New Concept for Harmonic Filtration in Distribution Networks of Industrial Firms
M.Z. El-Sadek
Electrical Engineering Dept.
Assiut university
Assiut-Egypt
G. Shabib
Electrical Engineering Dept
High Institute Of Energy
Aswan-Egypt
M.R. Ghallab
Upper Egypt Electrical
Distribution Company
Aswan- Egypt
Abstract:
This paper presents a new method for designing the
parameters of harmonic filters used with distorting loads in
industrial firms. It proposes using hybrid filters which
composed of groups of single tuned harmonic filters and a
shunt capacitor. The design takes into consideration as
minimum as possible values of capacitors capacitance, and
the avoidance of parallel resonance and considers the filter
elements deviations from their adjusted values at the
designed filters harmonic orders [1-9]. Economic and
technical aspects are considered.
Fig.(1):Rectification station and harmonic filter
arrangement.
The network and transformer short circuit reactance Xesc is
defined by:
Xesc=Xtsc+(N2/N1) ² Xsc
(1)
The active and reactive power consumed by the rectifier
bridge (RB) load are:
P=3E I cos φ
,Q=3E I sin φ
(2)
Where I is the fundamental current entering to the rectifier
bridge and φ the phase angle between the induced voltage
E and the fundamental current I1.The form of the current
which enters (RB) is given in fig (2).[2]
1-Introduction:
The large distorting loads of power system currents and
voltages are converters, which are used as rectifiers or
inverters that draw certain reactive power from the
distribution networks. The flow of these excessive reactive
power on the network, leads to heavy currents, excessive
losses, large conductors cross sections and high voltage
drops which may lead to voltage instability. The distorted
currents may lead to blackouts of lamps, stand still of
motors, annealing of lines, protection and control systems
failure and errors in metering of KWHR. It must then have
harmonic filtering devices and installation capable of
doing double roles: elimination of the existing harmonics
from the distribution network, and in the same time
improvement in the50HZ power factor currents.[2]
This paper presents an effective method, which allow to
design the filter parameters, for converters feeding DC
constant loads which works in permanent mode, such
aluminum smelter plants, arc furnaces, sugar separation.
This situation is also economical frequently in industrial
applications of network feeding electrical
traction systems (trains, trams,...etc) .
In this study the connection of distribution transformers
are assumed to be connected in such a manner that the line
currents do not contain harmonic orders of third and
triplen harmonics (connected to star/delta or isolated
star/star). The proposed method is applied to a six pulse
rectifier 3-phase bridge, with ideal characteristic currents
5, 7, 11 etc orders .
Fig.(2):Line current in 6-pulse rectifier bridge
Where α is the firing angle, γ is the commutation angle.
The current waveform of fig.(2) is valid for any of
transformer connection. The angle γ is a function of Xesc,
and I the harmonic analysis of the current represented in
fig.(2) allows for determination of the harmonic
components RMS values. The fundamental component of
this current is derived as follows:
3 2E 2max
sin(2α + γ) sin γ
4πX esc
(3)
3 2E 2max
[γ − cos(2α + γ) sin γ]
4πX esc
(4)
I 1 cos ϕ1 =
I1 sin ϕ1 =
2-Loads Reactive Power:
Taking into consideration these relations given in
(3),(4),the active and reactive power of equation (2)
become:
The equivalent schematic diagram of the studied system is
given in fig.(1).This system consists of high voltage
busbars of line voltage V,3-phase short-circuit power Ssc,,
transformer turns ratio (N1/N2) and its short circuit
reactance Xtsc, rectifier bridge (RB) and harmonic filter
(HF). The transformer secondary voltage values are [4]:
EA=E ejγc , EB= a²EA, EC= a EA .
Where a= exp( j2л /3)
P =
2
9 E max
sin( 2 α + γ ) sin γ
4 π X esc
(5)
2
(6) Q = 9 E max [ γ − cos( 2 α + γ ) sin γ ]
4πX
esc
In which, the reactive power consumed by the rectifier
bridge (RB)
is obtained. If we are interested in
1
compensating this reactive power at the 50 HZ
components, then the phase angle between the busbar
voltage and the fundamental current should be decreased
from φ to φ΄ . Therefore the filters should fed the busbar
by capacitive reactive power given by
Q1 = P( tan φ1 – tan φ′1 )
(7)
With cos φ΄1 is the new power factor, cos φ1 is the original
power factor and P is the load power in KW or MW.
V cm =
For realizing harmonic filters (HF) ,different procedures
are used .Frequently, we employ filters connected as single
tuned filters for certain harmonic orders in addition to a
high pass filter (damping filter) for higher harmonics [2].
This solution has the disadvantages of high losses in the
high pass filters
(damping filters) .Another more
advantageous solution is adopted in this study based on the
concept of simultaneous filters of the type single tuned
filters and shunt capacitors connected to the busbar, in
parallel with the single tuned filters. The shunt capacitors,
which can operate with fewer losses, assure certain degree
of harmonic filtering for the higher orders harmonics. In
the same time, it feeds capacitive reactive power to the
busbar, which are used for reactive power compensation at
the fundamental frequency. Noting that the capacitors of
the filters are subjected to voltages, which exceed those of
the feeding busbar. Also it is necessary for limiting
reactive power to minimum values, that the rest of the
reactive power which must be compensated is fed from the
shunt capacitor which is connected directly to the
busbar.The international specification limit the over
loading of capacitor in steady state conditions in the ranges
V≤(1---1.1)Vn, I≤ (1.3----1.8)In, Q≤ (1---1.35)Qn
(8)
Where Vn, In, Qn are the nominal values of voltage, current
and power of capacitors respectively [3].
we should have :
Q ck =
2
+
1
X
k 2
2
ck
I
2
k
m
(19)
k
a 2k V 12
1
+ X ck I 2k
X ck
k
(22) Q cm =
(21)
a 2m V12
1
+ X cm I 2m
X cm
m
If we perform the derivatives with respect to Xck,Xcm , and
quating these derivatives to zero
{(∂Qck/∂Xck)=(∂Qcm/∂Xcm)=0}, we obtain the minimum
values of capacitances as follows:
(23)
equal voltages at the filters capacitors terminals. If we
consider that the filters are connected for two harmonic
orders (k, m),the voltages at the capacitor terminals for
these two filters are given by the following relations:1
Vk
=
Vm
The reactive power fed by the capacitor of each filter is
found by the sum of the reactive power at the fundamental
frequency and that at the harmonic voltages and given by:
4.2 Dividing of Capacitor Capacitances for
Obtaining Equal Voltages at The Filters Capacitors
Terminals: This concept is based on assuming having
V
(11)
I 2m
4.4 Dividing of Capacitor Capacitances Based on
Minimum Capacitor Rating:
The capacitors are divided equally among the arms of
(9)
filters
C= Ctotal / n
Where n is the number of filter arms. This the simplest
concept.
2
k
2
cm
In the case of the rectangular line currents form, this
(20)
relation necessitates: Ck / Cm = ( m / k )3/2
4.1 Dividing Of Equal Capacitors:
a
1
X
m 2
This concept is based on obtaining equal specific losses in
capacitors. When this criteria is satisfied, the duration of
capacitors life of all filters will be the same. The losses per
capacitor unit (or what called specific losses) can be
determined by means of the following relations:
Pδk = ω tanδ (ak² V² + k Vk² )
(17)
Pδm= ω tanδ ( am²V² + m Vm² )
(18)
Where Vk,Vm represent harmonic voltage in the phase
voltage, tan δ is the loss angle in capacitor insulations.
When we assume that the loss angle
(tan δ) has the same value for the charectracitic harmonics
orders up to the order 13. Then, for Pδk = Pδm and ak ≈ am
There are different criteria for dividing the total capacitors
capacitance of filters among each shunt filter arms. Several
criteria are proposed in this study. Each criteria will has
some advantages and drawbacks. The optimal method is
that which present technical and economical advantages.
=
V 12 +
4.3 Dividing of capacitors Capacitances for
Obtaining Equal Specific losses:
4- Criteria For Dividing Capacitors Between
Filter Arms [9]:-
ck
2
m
(12)
With ak= k² /(k²-1), am= m² /(m²-1 )
Where Xck,Xcm represent the filter reactances at the
fundamental frequencies (50 or 60 HZ) ,V is the
fundamental phase voltage.(Ik,Im)are the harmonic current
branches of the order(k and m) .Having given that for the
harmonic frequencies ak=am ,then the voltages Vck,Vcm will
be surely equal when: Ck/Cm= mIk/ kIm
(13)
In this ideal case where the line current is of rectangular
form ,we found that : Ik= I1/ k , Im = I1/ m
(14)
Then, we obtain :
Ck /Cm = m²/ k²
(15)
These relations agree with:
k² Lk Ck ω² =m² Lm Cm ω² = 1
(16)
The condition in eqs (15),(16) necessitates certainly the
equality of the inductances of the filters (Lk = Lm).
3- Harmonic Filters: -
V
a
, Cm =
Im
ma mωV1
Ck =
Ik
k a k ωV1
From which the condition of minimum capacitors is :
Ck
= m
(24) (I k / I m ) .
k
Cm
(10)
4.5 Optimum Capacitors Division :
2
Comparing relations (20), (24), we notice that criteria
(4.3), (4.4) are equivalent. On the other hand, the condition
(20) is practically satisfied in the case when we look for
obtaining filter with minimum costs . Consequently from
techno-economic point of view the most reasonable
capacitor dividing technique is that used on equal specific
losses criteria (criteria 4.4 ).
With Q1k fundamental frequency system reactive
power,Qck filter capacitor reactive power of order k, Qbk
filter inductor reactive power.
Q1k = ak V1² / Xck
(28)
We can determine the absorbed reactive power by the
reactor by Calculating the difference Qbk = Qck – Q1k .
take into consideration the relation (22) and (28)we obtain:
5. Proposed Harmonic Filter Design Procedure:
5.1 Harmonic Filter Capacities Rating
Determination:
(29) Q
bk
a 2k V 12
1
+
X
2
k X ck
k
=
ck
I 2k
If we consider the capacitance Ck of the capacitor as
independent variable the expressions (21) and (29)
Become:
A
B
, Q ck = AC k + B
(30) Q bk = 2 C k +
k
Ck
C k
The capacitor of the filters connected for harmonic order k
is subjected to voltage according to the formula (10) while
the capacitor connected directly to the busbar is subjected
to the whole voltage. Having known that the capacitor in
the schematic diagram of (HF) has the same size. The
result is that the capacitors installed in the filters will have
more voltage than that those connected directly to the
busbar. For this reason the value of the capacitance of the
filter capacitors must be as small as possible. A proposed
method of calculation those minimum capacitors was
previously displayed in section (4-4), in equation (23). The
proposed filter design uses the minimum capacity rating
value.
Where
A = ω ak² V1² , B = Ik² /kω
5.2 Filter Inductance Determination:
Firstly we calculate the filters rating which is connected
for harmonic order number 5.The filter size is determined
by means of relation (20). The inductance of the coil of the
fifth order filter taking into consideration the relation (14)
will be:
L
k
=
1
ω
.
k
2
k
V
. 1
− 1 Ik
Fig.(3):Reactive powers (Qck,Q1k,Qbk) as a function in
capacitor Ck.
The curves Qck ,Qbk and Q1k are plotted in fig.(3), for
various capacitances Ck. We notice that for values of the
capacitance which exceed Ck min. , which corresponds to
Qckmin in fig.(3) consequently the gain of the reactive
power (Qck/Q1k) in this case is exceeded nearly in all bus
bars.
5.6 Calculation of Circulated Current: The circulating
current by the filter capacitor can be determined by means
of the relation:
(25)
5.3 Over Voltages And Over Currents:
After this, it is necessary to verify the capacitor
performance with respect to over voltages and over
currents at steady state conditions. The voltage is
determined by means of relation (9). By introducing the
minimum value of Ck in the reactance Xck,and by making
several calculations we obtain:
(26)
V ck = a k
I
( k + 1) / k V 1
I ck =
ωC
− ωL
k
=
k
V
X
2
ck
2
+ I
1
2
k
(32)
k
5.7 Calculation of Reactive Power at Minimum
Capacitance of Capacitors: The reactive power fed by
the filter capacitor used for the harmonic order k can be
evaluated by means of relation (21) which when the
capacitor capacitance is minimum becomes:
If not, it is advised to increase the capacitor capacitance by
nearly 30% in order that the terminal voltage does not
exceed 1.1 Vn .By this increase, an associated
supplementary reactive power will be available at the
fundamental frequency, it is given by Q1k=V1Ik1 or:
V1
( k + 1) / k I
2
k
Which will lead for k=5 to Ick = 1.1 Ik.
5.4 Determination of Filter Current:
1
ck
(31)
If we introduce Ck min.we obtain:
Which for k=5,it is Vck= 1.14V1 .Noting that the voltage
at the filter capacitor terminals which is used for the 5th
order harmonic exceeds 3.7% which is a limit value of
specification . If the nominal capacitors voltage used in
this filter is more than the network voltage, we can keep
the capacitor capacitance at minimum value.
(27) I k 1 =
a
=
(33) Q
a k V1
X ck
ck
= 2
a
k
k
V1I k
Noting that the reactive power fed by the capacitor will
fulfill the specification limits at all conditions.
5.8 Parallel Connected Capacitor Rating: When Q1
represent the total reactive power which must be
compensated and given by eq.(7) before, and when Q1k is
the reactive power provided by the filter of order k.The
5.5 Filter Reactive Powers Calculation (Qck,Qbk,Q1k) :
3
reactive power of the capacitor which is connected directly
to the busbar is given by : Qcb = Q1 - Q1k
This capacitor is directly connected to the busbar of
voltage V1.Therfore, this capacitor capacitance is given by
Cb = Qcb / ω V1²
(34)
We can estimate the possibility of appearance of over
voltages and over currents. In the capacitors, which are
connected directly to busbar, we should know the value of
distortion coefficient at that busbar, which represents the
following step of the calculations.
5.11 Check Of Parallel Harmonic Resonance:
In the circuit of fig.(4) ,besides the characteristic
harmonics, other non characteristic harmonics can arise
They are generated either by other distorting loads such as
arc furnaces or by dissymmetry of network or unbalance of
loads .In this case ,parallel resonance’s can happen. They
are usually associated by over voltages, which can destroy
the system devices. These conditions are attained when the
total susceptance of the circuit becomes zero. This total
susceptance, with frequency now is determined by the
relation (37) and using the following relations:
5.9 Calculation of the Distortion Coefficient :
For calculating this coefficient, the schematic diagram
given in fig.(4),is used here we have neglected the ohmic
resistances of the coil of the filters. Lesc represent the
equivalent short circuit inductance at the busbar. Firstly we
will consider only the filter connected for the harmonic
order number 5 (k=5).
(39) X cb =
Substituting of eq. (36) into eq. (33) yields:
25 n
1
ωC 5 −
+ nω C b
n 2 − 25
nω L esc
After some manual calculations ,we obtain :
ω2 Cb Lescn 4 −[25ω2 Lesc (C5 + Cb ) +1]n 2 + 25
(41) Bn =
nωLesc (n 2 − 25)
Therefore, there will be a current resonance when :
(40) B n = −
(42)
ω² Cb Lesc n4 − [25 ω² Lesc ( C5 + Cb)+1]n²+25 =0
It is evident that, a voltage resonance occurs with n=5.
There are two possible current resonance’s , the first at
frequency less than 250 HZ ,the other at higher frequency
.If the first resonance is very near to 200 HZ and the
distorted loads include arc furnaces producing harmonics
of order 4 , this indicate either the harmonic curve of the
filter which connected to eliminate the 5th order harmonic
current ,by connecting a damping resistance in parallel
with the filter coil ,or by using additional (other) filter for
eliminating the 4th order harmonic. The current resonance
at frequencies more than 250 HZ will create resonance
problems only if this frequency is sufficiently near one of
the characteristic harmonics. If in addition to the filter of
the 5th order harmonic, we use a 7th order harmonic filter,
it will result from the harmonic frequencies analysis of the
circuit in fig.(4),that a current resonance will be produced
at frequency between 250 to 350 HZ .The 6th order
harmonic is insignificant, over voltages cannot appear. We
will reach to similar conclusions with filters connected to
eliminate, the 11th and 13th order harmonics. In definite,
between all possible parallel current resonances,that near
200 HZ is most dangerous. If at least one of the harmonic
voltages (V7,V11,V13) exceeds the level 1% of the
fundamental voltage, it is necessary to connect a filter
tuned to an adequate order.Firstly,we introduce a filter
tuned to the 7th order and we determine the harmonic level
of the harmonic voltages V11,V13.If they are less than 1%
of the fundamental voltage, there is no need for additional
(supplementary) harmonic filters, if not (or in the inverse
case),we introduce a filter tuned to the 11th order and may
be a another one tuned to the 13th order harmonics.
For the filters which are tuned to the harmonic orders
7th,11th,13th,we determine the minimum values of
capacitors capacitances, using the relation(23). The
voltages across the terminals of those capacitors,(a
according to eq.(26) are:
Fig(4): Schematic diagram of proposed harmonic filter and
equivalent power system and harmonic source.
In this case the spectrum of the voltage at that busbar
contain the harmonic V7,V11,V13 which can be determined
by means of the relations:
V7 = I7/B7t , V11 = I11/B11t , V13 = I13/B13t
(35)
(36) B
nt
= −B
−
5n
1
n
+
nX esc
X cb
With:
where B5n is the susceptance of the filter connected for
harmonic order number 5, Xesc =ωLesc is the equivalent
system short circuit reactance and Xcb = (1/ωCb) is the
reactance of the capacitor connected directly to the busbar,
Bnt is the total susceptance of filter, system and shunt
capacitor. Both of these reactance’s (Xesc,Xcb) are
determined at the fundamental frequency. After making
some calculations the capacitor susceptance at order k will
become:
B
kn
= (
k
n
2
n
− k
1
2
2
)(
X
)
(37)
ck
5.10 Check Of Over Voltages And Over Currents:
In the following we allow that the distortion coefficient of
the busbar voltage is only acceptable, if each of the
harmonic voltage V7,V11,V13 does not exceed 1% of the
fundamental voltage, according to the recommendations of
certain specifications limits. In this condition there is no
danger of appearance of over voltage at the terminal of the
capacitor Cb (in steady state condition). On the other hand,
in all calculations, we attained that the RMS values of the
current flowing into the capacitor does not exceed the
value:
Ib = I12 + I72 + I112 + I132 ≤ 1.02I1
1
25n
B 5n = 2
ωC 5 , Xesc = ωLesc
ωC b
n − 25
(38)
Which proves that the over current in the current which
flow by the capacitors rest within the limits imposed by
the specification.
4
Vc7 =1.09 V1 ,Vc11 =1.05 V1 ,Vc13 = 1.04 V1
They are less than the limiting levels allowed in the
specification.
Table(1) gives a comparative study of the different values
of the filter capacitors and elements using the different
criteria. From which, criteria (4.3), (4.4) are the most
efficient. They give minimum capacitances. The table
shows checking voltages and reactive powers.
Table (4): Filters parameters for single tuned, damped
and new technique for an aluminum smelter plant.
(43)
5.12 Check of Resonance’s at Untuned
Frequencies: The last aspect which should be taken into
consideration for the correct appreciation of the function
of the shunt harmonic filters (HF) is that the effects of
untuning of the filters, which is usually an invoided
situation in practice .the factor which contribute to the
untuning of filters are the following: deviations in
fabricating the coils and capacitors with respect to their
nominal values of tuning; the variations of the network
frequency, the variation of the capacitance as a function in
temperature. For these reasons, each filter may has at its
nominal frequency a non-zero reactance. If we transform
,the deviations in the inductance and in the capacitance in
an equivalent deviation in frequency, we can show, by
equation (42), that when the filter is only tuned to the 5th
order harmonic and is connected to the bas bar, each
positive deviation of frequency lead to lowering the
parallel resonant frequencies ,while negative frequency
deviation leads to augmenting (increasing) the parallel
resonant frequency. A deviation of 2% of the network
frequency leads approximately to 1.25 % variation in the
parallel resonance frequencies. Similar analysis can be
made for the cases where other filters of frequencies are
connected to the network. The untuning of the filters has a
harmful effect on the level of the harmonic voltage. Also,
if the filter which used for the 5th order harmonic is the
only filter which connected to the network, it will also
exist harmonic voltage of order 5, in a manner that the
distortion in the voltage may become unacceptable. In
these situations, it is necessary to use the recent automatic
adaptive filters or active filter.
Filter
rating
C (µF)
L (H)
R (Ω)
Cb (µF)
Eq.
voltage
2.842
0.029
0.558
136.6
8.39
3.118
5.272
Min.
loss
2.186
0.038
1.014
138.26
8.109
4.087
4.02
Proposed
k=11))
2.186
0.038
1.318
Conclusions:
A new technique for design of harmonic filter with more
advantageous solution is adopted in this study. It is based
on the concept of simultaneous filters of the single tuned
filters type and shunt capacitors connected to the busbar,
in parallel with the filters. Minimum capacitor
capacitances are obtained and used in the filter design of
orders 5th, 7th,11th, 13th and 23rd . The voltage across the
terminals of those capacitors are found to be less than the
limiting levels allowed in the specification.
The resonance in the system is studied for the designed
filter and avoided by special measures.
References:
[1] M.Z.El-Sadek," Power Systems Voltage Stability and
Power Quality", Muchter Press, Assiut,Egypt,2002,ch 16.
[2] D.E.Staeper and R.P.Stanford;" Reactive
Compensation and Harmonic Suppression for Industrial
Power Systems Using Thyristor Converters” .IEEE
Trans,on.IA 12(1976) 3,P.232-254
[3] D.A.Gonzalez,J.C.Mccall,"Design of Filters to Reduce
Harmonic Distortion in Industrial Power Systems".IEEE
Trans.on Industry Applications, Vol.IA-23,No.3,May/June
1987,pp. 504-515
[4] Jos Arrillaga, Bruce C. Smith, Nevelle R. Watson,Alan
R. Wood, “Power System Analysis" ,Book, John Wilery
&Sons Ltd, England, 1997.
[5] C.K. Duffy,R.P.Stratford,"Update of harmonic
Standards IEEE-519.IEEE Recommended Practices And
Requirements For Harmonic Control In Electrical Power
System", IEEE Trans. On Industrial Applications, Vol.IA25, No.6 , Nov./Dec.1989,pp.1025-1034.
[6]J. Arrillage, D. A. Bradly ,P. S. Bodger ,"Power System
Hrmonics " John Wiley and Sons Inc.,New York, 1985.
[7]H. M. Bedies, G. T. Heydt " Power Systems Harmonics
Estimation and Monitors " Electric Machines and Power
Systems,1992,pp. 94-102.
[8]T.J .E. Miller, " Reactive Power Control in Power
System " Book ,John Wiley ,London ,1982
The aluminum smelter plant of Nag-Hammady, Upper
Egypt, is rated 400 MVA at average power factor of
0.9.The electrolysis rectification stations are 12-pulse
uncontrolled rectifiers. The results of harmonic analyzer
show that the 11th, 13th and 23rd order harmonic currents
exceed the standard limits. By using the design of
proposed technique filters for these three harmonic orders,
and deciding that these filters should correct the 50 HZ
power factor to 0.95. Having Q optimum =33, and Q coils
=100. System voltage =132 KV. If the 11th , 13th and 23rd
currents are found to be 10, 8 and 5 %.
Table (1): Filters parameters using different criteria for
dividing capacitors between filter arms ( k=11)
Eq.
Cap.
3.06
0.027
0.34
136.2
8.573
2.94
5.63
Damped
k=23))
3.4
0.006
12.1
-
Table (4) gives a comparison between the parameters of a
conventional single tuned filter, damped filter and the
proposed filter. Damped filter require more resistance and
has excessive losses.
6. Case Study:
Filter
rating
Ck(µF)
Lk (H)
Cb(µF)
Vck (KV)
Qck(Mvar)
Q1k ,,
Qbk ,,
Single
(k=11)
3.4
0.025
2.5
-
Min.
Cap.
2.186
0.038
1.014
138.26
8.109
4.087
4.02
5
[9] J. D. Ainsworth , "Filers, Damping Circuits and
Reactive VOLT/AMPS in HVDC Converters " Chapter 7
from "High Voltage Direct Current Converters in Systems
" Book, 1988.
6