24 18:13:24 19:03:24 19:53:24 20:43:24 21:33:24 22:23:24 23:13:24 0:03:24 0:53:24 1:43:24 2:33:24 3:23:24 4:13:24 5:03:24 5:53:24 6:43:24 7:33:24 8:23:24 (A)

Fig. 7. 7th harmonic inject into power system without TSF

Eleventh harmonic without TSF

0 5 10 15 20 25 30 35

12:23:24 13:13:24 14:03:24 14:53:24 15:43:24 16:33:24 17:23:24 18:13:24 19:03:24 19:53:24 20:43:24 21:33:24 22:23:24 23:13:24 0:03:24 0:53:24 1:43:24 2:33:24 3:23:24 4:13:24 5:03:24 5:53:24 6:43:24 7:33:24 8:23:24 (A)

Fig. 8. 11th harmonic inject into power system without TSF Thirteenth harmonic without TSF

0 5 10 15 20 25

12:23:24 13:13:24 14:03:24 14:53:24 15:43:24 16:33:24 17:23:24 18:13:24 19:03:24 19:53:24 20:43:24 21:33:24 22:23:24 23:13:24 0:03:24 0:53:24 1:43:24 2:33:24 3:23:24 4:13:24 5:03:24 5:53:24 6:43:24 7:33:24 8:23:24

(A)

(5)

0 3 5 7 11 13 23 25 0

10 20 30 40 50 60

harmonic order

h

a

rm

o

n

ic

c

u

rr

e

n

t

(

A

)

measured harmonic current by Power Analyzer

China nationalstandard value 95% probability value maximun value

Fig. 10. Harmonic current comparing with Chinese national standard

THD i

0 5 10 15 20 25

12:23:24 13:22:24 14:21:24 15:20:24 16:19:24 17:18:24 18:17:24 19:16:24 20:15:24 21:14:24 22:13:24 23:12:24 0:11:24 1:10:24 2:09:24 3:08:24 4:07:24 5:06:24 6:05:24 7:04:24 8:03:24

Fig. 11. THD of current of power system before TSF

power factor

0 0.2 0.4 0.6 0.8 1 1.2

12:23:24 13:30:24 14:37:24 15:44:24 16:51:24 17:58:24 19:05:24 20:12:24 21:19:24 22:26:24 23:33:24 0:40:24 1:47:24 2:54:24 4:01:24 5:08:24 6:15:24 7:22:24

Fig. 12. Power factor of power system before TSF

There were switchboard tripping, burn-out cable,

computer and TV was automatically turned on, lighting

flashing, fuse of consumer line blow out and etc in 35kV

bus of the steel mile which induced by terrible harmoni c

current.

Considering the high voltage, terrible harmonic

current, rapid varying reactive power and big

compensation capacity, TSF is applied to suppress

harmonic and compensate reactive power of DC furnace

of above steel mile.

IV. DYNAMIC MODELING OF TSF

Considering the effect of in-phase inverse parallel

rectifiers with asymmetrical 12 pulsetriggering signal of

DC furnace, a TSF consist of 5th, 7th, 11th and 13th single

tuning filter were presented. Third single tuning filter

and high pass filter of TSF were given also according to

actual measured harmonic current and power factor. The

topology of TSF was shown by Fig.13.

35kV

Ia

AC furnace

DC furnace

T1 T2

T3

13th

filter 11th

filter 7th

filter 5th

filter 3rd

filter

High passin

g filter

Fig. 13. The topology of TSF

3 L

3 R

3 C

5 L

5 R

5 C

7 L

7 R

7 C

11 L

11 R

11 C

13 L

13 R

13 C

h

C

h

R

h

L

f

i3 f

i5 i7f f

i11 i13f ihf

Lh

i

f d

i

s

L

u

d

L

f s

i

a) fundamental model

3

L

3

R

3

C

5

L

5

R

5

C

7

L

7

R

7

C

11

L

11

R

11

C

13

L

13

R

13

C

h

C

h

R

h

L

Lh

i

s

L

n

I

h

i3 i5h i7h i11h h

s

i

h

i13 ihh

b) harmonic model Fig. 14. Proposed model of TSF

When design the TSF, in order to obtain rated

voltage and rated current of corresponding reactor and

capacitor of TSF which were decided by fundamental

current of power system and harmonic current induced

by load, the fundamental model and harmonic model of

TSF were given and analyzed by Thevenin and Norton

theorem, respectively.

Fig.14 shows the fundamental and harmonic model

of TSF, respectively. There Ls 35.92mH and

mH 89 . 15  d

L denote the fundamental equivalent inductor

of power system and load, respectively. Variable u

denote the phase voltage of 35kV bus of steel

mine.Li(i3,5,7,11,13,h)andCi(i3,5,7,11,13,h) denote the

reactor and capacitor of TSF.

In Fig.14 a), suppose uCk(k3,5,7,11,13,h) and

) , 13 , 11 , 7 , 5 , 3

(k h

ikf  denote voltage of capacitor and the

loop current of every single tuning filter and high pass

(6)

equations were given ) , 13 , 11 , 7 , 5 , 3 (

/C k h

i

uck kf k  (6)

) 13 , 11 , 7 , 5 , 3 ( ) (         n L L i L u i R u i n s nf s cn nf n nf 

 (7)

s hf s ch Lh h

hf u Li u L i L

i [    ( )]/ (8)

) )( /

( h h hf Lh

Lh R L i i

i   (9)

) /( )] (

[ s d s d

df u L i L L

i     (10)

There df hf f f f f

f i i i i i i

i      



 ₃ ₅ ₇ ₁₁ ₁₃ (11)

In Eq.6 Variable

u

denote phase voltage of 35kV

bus of power system that satisfied following expression

) 2 ( ) 3 / 35 (

2 cons f t

u   (12)

There f denote fundamental frequency of power

system.

In fig.14 b), ikh(k3,5,7,11,13,h,s) denote the

harmonic current injected into ith filter and power system

respectively. Define following variables

s s j nfL

z  2 (13)

) 2 /( 2 2

/ h h h h h

h j nfC R j nfL R j nfL

z        (14)

) 13 , 11 , 7 , 5 , 3 ( ) 2 / 1 2 (   

R j nfL nfC i

z_i _i  _i  _i (15)

There z_s , z_h and z_i denote reactance of power

system, high pass filter and ith single tuning filter

respectively. Variable n( n1,2,3,,23,25) denote the

order of harmonic current. Applying symbolic

computation, the harmonic current injected into power

system is express as follows

n s h s I Z Z Z Z Z Z Z Z Z Z Z i 13 11 7 5 3 13 11 7 5 3 // // // // // // // // 

 （16）

The harmonic injected into ith filter may be

expressed as follows

n s i s h i I Z Z Z Z Z Z Z Z Z Z Z i 13 11 5 3 13 11 5 3 // // // // // // // // 

 （17）

There In



n1,2,3,,23,25



denote every harmonic

current induced by the load, i.e. DC furnace in this

paper.

Table II

Parameters of a phase of TSF by classical algorithm

Order

harmonic(A)

3 5 7 11 13 h

R （） 3.85 1.86 2.11 3.39 4.91 80.43

L （mH） 267.45 74.70 59.76 60.16 73.52 52.57

C

μF 5.00 6.00 3.72 1.46 0.85 0.33

kVar/unit 109 98.15 97.40 95.53 111.23 108

Value/phase 6 8 5 2 1 1

Tab. II and Tab. III show the parameters of TSF by

classical algorithm and GA respectively. Comparing

Tab.III with Tab. II, obtained parameters of TSF by

multi objective optimization of GA, especially

capacitors, were standardization product of China. It

denotes that the cost of TSF may be evidently decreased

by GA.

Table III

Parameters of a phase of TSF by GA

Order

harmonic(A)

3 5 7 11 13 h

R （） 4.06 1.79 2.02 3.20 5.40 36.30

L （mH） 272.06 70.46 56.51 56.31 80.30 25.17

C

μF 4.58 6.36 3.82 1.27 0.76 0.25

kVar/unit 100

Value/phase 6 8 5 2 1 1

V. PERTURBATION ANALYSIS OF TSF

In order to decrease the cost of reactor and

capacitor and avoid overcompensating, its grade of

voltage and current of TSF must be considered also.

Based on above analysis the influence of surge current,

flicker of voltage or perturbation of impedance and

frequency of power system to TSF are studied in this

paper.

As shown by Eq.6-Eq.12, the differential equations

that described dynamic behaviors of TSF were derived

according to KCL (Kirchhoff’s Current Law) and KVL

(Kirchhoff’s Voltage Law). Considering perturbation of

fundamental frequency f and inductor Ls of power

system is within ±1% and ±5% respectively, the

influence of perturbation to rated current of capacitor of

TSF were analyzed by dynamic numerical iterative

method. Corresponding calculation results are illustrated

by Fig.15 to Fig.20.

Fig.15a)-Fig.20a) show the response of

fundamental current injected into 3rd, 5th, 7th, 11th and

13th single tuning and high pass filter when the

perturbation of frequency of power system is within

(1±1%)×50Hz. It indicates that the surge current

induced by perturbation of frequency is evidently greater

than stationary fundamental current.

(7)

fundamental current injected into 3rd, 5th, 7th, 11th and

13th single tuning and high pass filter when the

perturbation of inductor L_sof power system is within

(1±5%)×35.93mH. It indicates that the surge current

induced by perturbation of power system is also

evidently greater than stationary fundamental current.

49.5 49.6 49.7 49.8 49.9 50 50.1 50.2 50.3 50.4 50.5 -80 -60 -40 -20 0 20 40 60 80

frequency of power system f (Hz)

fu n d a m e n ta l c u rr e n t in je c te d i n to 3 .t h f ilt e r ( A

) analysis of perturbation of the frequency

a)

30 32 34 36 38 40 42

-100 -50 0 50 100

reactor of power system Ls (mH)

) analysis of perturbation of reactor of power systemy

b)

Fig.15 Analysis of current injected into 3.th filter

49.5 49.6 49.7 49.8 49.9 50 50.1 50.2 50.3 50.4 50.5 -100

-50 0 50 100

a)

30 32 34 36 38 40 42

-300 -200 -100 0 100 200 300

b)

Fig. 16. Analysis of current injected into 5.th filter

More detail data of current are illustrated by Tab.4 .

Maximum fundamental currents injected into each filter

that was described by Fig.15-fig.20 in condition of

perturbation of power system are shown by boldface of

Tab.4. It must be considered when design the rated

current of the capacitor of TSF.

49.5 49.6 49.7 49.8 49.9 50 50.1 50.2 50.3 50.4 50.5 -100

-50 0 50 100

a)

30 32 34 36 38 40 42

-150 -100 -50 0 50 100

b)

49.5 49.6 49.7 49.8 49.9 50 50.1 50.2 50.3 50.4 50.5 -150 -100 -50 0 50 100 150

fu n d a m e n ta l c u rr e n t in je c te d i n to 1 1 .t h f ilt e r ( A

(8)

30 32 34 36 38 40 42 -200 -150 -100 -50 0 50 100 150

b)

In fact, the rated current of a capacitor is decided

by fundamental and harmonic current injected into the

capacitor.

For example, according to Tab.1 and Tab.4 the

current injected into 5th single tuning filter are satisfy

following expressions A 830 . 87 2 5 2 max 5 max

5  i f ih 

i （18a）

A 598 . 78 max 5  f

i （18b）

A 60 5 h

i （18c）

There, if5max and ih5 denote the maximum

fundamental and harmonic current injected into 5th

single tuning filter respectively.

49.5 49.6 49.7 49.8 49.9 50 50.1 50.2 50.3 50.4 50.5 -60 -40 -20 0 20 40 60 80

a)

30 32 34 36 38 40 42

-100 -50 0 50 100

) _{analysis of perturbation of reactor of power systemy}

b)

a)

b)

Fig. 20. Analysis of current injected into high pass filter Table IV

Current injected into each filter in condition of perturbation of power system

current

filter

fundamental Current

（A）

frequency f perturbation

（A）

Ls perturbation

（A）

3.th 29.398 72.153 67.155

5.th 39.198 78.598 159.153 7.th 24.499 82.746 27.004 11.th 9.799 105.855 42.804

13.th 4.900 74.701 28.426 high pass 4.900 28.401 15.431

Above principle of selecting perturbation current

accord with multi objective optimization method and

transient response of TSF that induced by perturbation

of parameters of power system. Maximum rated current

injected into each filter of TSF are shown by Tab. V.

Table V

Maximum rated current of each filter of TSF (A)

filter

current

3rd 5th 7th 11th 13th high _pass

Fundamental

f

i 72.15 78.60 82.75 105.86 74.70 28.40

Harmonic i_h 30 60 52 32 22 15.50

2 2

max h

f i

i  78.14 98.88 110.60 43.91 77.87 32.35

Rated current 60.12 76.06 75.18 85.07 59.90 24.89

(A)

30 32 34 36 38 40 42

-60 -40 -20 0 20 40

fu n d a m e n ta l c u rr e n t in je c te d i n to r e a c to r o f h .t h f ilt e r ( A )

analysis of perturbation of reactor of power systemy (A)

49.5 49.6 49.7 49.8 49.9 50 50.1 50.2 50.3 50.4 50.5 -30 -20 -10 0 10 20 30

fu n d a m e n ta l c u rr e n t in je c te d i n to r e a c to r o f h .t h f ilt e r ( A )

(9)

Considering the operating current of a capacitor is

usually 1.3 times larger than rated current, the rated

current of a capacitor of each filter are shown by fifth

row of Tab.5. The question is that, rated current of 5th

filter is 39.198A which is 1.94 times less than maximum

current injected into this filter. A topology of two groups

including 16 capacitors first connected in parallel then

they are connected in series each other is proposed.

Above topology is illustrated by Fig.21.

1

0

k

V

ar

Fig. 21. Topology of capacitors of 5.th single tuning filter

By fig.21 that consists of 32 capacitors which

capacity of every capacitor is 100kVar, the actual rated

current of capacitor of 5th single tuning filter was

described by following expression

5actual 39 198 2 78 396A 76 06A

i  .   .  . （19）

It indicates that proposed topology can bear

maximum current injected into 5th single tuning filter.

VI. FAULT ANALYSES OF TSF

A unit of 5th single tuning filter consists of 4

capacitors connected in parallel and series is shown by

Fig.22. There are total 8 same units in Fig.21.

C51 C53

C52 C54

51 i

53 i U

10

0k

V

a

r

52

i i54

fuse53 fuse51

fuse54 fuse52

C51 C53

C52 C54

51

i i₅₃

U

10

0k

V

a

r

52

i i54

fuse53 fuse51

fuse54 fuse52

a) work state b) fault state

Fig. 22. Topology of a unit of 5.th filter

Suppose I denote the total current injected into this

unit, in work state it satisfies following expression



51// 53 52// 52



/2 ₅/2 54

53 52

51 i i i U C C C C U C

i        

（20）

In Eq.20,

5 54 53 52

51 C C C C

C     （21）

In Eq.20 variablei₅₁,i₅₂,i₅₃ and i₅₄ denote the

current injected into capacitors that marked by C51, C52,

C53 and C54 respectively. Fig.22 b) illustrate the fault

state of capacitor that induced by surge current, flicker

of voltage or perturbation of impedance and frequency

of power system.

For example, if the capacitor C51 burn-out,

following expression was satisfied



53 52// 54



2 5/3 54

52

53 i i U C C C U C

i        （22a）

3 / 5 54

52 i U C

i    （22b）

Comparing Eq.20 to Eq.22a show that current

injected into capacitor C53 in fault state is 1.333 timers

greater than that one in work state, it must be considered

when designing a TSF.

Supposing the resonance point of the 5th tuning

filter in work state is n₅₀ that satisfy

85 . 4 2

0 . 1

5 5

50 

C L n

 （23）

There L₅ denote the reactor of 5.th filter.

 

2 5.94

3 3

/ 2 2

0 . 1

50 5

5

50  

 n

C L n

 （24）

It indicates that resonance point of 5th tuning filter

in fault state is 1.225 times greater than that one in work

state. Eq.24 implies that the 6th harmonic current will

inject into the 5.th tuning filter when the fault occur.

34 35.17 35.92 36.68 38

-460 -450 -440 -430 -420 -410

inductance of power system Ls (mH) analysis of perturbation of inductance of power

system

i3

+

i5

+

i7

+

i1

1+

i1

3+

ih

(

A

)

stability area period response instability area

chaos

instability area chaos

bifurcation point

Fig. 23. Analysis of perturbation of inductance of power system

Fig.23 indicate that when the perturbation of

inductance occur, the chaos of vector sum of

current



i₃i₅i₇i₁₁i₁₃i₂₃i₂₅



will appear in condition

of inductance L_s35.17mH orL_s36.68mH . Especially

there are bifurcations at L_s35.17mH or L_s36.68mH .

There is period response of



i₃i₅i₇i₁₁i₁₃i₂₃i₂₅



(10)

are the main reasons that influence the stability of

response of TSF.

The instability of TSF, i.e. the resonance induced

by perturbation of parameters of power system must be

avoided. Above discussing may give a reference to

designing the parameters of TSF.

VII.EFFECT ANALYSIS OF TSF

In order to predict the effect of TSF the characters

calculation method was applied to modeling and

simulating the TSF.

3 5 7 11 13 23 25

0 10 20 30 40 50 60

harmonic oeder n

h

a

rm

o

n

ic

c

u

rr

e

n

t

(

A

)

China standard

actual current harmonic current harmonic current by TSF

Fig. 24. Harmonic current injected into power system

Obtained detail data was shown by Fig.24 where

the symbol “△” denote the standard value of harmonic

current accord with national standard GB/T-14549-93 of

China. Symbol “o” denotes actual harmonic current

injected into the power system, symbol “*”denotes

harmonic current by TSF.

Fig.24 indicates that the harmonic current injected

into power system by TSF was evidently lower than

national standard GB/T-14549-93. As a matter of fact,

the effect of TSF may be influenced by the many

complex elements of power system such as perturbation

of frequency and inductance, load variation and etc..

Fig.25-Fig.29 illustrates the harmonic current

injected into second line of 35kV bus by TSF which data

are measured by U900F at one time. There “+” and red

line denote the ith harmonic current injected into power

system by TSF and not respectively.

0 5 10 15 20 25 30 35

12:23:24 13:13:24 14:03:24 14:53:24 15:43:24 16:33:24 17:23:24 18:13:24 19:03:24 19:53:24 20:43:24 21:33:24 22:23:24 23:13:24 0:03:24 0:53:24 1:43:24 2:33:24 3:23:24 4:13:24 5:03:24 5:53:24 6:43:24 7:33:24 8:23:24

Third harmonic without TSF Third harmonic with TSF

(A)

Fig. 25. 3.th harmonic inject into power system by TSF

0 10 20 30 40 50 60 70

12:23:24 13:13:24 14:03:24 14:53:24 15:43:24 16:33:24 17:23:24 18:13:24 19:03:24 19:53:24 20:43:24 21:33:24 22:23:24 23:13:24 0:03:24 0:53:24 1:43:24 2:33:24 3:23:24 4:13:24 5:03:24 5:53:24 6:43:24 7:33:24 8:23:24

Fifth harmonic without TSF Fifth harmonic with TSF

(A)

surge curren t

It indicates that the 3rd, 5th, 7th, 11th and 13th

harmonic current injected into second line of 35kV bus

by TSF are evidently less than that one when TSF wasn’t

applied.

An especially conditions were shown by Fig.26 and

Fig.27 there were some 5th or 7th harmonic current

wasn’t eliminated. For example, between 19:03:24 and

19:53:24 of Fig.26, there was a peak value of 5th

harmonic current that reached to 32A which overrated

national standard GB/T-14549-93 of China. This

problem for surges current that induced by switching

dynamic filter of TSF may solved by taking an ulterior

optimizing control stratagem of crossing zero of voltage.

0 10 20 30 40 50 60

12:23:24 13:13:24 14:03:24 14:53:24 15:43:24 16:33:24 17:23:24 18:13:24 19:03:24 19:53:24 20:43:24 21:33:24 22:23:24 23:13:24 0:03:24 0:53:24 1:43:24 2:33:24 3:23:24 4:13:24 5:03:24 5:53:24 6:43:24 7:33:24 8:23:24

Seventh harmonic without TSF Seventh harmonic with TSF

(A)

surge curren t

(11)

0 5 10 15 20 25 30 35

12:23:24 13:13:24 14:03:24 14:53:24 15:43:24 16:33:24 17:23:24 18:13:24 19:03:24 19:53:24 20:43:24 21:33:24 22:23:24 23:13:24 0:03:24 0:53:24 1:43:24 2:33:24 3:23:24 4:13:24 5:03:24 5:53:24 6:43:24 7:33:24 8:23:24

Eleventh harmonic without TSF Eleventh harmonic with TSF

(A)

0 5 10 15 20 25

12:23:24 13:13:24 14:03:24 14:53:24 15:43:24 16:33:24 17:23:24 18:13:24 19:03:24 19:53:24 20:43:24 21:33:24 22:23:24 23:13:24 0:03:24 0:53:24 1:43:24 2:33:24 3:23:24 4:13:24 5:03:24 5:53:24 6:43:24 7:33:24 8:23:24

Thirteenth harmonic without TSF Thirteenth harmonic with TSF

(A)

power factor

0 0.2 0.4 0.6 0.8 1 1.2

12:23:24 13:23:24 14:23:24 15:23:24 16:23:24 17:23:24 18:23:24 19:23:24 20:23:24 21:23:24 22:23:24 23:23:24 0:23:24 1:23:24 2:23:24 3:23:24 4:23:24 5:23:24 6:23:24 7:23:24 8:23:24

Fig. 30. Power factor of power system by TSF

THD i

0 2 4 6 8 10

12:23:24 13:22:24 14:21:24 15:20:24 16:19:24 17:18:24 18:17:24 19:16:24 20:15:24 21:14:24 22:13:24 23:12:24 0:11:24 1:10:24 2:09:24 3:08:24 4:07:24 5:06:24 6:05:24 7:04:24 8:03:24

Fig. 31. THD of power system by TSF

Comparing Fig.30 with Fig.12 show that, the power

factor of 35kV bus increases from 0.82 to 0.95 by TSF.

There isn’t any overcompensation of reactive power in

Fig.30.

Comparing Fig.31 with Fig.11 show that, the THD

of current of 35kV bus decreases from about 20% to

7.8%. It indicates that the harmonic current injected into

the power system was evidently suppressed.

VIII. CONCLUSIONS

In this paper the TSF was applied to suppressing

harmonic current and compensating reactive power of

the furnaces of a steel mile of China. In order to

decrease the cost of TSF the optimization method of GA

was applied to normalizing the parameters of TSF.

Based on Thevenin and Norton theorem a dynamic

model of TSF in condition of fundamental and harmonic

current that described the behavior of TSF was given

respectively.

Combining the dynamic modeling method with

KCL and KVL, the perturbation of impedance and

frequency of the 35kV power system was analyzed.

Expressions of harmonic current injected into every

filter of TSF were derived by character calculation.

Based on presented method the maximum rated current

of the capacitors and reactors of TSF may be decided.

The results of simulation model and measure

practice show that, the harmonic currents injected into

power system and power factor accord with national

standard GB/T-14549-93 of China. Except the analysis

of this paper, the proposed method may used to analyze

other similar system, such as suppress drop off voltage

and harmonic distortion of wind power system when it

was connected with the power system.

ACKNOWLEDGMENT

The authors would like to thank the support from “National Natural Science Foundation (50877016, 50877017)”.

REFERENCES

[1] Sameh K.M. Kodsi, Claudio A. Canizares, Mehrdad Kazerani, “Reactive current control through SVC for load power factor correction,” Electric Power Systems Research, vol.76, pp.701-708, 2006.

[2] Fan Ruixiang, Li Zheng, Zhao Gang, Sun Min, “The Design of Relocatable SVC and Its Application in Jiangxi Power Grid,” Automation of Electric Power System, vol.32, no.14, pp. 91-95, 2008.

[3] Shukla A, Ghosh A, Joshi A, “State Feedback Control of Multilevel Inverters for DSTATCOM Applications,” IEEE Trans. on Power Delivery, vol.22, no.4, pp. 2409-2418, 2007.

[4] Bor-Ren Lin, Bor-Ren Yang and Hui-Ru Tsai, “Analysis and Operation of Hybrid Active Filter for Harmonic Elimination,” Electric Power Systems Research, vol.62, pp.191-200, 2002.

[5] Murat Kale, Engin Ozdemir, “Harmonic and reactive power compensation with shunt active power filter under non-ideal mains voltage,” Electric Power Systems Research, vol.74, pp.363-370, 2005.

(12)

Systems Research, vol.53, pp.133-140, 2001.

[7] Yong Zhao, Hongying Deng, Jianhua Li, Daozhi Xia, “Optimal planning of harmonic filters on distribution systems by chance constrained programming,” Electric Power Systems Research, vol.68, pp.149-156, 2004. [8] Wang Li-guo, Xia Yu, Ren Xiang, Xu Dian-guo, Xu

Zhuang, “Passive Control on the Negative Effect of Thyristor Switched Capacitor (I),” Asia-Pacific Power and Energy Engineering Conference, number: 5748810. [9] A.Wolf and M.Thamodharan, “Reactive Power Reduction

in Three-Phase Electric Arc Furnace,” IEEE Transactions on Industrial Electronics, vol. 47, no. 4, pp. 729-733, 2000. [10] Rohani R, Porkar B, “Improved EHV Line Switching Surge

Control via Controlled Switching Technique,” IEEE PEDES，vol.1, no.1, pp.1-4, 2010.

[11] Gao JQ; He GX; Wang YS, “A new parallel genetic algorithm for solving multiobjective scheduling problems subjected to special process constraint,” International Journal of Advanced Manufacturing Technology, vol.43, no.1, pp. 151-156, 2009.

Liguo Wang was born in Heilongjiang

Province, China, in 1972. He received his Ph.D.

in Electrical Engineering from the Harbin Institute of Technology, Harbin, China, in 2002.

Since 2003, he has been with the Department of Electrical and Electronics Engineering, Harbin Institute of Technology, where he is currently an Associate Professor. His current research interests

include harmonic suppression and reactive power compensation of power system, parameter identification in ac machines, and nonlinear