G
M
THE NINTH INTERNATIONAL MIDDLE-EAST POWER SYSTEMS CONFERENCE, MEPCON’2003
Minoufiya University, Shebin El-Kom, Egypt, December 16-18,2003
A NEW RELATION BETWEEN FIRING ANGLE OF THREE-PHASE
SCR CONVERTER AND BEST REINJECTION CURRENT ANGLE
Ali M. Eltamaly, PhD
Electrical Engineering Department
Faculty of Engineering, Elminia University, Elminia, Egypt
Abstract: In this paper a new relation between
firing angle (α) of three-phase SCR converter
and optimum angle of reinjection current has
been achieved for lowest THD of line currents.
The THD of line currents depends not only on
the rms value of the reinjection current but
also on the angle of this current. Angle of
reinjection current plays a very important rule
with the value of THD of the line current of
the three-phase SCR converter. The best angle
for reinjection current has been derived for
different firing angle (α). A controllable single
switch boost converter connected in shunt is
employed to circulate the new reinjection
current shape. A method to implement the
proposed approach under varying the firing
angle (α) is shown. Analysis, design, and
simulation results are presented.
I. Introduction
In most power electronic applications SCR
rectifier/ inverter are commonly used. These
controlled converters are attractive due to their
inherent ruggedness, simplicity and cheap
price, market availability even for very high
rating applications and it is become now
mature technology. However, these converters
exhibit
nonlinear
characteristics
and
consequently generate harmonic currents into
the electrical utility system. The nonlinear
operation of SCR rectifier / inverter causes
highly distorted utility line current. The
distorted line currents flowing through the
system causes distorted voltages at the Point of
Common Coupling (PCC) where many other
sensitive loads are connected. Thus the
increase in harmonic contents in the utility line
currents result in increased volt-ampere ratings
of the equipment connected to the system such
as generators, motor loads, transformers,
transmission lines, etc. For the reasons of these
harmful effects of harmonics many standards
has evolved to specify utility power quality to
acceptable levels [1,2].
The controlled SCR converter can be used as
a rectifier or inverter in Adjustable Speed
Drive (ASD) [3] as well as wind energy
applications [4,5]. Line current of SCR
converter and its FFT components are shown
in Fig.1. This famous current shape contains
components at 5, 7, 11, 11ωt etc. and presents
high harmonics (THD ≅ 35%) and contributes
to many ill effects to the electric utility. For
good quality sinusoidal current interface of 3phase utility voltages various approaches have
been described in the literature. Earl1y work
has been done to reduce the THD in the line
currents by increasing number of pulses
[6,7,8,9] such as a 12-pulse converters [6], 18pulse converter [7] and 24-pulse system [8].
793
But, this technique suffer from the following
disadvantages
ƒ Large in size and heavy in weight and all of
these components has to be in the top of the
WTG tower.
ƒ High in cost.
ƒ Needs special transformer, complex,
expensive and it will not be ready available
from manufacturer [9].
network impedances, also it is expensive and
bulky especially in low order harmonics.
There are many active methods to reduce
harmonic currents by using PWM converters.
But, all these techniques suffer from the
following disadvantages:
• Complex control circuit is
required to control the system.
• High price switches (IGBTs).
• High switching losses.
There is another method to reduce harmonics
generated in utility line currents of SCR
converters by injecting third harmonic current
If as shown in Fig.2. A line frequency isolation
transformer is used to provide neutral terminal
and third harmonic current If circulated
between the DC and AC side by a DC-DC
converter as shown in Fig.2 [10]. This scheme
suffer from the following disadvantages:
• It requires Υ / ∆ isolation transformer.
• Two IGBTs on the DC side are in the
series path of the power flow.
• The DC-link voltage is higher than
nominal and warrants re-design of the
wind/PV fuel cell inverter stage.
• Suffer from increased loses.
Fig.1 Utility line current and its FFT of SCR
converter without any harmonic reduction means.
Two Step down DCDC converters
The waveform of the utility line current still
has harmonic contents especially in 12- pulse
converters(THD =13%). Where in 12- pulse
system results in the cancellation of 5th and
7th harmonics in the utility line currents and
kVA ratings of isolation transformer in 12 –
pulse transformer is 1.04 pu [9].
Passive filters can filter harmonics at the
terminal of the system and also are useful
improving the power factor. However, these
approaches can eliminates only specific
harmonic as well as it is not successfully for
varying harmonics applications specially in
wind energy applications where the frequency
depends on the wind speed. In addition, the
passive filter can cause resonance with other
SCR
Inverter
Isolation
Transformer
UG
Vd
o
If
Fig. 2 Harmonic reduction in LCI inverter by twostep down DC-DC converters.
Another reinjection of third harmonic current
If technique for utility interface of WTG using
LCI inverter has been presented in [11]. A
tuned LC branch connected in star is employed
to provide the neutral. This scheme suffers
from the following disadvantages:
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• The LC branches are bulky and draw reactive
power of fundamental frequency.
• The LC branch can resonate with other element
in the electric utility.
• The current in the reinjection branch is very
sensitive to the deviation of L and C values.
• This technique does not take into account the
harmonic level in the DC-link current.
II -Proposed Technique
Fig.3 shows the topology of the proposed
approach to reduce harmonics generated by
line commutated SCR inverter used in (ASD).
This approach consists of zigzag transformer
that presents high impedance for fundamental
frequency component and very low impedance
for the injection current. A single-phase
transformer is connected between the DC-link
mid-point ‘o’ and the zigzag transformer
neutral ‘n’. The secondary of single-phase
transformer is connected to a rectifier boost
converter stage feeding the DC link. By
operating the single switch the injected current
shape If can be regulated.
Previous results say; the best rms value of 3rd
harmonic current is equal to the average value
of DC link current [10,11,12]. But it is not the
only condition required. However; the angle of
reinjection current plays a very important rule
in the THD of line current. So, the main
purpose of this paper is to determine the
relation between the angle of reinjection
current, ψ and the firing angle α. For this
reason we’ll use RL series branch as shown in
Fig.3 instead of using boost converter to drive
this relation easily and then we can reflect the
results back to work with boost converter. In
this analysis the rms value of reinjection
current is maintained equal to the average
value of load current in the following analysis.
For firing angle α=20 degrees (as an
example), Fig.4 shows the utility line current
with respect to the voltage of phase ‘a’,
voltage between point ‘d’ and ‘n’’ Vdn, the
voltage between point ‘f’ and ‘n’ Vfn and the
voltage between ‘o’ and ‘n’ Von with respect to
phase ‘a’ voltage.
The third harmonic components of the
voltages Vdn , V fn and Von have been used to
inject third harmonic back to utility line
current to reduce the harmonic contents in
utility line currents. So a careful analysis for
these voltages is required to get the optimum
value of reinjection current and its angle ψ.
It is convenient to employ Fourier series in
the analysis of the distorted waveforms. In
general, a non-sinusoidal waveform f(x) can be
expressed as follows :
f ( x) = a 0 +
∞

∑  a n
n =1
bn =
2L
1
2L
a0 =
1
L
 nπx 
 nπx  
cos 
 + bn sin 
 
L


 L 
∫
f ( x) dx , a n =
0
2L
1
L
2L
 nπ x 
 dx
L 
∫ f ( x) cos 
0
 nπ x 
 dx
L 
∫ f ( x) sin 
0
Will apply the above equations to the
waveforms of V dn , V fn only to get the third
harmonic component. In this case we will use
2L =
2π
and x = ωt and n=1. Then, For Vdn3
3
a1 =
3
5π
+α
6
π
∫ Vm sin ωt * cos 3ωt dωt
π
6
=
b1 =
3 3 Vm
[2 sin (2α ) − sin (4α )]
8π
3
π
5π
+α
6
π
6
=
(1)
+α
∫ Vm sin ωt * sin 3ωt dωt
(2)
+α
3 3 Vm
[cos(4α ) − 2 cos(2α )]
8π
In the same way it is easy to fined V fn3 and
Von3 .
The third harmonic component of these
voltages are the same third harmonic
component as Vdn3 . From (1) and (2) we can
obtain , Von3 and its angle , θ as in (3) and (4).
795
Von3
rms
And θ
=
1
2
* a12 + b12 =
3 V LL
8π
1 + 8 sin 2 α
 2 sin (2α ) − sin (4α ) 
a

= tan −1  = tan −1
b
 
 cos(4α ) − 2 cos(2α ) 
(3)
(4)
Fig.3 The proposed approach.
150
100
50
0
0
50
200
100
150
φ opt
θ
100
Fig.4 Utility line current, V dn , V fn and Von with
0
respect to Va voltage.
-100
The angle of line current fundamental
component, β equal to the firing angle α
(with respect to fundamental frequency) and
3α (with respect to 3rd harmonic frequency).
(5)
So; β = α (In fundamental frequency)
rd
β = 3α (In 3 harmonic frequency)
(6)
Angle of reinjection current; Ψ is:
ψ = θ −φ
(7)
Where, φ is the angle of reinjection impedance.
The best angle of reinjection current with
respect to the fundamental component of line
current is 180. So, The optimum angle of
reinjection current is shown in (8). But from
(7) the optimum angle of reinjection
impedance φ opt is shown in (9).
ψ opt = 180 − 3α
φ opt = θ − 180 + 3α
So, θ , φ opt and ψ opt
(8)
(9)
can be drawn with
-200
ψ opt
0
50
100
alpha
150
Fig.5 Th variation of Von,3rd , θ , φ opt ,ψ opt with α .
III- Design Example
For V LL = 380 V , and firing angle α=30
degrees, the following values can be obtained
from Fig.5. θ ≅ 150 o , ψ opt = 180 − 3 * 30 = 90
φ opt = θ − ψ opt = 150 − 90 = 60 o , Von3
rms
From PSIM simulation, I o
= 22.87 A
So I f
So
rms
Zr =
= 22.87 A
Von3 rms ∠θ
If
average
= 78.28V
rms
∠ψ opt
= 3.423 ∠60 = 1.71 + i 2.964 Ω
So R r = 1.71, and Lr =
2.964
= 3.145 mH
2 * π *150
If we apply the above values of Rr , Lr into
the PSIM simulation program will get the
results shown in Fig.6.
respect to α as shown in Fig.5.
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It is clear from Fig.6 that the THD of the
utility line current is very low (THD =4%).
In case we use the same rms value of
reinjection current but we will change the
angle of reinjection impedance Z r to be 30
degrees instead of 60 degrees. So,
Z r = 3.423 ∠30 o = 2.964 + i1.71141
So, R r = 2.964, Lr =
1.71141
= 1.816 mH
2 * π *150
It is clear from the results shown in Fig.7
that the THD increased.
In case we use the same rms value of
reinjection current but the angle of reinjection
impedance Z r has been changed to be 0
degrees instead of 60 degrees. So,
Z r = 3.423 ∠0 o , then, R r = 3.423, Lr = 0 mH . It
is clear from the results shown in Fig.8 that
the THD increased.
It is clear from Fig.6, 7, and, 8 that the THD
of utility line current is highly affected by the
angle of reinjection current. A relation
between THD and impedance angle at
α = 30 o is drown as shown in Fig.9.
Fig.7 Utility line current and its FFT components
at impedance angle φ = 30 o
Fig.8 Utility line current and its FFT components
at impedance angle φ = 0 o
Fig.6 Utility line current and its at optimum
impedance angle = φ opt = 60 o
797
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1995
[5] R. M. Hilloowalla and A. M. Sharaf “A utility
interactive wind energy conversion scheme
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Conference Proceedings 1997., Twelfth
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IEEE.
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interface “, IEEE trans. On IA, vol. 32, No. 6,
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for utility interface of static converters”, Ph.D.
Thesis Texas A&M University, Augest 1998.
[10] R. Naik, N. Mohan, M.Rogers and A.
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photovoltaic, wind-electric, and fuel cell
systems with a controllable power factor of
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line current harmonics in interfacing
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[12] Ali M. El-Tamaly, P. N. Enjeti and H. H. ElTamaly “An Improved Approach to Reduce
Harmonics in the Utility Interface of Wind,
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th Annual IEEE Applied Power Electronics
Conference and Exposition, New Orleans,
Louisiana, USA, 6-10 February 2002.
25
20
THD
15
10
5
0
0
10
20
30
40
50
60
Impedance angle
70
80
90
Fig.9 The relation between THD and impedance
angle at α = 30 o
IV. Conclusions
In this paper a new relation between the
firing angle, α and the angle of reinjection
current has been driven for the minimum
THD in the utility line current of three phase
thyristor converter. A boost converter has
been connected in the reinjection path to
control the reinjection current under varying
firing angle α and to returen the power in the
reinjection path back to DC link voltage.
Simulation and experimental results prove
that the new relation plays a significant rule
in the reduction of THD.
V. References
[1] ANSI/IEEE Standard 519 1992 “ IEEE Guide
for
harmonic
control
and
reactive
compensation of static power converters”
[2] Limitations of emission of harmonic current
in low-voltage power supply systems for
equipment with rated current greater than
16A, IEC 61000-3-4, 1998.
[3] Robart A. Hanna “Harmonics And Technical
Barriers In Adjustable Speed Drives” IEEE
1989
[4] R. Naik, N. Mohan, M. Rogers and A.
Bulawka” A novel grid interface, optimized
for utility-scale applications of photovoltaic,
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