harmonic treatment in industrial power

IEEE PESC-02 JUNE 2002 1

HARMONIC TREATMENT IN INDUSTRIAL POWER SYSTEMS

Presented by

Stefanos Manias

JUNE 2002 IEEE PESC-02 2

CONTACT INFORMATION

Stefanos N. Manias

National Technical University of Athens

Phone: +3010-7723503

FAX: +3010-7723593

E-mail: [email protected]

Mailing Address

National Technical University of Athens

Department of Electrical and Computer Engineering

9, Iroon Polytechniou Str, 15773 Zografou

Athens, Greece
mailto:[email protected]


PLAN OF PRESENTATION

1. DEFINITIONS

2. CATEGORIES OF POWER QUALITY VARIATIONS

3. HARMONIC DISTORTION SOURCES IN INDUSTRIAL POWER

SYSTEMS

4. EFFECTS OF HARMONICS ON ELECTRICAL EQUIPMENT

5. HARMONIC MEASUREMENTS IN INDUSTRIAL POWER SYSTEMS

6. HARMONIC STANDARDS

7. HARMONIC MITIGATING TECHNIQUES

8. GENERAL PASSIVE AND ACTIVE FILTER DESIGN PROCEDURES

9. DESIGN EXAMPLES

10. CONCLUSIONS


WHY HARMONIC ANALYSIS ?

When a voltage and/or current waveform is distorted, it causes abnormal operating conditions in a power system such as:

Voltage Harmonics can cause additional heating in induction and

synchronous motors and generators.

Voltage Harmonics with high peak values can weaken insulation in

cables, windings, and capacitors.

Voltage Harmonics can cause malfunction of different electronic

components and circuits that utilize the voltage waveform for

synchronization or timing.

Current Harmonics in motor windings can create Electromagnetic

Interference (EMI).


Current Harmonics flowing through cables can cause higher

heating over and above the heating that is created from the

fundamental component.

Current Harmonics flowing through a transformer can cause

higher heating over and above the heating that is created by the

fundamental component.

Current Harmonics flowing through circuit breakers and switch-

gear can increase their heating losses.

RESONANT CURRENTS which are created by current harmonics

and the different filtering topologies of the power system can

cause capacitor failures and/or fuse failures in the capacitor or

other electrical equipment.

False tripping of circuit breakers ad protective relays.


a) Current Source nonlinear load

Diode rectifier for ac drives,

electronic equipment, etc

HARMONIC SOURCES

Thyristor rectifier for dc drives,

heater drives, etc.

Per-phase equivalent circuit

of thyristor rectifier

b) Voltage source nonlinear load

Per-phase equivalent circuit

of diode rectifier


010 20 30 40

-1.0

-0.5

0.0

0.5

1.0

Time (mS)

Curr

ent

010 20 30 40

-1.0

-0.5

0.0

0.5

1.0

Time (mS)

Curr

ent

010 20 30 40

-1.0

-0.5

0.0

0.5

1.0

Time (mS)

Curr

en

t

TYPE OF

NONLINEAR LOAD

TYPICAL WAREFORM

THD%

1-

Uncontrolled

Rectifier

80%

(high 3rd

component)

1-

Semicontrolled

Rectifier Bridge

2nd, 3rd, 4th ,......

harmonic

components

6 Pulse Rectifier

with output voltage

filtering and without

input reactor filter

80%

5, 7, 11, .

INPUT CURRENT OF DIFFERENT

NOLINEAR LOADS


010 20 30 40

-1.0

-0.5

0.0

0.5

1.0

Time (mS)

Curr

ent

0 10 20 30 40-1.0

-0.5

0.0

0.5

1.0

Time (mS)

Cu

rren

t

0 10 20 30 40-1.0

-0.5

0.0

0.5

1.0

Time (mS)

Cu

rren

t

6 - Pulse Rectifier

with large output

inductor

28%

5, 7, 11, ..

6 - Pulse Rectifier

with output voltage

filtering and with 3%

reactor filter or with

continues output

current

40%

5, 7, 11, ..

12 - Pulse Rectifier

15%

11, 13, ..


CURRENT HARMONICS GENERATED BY 6-PULSE CSI CONVERTERS

HARMONIC

P.U PULSE

1

1.00

5

0.2

7

0.143

11

0.09

13

0.077

17

0.059

19

0.053

23

0.04

CURRENT HARMONICS GENERATED BY 12-PULSE CSI CONVERTERS

HARMONIC

P.U PULSE

IEEE 519 std

1

1.00

-

5

0.03-0.06

5.6%

7

0.02-0.06

5.6%

11

0.05-0.09

2.8%

13

0.03-0.08

2.8%

THD

7.5%-14.2%

7.0%


RECENT CURRENT MEASUREMENTS TAKEN IN AN

INDUSTRIAL PLANT WITH 600 KVA, 20 KV/400 V

DISTRIBUTION TRANFORMER

Current waveform and its respective spectrum

at the inputs of a motor drive system



at the inputs of a motor drive system



at the secondary of the distribution transformer

( i.e. at the service entrance)


DEFINITIONS

f (t) = Fourier Series of a periodic function f (t) =

1hhho th cosCC (1)

T

oodttf

T

1C ,)( (2)

T

ohdt)thcos()t(f

T

2A (3)

T

oh dt)thsin()t(f

T

2B (4)

h = harmonic order

2h

2hh BAC


%THD

100V

V

1

2h

2h

(5)

%iTHD

100I

I

1

2h

2

h

(6)

Percentage of the Total Harmonic Distortion of

a nonsinusoidal voltage waveform

Percentage of the Total Harmonic Distortion of

a nonsinusoidal current waveform

hthVh

hthIh

harmonic component of the voltage

harmonic component of the current

V~

H RMS value of the voltage distortion V~

2h

2h


I~

1h

2hI

~ (7)

V~

V~

1h

2

h

(8)

100VAk SC

kVA DriveHF %THD (9)

15h

2h

2 I/Ih (10)

RMS value of a nonsinusoidal current =

RMS value of a nonsinusoidal voltage =

HF Harmonic Factor =

I~H RMS value of the current distortion

I~

2h

2h


kVA Drive

kVA SC

SINUSOIDAL VOLTAGE NONSINUSOIDAL CURRENT

1i,1 cosI~ V

~P

I~ V

~S , sinI

~ V

~Q 1i,1

(11)

(12)

(13)

Full load kVA rating of the Drive system

Short Circuit kVA of the distribution system at

the point of connection

222 QPS VA DistortionD


2h

2h,i

221,i

222 I~

V~

I~

V~

SD (14)

S

PFactor Power True 1

1,icos

I

I(15)

Factorment Displace Factor Distortion

NONSINUSOIDAL VOLTAGE AND NONSINUSOIDAL CURRENT

1h 1hhhh , hhh sinI

~V~

QcosI~

V~

P (16)

SSSSPower DistortionD

mnm n

*mn

*nm

mnmn

nm (17)


2222 DQPS(18)

2 N

21

2

HH

2

1H

2

H1

2

11

1h

2h

2h

SS I~

V~

I~

V~

I~

V~

I~

V~

I~

V~

S

(19)

111 I~

V~

PowerApparent lFundamenta S

PowerApparent ntalNonfundame SN

2HH

21H

2H1

2N I

~V~

I~

V~

I~

V~

S


Power DistortionCurrent I~

V~

H1 (20)

Power Distortion Voltage I~

V~

1H (21)

PowerApparent Harmonic I~

V~

HH (22)

Power ActiveNon Harmonic Total

Power Active Harmonic Total NP S 2H2H

2H (23)

phase32

L-LC VAR/V capacitor theof Reactance X


Harmonic sequence is the phase rotation relationship with respect to the fundamental component.

Positive sequence harmonics ( 4th, 7th, 10th , . (6n+1) th ) have the same phase rotation as the fundamental component. These harmonics circulate between the phases.

Negative sequence harmonics ( 2nd, 5th, 8th (6n-1) th ) have the opposite phase rotation with respect to the fundamental component. These harmonics circulate between the phases.

Zero sequence harmonics ( 3rd, 6th, 9th, .. (6n-3) th ) do not produce a rotating field. These harmonics circulate between the phase and neutral or ground. These third order or zero sequence harmonics, unlike positive and negative sequence harmonic currents, do not cancel but add up arithmetically at the neutral bus.


EXAMPLE 1

A periodic, sinusoidal voltage of instantaneous value tsin2200v

Is applied to a nonlinear load impedance. The resulting instantaneous current is

given by: ooo 60t3sin1060t2sin1045tsin202i

Calculate the components P, Q, D of the apparent voltamperes and hence calculate the displacement factor, the distortion factor and the power factor.

Solution

tsin2200v

ooo 60t3sin1060t2sin1045tsin202i

The presence of the nonlinearity causes frequency components of current (i.e. the

second and third harmonic terms) that are not present in the applied voltage.

The rms voltage and current at the supply are:

V200V~

2222 101020I~

22A106

SINUSOIDAL VOLTAGE -NONSINIMUSOIDAL CURRENT


The apparent voltamperes at the input is therefore given by

2622222 VA1024106200I~

V~

S

In this example only the fundamental frequency components are common to

both voltage and current. Therefore, the real power P and the apparent

power Q are

11cosI~

V~

P

o45cos20200

W2

4000

11sinI~

V~

Q

o45sin20200

VA2

4000

1 = displacement angle between the fundamental of the voltage and the fundamental of the current


21

222 I~

I~

V~

D

232

2 I~

I~

V~

26222 VA1081010200

22222 I~

V~

DQP

Displacement factor 707.02

1cos 1

Distortion factor 817.0600

20

I

I1

Therefore, the power factor is

577.06

2

2

1PF

1111 cosI

I~

I~

V~cosI

~V~

S

Pfactorpower PF


EXAMPLE 2

A periodic, sinusoidal voltage given by o30t5sin200tsin2002vis applied to a series, linear, resistance-inductance load of resistance 4 and

fundamental frequency reactance 10.

Calculate the degree of power factor improvement realizable by capacitance

Solution. The rms terminal voltage is given by

25

21 V

~V~

V~

Compensation when .HZ50f1

22 200200

V~

Therefore

V283V~

10j4Z1

8.10Z1

o2.684/10tan 11

NONSINUSOIDAL VOLTAGE -RL LOAD


505 15

50j4Z5

50Z5o1

5 4.854/50tan

The instantaneous load current is given by

ooo 4.8530t5sin50

2002.68tsin

8.10

2002i

The rms load current I~

is therefore given by

2

5

5

2

1

12

5

2

1

2

Z

V~

Z

V~

I~

I~

I~

222 A359452.18


Average power P In this case is

...cosI~

V~

cosI~

V~

cosI~

V~

Pn

1

222111Lnn

oo 4.85cos42002.68cos52.18200

W1440

The power factor before compensation is therefore

27.01072.28

1440

S

PPF

6

26222 VA1072.28I~

V~

S

Apparent voltamperes S at the load terminals in the absence of capacitance is

therefore


EXAMPLE 3

A periodic, nonsinusoidal voltage with instantaneous value given by

o30-t2sin200tsin2002v

Solution.

is applied to a nonlinear impedance.

The resulting current has an instantaneous value given by ooo

L 60t3sin1060t2sin1045tsin202i

Calculate the components LDLXLR S,S,S of the load apparent voltamperes

and compare thee with the classical values LLL D,Q,P respectively.

o30-t2sin200tsin2002v

oooL 60t3sin1060t2sin1045tsin202i

Note that the presence of the load nonlinearity causes a frequency component

of load current (I.e. the third harmonic term) that is not present in the supply

voltage.

NONSINUSOIDAL VOLTAGE AND NONSINIMUSOIDAL CURRENT


The rms voltage and current at the supply are given by

24222 V108200200V~

222222L A106101020I

~

The load apparent voltamperes LS therefore has a value defined in terms V~

and LI

~

262

L

22

L VA1048I~

V~

S

Instantaneous expressions of the hypothetical currents DXR i,i,i are given by

o0o

R 30t2sin30cos10tsin45cos202i

222o2o2

LR A104

1130cos1045cos20I

~

o0oX 30t2cos30sin10tcos45sin202i

222o2o2

LX A104

930sin1045sin20I

~

o

D 60t3sin10 2i

222

LD A10I~


Note that current components XR i,i contain only those harmonic terms which are common to both voltage and current. These are therefore consistent with the

1n terms.

The rms load current components LDLXLR I~

,I~

,I~

are found, as expected to sum

to the total rms load current LI~

2

L

222

LD

2

LR

2

LD I~

1064

9

4

11110I

~I~

I~

Components LDLXLR S,S,S of the apparent voltamperes can now be obtained

26422

LR

22

LR VA1022108104

11I~

V~

S

26422

LX

22

LX VA1018108104

9I~

V~

S

26422

LD

22

LD VA10810810I~

V~

S


The component voltamperes are seen to sum to the total apparent voltamperes

8182210SSS 62LD2LX

2LR

26 VA1048

2

LS

Components LLL D,Q,P of LS are found as follows: 2

n

1

1n1n1n2L cosI

~V~

P

2oo 30cos1020045cos20200

22 310220100

2

LR

662

6 S108.2064381032210


2n

1

1n1n1n2L sinI

~V~

Q

2oo 30sin1020045sin20200

2

LX

66 S106.1412210

2L

2L

2L

2L QPSD

2LD

266 SVA106.12106.148.2048

From the possible compensation viewpoint it is interesting to note that LXS

and LQ differ by significant amount.

LXS could be defined as that component of the load apparent voltamperes that

Is obtained by the combination of supply voltage harmonics with quadrature

Components of corresponding frequency load current harmonics.


Similarly the definition of active voltamperes LRS could be given by that

component of the load apparent voltamperes that is obtained by the combination

of supply voltage harmonics with in-phase components of corresponding

frequency load current harmonics.

Both LRS and LXS are entirely fictitious and non-physical. The active

voltamperes LRS Is not to be compares in importance with the average power

LP which is a real physical property of the circuit. Term LRS Is merely the

analytical complement of term LXS

Term LXS the energy-storage reactive voltamperes, is that component

of the load apparent voltamperes that can be entirely compensated (for sinusoidal

supply voltage) or minimized (for nonsinusoidal supply voltage) by energy-storage

methods.


Voltage and current profiles in a

commercial building


HARMONIC STANDARDS

International Electrotechnical Commission (IEC) European

Standards.

- EN 61000-3-2 Harmonic Emissions standards were first published

as IEC 55-2 1982 and applied only to household appliances. It was

revised and reissued in 1987 and 1995 with the applicability

expanded to include all equipment with input current 16A per

phase. However, until January 1st, 2001 a transition period is in

effect for all equipment not covered by the standard prior to 1987.

- The objective of EN 61000-3-2 (harmonics) is to test the equipment

under the conditions that will produce the maximum harmonic

amplitudes under normal operating conditions for each harmonic

component. To establish limits for similar types of harmonics current

distortion, equipment under test must be categorized in one of the

following four classes.


CLASS-A: Balanced three-phase equipment and all other equipment

except that stated in one of the remaining three classes.

CLASS-B: Portable electrical tools, which are hand held during normal

operation and used for a short time only (few minutes)

CLASS-C: Lighting equipment including dimming devices.

CLASS-D: Equipment having an input current with special wave shape

( e.g.equipment with off-line capacitor-rectifier AC input

circuitry and switch Mode power Supplies) and an active

input power 600W.

- Additional harmonic current testing, measurement techniques and

instrumentation guidelines for these standards are covered in IEC

1000-4-7.


IEEE 519-1992 United States Standards on harmonic limits

- IEEE limits service entrance harmonics. - The IEEE standard 519-1992 limits the level of harmonics at the

customer service entrance or Point of Common Coupling (PCC).

- With this approach the costumers current distortion is limited based on relative size of the load and the power suppliers voltage

distortion based on the voltage level.

IEEE 519 and IEC 1000-3-2 apply different philosophies, which

effectively limit harmonics at different locations. IEEE 519 limits

harmonics primarily at the service entrance while IEC 1000-3-2 is

applied at the terminals of end-user equipment. Therefore, IEC limits

will tend to reduce harmonic-related losses in an industrial plant

wiring, while IEEE harmonic limits are designed to prevent

interactions between neighbors and the power system.


POWER QUALITY STANDARDS

IEEE 519-1992 STANDARDS

TABLE I CURRENT DISTORTION LIMITS FOR GENERAL DISTRIBUTION SYSTEMS

(120-69000 V)

Isc/IL


TABLE II

LOW VOLTAGE SYSTEM CLASSIFICATION AND DISTORTION LIMITS

IEEE 519-1992 STANDARTS

Special

Applications

General

System

Dedicated

System

Notch Depth 10% 20% 50%

THD (Voltage) 3% 5% 10%

Notch Area

(AN)*

16,400 22,800 36,500

Source: IEEE Standard 519-1992.

Note: The value AN for another than 480Volt systems should be

multiplied by V/480 .

The notch depth, the total voltage distortion factor (THD) and

the notch area limits are specified for line to line voltage.

In the above table, special applications include hospitals and

airports. A dedicated system is exclusively dedicated to converter load.

*In volt-microseconds at rated voltage and current.


TABLE III

LIMITS OF THD%

IEEE 519-1992 STANDARDS

SYSTEM

Nominal Voltage

Special

Application

General

Systems

Dedicated

Systems

120-600V 3.0 5.0 8.0

69KV and below - 5.0 -


TABLE IV PROPOSED IEC 555-2 CLASS D STANDARDS for power from 50 to 600W

Harmonic Relative limits

Milliamps/Watt

Absolute Limits

Amps

3 3.4 2.30

5 1.9 1.14

7 1.0 0.77

9 0.5 0.40

11 0.35 0.33

13 linear

extrapolation

0.15 (15/n)


METHODOLOGY FOR COMPUTING DISTORTION

Step 1: Compute the individual current harmonic distortion at each dedicated bus using different Software programs (i.e. SIMULINK, SPICE, e.t.c.) or tables that provide the current distortion of nonlinear loads.

Step 2: Compute the voltage and current harmonic content at the Point of Common Coupling (PCC) which is located at the input of the industrial power system.

- Each individual harmonic current at the PCC is the sum of harmonic current contribution from each dedicated bus.

- The load current at PCC is the sum of the load current contribution from each dedicated bus.

- The maximum demand load current at PCC can be found by computing the load currents for each branch feeder and multiply by a demand factor to obtain feeder demand. Then the sum of all feeder demands is divided by a diversity factor to obtain the maximum demand load current.


Step 3: Choose a base MVA and base KV for the system use the following

equations in order to compute individual and total current and

voltage harmonic distortions at PCC and any other point within the

power system.

Ib= Base current in Amps Ampsb

3b

kV3

10MVA

= System impedance = p.u. MVA

MVA

sc

b

MVAb= Base MVA, MVAsc= short circuit MVA at the point of interest

VH= Percent individual harmonic voltage distortion =

Volts 100ZhI

Is

b

h

(24)

(25)

(26)

sZ


h = harmonic order

100V

21V

%THD1

2h

2h

100I

I

%THD1

2

2h

2h

i

IH = Percent individual harmonic distortion = 100I

I

L

h

Isc = Short Circuit current at the point under consideration.

IL = Estimated maximum demand load current

S.C. Ratio = Short circuit Ratio

D

sc

L

sc

MVA

MVA

I

I

MVAD = Demand MVA

(27)

(28)

(29)


K Factor = Factor useful for transformers design and

specifically from transformers that feed

Adjustable Speed Drives

1h

2

L

h2

I

Ih

ONCE THE SHORT CIRCUIT RATIO IS KNOWN, THE IEEE CURRENT

HARMONIC LIMITS CAN BE FOUND AS SPECIFIED IN TABLE I OF

THE IEEE 519-1992 POWER QUALITY STANDARDS

USING THE ABOVE EQUATIONS VALUES OF IDIVINDUAL AND

TOTAL VOLTAGE AND CURRENT HARMONIC DISTORTION CAN

BE COMPUTED AND COMPARED WITH THE IEEE LIMITS

(30)


Step 4: If the analysis is being performed for CSI-type drives then the area

of the voltage notch AN should also be computed.

- At this point an impedance diagram of the under analysis

industrial power system should be available.

- The Notch Area AN at the PCC can be calculated as follows.

AN = AN1 + AN2 + . V . microsec

AN1 , AN2 , are the notch areas contribution of the different busses

ANDR1 : Notch area at the input of the drive

1NDR1N Adrive the toPCC from sinductance of sum the inductance Source

inductance SourceA

(31)

(32)


Step 5: Determine preliminary filter design.

Step 6: Compute THDv and THDi magnitudes and impedance versus

frequency plots with filters added to the system, one at a time.

SIMULINK or PSPICE software programs can be used for final

adjustments.

Step 7: Analyze results and specify final filter design.


EXAMPLE OF A SYSTEM ONE LINE

DIAGRAM


System impedances diagram which can be used to

calculate its resonance using PSPICE or SIMULINK

programs


1) Parallel-passive filter for current-source nonlinear loads

TYPES OF FILTERS

Harmonic Sinc

Low Impedance

Cheapest

VA ratings = VT (Load Harmonic current + reactive current of the filter)


2) Series-passive filter for voltage-source nonlinear loads

Harmonic dam High-impedance

Cheapest

VA ratings = Load current (Fundamental drop across filter + Load Harmonic Voltage)


3) Basic parallel-active filter for current source in nonlinear loads


4) Basic series-active filter for voltage-source in nonlinear loads


5) Parallel combination of parallel active and parallel passive

6) Series combination of series active and series passive


7) Hybrid of series active and parallel passive

8) Hybrid of parallel active and series passive


9) Series combination of parallel-passive and parallel-active

10) Parallel combination of series-passive and series-active


11) Combined system of series-active and parallel-active

12) Combined system of parallel-active and series-active


A SIMPLE EXAMPLE OF AN INDUSTRIAL

POWER DISTRIBUTION SYSTEM


HARMONIC LIMITS EVALUATION WHEN POWER-FACTOR-CORRECTION CAPASITORS

ARE USED

- As it can be seen from the power distribution circuit the power-factor-

correction capacitor bank, which is connected on the 480 Volts bus, can

create a parallel resonance between the capacitors and the system

source inductance.

- The single phase equivalent circuit of the distribution system is shown

below.

Using the above circuit the following equations hold:

Source AC

totL SI

C

inZ

hI

fI

SV

HarmonicLoad

totR


, R

Xtancos

MVA

kVR 1

sc

2LL

sys 2

syssys

RR

, R

Xtansin

MVA

kVX 1

sc

2LL

sys2

syssys

XX

tr

2LL

putrkVA

kV1000RR

tr

2LL

putrkVA

kV1000XX

= The turns ratio of the transformer at PCC

(33)

(34)

(35)

(36)


trsystot XXX

cap

2cap

ckVAR

kV1000X

X

L tottot f2

X tot

X

1C

c

C

1Xc

trsystot RRR (37)

(38)

(39)

(40)

(41)

(42)


C

1jLjR

C/jLjRZ

tottot

tottotin

, C

1L

ototo

oo

2

1f

The impedance looking into the system from the load, consists of the

parallel combination of source impedance and the

capacitor impedance tottotjXR

inZ

The equation for can be used to determine the equivalent system

impedance for different frequencies. The harmonic producing loads can

resonate (parallel resonance), the above equivalent circuit. Designating

the parallel resonant frequency by (rad/sec) or (HZ) and equating

the inductive and capacitive reactances.

inZ

o of

(43)

(44)


- Harmonic current components that are close to the parallel resonant frequency are amplified.

- Higher order harmonic currents at the PCC are reduced because the capacitors are low impedance at these frequencies.

- The figure below shows the effect of adding capacitors on the 480 Volts bus for power factor correction.

This figure shows that by adding some typical sizes of power factor correction capacitors will

result in the magnification of the 5th and 7th harmonic components, which in turns makes it

even more difficult to meet the IEEE 519-1992 harmonic current standards .

- Power factor correction capacitors should not be used without turning reactors in case the

adjustable speed drives are >10% of the plant load.


Let us examine an industrial plant with the following data:

- Medium voltage = 20KVLL

- Low voltage = 0.4 KVLL

- Utility three phase short circuit power = 250 MVA

- For asymmetrical current, the ratio of system impedance R

X 4.2

The Transformer is rated:

1000 KVA, 20 KV-400 Y/230 V

Rpu = 1%, Xpu = 7%

- The system frequency is: fsys = 50 HZ.

- For power factor correction capacitors the following cases are examined:

a. 200 KVAR

b. 400 KVAR

c. 600 KVAR

d. 800 KVAR

EXAMPLE


The parallel resonant frequencies for every case of power factor correction is calculated as follows:

6154.04.2tancos250

20R 1

2

sys

4769.14.2tansin250

20X 1

2

sys

504.0

20

000246.0506154.0R 2sys

000591.0504769.1X 2sys

00160.01000

4.0100001.0R

2

tr

0112.01000

4.0100007.0X

2

tr


001846.00016.0000246.0Rtot

011791.00112.0000591.0X tot

H1055.37502

011791.0L 6tot

Case a:

8.0200

4.01000X

2

c

F1098.38.0502

1C 3

HZ18.412

1098.31050.372

1f

36o

For 200 KVAR, the harmonic order at which parallel resonance occurs is:

24.85018.412h


Case b:

4.0400

4.01000X

2

c

F1096.7C 3

HZ45.291fo

83.5h

Case c:

267.0600

4.01000X

2

c

F1094.11C 3

HZ97.237fo

76.4h


Case d:

2.0800

4.01000X

2

c

F1092.15C 3

HZ08.206fo

12.4h

It is clear for the above system that in the 600 KVAR case, there

exists a parallel resonant frequency close to the 5th harmonic. of


POWER FACTOR CORRECTION AND HARMONIC TREATMENT USING TUNED FILTERS

- Basic configuration of a tuned 3- capacitor bank for power factor

correction and harmonic treatment.

Simple and cheap filter

Prevents of current harmonic magnification


- IN ORDER TO AVOID HARMONIC MAGNIFICATION WE CHOOSE A

TUNED FREQUENCY < FITH HARMONIC (i.e 4.7)

- The frequency characteristic of the tuned filter at 4.7 is shown below

As it can be seen from the above figure significant reduction of the 5th

harmonic is achieved. Moreover, there is some reduction for all the other

harmonic components.


The single phase equivalent circuit of the power distribution system

with the tuned filter is shown below

Using the above circuit the following equations hold:


0C

1LL

ofototo

21

ftot

oCLL2

1f

C1LLjR

LjRII

ftottot

tottothf

cap2

os

2cap

2os

c2

os

fkVARf2

kV1000f

f2

Xf2

f2C

1L

(parallel resonance)

= resonance frequency of the

equivalent distribution circuit

21

f

osCL2

1f = Resonant frequency of the series filter

The new parallel combination is having resonant frequency when

Also

(45)

(46)

(47)

(48)


C

1jLjLjR

C

1jLjLjR

Z

ftottot

ftottot

in

C

1LL jR

C

1jLjLjR

ftottot

ftottot

tottotsh LjRIV

C1LL jR

C/1L jII

ftottot

fhs (49)

(50)

(51)


As it was discussed before Selecting HZ235fo or 4.7 th harmonic

With KVcap= 0.4 , KVARcap= 600

H45.38H1045.686002352

4.0100050L 6

2

2

f

The new parallel combination is having resonant frequency:

CLL2

1f

ftoto

with H1055.37L 6tot

H1045.38L 6f

F1094.11C 3

we have

HZ16.167

1094.1110762

1f

36o

43.350/16.167h (without Lf was 4.76)


The following table shows the variation of Parallel resonant frequency

With and without resonant inductor

KVAR

C(mF)

Parallel Resonant f0

Without Lf With Lf

200 3.98 8.80 115.3H

4.08

400 7.96 6.22 57.7H 3.66

600 11.94 5.08 38.45H 3.43

800 15.92 4.40 29.5H 3.08


voltage

motor

+i -

i tot

compens

chock2%5

chock2%3chock2%1

+-

v

Voltage Measurement3

+-

v

V1

+-

v

V

T1

T

Source1

Source

Series RLC Branch3 Series RLC Branch2

Series RLC Branch1

Series RLC Branch

Scope4

Scope3

Scope2

Scope1

Scope

Ground (output)1

Ground (output)

Ground (input)8

Ground (input)5Ground (input)4

Ground (input)3 Ground (input)2

Ground (input)1

Ground (input)

Gnd

+i-

Current Measurement6

+i-

Current Measurement5+

i -Current Measurement4

+i-

Current Measurement3

+i -Current Measurement1

+i-

C

Bus Bar (horiz)7

Bus Bar (horiz)6

Bus Bar (horiz)5

Bus Bar (horiz)4

Bus Bar (horiz)3

Bus Bar (horiz)2

Bus Bar (horiz)1

Bus Bar (horiz)

AC Voltage Source

AC Current Source8

AC Current Source7

AC Current Source6

AC Current Source5

AC Current Source4

AC Current Source3

AC Current Source2

AC Current Source1

AC Current Source

50m cable 4x1

380kw/490rpm

200m cable 4x240

.

SIMULATED RESULTS USING

MATLAB/SIMULINK


SIMULINK RESULTS


ACTIVE FILTERING

Parallel type Series type


-2500

-1500

-500

500

1500

2500

0 5 10 15 20 25 30 35 40

I

[A]

Time [ms]

0

5

10

15

20

25

30

2 5 8 11 14 17 20 23

[% I1

]

Harmonics

-5000

-2500

0

2500

5000

0 10 20 30 40

Time [ms]

I D

yn

aco

mp

[A

]

0%

5%

10%

15%

20%

25%

30%

35%

2 5 8 11 14 17 20 23

Harmonics

[%I1

]

RESULTS OF ACTIVE FILTERING

Input current of a 6-pulse Rectifier driving a DC machine without any input filtering

Input current with Active Filtering


-1000

-500

0

500

1000

0 5 10 15 20 25 30 35 40

U [

V]

Time [ms]

0

2

4

6

8

10

12

14

2 5 8 11 14 17 20 23

[% U

1]

Harmonics

-1000

-500

0

500

1000

0 5 10 15 20 25 30 35 40

U [V

]

Time [ms]

0

2

4

6

8

10

12

14

2 5 8 11 14 17 20 23

[% U

]

Harmonics

Typical 6-pulse drive voltage waveform

Voltage source improvement with active filtering


SHUNT ACTIVE FILTERS

By inserting a parallel active filter in a non-linear load location we can inject a harmonic current component with the same amplitude as that of

the load in to the AC system.

C

FL

Equivalent circuit


Low implementation cost.

Do not create displacement power factor problems and utility loading.

Supply inductance LS, does not affect the harmonic compensation of parallel active filter system.

Simple control circuit.

Can damp harmonic propagation in a distribution feeder or between two distribution feeders.

Easy to connect in parallel a number of active filter modules in order to achieve higher power requirements.

Easy protection and inexpensive isolation switchgear.

Easy to be installed.

Provides immunity from ambient harmonic loads.

ADVANTAGES OF THE SHUNT OR PARALLEL

ACTIVE FILTER


WAVEFORMS OF THE PARALLEL ACTIVE

FILTER

Source voltage

Load current

Source current

A. F. output current


G1

ZZ

VI

G1

ZZ

ZI

LS

SLH

LS

LS

G1

ZZ

V

G1

1I

G1

ZZ

G1

Z

IL

S

SLH

LS

L

L

hSh

L ZG1

Z

LhC II

0Z

VG1IG1I

L

ShLHhSh

(53)

(54)

(55)

(56)

(57)

1Gh

0G1

LC GII (52)

If

Then the above equations become

PARALLEL ACTIVE FILTER EQUATIONS


L

ShLHhLh

Z

VII (58)

G1I

I

LH

S

LHI

LZ

G

= Source impedance

= Is the equivalent harmonic current source

= Equivalent load impedance

= equivalent transfer function of the active filter

For pure current source type of harmonic source SL ZZ

and consequently equations (53) and (55) become

SZ

(59)

1G1 h

(60)

Equation (55) is the required condition for the parallel A.F. to cancel

the load harmonic current. Only G can be predesign by the A.F. while

Zs and ZL are determined by the system.

Equation (59) shows that the compensation characteristics of the A.F. are not

influenced by the source impedance, Zs. This is a major advantage of the A.F.

with respect to the passive ones.


The DC bus nominal voltage, , must be greater than or equal to line voltage

peak in order to actively control

The selection of the interface inductance of the active filter is based on the

compromise of keeping the output current ripple of the inverter low and the same

time to be able to track the desired source current.

The required capacitor value is dictated by the maximum acceptable voltage

ripple. A good initial guess of C is:

Cmax

t

0 C

v

dtimax

C

dt

dimax

VV3

2

LL

ndC

F

dCV

.iC

n V= peak line-neutral voltage

dC V= DC voltage of the DC bus of the inverter

L i = Line phase current

Cmax v = maximum acceptable voltage ripple,

Ci = Phase current of the inverter

dCV

C

Also


For identifying the harmonic currents in general the method of computing

instantaneous active and reactive power is used.

Transformation of the three-phase voltages and and the three-

phase load currents and into - orthogonal coordinate.

w

v

u

v

v

v

2/3

2/1

2/3

2/1

0

1

3

2

v

v

Lw

Lv

Lu

L

L

i

i

i

2/3

2/1

2/3

2/1

0

1

3

2

i

i

, vu vv wv, iLv Lui Lwi

P-Q THEORY


Then according to theory, the instantaneous real power and the

instantaneous imaginary (reactive) power are calculated.

L

L

L

L

i

i

vv

vv

q

p

where

LLLL p~ppp

LLLL q~qqq

DC + low frequency comp. + high freq. comp.

DC + low frequency comp. + high freq. comp.

Lp

Lq

q-p


The conventional active power is corresponding to , the conventional reactive

power to and the negative sequence to the 2 f components of and .

The commands of the three-phase compensating currents injected by the

shunt active conditioner, , and are given by:

q

p

vv-

vv

2/3

2/3

0

2/1

2/1

1

3

2

i

i

i 1

Cw

Cv

Cu

Lp~

Lq~

Lp Lq

Cui Cvi Cwi

p

q

= Instantaneous real power command

= Instantaneous reactive power command


L

L

q~q

p~p

LL

L

q~qq

p~p

LL

LL

q~qq

p~pp

Current Harmonics compensation is achieved

Current Harmonics and low frequency variation

Components of reactive power compensation

Current Harmonics and low frequency variation

Components of active and reactive power compensation

Substituting


HARMONIC DETECTION METHODS

i) Load current detection iAF= iLh

It is suitable for shunt active filters which are installed near

one or more non-linear loads.

ii) Supply current detection iAF= KS iSh

Is the most basic harmonic detection method for series

active filters acting as a voltage source vAF.

iii) Voltage detection

It is suitable for shunt active filters which are used as

Unified Power Quality Conditioners. This type of Active

Filter is installed in primary power distribution systems. The

Unified Power Quality Conditioner consists of a series and a

shunt active filter.


SHUNT ACTIVE FILTER CONTROL

a) Shunt active filter control based on voltage detection


Using this technique the three-phase voltages, which are detected at the point of

installation, are transformed to and on the dq coordinates. Then two first

order high-pass filters of 5HZ in order to extract the ac components and

from and . Next the ac components are applied to the inverse dq

transformation circuit, so that the control circuit to provide the three-phase

harmonic voltages at the point of installation. Finally, amplifying each harmonic

voltage by a gain Kv produces each phase current reference.

dv~

qv~

dv qv

dv qv

hVAF vKi

The active filter behaves like a resistor 1/KV ohms to the external circuit for harmonic frequencies without altering the fundamental components.

The current control circuit compares the reference current with the actual

current of the active filter and amplifies the error by a gain KI . Each phase voltage detected at the point of installation, v is added to each magnified error

signal, thus constituting a feed forward compensation in order to improve current

controllability. As a result, the current controller yields three-phase voltage

references. Then, each reference voltage is compared with a high frequency

triangular waveform to generate the gate signals for the power semiconductor

devices.

AFi

AFi

iv


b) Reference current calculation scheme using source currents (is),

load currents (iL) and voltages at the point of installation (vS).


3- HYBRID ACTIVE-PASSIVE FILTER

Compensation of current harmonics and displacement power

factor can be achieved simultaneously.


In the current harmonic compensation mode, the active filter improves the

filtering characteristic of the passive filter by imposing a voltage harmonic

waveform at its terminals with an amplitude

ShCh KIV


THDi decreases if K increases.

The larger the voltage harmonics generated by the active filter a better filter

compensation is obtained.

A high value of the quality factor defines a large band width of the passive

filter, improving the compensation characteristics of the hybrid topology.

A low value of the quality factor and/or a large value in the tuned factor

increases the required voltage generated by the active filter necessary to

keep the same compensation effectiveness, which increases the active

filter rated power.

SF

F

Lh

Sh

ZZK

Z

I

I

1S

2h SF

FLh

iI

ZZK

ZI

THD

If the AC mains voltage is pure sinusoidal, then


Displacement power factor correction is achieved by controlling the voltage

drop across the passive filter capacitor.

TC VV

Displacement power factor control can be achieved since at fundamental

frequency the passive filter equivalent impedance is capacitive.


HYBRID ACTIVE-PASSIVE FILTER

Single-phase equivalent circuit Single-phase equivalent circuit

for 5th Harmonic


This active filter detects the 5th harmonic current component that flows

into the passive filter and amplifies it by a gain K in order to determine its

voltage reference which is given by

5FAF iKv

As a result, the active filter acts as a pure resistor of K ohms for the 5th

harmonic voltage and current. The impedance of the hybrid filter at the 5th

harmonic frequency, Z5 is given by

KrC5j

1L5jZ f

FF5

0K The active filter presents a negative resistance to the external Circuit, thus improving the Q of the filter.

FrK, 0V 5BUS 5S

T5S V

L5j

1I


CONTROL CIRCUIT

The control circuit consists of two parts; a circuit for extracting the

5th current harmonic component from the passive filter iF and a circuit

that adjusts automatically the gain K. The reference voltage for the

active filter 5FAF iKv

HARMONIC-EXTRACTING CIRCUIT

The extracting circuit detects the three-phase currents that flow into

the passive filter using the AC current transformers and then the -

coordinates are transformed to those on the d-g coordinates by

using a unit vector (cos5t, sin5t) with a rotating frequency of

five times as high as the line frequency.


SERIES ACTIVE FILTERS

By inserting a series Active Filter between the AC source and the load

where the harmonic source is existing we can force the source current to

become sinusoidal. The technique is based on a principle of harmonic

isolation by controlling the output voltage of the series active filter.

Equivalent Circuit


- The series active filter exhibits high impedance to harmonic current and consequently blocks harmonic current flow from the load to the source.

SC KGIA.F. theof tageOutput vol V

KGZZ

V

KGZZ

IZI

LS

S

LS

LLS

(61)

(62)

= Equivalent transfer function of the detection circuit of

harmonic current, including delay time of the control

circuit.

G

, 0G1

1Gh

(63)


K = A gain in pu ohms

The voltage distortion of the input AC source is much smaller

than the current distortion. ShV

If hLZK and hLS

ZZK

Then

ShLhLC VIZV

0IS

(64)

(65)

(66)


HYBRID SERIES AND SHUNT

ACTIVE FILTER

At the Point of Common Coupling provides:

Harmonic current isolation between the sub transmission and the

distribution system (shunt A.F)

Voltage regulation (series A.F)

Voltage flicker/imbalance compensation (series A.F)


SELECTION OF AF S FOR SPECIFIC APPLICATION CONSIDERATIONS AF Configuration with higher number of * is more preferred

Compensation for

Specific Application

Active Filters

Active

Series

Active

Shunt

Hybrid of

Active Series

and Passive

Shunt

Hybrid of

Active Shunt

and Active

Series

Current Harmonics ** *** *

Reactive Power *** ** *

Load Balancing *

Neutral Current ** *

Voltage Harmonics *** ** *

Voltage Regulation *** * ** *

Voltage Balancing *** ** *

Voltage Flicker ** *** *

Voltage Sag&Dips *** * ** *


CONCLUSIONS

Solid State Power Control results in harmonic pollution above the tolerable limits.

Harmonic Pollution increases industrial plant downtimes and power losses.

Harmonic measurements should be made in industrial power systems in order (a) aid in the design of capacitor or filter banks, (b) verify the design and installation of capacitor or filter banks, (c) verify compliance with utility harmonic distortion requirements, and (d) investigate suspected harmonic problems.

Computer software programs such as PSPICE and SIMULINK can be used in order to obtain the harmonic behavior of an industrial power plant.

The series LC passive filter with resonance frequency at 4.7 is the most popular filter.

The disadvantages of the the tuned LC filter is its dynamic response because it cannot predict the load requirements.

The most popular Active Filter is the parallel or shunt type.

Active Filter technology is slowly used in industrial plants with passive filters as a hybrid filter. These filters can be used locally at the inputs of different nonlinear loads.

Active Filter Technology is well developed and many manufactures are fabricating Active filters with large capacities.

A large number of Active Filters configurations are available to compensate harmonic current, reactive power, neutral current, unbalance current, and harmonics.

The active filters can predict the load requirements and consequently they exhibit very good dynamic response.

LC tuned filters can be used at PCC and the same time active filters can be used locally at the input of nonlinear loads.


REFERENCES

RECOMMENDED PRACTICES ON HARMONIC TREATMENT

[1] IEEE Std. 519-1992, IEEE Recommended Practices and Requirements for Harmonic Control in Electric Power Systems, 1993.

[2] IEC Sub-Committee 77B report, Compatibility Levels in Industrial Plants for Low Frequency Conducted Disturbances, 1990.

[3] IEC Sub-Committee 77A report, Disturbances Caused by Equipment Connected to the Public Low-Voltage Supply System Part 2 : Harmonics , 1990 (Revised Draft of IEC 555-2).

[4] UK Engineering Recommendation G.5/3: Limits for Harmonics in the UK Electricity Supply System, 1976.

[5] CIRGE WG 36.05 Report, Equipment producing harmonics and Conditions Governing their Connection to the Mains power Supply, Electra, No. 123, March 1989, pp. 20-37.

[6] Australian Standards AS-2279.1-1991, Disturbances in mains Supply Networks-Part 2: Limitation of Harmonics Caused by Industrial Equipment, 1991.


DEFINITIONS

[7] J. Arriilaga, D.A. Bradley, and P.S. Bodger, Power System

Harmonics,New York: Wiley, 1985.

[8] N. Shepherd and P. Zand, Energy flow and power factor in

nonsinusoidal circuits, Cambridge University Press, 1979.

EFFECTS OF HARMONICS

[9] J.M. Bowyer, Three-Part Harmony: System Interactions Leading

to a Divergent Resonant System, IEEE Trans. on Industry

Applications, Vol. 31, No. 6, Nov/Dec 1995, pp. 1341-1349.

[10] R.D. Hondenson and P.J. Rose, Harmonics: the Effects on power

Quality and Transformers, IEEE Trans. on Industry Applications,

Vol. 30, No.3, May/June 1994, pp. 528-532.

[11] J.S. Subjak and J. S. McQuilkin, Harmonics-Causes, effects,

Measurements and Analysis: An Update, IEEE Trans. on Industry

Applications, Vol. 26, No. 6, Nov/Dec 1990, pp. 103-1042.

[12] P.Y. Keskar, Specification of Variable Frequency Drive Systems

to Meet the New IEEE 51 Standard, IEEE Trans. on Industry

Applications, Vol.32, No.2, March/April 1996, pp. 393-402.


[13] T.S. Key, Cost and Benefits of Harmonic Current Reduction for

Switch-Mode Power Supplies in a Commercial Building, IEEE

Trans. on Industry Applications, Vol. 32, No. 5,

September/October 1996, pp. 1017-1025.

PASSIVE HARMONIC TREATMENT TECHNIQUES

[14] M.F. McGranaghan and D.R. Mueller, Designing Harmonic

Filters for Adjustable-Speed Drives to comply with IEEE-519

Harmonic limits, IEEE Trans. on Industry Applications, Vol. 35,

No 2, March/April 1999, pp. 312-18.

[15] F.Z. Peng, Harmonic Sources and filtering Approaches, IEEE

Industry Applications Magazine, July/August 2001, pp. 18-25.

[16] J.K. Phipps, A transfer Function Approach to Harmonic Filter

Design, IEEE Industry Applications Magazine March/April 1997.

[17] S.M. Peeran, Application, Design, and Specification of Harmonic

Filters for Variable frequency Drives, IEEE Trans. on Industry

Applications, Vol. 31, No. 4, July/August 1995, pp. 841-847.


[18] J. Lai and T.S. Key, Effectiveness of Harmonic Mitigation Equipment for Commercial Office Buildings, IEEE Trans. on Industry Applications, Vol. 33, No. 4, July/August 1997, pp. 1104-1110.

[19] D.E. Rice,A Detailed Analysis of Six-Pulse Converter harmonic Currents, IEEE Trans. on Industry Applications, Vol. 30, No. 2, March/April 1994, pp. 294-304.

[20] R.L. Almonte and Ashley, Harmonics at the Utility Industrial Interface: A Real World Example, IEEE Trans. on Industry Applications, Vol. 31, No. 6, November/December 1995, pp. 1419-1426.

[21] K. A. Puskarich, W.E. Reid and P. S. Hamer, Harmonic Experiments with a large load-Commutated inverter drive, IEEE Trans. on Industry Applications, Vol. 37, No. 1, Jan/Feb. 2001, pp. 129-136.

[22] L.S. Czarnecki and O. T. Tan, Evaluation and Reduction of Harmonic Distortion Caused by Solid State Voltage Controller of Induction Motors, IEEE Trans. on Energy Conversion, Vol. 9, No. 3, Sept. 1994, pp. 528-421.


[23] R.G. Ellis, Harmonic Analysis of Industrial power Systems,

IEEE Trans. on Industry Applications, Vol. 32, No. 2, March/April

1996, pp. 417-421.

[24] D. Adrews et al, Harmonic Measurements, Analysis and Power

factor Correction in a Modern Steel Manufacturing Facility,

IEEE Trans. on Industry Applications, Vol. 32, No. 3, May/June

196, pp. 617-624.

[25] D. Shipp and W. S. Vilcheck, Power Quality and Line

Considerations for Variable Speed AC Drivers, IEEE Trans. on

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410.

[26] J. A Bonner et al, Selecting ratings for Capacitors and Reactors

In Applications Involving Multiple Single-Tuned Filters, IEEE

Trans. on Power Delivery, Vol. 10, No. 1, Jan. 1995, pp. 547-555.

[27] E. J. Currence, J.E Plizga, and H. N. Nelson, Harmonic

Resonance at a medium-sized Industrial Plant, IEEE Trans. on

Industry Applications, Vol. 31, No. 4, July/August 1995, pp. 682-

690.


[28] G. Lemieux, Power system harmonic resonance. A document case, IEEE Trans. on Industry Applications, Vol. 26, No. 3, pp. 483-487, May/June 1990.

[29] D. D. Shipp, Harmonic Analysis and Suppression for electrical systems, EEE Trans. on Industry Applications Vol. 15, No. 5, Sept./Oct. 1979.

ACTIVE HARMONIC TREATMENT TECHNIQUES

[30] H. Akagi, New trends in active filters for Power conditioning, IEEE Trans. on Industry Applications, Vol. 32, Nov/Dec. 1996, pp. 1312-1322.

[31] Bhim Singh et al, A Review of Active Filters for Power Quality Improvement, IEEE Trans. on Industrial Electronics, Vol. 46, No. 5, Oct. 1999, pp. 960-971.

[32] F. Z. Peng, Application Issues of Active Power Filters, IEEE Industry Applications Magazine, Sep./Oct. 1998, pp. 22-30.

[33] S. Bhattacharga et al, Active Filter Systems Implementation, IEEE Industry Applications Magazine, Sep./Oct. 1998, pp. 47-63.


[34] S. Bhattacharya et al, Hybrid Solutions for improving Passive

Filter Performance in high power Applications, IEEE, Trans.

on Industry Applications, Vol. 33, No. 3, May/June 1997, pp.

732-747.

[35] H. Akagi, Control Strategy and site selection of a shunt active

filter for damping of harmonies propagation in power

distribution systems , IEEE Trans. on Power Delivery, Vol. 12,

Jan. 1997, pp.354-363.

[36] H. Fujita, T. Yamasaki, and H. Akagi, A Hybrid Active Filter for

Damping of Harmonic Resonance in Industrial Power

Systems, IEEE Trans. on Power Electronics, Vol. 15, No. 2,

March 2000, pp. 215-222.

[37] H. Akagi et al, shunt Active Filter Based on Voltage Detection

for Harmonic Termination of a Radial power Distribution Line,

IEEE Trans. on Industry Applications, Vol. 35, No. 3, May/June

1999, pp. 638-645.

[38] D. Rivas et al, A simple control scheme for hybrid Active

Power Filter, IEE PESC-00, pp. 991-996.


[39] L. Zhou and Zi Li, A Novel Active Power filter Based on the Least compensation Current Control Method, IEEE Trans. on Power Electronics, Vol. 15, No. 4, July 2000, pp. 655-659.

MODELING

[40] IEEE Task Force on Modeling and Simulation, Modeling and Simulation of the propagation of harmonies in electric power networks, Part I: Concepts, models, and simulation techniques, IEEE Trans. on Power Delivery, Vol. 11, No. 1, Jan. 1996, pp. 452-465.

[41] IEEE Task Force on Modeling and Simulation Modeling and Simulation of the propagation of harmonies in electric power networks, Part II: Sample systems and examples, IEEE Trans. on Power Delivery, Vol. 11, No. 1, Jan. 1996, pp. 466-474.

[42] W. Jewel et al, Filtering Dispersed harmonic Sources on Distribution, IEEE Trans. on Power Delivery, Vol. 15, No. 3, July 2000, pp. 1045-1051.

[43] N.K. Madora and A. Kusko, Computer-Aided Design and Analysis of Power-Harmonic Filters IEEE Trans. on Industry Applications, Vol. 36, No. 2, March/April 2000, pp.604-613.

harmonic treatment in industrial power

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