Research on the Parallel Capacitor Series Reactance Rate Parameter Design Shi Hong, Chen Zheng, Feng Lei, Xu Xing Henan Electric Power Survey & Design Institute

Zhengzhou , P.R.China lindashihong@126.com

Abstract— Series reactance rate is the important part of the

reactive power compensation capacitor, if which of poor

choice may cause occurrence of resonance between

capacitor and the system, affecting the safety of equipment

and system stability. In this paper, with the actual project

cases integrated, according to the power capacitor

switching tests and field tests on one electrical substation,

we got series reactor parameters in reactive power

compensation capacitor do not match is the direct cause of

capacitor fuse explosion. Proposed a concept that in the

case substation has current limiting reactor, the capacitor

design in addition to select the appropriate series reactance

rate, should be considered the equivalent series reactance.

What’s more, according to the actual situation, the

corresponding solutions are given and the harmonic

situation in shunt compensating branch when capacitor

bank in different series reactance rate are analyzed.

Key words—series reactance, harmonic restrain, reactance rate choice, fuse explodes, substation test

I. INTRODUCTION Reactive power compensation is the important

means to improve the power factor, ensure the security of power system and ameliorate power quality. Series reactor is the important ancillary equipment of transformer substation reactive compensation capacitor, whose main function is to suppress harmonic current amplification and restriction of capacitor switching inrush current [1-3]. While in the practical power system, there are still many substation capacitor groups because of harmonic problem bulging, fuse and even explosion. The cause of this kind of accident is one of the main reasons for capacitor and series reactor bank reactance rate selection of misconduct, the capacitor group parameters and system parameters make a harmonic resonance circuit, which led to the harmonic current amplification or the occurrence of resonance [4-6]. Many of the low voltage side of transformer substation is connected in series with a current limiting reactor, when running capacitor group number change, because the current limiting reactor in the presence, the equivalent reactance changed, more

easily form a harmonic resonance condition, influence of the equipment safety and stability of the system.

This paper based on the brief analysis of capacitor on harmonic current amplification mechanism, combination of capacitor switching experiments on real data, analyses the function of reactive compensation capacitor group of series reactor parameters matching problem.

II. THEORETICAL ANALYSIS OF HARMONIC CURRENT AMPLIFICATION

The system wiring diagram and equivalent circuit are shown in figure 1.

Fig.1 Illustrative diagram of harmonic amplification

Defined /L CK X X= as the capacitor circuit of series reactance rate, the system and capacitor circuit of harmonic current is:

2

2

//

(1 ) /(1 ) /

L CSh h

S L C

Ch

S C

hX X hI IhX hX X h

h K X hIhX h K X h

−= ×+ −

− −= ×− −

（1）

2

/

(1 ) /

SCh h

S L C

Sh

S C

hXI IhX hX X h

hXIhX h K X h

= ×+ −

= ×− −

（2）

It can be seen when the capacitor group branch harmonic capacitive reactance and harmonic reactance is equal, the capacitor circuit of h harmonic generation series resonance, resonant frequency is:

1hK

= （3）

This format a loop filter, which flowing through the system harmonic current is zero. When the system harmonic inductance and capacitor bank branch harmonic impedance is equal, the capacitor circuit and system in h harmonic generation on parallel resonance, resonant frequency is: 1

/S C

hX X K

=+

（4）

978-1-4577-0547-2/12/$31.00 ©2012 IEEE

At this time, flowing through the capacitor group branch harmonic current theory tends to infinity. Actuality, due to the resistor it is far greater than the equipment can withstand the limited value. When /S S L ChX hX hX X h> + − ， Ch hI I> ，

flowing through the capacitor group branch harmonic current is amplified. It can get:

1 12 /S C

hX X K K

< <+

（5）

When /S S L ChX hX hX X h< + − ， Ch hI I< ，

flowing through the capacitor group branch harmonic current is limited. It can get: 1

2 /S C

hX X K

<+

or 1hK

> （6）

Since only K is adjustable, the reactance rate is the series reactor important parameters, selection of reactance rate is appropriate is related to the amplification of harmonic frequency and harmonic current value.

III. ACTUAL CASE ANALYSIS AND FIELD TEST A 220kV power substation with 2 main

transformer whose capacity is 2×150MVA, it has three voltage grade. When 1# main transformer capacitance put operation，the capacitance external fuse group frequently occur explosion accident. The bus is configured with a group of dry current limiting reactor and 4 group of capacitor whose capacity is 7200kvar. The capacitor is configured of series reactor whose reactance rate is 6%.

In order to find the cause of the accident, testing staff made a capacitor switching test in the substation using PS-8 power quality analyzer monitored 10kV system background harmonic and the first capacitor branch current, using Nicolet Waveform Recorder recorded transient waveform of capacitor operation process. The results obtained are as follows.

A. THE 10kV BUS VOLTAGE BACKGROUND TEST

In the absence of condenser operation condition, the 10kV bus voltage harmonic test case as figure 2 and tables 1 show.

Fig.2 Bus voltage waveform and the frequency spectrum when

no capacitor puts operation

Tab.1 10kV bus voltage background harmonic

Harmonic

order 3 5 7 9 11 THD（%）

THDU（%） 0.499 2.041 0.435 0.210 0.970 2.306

Table 1 shows, the substation 10kV bus background total harmonic voltage distortion rate of 2.306%, meet the national standard. Among them 5 and 11 harmonic content are bigger, it is because the substation has electrical railway load.

B. PUT INTO OPERATION IN THE CASE OF 3 GROUP CAPACITORS

Test staff has conducted a total of more than 10 capacitor switching operations. Through the test, it found when put into operation in the case of 3 group capacitors, the capacitor circuit transient process is more apparent, as shown below.

Fig.3 Bus voltage transient waveform and the frequency

spectrum when 3 capacitors put operation

Fig.4 Capacitor branch current transient waveform and the

frequency spectrum when 3 capacitors put operation

As figure 3 and figure 4 shows, when the third group of capacitors put operation voltage and capacitor current spectrum component is relatively abundant, mainly between 100HZ and 300HZ. It is because as the capacitor parallel branches grow, the branch impedance and 10kV bus circuit impedance are related change.

Fig.5 Bus voltage stable state waveform and the frequency

spectrum when 3 capacitors put operation

Fig.6 Capacitor branch current stable state waveform and the

frequency spectrum when 3 capacitors put operation

As figure 5 and figure 6 shows, when the third group of capacitors put operation, causing the three harmonic current amplification which bus voltage distortion rate achieve 2% above. The 3 harmonic current content of capacitor branch is more than 10%. Considering the current limiting reactance and capacitor series resistance, for the 3 harmonic, capacitor branch and system impedance has three harmonic resonance trends.

C. TEST RESULTS WHEN DIFFERENT GROUPS OF CAOACITOR PUT INTO OPERATION

When a capacitor in the series reactance rate of 6%, put different groups of capacitors into operation respectively, the measured capacitor branch current data is shown in table 2.

Tab.2 Current date that several capacitors put operation when the series reactance rate is 6%

REACTANCE RATE 6% HRI（%）

GROUPS 1I 3I 5I 7I 3 1/I I

5 1/I I 3 1/I I

1 393.87 14.86 31.8 2.53 3.77 8.07 0.64

2 401.35 27.34 22.05 1.98 6.81 5.49 0.49

3 409.11 70.02 16.88 1.63 17.11 4.12 0.39

4 417.18 29.68 13.66 1.39 7.11 3.27 0.33

As can be seen from table 2, when the capacitor series resistance rate is 6%, three sets of capacitors in the case, 3 harmonic current amplification is relatively serious, capacitors branch and system impedance has parallel resonance trend. 3 harmonic content is high up to 17%. With the increase of the number of capacitors operation group, the 5 harmonic filtering effects is reduced, this is because capacitive reactance value according to 1/n decline, the capacitive reactance value change quantity changes smaller.

IV. SIMULATION ANALYSIS OF DIFFERENT SERIES REACTANCE RATE

In order to study the capacitor branch harmonic condition when capacitor in different series resistance rate, this paper uses PSCAD/EMTDC software to carry out simulation and analysis. The system parameters and operation parameters remain the same, the simulation results are as follows.

A. CAPACITOR SERIES RESISTANCE RATE OF 4.5% CASE

When capacitor series resistance rate of 4.5% case, put into operation one group of capacitor, two groups of capacitor, three groups of capacitor, four groups of capacitor, the current waveform of 1# capacitor branch is shown respectively in figure 7 (a), (b), (d), (d). The corresponding current value is shown in table 3.

Fig.7 Capacitor branch current waveform when the series

reactance rate is 4.5%

Tab.3 Current date that several capacitors put operation when the series reactance rate is 4.5%

REACTANCE RATE 4.5% HRI（%）

GROU

PS 1I 3I 5I 7I 3 1/I I

5 1/I I 3 1/I I

1 387.59 10.4 54.58 3.48 2.68 14.08 0.89

2 394.82 15.42 31.01 2.53 3.90 7.85 0.64

3 402.34 28.51 21.65 1.98 7.08 5.38 0.49

4 410.14 56.16 16.63 1.64 13.69 4.05 0.39

It can be seen by graph 7 and table 3, along with the capacitor operation group number increase, the transition time decreases, the three harmonic content increased gradually, and the 5 harmonic content is gradually reduced, the filtering effect is reduced.

B. CAPACITOR SERIES RESISTANCE RATE OF 1% CASE

When capacitor series resistance rate of 1% case, put into operation one to four group of capacitor, the current waveform of 1# capacitor branch is shown respectively in figure 8 (a), (b), (d), (d). The corresponding current value is shown in table 4.

Fig.8 Capacitor branch current waveform when the series

reactance rate is 1%

Tab.4 Current date that several capacitors put operation when the series reactance rate is 1%

REACTANCE RATE 1% HRI（%）

GROUPS 1I 3I 5I 7I 3 1/I I

5 1/I I 3 1/I I

1 373.71 6.12 76.49 25.11 1.64 20.46 6.72

2 380.38 7.58 183.36 6.88 1.99 48.20 1.81

3 387.38 9.94 60.17 3.94 2.56 15.53 1.02

4 394.61 14.28 33.13 4.47 3.62 8.39 1.13

It can be seen by graph 8 and table 4, when put two groups of capacitor, capacitor branch and system impedance get 5 harmonic resonant, the 5 harmonic current amplified serious.

V. CAPACITOR EQUIVALENT SERIES RESISTANCE RATE ANALYSIS

If the substation low voltage side has series current limiting reactor, put into operation different group of capacitor will change the parallel compensation device equivalent series resistance rate. It is necessary to choose the right string of rate, also should consider the capacitor equivalent series resistance in capacitor design to avoid the accidents because of parameter choice undeserved.

Fig.9 Series reactance equivalent circuit diagram

Figure 9 is the diagram of equivalent series resistance of series reactor, its equivalent string of rate is :

1 21 2

1

% 1L L

L Le

CC

X X nX XnKXX

n

+ += = （7）

It can be seen along with the capacitor operation group increase, the equivalent series resistance rate also increased. The substation in the series resistance rate of 6% and 4.5%, respectively, when put into operation one group, two groups, three groups and four groups of capacitor, the capacitor equivalent series resistance rate as shown in table 5.

Tab.5 Equivalent series reactance rate when several capacitors put operation

eK （%） 1 2 3 4

REACTANCE RATE 6% 6.82 7.64 8.46 9.28

REACTANCE RATE 4.5% 5.32 6.14 6.96 7.78

When series reactance rate is 6%, the four group of capacitors all put into operation, the equivalent series resistance rate is 9.28%, already close to three harmonic resonance equivalent series resistance rate 11%, capacitor branch circuit and system impedance of parallel resonance trend.

Combined with the actual test, the occurrence of explosion accidents of substation fuse are all happened when an additional third groups of capacitor. It can be concluded that the cause of the accident was the unreasonable design of capacitor series resistance, shunt compensation capacitor equivalent series resistance rate is close to three harmonic resonance level, caused by harmonic current amplification which leading fuse.

VI. CONCLUSION Substation shunt compensation capacitors in

series reactor parameters should be carefully chosen. It need considered the background harmonics where the equipment installation point. If the substation has limited current reactor, it also should consider the capacitor equivalent series resistance rate effect, to avoid the parameter choice is undeserved, cause harmonic current amplification or resonance phenomenon.

VII. REFERENCES [1] Chen Bo-sheng．Harmonics restraining function of serial reactor and

selection of reactance rate [J]．Power System Technology，2003，27(12)：92-95(in Chinese)．

[2] Ju Fei．Parameters selection of series reactor in shunt reactive compensation installation [J]．Power Capacitor，2006，(6)：4-7(in Chinese)．

[3] Wang Xing-hua，Yu Xin-mei．Optimal configuration of series reactors in capacitor banks [J]．Power System Protection and Control，2008，36(16)：42-47(in Chinese)．

[4] Xu Lin-feng，Lin Yi-feng．Failure analysis of capacitor bank in 500kV substation [J]．Power Capacitor，2004，(4)：43-45(in Chinese)．

[5] Shi Cheng-kui ． Study on harmonic resonance and harmonic enlargement of power network capacitor bank [J]．Electric Power Automation Equipment，2001，21(7)：36-39(in Chinese)． [6] Pan Yan， Liu Lian-guang， Hu Guo-xin． Affection of compensating capacitor bank in series with reactor on performance of passive filter