Double Tuned Filters

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lgorithm for the Parameters

of

Double Tuned Filter

Xiao Yao

Hubei Electric Power Test & Research Institute

Wuhan, P.

R.

China

Abstract: On the basis of analyzing the characteristics of the

simplest and the basic type

of

double tuned filter,

an

algorithm

for

precisely determining its parameters is presented here. Using this

method, the inductances and the capacitances of the filter can be

calculated h m he

known

data such as the reactive compensation

capacity, the tuned freque ncies and the parallel resonant frequency,

etc.

There are various damped types of double tuned filters, they

have three pain of tuned frequencies under the conditions

of

i) the

equivalent impedance being minimum;

ii)

the total

reactance

being

zero; iii) when the damping resistorsare out

of

service. Usually the

tuned frequencies of condition i) or ii) are

selected

to determine

the parameters of the filter in designing process. The diagram for

determining the parameters

of

damped-types s also developed.

Keywords:

powersystemharmonics, power filter, filter

I.

INTRODUCTION

There are m any types of doub le tuned filters. The simplest

and the basic one is shown

as

Fig.

1,

others are damped types

illustrated in Fig.

2.

They a re widely used in HVDC projects

[l ] [2]. Besides bypassing the appointed harmonic currents

near the tuned frequencies, the filter also provide the

fundamental reactive power needed by the converter.

Compared to the single tuned filters with same performance,

they enjoy a lot of advantages such

as

only one reactor is

subjected to full line voltage, occupies less site, and only

one switchgear is needed, etc.

The parameters of the doub le tuned filter estimated from

two

banks of single tuned filters has been introduced in [3],

which is subject to that their equivalent impedance near the

resonant frequencies are approximately equal, but this is not a

pragmatical method. How to calculate the parameters of

double tuned filters accurately and directly from the known

data such

as

the tuned frequencies, the reactive capacity of

the filter, and the rated voltage of the

system

has not been

introduced in detail so far.

The relationships among the parameters of basic type

double tuned filter (Fig.

1

are analyzed,

so

an algorithm for

precise calculating the parameters of it according to the

known data is conducted in this paper.

Based

on

he analyzing of relationships among the

Paper accepted

for

presentation

at the 8u International

Conference on Harmonics and Qualio of Power

ICHQP

98,

ointly organized

by IEEEPES

and

NTUA,

Athens Greece October

1416,1998

0-7803-5105-3/98/ 10.00 1998 EEE

parameters of the simplest filter, the characteristics

of

the

damped-type filters are discussed. There are three pairs of

tuned frequencies

on

the damped-type filters under the

conditions o f (i) the total impedance being minimum;

(ii)

the

total reactance being zero; (iii) the damping resistors being

out of service. Usually tuned frequencies of condition

i)

or

(ii)

are

selected to determine the parameters of the filters in

designing process. The diagram for determining the

parameters of them is also developed accordingly.

11.

THE RELATIONSHIPSAMONG THE PARAMETERS

OF

THE BASIC DOUBLE

TUNED

FILTER

The configuration of the basic do uble tuned filter is shown

as Fig. 1, which is the combination of a series resonant circuit

L,,

,)

nd a parallel resonant circuit

L,

z).

Under the conditions of ignoring the resistance in reactors

and dielectric losses

in

capacitors, the impedance of the series

circuit is

1)

1

where w is the angu lar frequency in radians, therefore the

ZJW =Ad - 1,

cut,

Fig.

1

The configurationof the basic double tuned filter

-.

(4

(4

Fig.

2 Variousdampedtypes of double tuned filters

154



a?

a4 f n q u e w J

c )

Fig 3

The characteristicsofthe simplest doubletuned

Filter,

a) series

circuit;

b)

parallel

circuit; c)

total

impedance

of

the

filter

l

series resonant frequency is

w ,=m

When w

<a,, z s w

is capacitive; and

w >

w ,

, w

is inductive. The impedance of the parallel

circuit is

3)

and

its

parallel resonant frequency is

up=JG 4)

When

w < w p , z p w )

is inductive; and CI )

> u p ,

z p w ) is

capacitive. The curves of the impedance versus

frequency z w and

z , w)

are show n in Fig.3 (a) and (b)

respectively. Fig.3 (c)

is

the series combination

characteristicsof the above two circuits, From which, another

two resonant frequencies 4,), that

is

the tuned

frequencies of the filter can be seen clearly. At the tuned

fkquencies, the total impedance of the filter is zero.

frequencies will

be

derived from the following equation:

If the parameters L,,C, and

L, C ,

are given, the tuned

z 0 )

=

ZS(@)

+

Z p ( @

This equation can be rewritten

as

o4L1L2C1C2 - tu2(L2C1 + LlCl + L 2 C 2) + 1 = 0 . ( 6)

Two real roots and y

of

equation 6) are tuned

frequencies of the do uble tuned filter. According to V ida s

theory, the relationship between the roots and the coefficients

of

the equation 6)

is

i.e.

8)

The hannonic currents at tuned frequenciesq nd y will

be bypassed by the filter. According to the project

requirement, the tuned frequencies are defined at

first

and

then the parameters

L,,

C, and L f , Cf will be derived. The

filter impedan ce is infinite at the parallel fiequen cy CO= , To

prevent some harmonic currents near

w

rom being severely

amplified, engineers should take account

of

the network

impedance-fkequency characteristics and select a parallel

resonant frequency properly in the designing process. If

CUI

0 2 and w s determined, is certainly defined by

equation 8). Substituting equations

2)

and 4) into equation

(6) yields

1

1

@ p

w , w 2

=

E

Forwlbeing one

of

the solutions

of

equation

9) ,

substituting w by

w 1

, the relationship between the

capacitances C , and

C,

can be obtained:

10)

There are other two relationships between

L,

nd C , ,

L,

and

C2

etermined by equation ( 2 ) and equation 4), which

can be rewritten as:

--, -4

4

m i -

2

c2

U S

Besides bypassing the harmonic current, the double tuned

filter has another performance

of

supplying the reactive

compensation power. If the network findamental rated

voltage is

U,

nd the hdamental reactive power supplied by

the filter is Q, then the impedance

of

the filter at hndamental

frequency

is

155



From equation

5 ) ,

the impedance of the filter at the

fundamental frequency has a nother form:

where OF

is

the fundamental frequency

in

radians. From

above two equations, the follow ing equation is obtained:

15)

By equations 1

0)

to 1 2) and I

5) ,

if

wI

nd

Q

are

given, and

a+,

is determined at first, the parameters of the

basic double tuned filter can be obtained imm ediately.

By

scanning the impedance frequency characteristics of

the double tuned filter after getting its parameters, it can be

seen that the tuned frequencies

are

just expected, and the

fimdamental reactive capac ity is the same as the given one.

111.

A SPECIAL CASE

Specifically, if os w p = wo =6 he

retationships among the parameters can be simplified as the

following:

(16)

,

I c, = (h2 - h , )2 (h lh2)

1 9 )

IV. THE FEATURE

OF

THE DAMPED-TYPE

DOUBLE TUNED FILTERS

The impedance

of

the simplest double tuned filter is

almost pure inductive or capacitive over the whole

frequencies. If the impedance of the system

is

approximately

equal and opposite to that of the filter at some harmonic

frequencies, the resonance will be resulted in, which in

turn

leads to the harmon ic currents being seve rely amplified with

harmonic overvoltage of the components in the filter and

in

system.

To

prevent such a phenomenon, dam ping resistors are

added to it in different ways, therefore various damped types

of double tuned filters are con figurated in Fig. 2.

The Gezhouba-Nanqiao

HVDC

project

is

the first long

distance (=1045.7km) transmission scheme

in

China. Fig.

4

illustrates one pole of this f 00kV DC bipolar scheme from

Gezhouba (rectifier station) located in Central China to

n n

DC ine

5OmH

I5OmH

I I

38.93mH

b

71.0bmH

9

+ 23uF

Filter A

Filter

B

12/24 12/36

Fig.

4 ConfigurationofDCside in Gezhouba-Shanghai

HVDC

transmission

projects

Nanqiao (inverter station) located in Shanghai area with its

DC filter being the basic type of double tuned filters at first.

When

it

was put into operation in 1990, the equivalent

disturbing currents in DC line e xceede d 450mA and reached

to the level of 2618.2mA two levels are specified for the

equivalent disturbing current, level A: 500mA for bipolar,

1500mA for monopolar; level B: 150mA or bipolar, 450mA

for monopolar). One of the reasons is the resonance between

the filter A and the smoothing reactors at 181h harmonic.

Finally, a resistor of 500R was added to filter A in the way

illustrated

as

Fig. 2(a) to weaken the resonance, which

efficiently reduces

181h

harmonic current in DC line and so

reduces the equivalent disturbing current to 947mA in

monopolar operation.

The performance of each damped type of double tuned

filter is slightly differ from the others. The impedance of

Filter 2(a) at w p is on the order of R; the impedance of filter

2(b) takes R as asymptotic line when o s above q he

parameters in filter 2(c) should meet the relationship of

R

>,/m,

ts

impedance at is very large , but the

impedance above

w

is on the order of

R;

Fig. 2(d)

i s i n

fact

an third order filter being in series connection with a reactor,

it behaves as a high pass filter above

y;

ilter 2(e) has

limited impedance both at op and above y with its

parameters should meet the relationship of that

RI> m.

inally, the filter of Fig 2(f) with its

impedance both at oIJnd above are limited to the lower

value ofA, and

R2.

By scanning the impedance and frequency, it can be found

that there are three pairs

of

tuned frequenc ies on the damped-

type filters, they are:

(i) The frequencies

el

.., at which the impedance of the

filter are minimum;

(ii) The frequenciesel x2, at which the total reactance of

the filter equal zero.

(iii) Another is the solutions CO,,y f equation (6 ) , hey are

tuned frequencies of the simplest one. If damping

resistors are out of service, the filter will

be

tuned

at 01 andwz ;

Take Fig. 2(e) for example, the param eters of it are

156



Inductance (mH)

LI ] U

3.16

I

4.39

Table

2 Frequencies relating

to

Fig. 2(e) and Table

1

Capacitance

pF)

Resistor (Q )

C I c 2 R I R 2

6.96 8.53 476 2744

I

f i (Hz ) h (Hz )

Solutions of Equ. (6) 797.5 2213.5

Minimum impedance I 248.5 1130.

Total rca c ta nc d

I

250.6 I

1264.

Select the type

of

damped dou ble tuned filter and input:

Q,he size of the filter

U,

the rated voltage of the system

,,,the parallel resonant frequency of the filter

q

.

o2

tuned frequencies ofth e filter

R,,Rz, esistance ofthe filter

terative precision

1

Select the

sorts

of tuned frequencies:

k m j =

min

or x ( c o ) = o

I

according to their relationships

El <E?

Calculate the pass band of the filter and

Fig 5 Diagram for determining the parameters of

damped double tuned filters

In designing process, the resistance of

R (RI

and

R 2 )

is

given, and so it is with the rated voltage of the system, the

compensation capacity and the tuned frequencies of the filter

prior to the calculation of

LI , L ,

and

CI,C,.

Parameters of

inductances and capacitances can be firstly calculated out

with the tuned frequencies given, then the resistance R R,

and

R2)

s added and the resistances in reactors

are

also taken

into account to calculate the actual tuned frequencies {

,az,,

wz2

} or

{

oxI,

w x 2 } by scanning. if the tuned frequencies

are not what demanded, recalculate

LI,

L, and C I ,

C

again by

adjusting 0 1 and

0 2 .

Finally the performance of the filter

should be inspected with the consideration of harmonic

impedance of the system and other filters to be installed. If

necessary, resistance

R ( R I

and R2)

should

be corrected and

repeat the calculating procedure s above.

The diagram for designing the damped-type double tuned

filters is as Fig. 5

IV. CONCLUSION

A simpler and accurate way to calculate the parameters of

the basic type of double tuned filter has been introduced in

this paper, and the diagram for determining the parameters of

damped-type double tuned filters

is

also developed. Other

parameters such

as

rated voltage, current and capacity of the

components

in

the filter can

be

further calculated after the

parameters R, L, C are determined.

A

software of this

algorithm for parameters of the filters is developed in

Visual Basic.

For

its advantages compa red to the single tuned

filter with same performance, the double tuned filter should

be cons idered at first

in

filtering projects.

V. REFERENCE

[ I

ClGR E WG 14.03, AC harmonic

filters

and reactive compensation for

HVDC,

general survey , Electra No.63, 1979

[2]

CIGRE

WG 14-03, AC harmonicjilrersandreactive compensation for

HVDC

w i th particular reference lo non-characferistic harmonics:

complemenr

to

the paper published in Electra

No.63 1979),ClGRE

report , une, 1990

[3] J. h i l l a g a , D. A. Bradley, P. S.Bodgcr,

Power Sysrem harmonics.

John Wiley & Sons, 985

VI.

BIOGRAPHY

Xiao

Yao,

was

born on

March, 28,

1960 in

Hubci Province, China.

He received

his

B.E. and M.E. degree in Electrical Engineering

from Tsinghua U niversity, China in 1983 and 1986nspectively. He

jointed Hubei Electric Power Test & Research Institute in china in

1986, and has been working in the field of power system harmonics

and quality ever since. He has some articles published in various

Chinese periodicals.

listed in Table 1, and the frequencies relating to above

conditions are listed in Table

2.

Usually, { w q , wz2 } or { w,yl,

o B

are selected to

absorb main harmonic currents, while frequencies {

w I

D

}

are used to determine the parameters

of LI, ,

and

C,,

C2 in

designing process.

157

Double Tuned Filters

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