1

A Reviewof

ACTIVE POWER FILTERS

Prepared byPARK KI-WON

R&D Center , POSCON

2001. 02. 09

2

1. Issues on Harmonics

Nature of Harmonics• Generalized power theory• Measurement / Metering

Impacts of Harmonics• Parallel / Series Resonance, RMS / Peak Value Increase

Source of Harmonics• Voltage source vs.Current source• Static vs. Dynamic

Standards on Harmonics: Harmonic Limits• Utility companies / Customers / Manufacturers• IEC / IEEE

Harmonics Reduction/Elimination

3

2. Source of Harmonics

Non-linear magnetization of a transformer• Very small compared to rated current

Power electronics based equipment• UPS, PC, Welder, Printer• Rectifier, Variable Speed Drive• Due to discontinuous current flows

[ ]Wbφ

[ ]Ai [sec]t

( )tφ ( )ti

4

( )tiline

CLoadLoadLoadLoad

ACACACACSupplySupplySupplySupply

Voltage Source Type Harmonic• Diode rectifiers with capacitive filtering

5

Current Source Type Harmonic• Thyristor converters with inductive filtering

( )tiline

L

LoadLoadLoadLoadACACACACSupplySupplySupplySupply

6

3. Standards/Guides on Harmonic Limits

IEC 1000-3-2( International Electrotechnical Commission )• Harmonic current emission limits for individual equipments• Small equipments < 16A• European standard (CELENEC)

IEC 1000-3-4• Harmonic current limits of overall installation• Medium to large installations >16A• Related to line stiffness (SCC)

IEEE 519-1992• Limits at PCC (Interfacing)• Harmonic voltage limits for utility company• Harmonic current limit for customers(<69kV)• Related to line stiffness

7

4. How Harmonic Reduction/Elimination?

Line-Friendly Load• Multi-pulsed system : Series and/or parallel• Active current shaping( PFC converter )

Passive Filters• Simple, low cost, robust• Sensitive to environments: line impedance, load change, ageing of component• Subject to parallel/series resonance• Easily overloadable : switch off or be damaged, plant modification• Over Compensation at which have already a good power factor

Active Filters

8

Series vs. Shunt

Shunt Tuned Filter• High voltage: 50 < Q < 150• Low voltage: 10 < Q < 50

LC1

C

L

R

ω

CL

RQ 1=

Cω1

Lω

R

FZ

)(ωFZ

5. Passive Filters

9

LC1

C

L

R

FZ

ω

Cω1

Lω

R

)(ωFZ

bR

bR

CRb

1

Damped High-Pass Filter (2nd order)

10

Non-linear load

Power system

I5 I7 I11 Ih IS ≅ I1

IL

5th tuned filter

7th tuned filter

11th tuned filter

High-pass filter

Typical Passive Filter System

11

6. Parallel Resonance

• Due to load current harmonic • Voltage distortion will be very high• Overvoltage

ACACACACSupplySupplySupplySupply

L

C

parallelZ

hihi

)1(11

12

2 =∞⇒−

=+

= LCwhenLC

Lj

CjLj

CjLj

Z parallel ωωω

ωω

ωω

12

Parallel Resonance with Passive Filter

FZ

SZ

LhI

ShI LhI

FhI

FSSF ZZZ ||=

LC1

R

ω

Cω1

Lω

)||( LLSω

SLω

1 (0dB)

CLS

1 CLLS )||(

1

Lh

ShII

SFZ

LLL

S +

CLS21

ω

Parallel resonance Tuned frequency

CLLS )(1+

CLLSp

)(1+

≈ω

CLL

RRQ S

Sp

++

≈ 1

13

Possible Cause of Parallel Resonance• Detuning Filter : shift of resonance frequency• Capacitance change due to fuse blow• C and L may be damaged• Temperature• Line structure change

Typical Design Practice• Tuned to slightly lower harmonic frequency (3~10%)

Effect of Ls (SCC)• High Ls : good for avoiding parallel resonance• Higher Ls : Higher Q for parallel resonance

14

7. Series Resonance

hv

DistortedDistortedDistortedDistortedSupplySupplySupplySupply

L

C

seriesZ

hi

hv

)1(011C

LwhenC

LjCj

LjZseries ωω

ωω

ωω =⇒

−=+=

• Due to line voltage harmonics• Excessive harmonic current flow• Overload, Breakdown

15

Series Resonance Due to Neighborhood Harmonic Source

1TRZPCCPCCPCCPCC

hi

............

Plant #1Plant #1Plant #1Plant #1

2TRZ

Plant #2Plant #2Plant #2Plant #2

ACACACACSupplySupplySupplySupply

FilterFilterFilterFilter

16

Equivalent Circuits Transforms

hI

2TRZ

LIFZ1TRZ

ShV LIFZ

1TRZ 2TRZ

SZ

1TRhSh ZIV =

PCC

• Series Resonance

will be occurred

17

8. Troubles due to Harmonic Pollutions

• Heating of the electrical equipment• Trip of circuit breaker• Fuse blown• Capacitor damage• kWh fault• Loss of motor winding and iron• Perturbing torques on the motor shaft• Damage of Sensitive electronic equipment• Malfunction of PLL circuit• Communication interference

• Parallel and Series Resonance will occured• Increase of RMS and Peak Value• Excessive Neutral Currents

18

9. Motivations for taking action against Harmonics

Harmonics lead to premature ageing of the electrical Installation

• Excessive amount of harmonics must eliminatefor economic reasons

The utility company impose penalties on users

• Harmonic pollution may disturb equipment in other plants• THD limitation of voltage / current present at PCC• IEC 1000-3-6 : “Assessment of emission limits for disturbing loads

in MV and HV power systems”

19

10. Function of APFs

Main function• Compensate current and voltage harmonic.

Additional functions• Current-related compensation

• Reactive power, current unbalance, neutral current• Using shunt-APF for the most part

• Voltage-related compensation• Voltage unbalance, flicker, spikes, regulation• Using series-APF for the most part

20

Converter-based classification• VSI (Voltage Source Inverter) bridge structure• CSI (Current Source Inverter) bridge structureTopology-based classification• Shunt APF• Series APF• UPQC : Shunt APF + Series APF• Hybrid APF : Shunt or Series Active Filter + Passive Filter

Supply-system-based classification• Two-wire APF• Three-wire APF• Four-wire APF

11. Classification of Active Filters

21

12. Converter based classification

CSI

• Switching frequency is restricted

• Higher losses

• Cannot be used in multilevel

VSI

• Self-supporting dc voltage

• Lighter, cheaper

• Expandable to multilevel

22

Shunt APF stand-alone

• Eliminate current harmonics

• Reactive power compensation

• Balancing unbalanced current

NonlinearLoad

Shunt Active FilteriF

NonlinearLoad

Seies Active Filter

vF

13. Topology based classification

Series APF stand-alone

• Eliminate voltage harmonics

• Regulate and balance the terminal voltage

• Damp out harmonic propagation

23

Nonlinear Load

optional

Series Shunt

UPQC : Unified Power Quality Conditioner

• Eliminate voltage and current harmonics• Damp out harmonic propagation• Load voltage regulation and current balancing• Another name is “Universal APF”• Fundamental power flow control: Low power version of UPFC in FACTS• Large cost and control complexity

24

Hybrid APF( Combinations of Passive-Active )

Parallel combination of shunt-APF and shunt passive filter• Current source vs. Harmonic sinkSeries combination of series-APF and series passive filter• Voltage source vs. Harmonic dampingHybrid of series-APF and shunt passive filter• Harmonic isolation vs. Harmonic compensation• Reduced size and cost : Quite popularHybrid of shunt-APF and series passive filter• Harmonic isolation vs. Harmonic blocking Series combination of shunt-APF and shunt passive filter• Resonance damping vs. Harmonic compensationParallel combination of series-APF and series passive filter• Enhancing passive filter vs. Harmonic blocking

25

NonlinearLoad

Shunt Active Filter

Nonlinear

Load

Series Active Filter

• Harmonic cancellation• Q control• Optimal sharing is needed• Commercialized

• Harmonic damping• Existing passive filter• Low power• More circuit for Q control• Overcurrent protection

is difficult

Parallel combination ofshunt-APF and shunt passive filter

Hybrid ofseries-APF and shunt passive filter

26

NonlinearLoad

Series Active Filter

• Harmonic cancellation and damping• Series-APF enhanced existing passive filter• Easy protection is possible• Current Transformer is minimized• No Q control• Under developed

Series combination ofseries-APF and shunt passive filter

27

14. Supply-system based classification

Two-wire APF

• Single-phase nonlinear loads, such as domestic appliances

• Smaller rating

Three-wire APF

• Three-phase nonlinear load without neutral, such as ASD’s

Four-wire APF

• Single-phase nonlinear loads fed from four-wire supply system,

such as computers, commercial lighting

• Eliminate excessive neutral current and unbalance

28

Capacitor midpoint four-wire shunt APF• Used in smaller ratings,

because entire neutral current flows through dc bus capacitor

Sae

Sbe

Sce

Sai

Sbi

Sci

Lai

Lbi

Lci

Cav

Cbv

Ccv

cL

n

CaiCbiCciCni

Sni

dcC

Non-Linear Four-wireUnbalanced Loads

Lni

n

dcC

29

Four-pole four-wire shunt APF• Fourth pole is used to stabilized the neutral of APF

Sae

Sbe

Sce

Sai

Sbi

Sci

Lai

Lbi

Lci

CavCbv

Ccv

cL

n

CaiCbiCciCni

Sni

dcC

Non-Linear Four-wireUnbalanced Loads

Lni

n

30

Three-bridge four-wire shunt APF• Quite common type• Proper voltage matching for IGBT, Enhances the reliability of APF

Sae

Sbe

Sce

Sai

Sbi

Sci

Lai

Lbi

Lci

Cbv Ccv

n

Cai Cbi Cci

Sni

dcC

Non-Linear Four-wireUnbalanced Loads

Lni

Cav

31

First stage : Signal conditioning• Sensing system information by PT, CT, Isolation amplifiers• Monitor, measure, record

: THD, power factor, active/reactive power, crest factor…Second Stage : Derivation of compensating signal• Current level and/or voltage level• Frequency domain

: Based on Fourier transformation: Cumbersome computation, large response time

• Time domain: Based on instantaneous derivation: pq theory, synchronous dq reference frame method, synchronous

detection method, flux-based controller, notch filter method…Third stage : Generation of gating signal• Hysteresis, PWM, SVPWM, sliding mode, fuzzy-logic…

15. APF Control Strategies

32

16. Component considerations of APF

Series inductor : buffer between supply and PWM voltagePassive ripple filter : suppress switching harmonic and improve source THDDC bus capacitor : reduces dc ripples

Cai

Cbi

Cci

Cav

Cbv

Ccv

cL

dcCdcv

p

n

dci

dc bus capacitor

passive ripple filter

series inductor

IGBT

33

17. Basic Concept of Active Filter Control

Active Filter as a “Harmonic Canceller”

Harmonic current detection

And

Current control method

Harmonic voltage detection

And

Voltage control method

SL

Shunt-APF

fS ii = hfL iii +=

hC ii =

detectionih

Sv Li

SL

Series-APF

hC vv =

hf

S

vvv

+=

detectionvh

Sv LifL vv =

34

Active Filter as a “Harmonic Damper”

SL

Shunt-APF

h

hC Z

vi =

detectionvh

Sv Li

SL

Series-APF

hhF iZv =

detectionih

Sv Li

Harmonic voltage detection

And

Current control method

Harmonic current detection

And

Voltage control method

35

18. Control Based on Synchronous d-q Transformation

• Definition of Synchronous d-q transformation

32,

)sin()sin(sin)cos()cos(cos

32 πγ

γθγθθγθγθθ

=

+−−−−

+−=

where

fff

ff

c

b

a

q

d

−

=

−=

s

q

sd

ee

eee

q

ed

eq

ed

ee

ees

q

sd

ff

ff

ff

ff

θθθθ

θθθθ

cossinsincos

,cossinsincos

∑∑

=

=

+=+=

+=+=

mkqkm

eqh

eq

eq

mkdkm

edh

ed

ed

iIiii

iIiii

311

311

sin

cos

φ

φ

• Transformed current with harmonics

( ) ( )

( ) ( )[ ]

( ) ( )[ ]kek

mkemb

kek

mkemb

kek

mkema

kIIi

kIIi

kIIi

φγθφγθ

φγθφγθ

φθφθ

−++−+=

−−+−−=

−+−=

∑

∑

∑

∞

=

∞

=

∞

=

coscos

coscos

coscos

21

21

21

36

Axes relation between abc and dq

• Stationary frame • Synchronously rotating frame

aa ff =

32πj

bb eff ⋅=

32πj

cc eff−

⋅=

sdf

sqf

γ

γ−

aa ff =

32πj

bb eff ⋅=

32πj

cc eff−

⋅=

sdf

sqf

eθγ +

eθγ +−

edfe

qf

eθ

37

D-Q variable in time domain

Sae Sbe Sce

mE

π π2

π

π−

teω

t

sSqes

Sde

mE

π π2teω

eSde

eSqe

mE

π π2teω

• Stationary

• Synchronously

38

Harmonic locus in Space Vector

5th in stationary frame 7th in stationary frame

tjm

tjm

sssdq

ee eFeFfff ωω 551 5

151 −+=+= tj

mtj

msss

dqee eFeFfff ωω 7

71 71

71 +=+=

sdqf

eω

sf1

sf5eω5−

sdf

sqf

sdqf

eωsf1

sf7eω7

sdf

sqf

39

5th and 7th in stationary frame 5th and 7th synchronous rotating variable in stationary frame

tjm

tjm

tjm

ssssdq

eee eFeFeFffff ωωω 75751 7

151

71

51 ++=++= −

tjm

tjmm

eeeedq

ee eFeFFffff ωω 66751 7

151

71

51 ++=++= −

sdf

edqf

sqf

sdqf

eωsf1

sdf

sqf

40

Overall block diagram of shunt-APF controller

Lai

Lbi

eLdi

eLqi

LPFeLdi

===

)1(0)0(

KKii

eLde

Sd

+ −

LPF

+ −

1-K

eLqi e

LqeSq ii =

*eCdi

*eCqi+ −

IPcontroller

*dcv

dcv

+

−

synchronousPI-controller

eθeθ

*eCdv

*eCqv

seTjke ω

*'eCdv

*'eCqv

e→φ3 se →

*sCdv

*sCqv

SVPWM

*aT

*bT

*cT

e→φ3

Cai

Cbi

eCdi

eCqi

HarmonicPhase DelayCorrection

41

Harmonic Phase Delay Correction Method

)(* ki eC

LPF

)(*1 ki e

C

)(*5 ki e

C

)(*7 ki e

C

5CI

7CI

seTje ω6−

LPF

5th Harmonic detection

7th Harmonic detection

+

−

seTje ω6

)(*11 ki e

C

)(*13 ki e

C

+

+

+

+

LPF1CI

Fundamental detection

+

+

+

)1(*1 +ki e

C

)1(*5 +ki e

C

)1(*7 +ki e

C

+

+

+

+

+

+

)1(*11 +ki e

C

)1(*13 +ki e

C

+

+)1(* +ki e

C

eje θ6

eje θ6 eje θ6−

eje θ6−

Harmonic phase delay correction in synchronous rotating frame

42

19. Control Based on p-q Theory

=

−

−−=

c

b

a

c

b

a

eee

Ceee

ee

αββ

α

23

230

21

211

32

=

−

−−=

c

b

a

c

b

a

iii

Ciii

ii

αββ

α

23

230

21

211

32

aa ie ,

bb ie ,

cc ie ,

32π

32π

32π

a-Axis

b-Axis

c-Axis

0

αα ie ,

ββ ie ,

α-Axis

β-Axis

0

αααα- ββββ Transfomations

43

ccbbaa ieieiep ++=

ββαααβαβββαα ieieiepieiep ⋅+⋅=⋅=+= ,

αββααβαβαββα ieieieqieieq ×+×=×=−= ,

• Conventional instantaneous power

βα ie ×

αβ ie ×

αeαi

βiβe

REAL PLANE

IMAGINARY AXIS

α-Axis

β-Axis • Instantaneous real power

• Instantaneous imaginary power

−

=

−

=

−

qp

eeee

ii

ii

eeee

qp

1

,αβ

βα

β

α

β

α

αβ

βα

• Instantaneous power vs. current

44

p and q in Sinusoidal Case

tVva ωcos2=

)cos(2 γω += tVvb

)cos(2 γω −= tVvc

)cos(2 φω −= tIia

)cos(2 γφω +−= tIib

)cos(2 γφω −−= tIic

tVv ωα cos3=

tVv ωβ sin3=

)cos(3 φωα −= tIi

)sin(3 φωβ −= tIi

φββαα cos3VIivivp =+=

φαββα sin3VIivivq =−=

45

p and q in Non-Sinusoidal Case

46

Overall block diagram of series-APF controller

Fav

Fbv

Fcv

HPF

HPF

αFv

βFv

Sai

Sbi

Sci

αSi

βSi

p

q

hp

hq

a

b

c

d

q

0=θ

a

b

c

d

q

0=θ

−

=

β

α

αβ

βα

S

S

FF

FF

ii

vvvv

qp

−

=

−

h

h

FF

FF

hS

hS

qp

vvvv

ii 1

αβ

βα

β

α

hSi α

hSi β

a

b

c

d

q

0=θ

K

K

K

Sahi

Sbhi

Schi

*Cav

*Cbv

*Ccv

47

20. Selection of APF for specific considerations

9. Voltage Sag & Dips

8. Voltage Flicker

7. Voltage Balancing

6. Voltage Regulation

5. Voltage Harmonics

4. Neutral Current

3. Load Balancing

2. Reactive Power

1. Current Harmonics

UPQCHybrid-APFSeries-APFShunt-APF

Active Power Filters TopologyCompensation for specific application

Higher number of ‘ ’ is more preferred