Power Quality Conditioning using Bridged-T Filters for Passive Rectifiers

Steven Fredette UTC Power

195 Governors Hwy. South Windsor, CT, 06074

steven.fredette@utcpower.com

Giri Venkataramanan Dept. of Electrical and Computer Engineering

University of Wisconsin – Madison Madison, WI 53706

giri@engr.wisc.edu

Abstract— Harmonic standards such as IEEE 519 have prompted the adoption of active rectifiers or the use of multiple pulse rectifiers for three phase ac-dc conversion system in variable speed drives and other applications. Although active rectifiers are capable of excellent line current waveforms and dc bus regulation, they do result in increased EMI at the input terminals. On the other hand, passive filters typically require a modest amount of reactive elements if configured appropriately. This paper presents the application of a passive filter for input current filtering for passive rectifiers. Filter design equations and operation during voltage imbalances are discussed. Computer simulation and experimental results are presented that verify the operation of the filter.

Keywords- Three phase rectifier harmonics, harmonic filtering, bridged-T filters, voltage imbalance mitigation

I. INTRODUCTION Adjustable speed drives containing passive rectifiers are

prevalent in general-purpose applications including pumps and blowers. The poor power quality of these drives is well known [1-3]. Traditional techniques for improving current harmonic distortion include the addition of three-phase ac line reactors, dc link choke and matrix filters [4-5].

Recent focus has highlighted the performance of these drives under utility voltage unbalanced conditions [6-8]. Approximate closed-form analyses highlighted the negative impact of the voltage unbalance and reduced power quality, however, solutions to improve the design are not readily applied.

This paper focuses on providing a solution that allows the adjustable speed drive to operate under voltage unbalance conditions, which would otherwise cause the system to enter a single-phasing condition. A bridged-T filter based on the matrix filter is proposed as a solution and is located between the utility and passive rectifier input terminals. Design guidelines and analyses of the filter are provided along with a comparison to an inductor filter. Utilization of the bridged-T filter capacitor for sourcing reactive power is also investigated for applications were power factor correction is desired.

A comparison of the positive to negative sequence impedance of the bridged-T filter to the inductor filter

provides insight into the workings of the bridged-T filter during unbalanced voltage input. Simulation and experimental results are provided to verify the functionality of the proposed solution.

II. THREE PHASE RECTIFIER HARMONICS For most adjustable speed drives, a three-phase rectifier is

provided at the utility interface. In order to reduce harmonic currents to reasonable levels, ac line inductance is added as shown in Figure 1. The current drawn from the utility for this system is rich in harmonics as indicated in Figure 2. The time domain waveform is represented by a classic “double humped” signature while the frequency domain is characteristic of a 1/n roll-off of magnitude with frequency. The harmonic distortion can be easily calculated and compared with appropriate standards. Such an arrangement of line inductance in series with the rectifier input is limited to a theoretical maximum of about 30% current harmonic distortion and lies well above the 5% level recommended by IEEE 519 [9]. Therefore, additional passive or active filtering is necessary to mitigate the harmonic currents.

Figure 3 illustrates the odd non-triplen harmonics of the line current normalized to the fundamental component in dB, with a logarithmic scale in frequency up to the 40th harmonic. Along with the current harmonics, recommended limits conforming to the recommendations of IEEE 519 standards and the amount of attenuation required for mitigating the harmonics to meet the standards are also illustrated in the figure. Not surprisingly, it may be observed that the attenuation required for meeting the harmonics is a function of the frequency. Since the inherent harmonics required for the attenuation are a decreasing function of frequency, and the IEEE 519 limits are also a decreasing function of frequency, the amount of attenuation required to conform to the standard is roughly constant.

This is an interesting observation, particularly in the light of typical transfer functions of typical multiple order low pass LC filters that tend to have attenuation characteristics that increase in multiples of 20db/decade depending on the order of the filter. Based on this observation, one would seek a cascade filter that has a box-car transfer characteristics that have 0 dB gain in the neighborhood of 60Hz and a 30~40 dB attenuation beyond 200 Hz. Realization of the bridged-T filter as illustrated

978-1-4244-2279-1/08/$25.00 © 2008 IEEE 1

Figure 1. Simplified schematic of the three-phase passive rectifier.

Figure 2. Waveform of rectifier line currents and its harmonic spectrum obtained from computer simulations

Figure 3. Normalized harmonic components of line current at various

frequencies (+ – current harmonics in dB, X – normalized IEEE 519 limits, and O – attenuation required for mitigation of harmonics in dB)

in the following sections approximates such a frequency response transfer function, given the constraints of a finite sized components with acceptable damping properties.

III. IDEAL BRIDGED-T FILTER TOPOLOGY The bridged-T filter that provides an approximation of the

desired frequency response characteristics is illustrated in Figure 4. It consists of two reactors, a capacitor and a damping resistor. As the frequency is swept from dc to high frequencies, the behavior of the filter approximates various circuits as illustrated in dark in Figures 5(a)-(d).

L1

LfR

I in

Cf

Io

Figure 4. Simplified schematic of the ideal bridged-T filter.

L1

LfR

I in

Cf

Io

(a)

L1

LfR

I in

Cf

Io

(b)

L1

LfR

I in

Cf

Io

(c)

L1

LfR

I in

Cf

Io

(d)

Figure 5. Current transfer behavior of the bridged-T filter at (a) low (b) parallel resonant (c) series resonant, and (d) high frequency bands

10 100 1 .103 1 .10460

40

20

0

20

Frequency [Hz]

Nor

mal

ized

har

mon

ic c

urre

nts [

dB]

2

At low frequencies in the neighborhood of the power frequency, the impedance of path formed by L1 between the harmonic current source Iin and the line current Io is the smallest and all the current flows through the path illustrated in Figure 5(a). As the frequency increases, the filter capacitor Cf and the inductors L1 and Lf together form a parallel resonant path illustrated in Figure 5(b), and leads to large circulating currents in the resonant tank even with very little excitation from Iin. As the frequency increases even more, the filter capacitor Cf and the inductor Lf form a series resonant path, bypassing the excitation current from flowing through the line as illustrated in Figure 5(c). At even higher frequencies, the capacitor Cf acts as a short circuit and the excitation current follows a current divider network formed by the inductors Lf and L1 as illustrated in Figure 5(d). While the reactors and the capacitors form the resonant networks, the resistor provides adequate damping and also provides a preferential path for the current through L1 as opposed to Lf at low frequencies.

The transfer function between the excitation current and the line current may be determined using circuit properties with the application of extra element theorem [10] as

2

2

2

2

11

11

)()(

dd

nn

in

o

sQ

s

sQ

s

sIsI

ωω

ωω

++

++= (1),

where

f

f

fn

ffd

CLL

RQ

CL

CLL

1

1

1

,1

,)(

1

+=

=

+=

ω

ω

Magnitude and phase vs. frequency plots of the filter transfer function for typical numerical parameters are illustrated in Figure 6. The presence of the parallel and series resonant frequencies at ωd and ωn respectively are readily evident from the frequency response graphs. Moreover, the 0-db gain in the pass band neighborhood of the power frequency, 60 Hz and a constant attenuation at high frequencies beyond the resonant frequencies may also be observed from the figure.

IV. BRIDGED-T FILTER IN A RECTIFIER The bridged-T filter can be utilized in three phase rectifier

systems to attenuate harmonics created by the rectifier to saty within limits of IEEE 519. A schematic of such a filter in the three phase system is shown in Figure 7. A per phase equivalent circuit while representing the rectifier bridge as a harmonic current source and the supply side voltage source as an ammeter for measuring the current transfer function as shown in Figure 8. The ideal bridged-T filter is shown shaded while the additional components are not. The inductors on either side of the filter are added to ensure a current stiff

source on either side of the filter. Figure 9 illustrates the magnitude and phase frequency response of the transfer function of the three phase bridged-T filter in series with the passive rectifier.

10 100 1 .103 1 .10420

10

0

10

20

Frequency [Hz]

Filte

r gai

n [d

B]

10 100 1 .103 1 .104180

90

0

90

180

Frequency [Hz]

Filte

r pha

se [d

egre

es]

Figure 6. Magnitude and phase characteristics of the bridged-T filter for typical power circuit parameters

L1

LfR

Cf

Rs Ls L2

L1

LfR

Rs Ls L2

L1

LfR

Rs Ls L2

Cf

Cf

Cdc

Rdc

Figure 7. Use of bridged-T filter in a passive rectifier system with line impedance and interface reactor at the rectifier terminals

L1

LfR

I in

Cf

Io

Rs L2+Ls

Figure 8. Simplified per phase equivalent circuit model of the bridged-T filter in the rectifier system, which represented by a harmonic current source

3

10 100 1 .103 1 .104 1 .10540

20

0

20

Frequency [Hz]

Filte

r gai

n [d

B]

10 100 1 .103 1 .104 1 .105180

90

0

90

180

Frequency [Hz]

Filte

r pha

se [d

egre

es]

Figure 9. Magnitude and phase characteristics of the bridged-T filter for typical power circuit parameters

The presence of the line impedance and the series reactor at the rectifier terminals introduce a high frequency pole at R/(L1+L2+Ls), which provides additional attenuation for higher frequency harmonics. The transfer function of the filter system may be developed by introducing a correction term to the ideal bridged-T filter to be,

⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟

⎟⎠

⎞⎜⎜⎝

⎛++

++=

pdd

nn

in

o

ssQ

s

sQ

s

sIsI

ωωω

ωω

111

11

)()(

2

2

2

2

(2),

where

21 LLLR

sp ++

=ω , and all other parameters as defined in (1).

The transfer function of the filter consists of a denominator polynomial having complex conjugate poles at the parallel resonant frequency and a real higher frequency pole. The numerator polynomial has complex conjugate zeros at the series resonant frequency. Design of the filter follows through from the selection of various poles and zeroes of the transfer function that leads to separation of various reactive elements and the damping resistor.

V. FILTER DESIGN CONSIDERATIONS An application for the bridged-T harmonic filter is shown in

Figure 9. An induction machine-based distributed generator is in parallel with the utility grid. A variable speed drive (VSD) is included in the system as an ambient nonlinear load with harmonic filtering.

Figure 10. Magnitude and phase characteristics of the bridged-T filter for typical power circuit parameters

As the dominant harmonic in three phase rectifier systems is

the 5th, it is desirable to place the series resonance at this pointing order to provide the most attenuation. The parallel resonant frequency has to be situated between the fundamental power frequency and the fifth harmonic frequency. It is desirable to place this near the third harmonic frequency, since ambient third harmonic currents in floating neutral three phase systems are naturally rejected, thereby minimizing the possibility of exciting any possible resonance. The parallel resonance is selected at about the 3.4th harmonic as a first approximation to allow for some separation from residual 3rd harmonic, which may be present during unbalanced cases. A quality factor of at least ten for both the series and parallel resonance was found to be a good choice for meeting the requirements of IEEE 519 while maintaining reasonably low loss in the system. Once the resonant frequencies are selected, separation of Cf and L are required. The value of Cf may be chosen to provide a set amount of fundamental reactive power as may be necessary under ambient conditions. Figure 11 illustrates a flow chart, which has been developed for the filter design.

The first step is to select the filter capacitance (Cf) based on no load or minimal loading conditions. The capacitance is sized to provide near unity power factor at this condition so as not to provide leading power, which could have a destabilizing effect on the power system. Upon sizing the capacitor, the inductors (L1 and Lf) can be sized according to the parallel and series resonances. The filter damping resistor (R) can then be sized based on a quality factor for the series resonance (e.g. at least a factor of 10). The inductors Ls and L2 have minimal impact on the filter performance and are usually sized based on other system requirements, to provide a total reactance of a few percent at the power frequency.

VI. MITIGATION OF VOLTAGE UNBALANCE EFFECTS It has been known that single phase operation of a three-

phase passive rectifier can occur due to grid voltage unbalance [1]. The inclusion of a bridged-T filter between the grid and the rectifier also prevents the system from entering single phasing operation. Figure 12 illustrates the equivalent circuit when the rectifiers of phase A and C are conducting during such an instance of lower voltage on phase B.

4

INPUTSPvsd, PFgrid

CALCULATEQgrid

INPUTSQ, ωd, ωn

CALCULATECf, Lf, L1, R

CALCULATELs, L2

INPUTSLs, Rs, %Z

Frequency response&

Circuit simulationOK?

FINISHED

ADJUST

Figure 11. Flow chart describing filter design process

L1

LfR

Cf

Rs Ls L2

L1

LfR

Rs Ls L2

L1

LfR

Rs Ls L2

Cf

Cf

Cdc

Rdc

Figure 12. Magnitude and phase characteristics of the bridged-T filter for typical power circuit parameters

Since closed form analytical evaluation of the operation of the circuit shown in Figure 12 is beyond linear circuit modeling techniques, sequence impedances are evaluated using computer simulations in order to illustrate the effects of the bridged-T filter to voltage imbalances. The positive (Zp) and negative (Zn) sequence impedances are defined as the ratio of sequence components of the voltage to the corresponding sequence components of the currents. If a system has a large negative sequence impedance in comparison to its positive sequence impedance, it may be said to reject ambient voltage imbalances. Thus the ratio of positive sequence impedance to the negative sequence impedance is a figure of merit that is ideally zero for a desirable system capable of rejecting all negative sequence voltages. The sequence impedance ratio was evaluated as a function of the percentage of voltage unbalance value using computer simulations of the rectifier system with and without the use of bridged-T filter.

The results from the simulation are illustrated in Figures 13-15. It can be observed from Figure 13 that the use of bridged-T filter leads to a small sequence impedance ratio in comparison to the baseline case for even insignificant amount of voltage imbalance levels. Figures 14 and 15 illustrate the line current waveforms drawn by the rectifier system without and with the bridged-T filter respectively. The waveforms were developed for a case with a line voltage imbalance of 4.5%. The improvement of the grid currents is readily evident in the figures. The absence of the “single hump” phenomenon in two of the phases is particularly evident in Figure 15 in comparison to Figure 14.

VII. FILTER PERFORMANCE EVALUATION Evaluation of the bridged-T filter for three phase rectifier

systems was conducted in PSpice using the circuit in Figure 7 with the values shown in the Appendix. The time domain and frequency domain results are presented in Figure 16 respectively for balanced three phase input voltage. The top traces on Figure 16 shows the rectifier and line currents for one phase along with the phase voltage and the bottom traces show the frequency spectrum of the rectifier current and the line current. Table 1 summarizes the data in relation to IEEE 519 limits.

|(Zp/Zn)| vs. Vn

05

1015202530354045

0 5 10 15 20

Vn (%)

|Zp/

Zn|

With Bridged-T Filter Without Bridged-T Filter

Figure 13. Sequence impedance ratio of the rectifier system with and

without bridged-T filter

5

1 0 0 m s 1 2 0 m s 1 4 0 m s- I ( V a ) - I ( V b ) - I ( V c )

- 4 0 0 A

- 2 0 0 A

0 A

2 0 0 A

4 0 0 A

Figure 14. Three phase current waveforms of the rectifier system without bridged-T filter

1 0 0 m s 1 2 0 m s 1 4 0 m s- I ( V a ) - I ( V b ) - I ( V c )

- 4 0 0 A

- 2 0 0 A

0 A

2 0 0 A

4 0 0 A

Figure 15. Three phase current waveforms of the rectifier system without bridged-T filter

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018-400

-300

-200

-100

0

100

200

300

400

Vgrid

IgridIvsd

Frequency

0Hz 0.4KHz 0.8KHz 1.2KHz 1.6KHz 2.0KHz 2.4KHzI(Lin_a)

1.0A

100uA

1.0KAI(L2_a)

1.0A

100uA

1.0KA

SEL>>

Figure 16. Line voltage, rectifier current and waveforms (top) and rectifier current frequency spectrum (middle) and line current frequency spectrum

(bottom) of the rectifier system from simulation

TABLE I. LINE CURRENT HARMONICS OF THE RECTIFIER SYSTEM WITHOUT AND WITH BRIDGED-T FILTER

An experimental test setup shown in Figure 17 was

constructed to verify the operation of the bridged-T filter. It consisted of an off-the-shelf 70hp VSD and a harmonic filter with of the values of components shown in the Appendix. Figure 18 illustrates the three-phase currents at a full load operating point, corresponding to the simulation waveforms illustrated in Figure 16.

VIII. CONCLUSIONS This paper has presented the application of the bridged-T

filters for mitigation of harmonic currents drawn by three phase passive rectifiers. After a brief discussion of the requirements of harmonic mitigation techniques, the bridged-T filter topology was presented as a solution for harmonic mitigation. Transfer function of the filter as a stand-alone and in the presence of rectifier was presented followed by a design example case study. The effect of the bridged-T filter in mitigating the effects of line voltage imbalance was discussed. Simulation and experimental results verifying system performance were presented.

Figure 17. Photograph of the experimental set-up

VSD

Bridged-T Harmonic Filter

6

Figure 18. Three phase line current waveforms from the experimental test set-up.

REFERENCES [1] M.F. McGranaghan and D. R. Mueller, “Designing harmonic filters for

adjustable-speed drives to comply with IEEE 519 harmonic limits,” IEEE Trans. on Ind. Appl., vol. 35, no. 2, pp. 312-318, Mar./Apr. 1999.

[2] J. W. Schwartzenberg, E. L. Stagliano, M. N. Kaplan and R. F. Chu, “Characterization of ASD operation”, APEC Conference Proceedings, Seventh Annual, pp. 139-146, Feb 1992.

[3] G. Carpinelli, F. Iacovone, A. Russo, P. Varilone and P. Verde, “Analytical Modeling for Harmonic Analysis of Line Current of VSI-Fed Drives”, IEEE Trans. on Power Delivery, vol. 19, no. 3, July 2004.

[4] MTE Corp., “Performance of Harmonic Mitigation Techniques”, as found at http://www.mtecorp.com/mitigation.pdf

[5] Myron Zucker, Inc., “Application Guide for Solving Harmonic Problems” at http://www.myronzucker.com/docs/HARMONIC%20APPL%20GUIDE.pdf

[6] K. Lee, T. Jahns, W. Berkopec and T. Lipo "Closed-Form Analysis of Adjustable Speed Drive Performance Under Input Voltage Unbalance and Sag Conditions”, IEEE Trans. on Ind. Appl., vol. 42, no. 3, pp. 733-741, May/June 2006.

[7] M. H. J. Bollen and L. D. Zhang, “Analysis of voltage tolerance of AC adjustable speed drives for three-phase balanced and unbalanced sags,” IEEE Trans. Ind. Appl., vol. 36, no. 3, pp. 904-910, May/Jun. 2000.

[8] Lee, K.; Jahns, T.M.; Venkataramanan, G.; Berkopec, W.E., “DC-Bus Electrolytic Capacitor Stress in Adjustable-Speed Drives Under Input Voltage Unbalance and Sag Conditions”, IEEE Trans. Ind. Appl., vol. 43, no. 2, pp. 495-504, Mar./Apr. 2007.

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

[10] R.D. Middlebrook, “Null Double Injection and the Extra Element Theorem”, IEEE Trans on Education, vol. 32, no. 3, pp. 167-180, August 1989.

APPENDIX: PARAMETERS USED IN SIMULATIONS AND EXPERIMENTS

Parameter Value Units Z @ 60Hz Units Ls 0.110 mH 0.0415 Ω Rs 2.5 mΩ 2.5 mΩ Lin 0.240 mH 0.090 Ω L1 0.587 mH 0.220 ΩL2 0.240 mH 0.090 ΩLf 0.755 mH 0.285 ΩCf 400 μF 6.63 ΩR 27 Ω 27 Ω

7