202

A Discrete Frequency Tuning Active Filter forPower System Harmonics

Tzung-Lin Lee∗ Jian-Cheng Li∗ Po-Tai Cheng∗∗∗ Department of Electrical Engineering, Chang Gung University, TAIWAN

∗∗ CAPT, Department of Electrical Engineering, National Tsing Hua University, TAIWAN

Abstract— Severe voltage distortion due to power systemharmonic resonance has been reported in recent years. Thetermination installation active filter was presented to resolve thisproblem. It operates as similar conductance for all harmonicfrequencies whether in a fixed conductance command or inan automatic gain adjustment control. Therefore, its filteringcapability is impeded by mismatching between the active filterand the radial line, and the voltage distortion may still be signif-icant throughout the line. Distributed installation of active filterspresented previously can address this issue effectively, but thepractical application is limited due to their cost-ineffectiveness.This paper proposes a discrete frequency tuning active filter tosuppress power system harmonics. The active filter operates asvarious conductance for individual harmonic frequency. Eachharmonic conductance is dynamically adjusted according to thecorresponding voltage distortion of the active filter installationpoint in response to increase or decrease of nonlinear loads,or variation of resonant frequency in the power system. Themismatching problem between the feeder and the active filtercan be avoided effectively. Therefore, harmonic voltage distortioncan be maintained at an allowable level throughout the feederwith lower peak current and lower rms current consumption, andvarious loads installed in the power system receive more uniformvoltage waveform. Operation principles are explained in detail,and computer simulations and experimental results validate theeffectiveness of the proposed approach.

I. INTRODUCTION

With the advance of semiconductor devices, power electron-ics technologies have been developed extensively for variousapplications, such as lighting, adjust speed driver, and unin-terruptible power supply systems. Due to the nonlinear nature,most power electronics equipment produces non-sinusoidalcurrent, and thus results in significant harmonic pollution inthe power system. The amplification of harmonic voltage alonga power feeder resulting from the resonance between powerfactor correction capacitors and system inductances, includingtransmission line inductance and transformer leakage induc-tances, has been reported [1], [2], [3]. The harmonic reso-nant may become unpredictable and variable in a renewable-generated electric power system due to a large number ofhousehold capacitors and inverter output capacitors [4]. It hasbecome a serious concern of power quality recently.

Akagi et al. have proposed a voltage detection active filterinstalled at the end of a radial line to suppress such harmonicresonance [5], [6]. The damping performance is subject tothe matching degree between the harmonic conductance ofthe active filter and the characteristic impedance of the radialline. Therefore, the capability of the active filter with fixedconductance declines due to variation of the characteristic

impedance in the real power system. In order to enhancefiltering performance, an automatic gain adjustment schemeis added to reduce the voltage distortion at the installationpoint [7]. In this scheme, the operating conductance of theactive filter is adjusted according to the total voltage distortionof the active filter installation point. However, the harmonicresonance is frequency-dependent and variable with the damp-ing degree. The active filter operating at similar conductancefor all harmonic frequencies may suffer the mismatched prob-lem. This is the so-called ”whack-a-mole” problem, whichillustrates unintentional induction of another harmonic res-onance when supplying damping for a specific harmonicfrequency [6]. Therefore, the filtering performance is limited,and some harmonic voltage components may become worse atcertain locations along the line. Distributed installation activefilter systems presented previously can address this issue.They demonstrate effective filtering performances whether bya communication-coordinated or harmonics-drooped control,but the practical application is limited due to their cost-ineffectiveness [8], [9], [10].

This paper proposes a discrete frequency tuning active filterto suppress power system harmonics. The active filter operatesas various conductance at each harmonic frequency. Thedamping conductance for individual harmonic frequency isdetermined by the corresponding harmonic voltage distortionof the active filter installation point. Based on this scheme,the active filter can dynamically adjust the filtering capabilityin response to increase or decrease of nonlinear loads andsystem resonant frequency variation. The annoying ”whack-a-mole” problem due to mismatching between the feeder and theactive filter can be avoided effectively. Therefore, harmonicvoltage distortion throughout the feeder would be definitelymaintained at an allowable level with lower peak current andlower rms current consumption in the proposed approach.

II. OPERATION PRINCIPLES

A simplified one-line diagram of the proposed discretefrequency tuning active filter is shown in Fig. 1(a). The activefilter unit (AFU) is installed at the end of a radial line toterminate harmonic voltage propagation. The AFU operatesas various conductance at each harmonic frequency as given,

i∗abc =∑

h

G∗

h · Eabch(1)

where h represents the harmonic frequency order. The indi-vidual conductance command G∗

h is a control gain to suppressthe associated harmonic voltage component Eabch

of the

978-1-4244-1668-4/08/$25.00 ©2008 IEEE

203

EabciabcL

CLi

gulator

AFU

Vs

(a) One-line circuit diagram of the proposed active filter in a radial line.

abcto

dqeh

abcto

dqe5

abcto

dqe7

dqeh

toabc

dqe5

toabc

dqe7

toabc

Eabc

Eabc

Eabc

Eabc

iabc

Eeqdh

Eeqd5

Eeqd7

Eeqdh

Eeqd5

Eeqd7

Eabch

Eabc5

Eabc7

G∗

h

G∗

5

G∗

7

ωh ωh

-ω5-ω5

ω7ω7

i∗abc

v∗

abc

LPF

LPF

LPF

CurrentRegulator PWM

AFU

(b) Control block diagram of the proposed active filter.

ωf

s+ωf

ωf

s+ωf

kp + ki

s

SQRTSQRT

Eah

Ebh

Ech

Ea

Eb

Ec

VD∗

h

VDh

G∗

h

(c) Conductance tuning control for individual harmonic frequency.

Fig. 1. The proposed discrete frequency tuning active filter in a radial line.

AFU installation point. Harmonic voltage components canbe derived according to the synchronous reference frame(SRF) transformation [11], [12]. The specific harmonic voltagecomponent Eabch

becomes a dc value in the SRF at ωh,so it can be extracted by using a low pass filter (LPF), asshown in Fig. 1(b). The current command is then generatedby multiplying the voltage harmonics and its correspondingconductance command. Based on the current command i∗abc,the measured current iabc, and the measured voltage Eabc,the current regulator calculates the voltage command v∗abc asfollows,

v∗abc = Eabc −Li

ΔT(i∗abc − iabc). (2)

Li is the output inductor of the AFU, and ΔT is the samplingperiod [13]. The current regulator operates the inverter to

synthesize the current as in (1) to accomplish the dampingfunctionality.

Fig. 1(c) shows the proposed discrete frequency tuningscheme for harmonic order h. The conductance command G∗

h

is determined according to the voltage distortion VDh at theAFU installation point Eabc. The voltage distortion VDh isdefined as the harmonic voltage component rms value at ωh

divided by the voltage rms value as given,

VDh =Eabch,RMS

Eabc,RMS

· 100%. (3)

The derivation of VDh can be approximately evaluated byusing two LPFs with cut-off frequency at ωf , which areto filter out ripple components in the calculation. The errorbetween the allowable voltage distortion VD∗

h and the actualvoltage distortion VDh is then fed into a proportional-integral

204

1 2 3 4 5 6 7 8 9L

C

AFUNLA NLB

iaf

220 V

60 Hz

20 kVA

(a) Simulation circuit configuration.

−500

0

500bus1

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500bus2

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500bus4

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500bus6

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500bus7

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500bus9

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0

20

3.6%

5.6%

5.6%

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2.9%

2.9%

4.5%

5.6%

6.1%

iaf

(b) AFU is off.

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1.41 1.42 1.43 1.44−20

0

20iaf

2.8%

4.3%

4.6%

4.1%

3.4%

3.5%

4.1%

4.3%

4.4%

3.7 A

(c) Discrete frequency tuning AFU.

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500bus1

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500bus9

2.41 2.42 2.43 2.44−20

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20iaf

2.8%

4.0%

4.9%

5.2%

4.9%

4.7%

4.2%

3.5%

3.0%

6.2 A

(d) Automatic gain adjusted AFU.

1 2 3 4 5 6 7 8 90

1

2

3

4

5

6No AFUsDiscrete frequency tuning AFUAutomatic gain adjustment AFU

VD5

Bus number

(e) Fifth harmonic voltage distortion on all buses.

1 2 3 4 5 6 7 8 90

1

2

3

4

5

6No AFUsDiscrete frequency tuning AFUAutomatic gain adjustment AFU

Bus number

VD7

(f) Seventh harmonic voltage distortion on all buses.

Fig. 2. Simulation circuit and steady-state simulation results.

(PI) regulator to adjust the conductance command G∗

h. Thedefinition of the PI regulator is defined as

TPI = kp +ki

s(4)

where s is the Laplace operator, kp and ki are proportionaland integral gain, respectively. Since harmonics variation inthe power system is usually slow, the PI controller with a verylow bandwidth can function well. Thus, various conductance

commands G∗

h of all harmonic frequencies are generated toprovide damping for different harmonic frequencies, as shownin Fig. 1(b). Based on this control, the AFU can dynamicallyadjust the individual harmonic conductance command G∗

h,so the AFU would provide effective harmonic damping toresonant frequencies, and the voltage distortion throughout thefeeder can be maintained at an allowable level.

205

III. SIMULATION RESULTS

The proposed discrete frequency tuning active filter isapplied to a radial power distribution line to demonstratethe harmonic filtering performance by using the alternativetransient program (ATP). Fig.2(a) shows the simulation circuitand circuit parameters are given as follows:

• Power system: 220 V(line-to-line), 20 kVA, 60 Hz,L=0.2 mH(3.1 %), C=150 μF(13.7 %).

• Nonlinear loads NLA and NLB: Both nonlinear loadsare diode rectifiers with filter inductor, DC capacitor, andload resistor. NLA and NLB are rated at 5.3 kVA(30 %),respectively.

• The reference fifth and seventh harmonic voltage distor-tion is 3%, respectively.(VD∗

5=VD∗

7=3.0%)• The AFU is implemented by conventional three-phase

voltage source inverter. The PWM frequency is 10 kHz.

From the point of the view of the distributed-parameter circuitmodel of Fig.2(a), Both fifth harmonic wavelength and seventhharmonic wavelength are near the feeder length. They becomemajor harmonic concerns and other higher order componentswill not excite resonances in this circuit arrangement [6], [14].Therefore, only G∗

5 and G∗

7 are implemented by the proposeddiscrete frequency tuning method, and G∗

h is set as 0.2 Ω−1

for h > 7 in the simulation.

A. Steady-state operation

Due to harmonic resonance, the bus voltages are severelydistorted, as illustrated in Fig.2(b). After the AFU is engaged,Fig. 2(c) shows total voltage distortion along the line issignificantly reduced. Both fifth voltage distortion VD5 andseventh voltage distortion VD7 are maintained below 3%, asdemonstrated in Fig. 2(e) and Fig. 2(f). At the steady state, theAFU consumes 1.7 kVA (peak current = 10 A, rms current =3.7 A) at G∗

5 = 0.61 Ω−1 and G∗

7 = 0.49 Ω−1.The AFU with the automatic gain adjustment scheme are

tested, where the AFU operates as the same conductancecommand G∗ for all harmonic frequencies [7]. Fig.2(d) showsthe total voltage distortion at bus 9 can be maintained at 3%,but the improvement on the mid section of the line is notclear. Fig. 2(e) indicates VD5 at bus 3, 4, 5, 6, 7 becomeshigher than 3% due to the fifth harmonic resonance. Thisis so-called ’whack-a-mole” phenomenon, which illustratesunintentional induction of another harmonic resonance whensupplying damping for a specific harmonic frequency [6]. TheAFU consumes 2.9 kVA (peak current = 17 A, rms current= 6.2 A) at G∗ = 1.35 Ω−1. Therefore, the proposed activefilter can maintain both VD5 and VD7 below 3% throughoutthe feeder with lower peak current and lower harmonic var(volt-ampere reactive) consumption.

Resonant frequency of the power system is usually vari-able and difficult to be predicted, which may trouble damp-ing performance in the conventional active filter design.In the following, the impact of variable capacitors onAFU damping performance is evaluated. Fig. 3 shows theconductance commands G∗

5, G∗

7 for various capacitors C(50, 75, 100, 125, 150, 175, 200 μF). Test results demonstrate

50 75 100 125 150 175 2000

0.2

0.4

0.6

0.8

1

G

C (u F)

G∗

5

G∗

7

Fig. 3. Conductance commands of the AFU in variation of resonantcapacitors.

G∗

5 and G∗

7 are adjusted to neutralize the harmonic ampli-fication at different resonant conditions. If C=125 μF, fifthharmonic resonance is worsened and a larger G∗

5 is required toreduce VD5. As the capacitor is larger than 175 μF, fifth har-monic resonance no longer occurs, so fifth harmonic dampingis not needed (G∗

5 = 0). On the other hand, seventh harmonicresonance changes fast compared to fifth harmonics due tosmall wavelength. G∗

7 can also respond with the variation ofcapacitors to accomplish harmonic damping functionality byusing the proposed approach.

B. Transient operation

Fig. 4 shows the conductance commands G∗

5, G∗

7 and thevoltage distortion VD5, VD7 of the AFU under nonlinearload variation. NLA increases to 6.6 kVA at t=2.0 s andsubsequently NLB increases to 6.6 kVA at t=3.0 s. The in-crease of nonlinear loads causes higher voltage distortion, thusthe PI regulator raises both G∗

5 and G∗

7 commands to drawmore harmonic current, as indicated in Fig. 4(a). The voltagedistortion VD5, VD7 at the AFU installation point would bemaintained at 3%.

Fig. 5 illustrates the transient when the capacitors on bus 4and bus 7 are disconnected at t=2.0 s and t=3.0 s, respectively.Due to uneven distribution of the feeder capacitors, the reso-nant pattern of the circuit cannot be predicted easily. However,G∗

5 and G∗

7 can still be tuned effectively according to VD5,VD7 in the proposed approach. As indicated in Fig. 5(a), G∗

5

and G∗

7 are decreased because the capacitor on bus 4 gettingoff line causes lower voltage distortion. Particularly, G∗

7 isreduced significantly. On the other hand, the capacitor on bus7 switching off line would cause both VD5 and VD7 increased.Therefore, G∗

5 and G∗

7 are raised to maintain VD5 and VD7

at 3%.

IV. LABORATORY TEST RESULTS

Fig. 6 shows a test circuit in the laboratory. The AFU withthe proposed discrete frequency tuning control is installed atthe end of the bus to evaluate harmonic damping performance.System parameters are given as follows,

206

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0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

G

Time

G∗

5

G∗

7

(a) Active filter conductance commands.

1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 42.5

2.6

2.7

2.8

2.9

3

3.1

3.2

3.3

3.4

3.5

VD

Time

VD5

VD7

(b) Voltage distortion.

Fig. 4. Conductance commands and voltage distortion of the AFU when NLA and NLB are added at t=2.0 s and t=3.0 s, respectively.

1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 40

0.2

0.4

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1

1.2

1.4

1.6

1.8

2

G

Time

G∗

5

G∗

7

(a) Active filter conductance commands.

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2.6

2.7

2.8

2.9

3

3.1

3.2

3.3

3.4

3.5

VD

Time

VD5

VD7

(b) Voltage distortion.

Fig. 5. Conductance commands and voltage distortion of the AFU when the capacitors on bus 4 and bus 7 are switched off line at t=2.0 s and t=3.0 s,respectively.

2 31

L1 L2LlLi

C C

iaf220 V

60 Hz

VTHD=2.8%VD5=2.8%

VD7=0.3%

AFU

Fig. 6. Experimental circuit.

TABLE I

VOLTAGE DISTORTION WITHOUT ANY FILTERING.

Bus 1 Bus 2 Bus 3VTHD 3.1% 4.7% 7.5%VD5 3.0% 4.4% 6.8%VD7 0.4% 1.2% 3.1%

TABLE II

VOLTAGE DISTORTION AFTER THE ACTIVE FILTER IS ENGAGED.

Bus 1 Bus 2 Bus 3VTHD 2.2% 2.9% 3.3%VD5 2.2% 2.8% 3.0%VD7 0.4% 0.8% 1.4%

• Power system: 220 V(line-to-line), 60 Hz. The harmonicsource is background voltage distortion of the powersystem. VTHD=2.8%, VD5=2.8%, VD7=0.3%. Ll rep-resents leakage inductance of the power system.

• Experimental circuit: L1 = 0.2 mH, L2 = 0.4 mH, C =180 μF.

• Active filter: Li=1.0 mH, inverter frequency is 20 kHz.• Damping controller: VD∗

5=VD∗

7=3.0% , G∗

h,max=1.0 Ω−1

and G∗

h,min=0.1 Ω−1 (h = 5, 7), G∗

h=0 Ω−1 (h > 7).Before the AFU is started, Fig. 7(a) shows bus voltages are

amplified substantially toward the end of the bus. Particularly,fifth harmonic voltage is severe, such as VD5 = 4.4% at bus 2and VD5 = 6.8% at bus 3, respectively. Voltage distortion onall buses is given in Table I. After the AFU with the proposeddiscrete frequency tuning method is in operation, voltagedistortion is significantly improved. Voltage waveforms andvoltage distortion are shown in Fig. 7(b) and Table II. VD5 isreduced to 2.8% and 3.0% at bus 2 and bus 3, respectively.The AFU operation is in Fig. 8. It indicates the AFU currentiaf can track the reference current i∗af generated from (1) for

207

Vbus1

Vbus2

Vbus3

(a) Bus voltages before the AFU is started.

Vbus1

Vbus2

Vbus3

(b) Bus voltages after the AFU is in operation.

Fig. 7. Bus voltage waveforms.

supplying damping functionality. At the steady state, the AFUconsumes iaf,RMS = 8.1 A, and iaf,peak = 13 A.

Fig. 9 shows G∗

5 and G∗

7 when the AFU starts up andexperiences transience due to resonant capacitor at bus 2switching off line. At t = T0, the AFU is turned on. G∗

5

and G∗

7 would settle at t = T1. Based on voltage distortionVD5, G∗

5 is adjusted to supply adequate damping. Whenreaching the steady state, G∗

5 is approximate to 0.65 Ω−1.On the other hand, G∗

7 is always maintained to the minimumvalue (0.1 Ω−1) because VD7 is slightly larger than 3.0%. Att = T2, the capacitor connected at bus 2 is switched off line.The voltage distortion on all buses is reduced. Finally, G∗

5 isreduced to 0.5 Ω−1.

The AFU with the automatic gain adjustment scheme isalso implemented. The AFU operation and test results areshown in Table III and Fig. 10. The damping performance

i∗af

iaf

Fig. 8. Active filter currents in the proposed discrete frequency tuningmethod. Y axis(i∗

af, iaf : 2.8 A/V )

|||||||||||||||||||||||||||||||||||||

|||||||||||||||||||||||||||||||||||||

|||||||||||||||||||||||||||||||||||||

G∗

5

G∗

7

T0 T1 T2

Fig. 9. Fifth and seventh conductance commands in AFU startup andcapacitors at bus 2 switching off line. Y axis(G: 0.5 Ω

−1/V )

TABLE III

VOLTAGE DISTORTION IN THE AUTOMATIC GAIN ADJUSTMENT CONTROL.

Bus 1 Bus 2 Bus 3VTHD 2.2% 2.9% 3.0%VD5 2.2% 2.7% 2.8%VD7 0.4% 0.5% 0.5%

208

i∗af

iaf

Fig. 10. Active filter currents in the automatic gain adjustment control. Yaxis(i∗

af, iaf : 2.8 A/V )

is similar to the proposed discrete frequency tuning methodbecause the ”whack-a-mole” phenomenon is not clear in theshort circuit. At the steady state, the AFU would consumeiaf,RMS = 8.1 A, and iaf,peak = 16 A. Harmonic currentcomponents of the AFU in both the discrete frequency tuningmethod and the automatic gain adjustment control are shownin Fig. 11. Compared with the proposed method, the peakcurrent of the automatic gain adjustment control is largerbecause the AFU emulates the same damping conductance forall harmonic components, as expected in Section III-A.

0

1

2

3

4

5

6

7

8

9

10

5th 7th 11th 13th5th 7th 11th 13th

Discrete frequency tuning methodAutomatic gain adjustment control

iaf,h

Fig. 11. Harmonic current components of the AFU in the discrete frequencytuning method and the automatic gain adjustment control. Y axis: A.

V. SUMMARY

A discrete frequency tuning active filter is proposed inthis paper to suppress power system harmonics. This activefilter is installed at the end of the radial line to terminatethe propagation of harmonic resonance. It operates as variousconductance according to voltage distortion at each harmonic

frequency. By dynamically adjusting damping conductanceof individual harmonic frequency, the mismatching problembetween the feeder and the AFU can be avoided effectively,and voltage distortion of each harmonic frequency would bedefinitely maintained below an allowable level either at theAFU installation point or on other location of the feeder. Thisis the significant advantage of the proposed approach.

Variation of resonant capacitors in the power system wouldshift resonant frequency and change system impedance. Thisphenomenon may deteriorate AFU damping functionality orcause unintentional harmonic amplification on certain loca-tions of the feeder whether a fixed gain or an automatic gainadjustment is employed due to similar conductance for allharmonic frequencies. Thanks to discrete frequency tuningmethod of the proposed AFU, power system harmonics wouldbe maintained at an allowable level and become insensitive tosystem variation. Therefore, entire loading installed throughoutthe feeder would receive similar voltage quality.

ACKNOWLEDGMENT

This research is funded by the National Science Council ofTAIWAN under grant NSC 97-2218-E-182-004.

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