Single-tuned Passive Harmonic Filter Design Considering

Journal of International Council on Electrical Engineering Vol. 1, No. 1, pp. 7~13, 2011

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Single-tuned Passive Harmonic Filter Design Considering Variances of Tuning and Quality Factor

Young-Sik Cho* and Hanju Cha†

Abstract - This paper presents how to select tuning factor and quality factor in designing of a single-tuned passive harmonic filter. Tuning factor and quality factor must be considered before a decision of filter parameters(R, L and C). In literature, the study about these two factors has not been performed and only empirical values have been used in the passive harmonic filter design so far. As an empirical value, in cases of 5th and 7th filter, tuning order has been used 4.8th and 6.8th respectively and quality factor has been used in a range of 30 and 60; therefore, we will propose how to decide these two factors in this paper. If a single-tuned passive harmonic filter were off-tuned, its performance would be deteriorated substantially and resulted in a parallel resonance between grid inductance and filter capacitance. In order to avoid this side effect from off-tuning, the filter must be tuned on some preceded order not on the exact order. In other words, total filter impedance must have reactive impedance on a tuned frequency. In this paper, tuning factor is derived by using a bode-plot based method and then performance of filter is confirmed as a harmonic current absorption rate which harmonic source flows through filter; and quality factor is also derived by using the same method and then the performance is confirmed by the same filter current absorption rate. Finally, the performance of proposed passive harmonic filter design using the tuning factor and quality factor is verified by experiment. Experimental results show that the 5th, 7th, 11th and 13th current harmonic distortions meet IEEE-519 requirement.

Keywords: Passive filter, Harmonic, Passive harmonic filter, Tuning factor, Quality factor

1. Introduction The utility grid voltage is normally assumed to be a pure

sinusoid at a fundamental frequency of 60 Hertz. Applying a sinusoidal voltage to a linear load produces sinusoidal current which is also at the same fundamental frequency. However, applying the sinusoidal voltage to a non-linear load does not result in a sinusoidal current waveform, although the current can be identified to be repetitive at the fundamental frequency. Harmonic currents and voltages are caused by the interaction of non-linear loads with the utility. The traditional approach to solve aforementioned harmonic problem has been done by the use of passive harmonic filter[1-3]. Currently, Passive harmonic filter application is used as a common practice and readily available to power system engineers and designers for reducing harmonic voltage and current distortion through alternate circuit path operation. Several IEEE transaction papers have been written and published which introduce the theory and implementation of advanced techniques for controlling

harmonic current flow such as magnetic flux compensation, harmonic current injection, dc ripple injection, series/shunt active filter systems, and pulse width modulated static var harmonic compensators. However, practical systems have not been extensively installed and are not available on the market yet. It may take more time before these advance techniques are fully developed and readily available for a successfully competition with Passive harmonic filter systems. Passive harmonic filters will be installed in the industry field and applied alone, or in combination with transformer phase shifting and/or higher pulse number rectifier configurations to waveform distortion on the power system[4]. This paper presents how to select tuning factor and quality factor in a single-tuned passive harmonic filter design.

2. Single-Tuned Passive Harmonic Filter

2.1 Passive Harmonic Filter Passive filters are well understood and represented a

conventional technology as the way to mitigate for harmonics. These filters, which consist of reactor and capacitor, typically provide an alternative impedance path

† Corresponding Author: Dept. of Electrical Engineering, Chungnam National University, Korea ([email protected])

* Dept. of Electricity and Control, Korea Institute of Nuclear Safety, Korea ([email protected])

Received: May 1, 2010; Accepted: October 16, 2010


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for harmonic currents generated by the nonlinear load, result in the lower harmonic current components in the utility current. Most passive filters need to be custom designed in the specific system impedances, the load current harmonics, the back ground voltage distortion, as well as interactions with other loads and sources in close vicinity. Filter design without considering some of the above identified issues can result in poor performance due to interactions, and overall system performance may be poorer than it was prior to filter installation in some cases [1, 5, 6]. The site specific engineering costs of specifying, purchasing, installing and commissioning a passive filter can often be higher than its actual cost.

2.2 Single Tuned Filter

A single tuned filter which is a series RLC circuit tuned

to a single harmonics frequency provides a low harmonic impedance characteristic generally. Its total impedance is given by

( 1/ )n n n nZ R j L Cω ω= + − (1)

At a resonance frequency 1/n nL Cω ω= From (1) n nZ R= An ideal single-tuned filter is said to be tuned on the

frequency that makes its inductive and capacitive reactance to be equal[5]. The quality factor(Q) of filter determines the sharpness of tuning, and in this respect filters may be either a high or a low Q type. The filter with low Q is sharply tuned to one of the lower harmonic frequency, and a typical value is between a range of 30 and 60. The filter with high Q typically in the region of 0.5-5.5 has low impedance over a wide range of frequency. When using to eliminate the higher-order harmonics it is also referred to as a high-pass filter. In the case of a tuned filter, Q is defined as the ratio of the inductance (or capacitance) to resistance at the resonant frequency[5, 6].

i.e.,

/Q X R= (2)

As shown in Fig. 1, the filter pass band(PB) is defined as being bounded by the frequencies at which the filter reactance is equal to its resistance; i.e., the impedance angle is 45˚and the magnitude is 2R . Relationship between the quality factor and pass band can be expressed as follows:

/nQ PBω= (3)

Where, nω is the tuned angular frequency(rad/s). Fig. 1 shows a single-tuned filter circuit and its characteristic

curve.

(a) Circuit (b) Impedance characteristic

Fig. 1. Impedance characteristic curve versus frequency.

3. Determination of Tuning and Quality Factors We have to decide two design parameters before the

decisions of R, L and C. They are tuning factor(δ) and quality factor(Q); these are considering the fact that in advanced, the resonance phenomenon in frequency caused by variations of parameter value[7, 8]. In order to express the filter impedance in terms of δ and Q, the following relationships are applied;

(1 )nω ω δ= + (4) 1

L Cω =

⋅ (5)

The reactance of inductor or capacitor in ohms at the

tuned frequency is

0

1n

n

LX LC C

ωω

= = = (6)

0XQ

R= (7)

0

1 1

n n

CX RQω ω

= = (8)

0

n n

X RQLω ω

= = (9)

Substituting equation (4), (8) and (9) into equation (1)

yields

(1 ) (1 )nn

RQL RQω ω δ δω

= + ⋅ = + (10)

Young-Sik Cho and Hanju Cha

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1 11 (1 )(1 )n

n

RQC

RQω δω δ

ω

= =++ ⋅ (11)

1 (2 )( )1fZ R j L R j RQ

Cδ δω

ω δ⎡ + ⎤⎧ ⎫= + − = + ⎨ ⎬⎢ ⎥+⎩ ⎭⎣ ⎦

21 ( )1fZ R jQ δδ

δ+⎧ ⎫= +⎨ ⎬+⎩ ⎭

(12)

Or, considering that δ is relatively small as compared

with unity,

1

0(1 2 ) ( 2 )fZ R j Q X Q jδ δ−≈ + = + (13)

And

2 2 1/ 2(1 4 )fZ R Qδ≈ + (14)

3.1 Determination of a Tuning Factor(δ) The extent of filter detuning from the nominal tuned

frequency is represented by the tuning factor(δ). This filter detuning is occurred by various causes as following: (i) variations in fundamental frequency, (ii) variations in the filter capacitance and inductance caused by aging or temperature, and (iii) initial off-tuning caused by manufacturing tolerances and finite size of tuning steps. Equation (15) shows the overall detuning in per unit of the nominal tuned frequency[6-8].

( ) /n nδ ω ω ω= − (15)

Moreover, the 2% change of L or C causes the same

detuning as change of 1% system frequency. Therefore δ is often expressed as

1 ( )2

f L Cf L C

δ Δ Δ Δ= + + (16)

Equation (17) shows relationship between ideal tuning

order and actual tuning order.

( )n nh h hδ= + × (17)

where, nh is ideal tuning order, h is tuning order considered tuning factor(δ). From equation (16) and Table 1, we can decide that optimized tuning factor(δ) is -0.0375.

Table 1. Anticipated error

Items Anticipated errors

Frequency △f : 2%

Inductance(L) variations △L : -10~+20%

Capacitance(C) variations △C : -4.5~+6.5%

Table 2 shows the tuning order of each harmonic and

they are calculated from equation (16), (17) and considered the errors of in Table 1.

Table 2. Tuning orders in an applied tuning factor

Order 5th 7th 9th 11th

Tuning 4.813 6.734 8.663 10.59

Order 13th 15th 17th 19th

Tuning 12.51 14.44 16.36 18.29

3.2 Current Absorption Rate in an Off-tuned Filter

For the assessment of tuning factor compatibility, we use

the amount of harmonic current absorption rate in filters. If filters were tuned at harmonic frequency accurately, most harmonic current flows into filter side. That is, harmonic current absorption in a 5th filter is about 5 /f aI I =95.7%. But, if the filter capacitance were increased to +6.5% compared with designed value, harmonic current absorption rate would be decreased to 70.17% sharply. The rest 30% of harmonic current flows out power source, it makes an adverse effect for adjacent system or equipment. Also, if the capacitance of filter were decreased to -4.5% compared with designed value, harmonic current absorption rate would be decreased to 83.87%. In this case, about 20% of harmonic current flows out power source, too. If filter inductance were increased 20% result in off-tuning, current absorption rate would be 29.49% and filter could not be functioned. The results of 7th filter case are similar to those of 5th filter case. Table 3 shows the performances of 5th and 7th filers by filter capacitance and inductance variations.


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Table 3. Filter absorption effects

Filter Current(If) Absorption rate(%)

5th

filter

original 4.785 95.7

XC+5% 3.509 70.17

XC-4.5% 4.194 83.87

XL+20% 1.475 29.49

XL-10% 2.598 51.95

7th filter

original 4.873 97.46

XC+5% 3.938 78.76

XC-4.5% 4.350 87.00

XL+20% 1.984 39.68

XL-10% 3.244 64.88

3.3 Definition of Quality Factor(Q)

The quality factor(Q), which determines the sharpness of

tuning, is related with a scale which shows the degree of harmonic current absorption quantity. In this respect, all filters will be one of the high or a low Q type according to use. Fig. 2 shows the definition and magnitude of quality factor(Q).

3r r

HI LO

f fQf f dB

= =−

, or

0

2 1( ) m n

loss n

W LQ series LC

P R RCω

ωω

⋅ = = =

• Q is depended on R; if it wants to high Q, it should get

lower R • Band width is an inverse proportion to Q. Therefore,

the frequency selectivity of filters decided on Q. For example, high Q has a small BW and can select frequency precisely.

(a) definition (b) comparison of magnitude

Fig. 2. Definition and Magnitude of Quality factor(Q).

3.4 Decision of Quality Factor(Q) by Bode Plot The bode-plot method is used to decide the quality factor

because it provides us a convenient tuning characteristic of filters. The changes of tuning sharpness by Q variations are shown in Fig. 3 and Fig. 4, where Fig. 3 shows gain curve of 5th harmonic filter and 7th harmonic filter in separate use, and Fig. 4 shows in case of combination 5th and 7th harmonic filter. As shown from Fig. 3 and Fig. 4, when quality factor is bigger than 50, filter sharpness is nearly similar. Therefore, the quality factor is chosen as 50.

(a) in case of 5th filter

(b) in case of 7th filter

Fig. 3. Sharpness changes by quality factor(Q).

Fig. 4. Sharpness changes in combination of 5th&7th filters.


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3.5 Comparison of Current Absorption Rate by Q To evaluate the filter performance, we used the amount

of harmonic current absorption rate in a filter, when quality factor is chosen as 5, 10, 30, 50, 70 and 100 respectively. The amount of current absorption rates are shown in Table 4.

Table 4. Current Harmonic Content after filter installation Filter Q5(%) Q10(%) Q30(%) Q50(%) Q70(%) Q100(%)5th 28.6 51.2 87.28 94.48 97.98 98.667th 38.54 64.12 92.90 97.98 98.58 99.38 As shown in Table 4, the harmonic current absorption

rate of a 5th filter, in case of Q=5, is 5 /f aI I =28.26%. In this case, the filter cannot do its function. In case of Q=10, the current absorption rate of a 5th filter is 5 /f aI I =51.2%, in this case, filter can only reaches a half of its capability. In case of Q=30, the current absorption rate of a 5th filter is

5 /f aI I =87.28%, about 10% current flows into power source. In case of Q=50, 70 and 100, the current absorption rates of a 5th filter are 5 /f aI I = 94.48%, 97.98 and 98.66 respectively. In these cases, most harmonic currents are absorbed in a filter. These results are similar to in a case of 7th filter. Therefore, the quality factor(Q=50) decided in this paper is suitable.

4. Experimental Result

In order to verify the performance of designed filters considering the tuning and quality factor, the experiment has been carried out by using the designed filters for a three-rectifier load. The experimental results are shown in some separate cases: without filter, only 5th filter installation, only 7th filter installation and an arrangement of 5th and 7th filter orders as follows:

4.1 Without Filter

The case which is not filter, current harmonic content in

all orders was exceeded on IEEE 519 current limits[9]. Without filter, measured the harmonic content of source current( sI ), current waveform and current spectrum are below.

Table 5. Current Harmonic Contents without filter

Orders Fund. 5th 7th 11th 13th Before 100% 72.6% 61.8% 20.9% 13.2%

IEEE 519 - ≤12% ≤5.5%

(a) Current Waveform (b) Current Spectrum

Fig. 5. Without filter.

4.2 After 5th Harmonic Filter Installation

The current waveform and its frequency spectrum are

illustrated in Fig. 6(a) and (b), respectively. As shown by Fig. 6, after 5th harmonic filter installation, the 5th harmonic content is decreased to 16.5% from 72.6%. This result did not meet the IEEE-519 limitation. The differences between actual value and ideal value of circuit parameters may cause this problem. The system response can be improved by using a combination of 5th and 7th filter.


Fig. 6. After 5th Filter Installation.

4.3 After 7th Harmonic Filter Installation

As In this case, the current waveform and its frequency

spectrum are illustrated in Fig. 7(a) and (b), respectively. As shown in Fig. 7, the 7th harmonic content is decreased to 4.8% from 61.8%. After 7th harmonic filter installation, the response can meet the IEEE-519 harmonic requirement.


Fig. 7. After 7th Filter Installation.


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4.4 Installation of 5th and 7th Filter Combination The current harmonic contents in this case are shown in

Table 6. Fig. 8(a) and (b) shows the current harmonic waveform and its frequency spectrum after 5th and 7th harmonic filter installation, respectively. In this case, the content of 5th harmonic current is decreased to 7.9% from 16.5%, but 7th harmonic is increased to 11.2% from 4.8% on the contrary. It means that, the 5th filter in arrangement has better operation than only 5th filter case, but the 7th filter in arrangement is slightly reduced in filtering function when compared with only 7th filter case. Although the interaction between circuit parameters of 5th and 7th filter in the arrangement causes their aforementioned results, the final current harmonic component responses obtained by the filter combination can meet the IEEE-519 requirement.

Table 6. Harmonic Content After 5th&7th Filter Combination

Filters Fund. 5th 7th 11th 13th Only 5th 100% 16.5% 10.5% 6.6% 3.0%Only 7th 100% 39.9% 4.8% 4.9% 2.5%5th+7th 100% 7.9% 11.2% 4.5% 2.9%

IEEE 519 - ≤12% ≤5.5%


Fig. 8. After Installation 5th and 7th Combination.

5. Conclusion

This paper presents how to select tuning factor and quality factor single-tuned passive harmonic filter design. In passive filter design, the tuning factor and quality factor must be taken into account before calculating filter parameters (R, L and C). In this paper, the tuning orders of 5th and 7th filters have been determined as 4.813th and 6.734th, respectively. And the quality factor (Q) has been chosen as 50. The designed passive harmonic filter performance has been verified by experiment and the experimental results show that 5th, 7th, 11th and 13th harmonics could meet the IEEE-519 requirements,

respectively. Compared the before and after filter installation cases, the 5th harmonic was decreased from 72.6% to 7.9%, the 7th harmonic was decreased from 61.8% to 11.2%, the 11th harmonic decreased from 20.9% to 4.5% and the 13th harmonic decreased from 13.2% to 2.9%, respectively. Therefore, the proposed tuning factor and quality factor decision method for passive harmonic filter design in this paper has been certified.

Acknowledgment This work was supported by the Human Resources

Development of the Korea Institute of Energy Technology Evaluation and Planning(KETEP) grant funded by the Korea government Ministry of Knowledge Economy (No. 20104010100600)

References

[1] M. E. Habrouk, M. K. Darwish and P. Mehta, “Active Power Filter; A review”, IEE Proc. Electr. Power Appl., Vol. 147, no. 5, pp. 403-413, September 2000.

[2] H. Fujita and H. Akagi, “A Practical Approach to Harmonic Compensation in Power System Series Connection of Passive and Active Filter”, IEEE Trans. On Industry Applications, Vol. 27, No. 6, pp. 1020-1025, 1991.

[3] F. Z. Peng, H. Akagi and A. Nabae, “A New Approach to Harmonic Compensation in Power System A Combined System of Shunt Passive and Series Active Filter”, IEEE Trans. On Industry Applications, Vol. 27, No. 6, pp. 983-990, 1990.

[4] J. K. Phipps, “A Transfer Function Approach to Harmonic Filter Design”, IEEE Industry Applications Magazine, pp 68-79, March/April 1997.

[5] J. Arrilaga and N. R. Watson, “Power System Harmonics”, Second Edition, University of Canterbury Christchurch, New Zealand, John Wiley & Sons, pp. 228-237, 2003

[6] Y. S. Cho, “Analysis and Design of Passive Harmonic Filter for a Three-phase Rectifier”, KIEE Magazine, 58P-3-13, pp. 316-322, September 2009

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[8] H. L. Willis, “Power System Capacitors”, Taylor & Francis, pp. 389-414, 2005

[9] IEEE Std. 519-1992, “IEEE Recommended Practices and Requirements for Harmonic Control in Electrical Power Systems”, pp. 77-80, 1992.


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Young Sik Cho received his B.S. degree in Electrical Engineering from Changwon National University and M.S degree in the same field from Chungnam National University, Korea in 1990 and 2009, respectively. He is in the course of PhD in Electrical

Engineering from Chungnam National University, Deajen Korea from 2009. He was with KEPCO in Ulchin NPP from 1992 to 2000. He worked at LG and KESCO From 2000 to 2005 respectively. From 2005 until now, He joined the department of electricity and control, Korea Institute of Nuclear Safety, Daejeon, Korea. His research interests are power quality; power reliability; UPS; harmonic mitigation; passive harmonic filter; active harmonic filter; hybrid harmonic filter.

Hanju Cha received his B.S. degree in Electrical Engineering from Seoul National University, Korea, and M.S degree in the same field from Pohang Institute of Science and Technology, Korea in 1988 and 1990, respectively. He obtained his PhD in Electrical

Engineering from Texas A&M University, College Station, Texas in 2004. From 1990 to 2001, he was with LG Industrial Systems in Anyang, Korea where he was engaged in the development of power electronics and adjustable speed drives. In 2005, he joined the Department of Electrical Engineering, Chungnam National University, Daejeon, Korea. He worked as a visiting professor in the United Technology Research Center, Hartford CT, USA in 2009. His research interests are advanced ac/dc, dc/ac, and ac/ac converters; renewable energy system; power quality; energy storage system and micro-grids.

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Single-tuned Passive Harmonic Filter Design Considering