20120140506014

International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online) Volume 5, Issue 6, June (2014), pp. 89-98 © IAEME
89
SINUSOIDAL FRONT END CONVERSION WITH HIGHER ORDER INPUT
FILTER
Renjith Kumar D
Assistant Professor, Department of Electrical and Electronics Engineering,
College of Engineering Adoor, Kerala, India
ABSTRACT
The fast development of consumer electronics and increase in growth of power electronic
devices resulted in a plethora of nonlinear loads which invariably uses mains rectification circuits
using line commutated devices at the front end, acting as the dominant cause of current harmonic
distortion. The non sinusoidal currents drawn from the supply at the various harmonic frequencies
produce individual voltage drops creating voltage distortions and consequent losses. To reduce those
issues, Pulse Width Modulation (PWM) based Voltage Source Converters (VSC) employed as
Sinusoidal Front End Converters (SFECs) interfacing the grid and the load are being used. Their
main characteristics are the generation of reduced low frequency line current harmonics, better
overall input power factor, substantially smaller filter requirements, consistent dc bus voltage and
inherent regeneration capability. Compared with an L filter at the input side of SFEC, an LCL filter
is preferred for the grid tied voltage source converter to limit the switching current ripple emitted
into the grid. The advantages of using LCL filter include better attenuation of harmonics, reduction
in filter inductance value and high dynamic performance. This paper analyzes how LCL filter acts as
a better alternative to conventional L filter for improving the input spectral quality at the input of
Pulse Width Modulated Voltage Source Converter based Front End Conversion, thereby meeting the
prescribed harmonic standards. Passive damping techniques are utilized to settle down the resonance
issues that are caused due to interaction of energy storage elements present. Successful simulations
are also carried out with designed values for establishing the merits of using the higher order filter at
the input.
Keywords: EMI (Electro Magnetic Interference), FFT (Fast Fourier Transform), LCL Filter,
PI Control, PWM (Pulse Width Modulation), SFEC (Sinusoidal Front End Converter), THD (Total
Harmonic Distortion), VSC (Voltage Source Converter).
INTERNATIONAL JOURNAL OF ADVANCED RESEARCH
IN ENGINEERING AND TECHNOLOGY (IJARET)
ISSN 0976 - 6480 (Print)
ISSN 0976 - 6499 (Online)
Volume 5, Issue 6, June (2014), pp. 89-98
© IAEME: http://www.iaeme.com/IJARET.asp
Journal Impact Factor (2014): 7.8273 (Calculated by GISI)
www.jifactor.com
IJARET
© I A E M E

90
1. INTRODUCTION
Conventional diode and thyristor rectifiers employed as front end converters for the ever
increasing number of power electronic loads draw highly distorted current and have a poor overall
input power factor. A large number of these devices distributed in a grid may severely distort the grid
voltage in a cumulative way causing mal operation and premature failure of other sensitive loads [1].
This led to the wide acceptance of active power filters and Front End Converters based on force
commutated devices. The high frequency components associated with Pulse Width Modulation of
the SFEC may cause disruption to other Electro Magnetic Interference (EMI) sensitive loads
connected on the grid. To mitigate this effect in high power systems, the input filter inductance value
of the SFEC has to be increased which can cause unstable operation of the system. Also, the
dynamics of the response becomes poorer causing long time responses, more losses and cost [2].
Using LCL filter at the input side reduces the filter size, cost etc. and improves the harmonic
performance [3]. The shunt capacitor in the filter circuit offers more attenuation to the switching
ripple present in the input current of the rectifier favoring lower values of inductors. But resonance
problems can occur due to the interaction of inductive and capacitive elements giving rise to
instability issues [4]. The oscillations due to resonance can be easily damped out by using damping
resistors in the circuit.
2. CONFIGURATION AND CONTROL OF PWMVSC WITH LCL FILTER
The converter consists of a three phase IGBT bridge converter, a high capacitance on the dc
side and three single phase LCL filters on the line side [4]. The Pulse Width Modulated pole voltage
consists of a fundamental component at line frequency besides harmonic components around the
switching frequency of the converter. Being at high frequencies, these harmonic components are well
filtered by the input filter, hence the mains current is nearly sinusoidal. The fundamental component
of pole voltage controls the flow of real and reactive power. High capacitance at the dc side
maintains a stable dc bus voltage. Input power factor is normally kept at unity. Besides inverter
current sensor, an additional current sensor which senses either line current or capacitor current is
used for current detection. The use of line current feedback is justifiable since line current phase
angle can be directly adjusted to control the power factor at the point of grid connection. Based on
the feedback variables and input commands, proper control signals are derived from the controller
for sinusoidal PWM switching of the converter as shown in Fig. 1.
Fig. 1: Basic configuration of Voltage Source Converter with LCL filter and its control

91
Presence of capacitor in the filter can lead to undesirable resonance oscillations due to zero
impedance at resonance frequency causing both dynamic and steady state input current distortions
and instability problems [1]. Proper damping will move the unstable poles more inside the stability
region and absorbs a part of the switching frequency ripple to avoid the resonance, making the
attenuation effective. As parasitic losses of the filter elements yield only slight damping at resonance
which is not sufficient, passive damping has to be achieved by introducing an element like resistance
in the filter circuit. The guidelines to select the appropriate seat of damping resistor are minimum
losses and size, minimum effect on switching ripple attenuation, effective damping at resonance etc.
Considering all these guide lines, based on frequency response analysis, a resistor in series with the
capacitor is considered for passive damping analysis [5].
3. MATHEMATICAL MODELING OF DAMPED LCL FILTERS
Let vg be the grid voltage, ig be the grid current, vi be the inverter ac side voltage, ii be the
inverter ac side current, vc be the capacitor voltage, Lg be the grid side inductance, Li be the inverter
side inductance, Cf be the filter capacitance, Rd be the damping resistance, ic be the filter capacitance
current, C be the dc bus capacitance, Idc be the dc current from the rectifier, Io be the load current and
Vdc be the dc bus voltage. The single phase representation of the converter with LCL filter using
passive damping is shown in Fig. 2.
Fig. 2: Single phase representation of SFEC with LCL filters using passive damping
Fig. 3: Block diagram of the transfer function of the LCL filter using passive damping
Fig. 3 shows the block diagram of the transfer function of the LCL filters with damping
resistor where the parasitic resistors in the filter elements are ignored [2]. Corresponding open loop
transfer function connecting converter voltage and grid current can be written as
ܑ܏ሺ‫ܛ‬ሻ
‫ܞ‬ܑሺ‫ܛ‬ሻ
ൌ
‫܀‬‫܌‬۱܎‫ܛ‬ା૚
൫‫ۺ‬ܑା‫ۺ‬܏൯‫ܛ‬ቈ
‫ۺ‬ܑ‫ۺ‬܏۱܎‫ܛ‬૛
‫ۺ‬ܑశ‫ۺ‬܏
ା۱܎‫܀‬‫܌‬‫ܛ‬ା૚቉
(1)

92
In the grid connected system with L filter alone, the relationship between grid current (ig = ii)
and converter voltage is
ܑ܏ሺ‫ܛ‬ሻ
ൌ
૚
‫ۺܛ‬
(2)
The LCL filter transfer function relating converter voltage and grid current with no damping
is given by
ܑ܏ሺ‫ܛ‬ሻ
ൌ
૚
‫ۺ‬ܑ‫ۺ‬܏۱܎‫ܛ‬૜ା൫‫ۺ‬ܑା‫ۺ‬܏൯‫ܛ‬
(3)
4. DESIGN CONSIDERATIONS
Usually the converter side reactor attenuates most of the switching ripple generated by the
converter and hence should be normally bigger than that at the grid side. The higher the ratio Li/Lg is
chosen, the better the attenuation of switching frequency components. However if Lg is very small,
the dependency on grid stiffness is highly increased such that the influence of line impedance
variations on the resonance frequency is increased causing stability problems, especially in weak
grids. The total inductance Li+Lg can be up to 10% of base inductance so that voltage drop can be
limited [2].
Capacitors are selected based on power factor, reactive power, resonant frequency, bandwidth
of closed loop system etc. Larger capacitor results in good damping of high frequency switching
current components and leads to smaller size of magnetic components, lesser filter volume, losses
and cost [3]. However it can result in high inrush current, too low resonance frequency, grid side
resonance, stability problems, increased reactive power consumption, dependence of grid impedance
on overall harmonic attenuation and a higher harmonic current through the capacitor and inductor.
Small filter capacitance causes resonance at higher frequency and thus the controller design becomes
more difficult. Thus an optimal design of capacitor is appreciated.
The best seat of resonant frequency is in a range between ten times the supply line frequency
and one half of the switching frequency to avoid resonance problems in the lower and higher parts of
the harmonic spectrum [2]. Damping resistor must be a compromise between reduction of
oscillations and increased power losses.
The filter capacitor value is referred in % of the following base values
Base impedance value, ‫܈‬‫܊‬ ൌ
‫܄‬܏
૛
‫۾‬
(4)
Base capacitance value, ۱‫܊‬ ൌ
૚
૛મ܎‫܈‬‫܊‬
(5)
where P is the rated active power of the system, Vg is the RMS value of grid line voltage and f is the
frequency of grid voltage.
Generally, the fundamental reactive power absorbed by filter capacitors should be less than
5% of rated power of VSC to avoid excess power factor decrease. Hence it is considered that the
maximum power factor variation seen by the grid is 5%. Thus,
۱܎ ൌ ૙. ૙૞۱‫܊‬ (6)

93
As in SFEC with L filters, assuming current ripple to be largest for a duty cycle of 50%
‫ۺ‬ܑ ൌ
‫܄‬‫܋܌‬
ૡ√૜∆۷܎‫ܟܛ‬
(7)
where ∆I is the permitted rms current ripple and fsw is the switching frequency.
The relation between the harmonic current generated by the inverter and the current injected
in the grid is explained by the following transfer function
ܑ܏ሺ‫ܛ‬ሻ
ܑܑሺ‫ܛ‬ሻ
ൎ
૚
૚ା‫ܛ‬૛‫ۺ‬܏۱܎
(8)
Considering a suitable ripple attenuation factor on the grid side with respect to the current
ripple on the inverter side, the ratio ‘r’ between the inductance at the grid side and the one at the
inverter side can be computed such that
‫ۺ‬܏ ൌ ‫ۺܚ‬ܑ (9)
To avoid resonance, the resonance frequency (fres) should be such that
૚૙܎ ൑ ܎‫ܛ܍ܚ‬ ൑ ૙. ૞܎‫ܟܛ‬ (10)
܎‫ܛ܍ܚ‬ ൌ
૚
૛મ
ට
‫ۺ‬ܑା‫ۺ‬܏
‫ۺ‬ܑ‫ۺ‬܏۱܎
(11)
The value of the damping resistor should be at least one third of the impedance of the filter
capacitor at the resonant frequency. Hence
‫܀‬‫܌‬ ൑
૚
૟ૈ܎‫ܛ܍ܚ‬۱܎
(12)
The allowable ripple component on the dc bus voltage decides the value of the required
capacitor. The dc bus capacitance is given by
۱ ൌ
‫۾‬ܑ‫ܖ‬ઢ‫ܜ‬
‫܄‬‫܋܌‬ઢ‫܄‬
(13)
where Pin is the input power at rated condition, ∆t is the discharge period (to load) and ∆V is the
ripple voltage allowed at the dc bus.
5. CONTROL STRATEGY
The control scheme modulates the inverter to regulate the magnitude and phase angle of the
grid supply current, so that the real and reactive power entering the network can be controlled. The
transient operating conditions resulting from change of load and load voltage reference will be taken
care of by the charge or discharge process of the capacitor. The outer dc bus voltage control loop
keeps a constant value of the dc link voltage and provides the d axis reference current for the current
loop which influences the active power flow. The q axis reference current is set to zero so as to make
input power factor unity. Synchronous reference frame based PI controls have been adopted that has

94
the d axis oriented on the grid voltage [2]. The parameters involved, transformations and control
topology are applicable to both d axis parameters and q axis parameters. The single phase model of
the current control loop representing the system without damping is shown in Fig. 4. Bode analysis
are used to assess the stability of the system.
Fig. 4: Single phase representation of the control strategy without damping
The corresponding closed loop transfer function without damping is given by
ܑ܏ሺ‫ܛ‬ሻ
ܑ܏‫܎܍ܚ‬ሺ‫ܛ‬ሻ
ൌ
۹‫ܘ‬‫ܛ‬ା۹ܑ
‫ۺ‬ܑ‫ۺ‬܏۱܎‫ܛ‬૝ା൫‫ۺ‬ܑା‫ۺ‬܏൯‫ܛ‬૛ା۹‫ܘ‬‫ܛ‬ା۹ܑ
(14)
Obviously the system is unstable. The system can be made stable by inserting a proper
resistor in series with the capacitor filter indicating passive damping as shown in Fig. 5.
Fig. 5: Single phase representation of the control strategy with passive damping
The closed loop transfer function for the current control loop with passive damping is then
ܑ܏ሺ‫ܛ‬ሻ
ܑ܏‫܎܍ܚ‬ሺ‫ܛ‬ሻ
ൌ
۹‫ܘ‬‫܀‬‫܌‬۱܎‫ܛ‬૛ା൫۹‫ܘ‬ା۹ܑ‫܀‬‫܌‬۱܎൯‫ܛ‬ା۹ܑ
‫ۺ‬ܑ‫ۺ‬܏۱܎‫ܛ‬૝ା൫‫܀‬‫܌‬۱܎‫ۺ‬ܑା‫܀‬‫܌‬۱܎‫ۺ‬܏൯‫ܛ‬૜ା൫‫ۺ‬ܑା‫ۺ‬܏ା۹‫ܘ‬‫܀‬‫܌‬۱܎൯‫ܛ‬૛ା൫۹‫ܘ‬ା۹ܑ‫܀‬‫܌‬۱܎൯‫ܛ‬ା۹ܑ
(15)
6. STABILITY ANALYSIS AND SIMULATION RESULTS
The system parameters taken for the calculation of the filter components of the SFEC using
both L and LCL filters are P = 7 kW, Vg = 415 V, f = 50 Hz, fsw = 10 kHz, Vdc = 700 V. Current
controller time constant, Ti = 150 µs and voltage controller time constant, Tv = 20 ms.
Assuming unity input power factor and an efficiency of 95% for the SFEC, rated input grid
current, I୥ ൌ 10.26 A
From Eqn. (4), (5) and (6), filter capacitance, C୤ ؆ 7 µF
From Eqn. (7), inductance on the converter side for 10% rms current ripple, L୧ ؆ 5 mH

95
Considering a ripple attenuation factor of 5%, from the sinusoidal transfer function of Eqn.
(8) and from Eqn. (9), r = 0.14 and grid side inductance, L୥ ؆ 700 µH
From Eqn. (11), resonant frequency, f୰ୣୱ ؆ 2450 Hz this satisfies Eqn. (10).
Consequently resonant angular frequency, ω୰ୣୱ ؆ 15300 rad/sec
From Eqn. (12) damping resistor, Rୢ ൑ 3.3
For 2% dc voltage ripple and a discharge period of 1 ms, from Eqn. (13), C ൌ 700 µF
For the simulation of SFEC, the inductance of the L filter has been chosen as the sum of the
inductances in LCL filter for an easy comparison of harmonic performance.
The frequency response plots of the SFEC with different filters and control loops are given in
Fig. 6 to Fig. 9. Designed values of filter elements are taken for the analysis.
Fig. 6: Frequency response of ig(s)/vi(s) for L and LCL filters without damping
In the lower part of the spectrum, the LCL type filter behaves like an L type filter as the
effect of filter capacitance can be neglected. If no damping is applied, resonance occurs at the
resonant frequency (15300 rad/sec) causing very high gain, promoting instability. In the higher part
of the spectrum, LCL filtering effectiveness is highly improved by attenuating high-frequency
harmonics. Thus to obtain a given attenuation of switching frequency ripple, lower values of
inductances are sufficient in case of LCL filter. This reduces the size of filter components and also
the cost.
Fig. 7: Frequency response of ig(s)/vi(s) for LCL filter with different Rd
-100
-50
0
50
100
150
Magnitude(dB)
System: sys
Frequency (rad/sec): 1.53e+004
Magnitude (dB): 104
10
2
10
3
10
4
10
5
-540
-360
-180
0
Phase(deg)
Bode Diagram
Frequency (rad/sec)
L
LCL
-80
-60
-40
-20
0
20
40
Magnitude(dB)
10
2
10
3
10
4
10
5
-225
-180
-135
-90
Phase(deg)
Bode Diagram
Frequency (rad/sec)
Rd=5 ohm
Rd=20 ohm

96
Fig. 8: Open loop frequency response of current control loop without damping
Fig. 9: Open loop frequency response of current control loop with passive damping
The simulation results using PSIM for the SFEC with LCL filter at full load and Iqref = 0 A
are given in Fig. 10 and Fig. 11. Designed values of filter elements and controller time constants are
taken for the simulation analysis.
Fig. 10: Grid current when no damping is applied
10
2
10
3
10
4
10
5
-675
-630
-585
-540
-495
-450
Phase(deg)
Bode Diagram
Frequency (rad/sec)
-100
0
100
200
300
400
Magnitude(dB)
System: sys
Magnitude (dB): 309
No damping
-60
-40
-20
0
20
40
Magnitude(dB)
System: sys
Magnitude (dB): -4.77
10
2
10
3
10
4
10
5
-225
-180
-135
-90
Phase(deg)
System: sys
Phase (deg): -180
Bode Diagram
Frequency (rad/sec)
Passive damping

97
Fig. 11: Grid voltage, grid current (scaled by 10), inverter current and capacitor current on passive
damping
Fig. 12 shows the effect of damping on the FFT (Fast Fourier Transform) of the grid current
drawn by the SFEC.
Fig. 12: FFT of grid current
The THD of the input current (THDi) measured after connecting each of the input filters to
the front end converter is indicated in the Table 1.

98
Table 1: THD comparison
Input filter THDi at full load THDi at half load
L filter 6 mH 3.59% 7.02%
LCL filter 5 mH, 7 µF, 1 mH 2.13% 4.29%
7. CONCLUSION
Improved harmonic performance is obtained from SFEC when L filter is replaced with LCL
filter. The size of filter inductors in the case of the LCL filters can be made smaller than that of L
filters for the same filtering effect of harmonic components. This topology provides a better
decoupling between filter and grid impedance and the ripple current stress is lower across the grid
inductor. The simulation results proved that the high frequency grid current ripple due to PWM
switching is considerably reduced using properly damped LCL filter, improving the input spectral
quality and harmonic performance. Passive damping technique has been effectively utilized for
limiting the resonance issues associated with LCL filters.
8. ACKNOWLEDGEMENT
The author would like to thank CDAC Trivandrum and Faculty Members of Department of
EEE, NIT Calicut for their immense help and support extended for completing the task.
REFERENCES
[1] I. C. Evans and A. H. Hoevenaars, “ Meeting harmonic limits on marine vessels”, Electric
Ship Technologies Symposium, ESTS’07, IEEE, May 2007, pp. 115-121.
[2] M. Liserre, F. Blaabjerg and S. Hansen, “Design and control of an LCL filter based three
phase active rectifier”, IEEE Transactions on Industry Applications, vol.41, Sep/Oct 2005,
pp.299-307.
[3] H R Karshenas and H Saghafi, “Performance investigation of LCL filters in grid connected
inverters”, IEEE PES Transmission and Distribution Conference and Exposition Latin
America, Venezuela 2006, pp. 1-6.
[4] Fei Liu et al. “Design and research on parameter of LCL filter in three phase grid connected
inverter”, IPEMC 2009, pp. 2174-2177.
[5] Wenqiang Zhao et al. “A double-loop current control strategy for shunt active power filter
with LCL filter”, IEEE International Symposium on Industrial Electronics (ISlE 2009), Seoul
Olympic Parktel, Seoul, Korea, July 5-8, 2009, pp. 1841-1845.
[6] Narayan G. Apte and Dr. Vishram N. Bapat, “Indirect Current Controlled Single Phase Shunt
Active Filter”, International Journal of Electrical Engineering & Technology (IJEET),
Volume 4, Issue 4, 2013, pp. 264 - 273, ISSN Print : 0976-6545, ISSN Online: 0976-6553.
[7] Mihail Antchev, Ivailo Pandiev, Mariya Petkova, Eltimir Stoimenov, Angelina Tomova and
Hristo Antchev, “PLL for Single Phase Grid Connected Inverters”, International Journal of
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ISSN Print: 0976-6545, ISSN Online: 0976-6553.
[8] Dr. Leena G, Bharti Thakur, Vinod Kumar and Aasha Chauhan, “Fuzzy Controller Based
Current Harmonics Suppression using Shunt Active Filter with PWM Technique”,
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20120140506014

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