INTRODUCTION
The growth of the power converters raises the issue of the power quality problems.
The major power quality problem is the harmonics which distorts the supply voltage,
derating the electrical equipment and there is a mal functioning of the protective
devices (Bashi et al., 2006). This load also
consumes reactive power from the mains. The bank of capacitors is connected
to reduce the reactive power (Q) so that power factor is reduced. But there
is harmonic amplification caused by the capacitor and the line impedance. The
diode rectifier with boost converter improves the power factor (Bashi
et al., 2005). But the THD does not meet the IEEE standard. The side
filter such as passive filter and active filter reduces the harmonics as well
as improves power factor (Vahedi, 2012). The Shunt Active
Filter (SAF) was used to reduce the supply current harmonics and also minimizes
Q. But the active filter cost is high and it is difficult to construct the filter
with quick current response (Kouzou et al., 2010;
Singh and Verma, 2006). Various hybrid filter topology
was investigated in the recent years. The hybrid filters are connected to the
supply line through a transformer. By removing the transformer, the expenditure
of the active filter is reduced to 10% (Mattavelli, 2001).
Series hybrid filter carriers the fundamental reactive current (i_{q})
and the total harmonic current (Sriranjani and Jayalalitha,
2011). But in the Shunt hybrid filter (Rahmani et
al., 2012) the SAF carries the (i_{q}) and the other harmonic
current. The dominant harmonic current is flowing in tuned passive filter which
is connected to supply as shown in Fig. 1.

Fig. 1: 
Schematic representation of shunt hybrid filter 
This study presents a SHF without transformer is used to decrease the rating
of the SAF (Luo et al., 2009).
The control of active filter is done by detecting the harmonics by the theory
of instantaneous reactive power or synchronous reference frame (Sriranjani
and Jayalalitha, 2012a). This theory needs more computation and also Phase
locked loop has many disadvantages. Many control strategy uses harmonic detection
methods (Tao et al., 2009). In this study, the
fundamental current is detected from the supply using Least mean square algorithm
which simplifies the control circuit (Sriranjani and Jayalalitha,
2012b). There is no intermediate transformer between the supply line and
the active filter. This reduces the cost of the filter design. The inverter
losses are minimized by managing the dc bus voltage using PI.

Fig. 2: 
Shunt hybrid filter equivalent circuit 
Hysteresis current controller based Shunt hybrid filter is analysed in MATLAB
simulink.
MATHEMATICAL MODELLING
Non linear load: The 3φ full bridge rectifier with RL load act
as a non linear load which distorts the line current.
Source voltage is given by:
Due to the diode rectifier load, the supply current contains fundamental component
and harmonics component:
Where:
I_{1} 
= 
Fundamental current 
I_{k}k^{th} 
= 
Harmonic current 
V_{m} 
= 
Peak supply voltage 
ω_{s} 
= 
Fundamental frequency at rad/sec 
φ_{k} 
= 
Phase angle between the supply voltageand current of the k^{th}
harmonic component 
Shunt hybrid filter: The Shunt Hybrid filter contains the passive filter
which is tuned for the dominant harmonic frequency of the line current. The
SAF provides the reactive power compensation and harmonic compensation. The
equivalent circuit of the system is shown in Fig. 2. The switching
ripples are reduced by the inductance coupled with the active filter.
The distorted current is given by:
For harmonic compensation and power factor improvement, the supply current
should have the fundamental component and it should be in phase with the supply
mains.
Thus the line current is:
where, I_{m} is the maximum fundamental component current of the mains
and ω_{1} is the supply frequency (50 Hz). In this study the resonant
filter is tuned for the fifth order harmonic frequency:
where, L_{r} and C_{r} are the inductor and capacitor of the
resonant filter.
The resonant filter current and the active filter current is given by:
where, I_{r1} is the fundamental reactive current component, I_{d}
is the dominant harmonic current, d is the dominant harmonic order and I_{hr}
represents the remaining harmonic component of the line current. n denotes the
phase angle between the current and supply voltage. The Z_{pf} is the
passive filter tuned for the dominant frequency so that it will inject the i_{pf}
to the supply mains. The shunt active filter will inject the I_{hr}
and I_{r1} current so that the supply is free from harmonics and reactive
power is minimized.
Reference current extraction: With the intention of tuning the active
filter, the reference current at the fundamental frequency is extracted by the
least mean square algorithm from the line current.

Fig. 3: 
Adaptive linear combiner 

Fig. 4: 
Block diagram of generation of pulses for Mosfet 
The distorted line current is filtered out by the adaptive linear combiner
shown in Fig. 3. Pulse generation of SAF is shown in Fig.
4. In this proposed control circuit, the fundamental current is detected
from the supply current.
The actual output is the fundamental current I_{f} determined by the
LMS algorithm (Bernard and Stearns, 2002).
The harmonic current is:
The adaptive linear combiner with desired output and error signal is given
by:
Where:

Fig. 5: 
Comparison of supply current and reference
current using hysteresis controller 
Weight matrix is updated by:
where, ε_{n} is error signal, d_{n} is the desired output,
y_{n }is the actual output and μ is gain constant. From Eq.
1, 3, 10 and 12:
So the fundamental current is extracted by updating the weight matrix w_{n+1}.
Inverter dc bus voltage control: The capacitor is charged or discharged
due to the switching of the Mosfet. The increasing of the capacitor voltage
is limited by PI controller and while switching pattern are formed by considering
the reference voltage of the dc bus shown in Fig. 4. This
minimizes the losses of the inverter.
where, k is the controller gain and I_{f} is the fundamental reference
current.
Hysteresis current control (HCC): The switching patterns for the each
leg is obtained by comparing the instantaneous value of the line current and
the fundamental current at supply frequency is shown in Fig. 5.
The fixed band HCC is used because of fast response and high accuracy compare
to PWM control (Abedi and Vahedi, 2013). The Switching
pattern for leg 1, the upper switch is ON when the supply current is more than
the reference current within the hysteresis band and the lower switch is ON
when the supply current is less than the reference current.
Design of SAF: The ripples of the SAF is filtered by an inductor which
is designed by:
Table 1: 
Specification shunt hybrid filter 


Fig. 6: 
Supply voltage waveform 

Fig. 7: 
Supply current waveform without filter 
and the active filter capacitor is given by:
where, I_{L} is load current, T is the switching period, V^{*}_{dc}
is the reference active filter dc voltage. V_{dc} is the actual voltage.
MATLAB SIMULATION
Shunt Hybrid filter is simulated in Matlab. Power gui is used to measure THD.
Here the full bridge rectifier with RL load is used and power is measured. The
passive filter is designed in such way that it will reduce the Fifth order harmonics.
Finally the SAF is connected and the power, power factor and harmonics are measured.
The rating of the active filter is calculated. Table 1, shows
Selection of parameters.
SIMULATION ANALYSIS
Figure 6 and 7 shows supply voltage waveform
and the supply current waveform before the connection of SHF.

Fig. 8: 
Active filter current 

Fig. 9: 
Fifth order Harmonic current waveform
of the passive filter 

Fig. 10: 
Suply crrunt waveform after compesation 
The current waveform is distorted and the power factor is less than 0.95.
Figure 8 and 9 shows the passive filter
current waveform and active filter current waveform. The passive filter injects
the fifth order harmonics to the load and the active filter injects the fundamental
reactive current and other harmonic current. The HSAF gives near to unity power
factor and reduces the current harmonics which is shown in Fig.
10. When the Hysteresis controlled SHF is connected, the supply is free
from harmonics. Figure 11 and 12 shows
the frequency spectrum of supply current before and after connection of the
filter. The Total harmonic distortion of the line current is trim down from
20.85 to 0.15% and there is an improvement in power factor. The KVA rating of
the active filter is 1.3 KVA. Figure 13 shows the dc bus
voltage waveform. It finally settled to its reference dc voltage value. When
the reference voltage is reduced below the set value (300 V), the harmonics
are increased. Thus the shunt hybrid filter overcomes the drawbacks of the resonant
filter and SAF.

Fig. 11(ab): 
Frequency spectrum of the line current without SHF 

Fig. 12(ab): 
Frequency spectrum of the line current with SHF 

Fig. 13: 
Dc bus voltage of the active filter 
Table 2: 
Individual harmonics of the supply current 

Table 2 shows the results of power, harmonics and power factor
before and after the connection of SHF. The nonlinear load absorbs very high
reactive power from the supply line. After the Shunt Hybrid filter is implemented
in the supply line, the reactive power is reduced from 272 to 3 VAR. Thus the
harmonic and reactive power compensation is done by Shunt Hybrid filter with
LMS algorithm.
CONCLUSION
Using Hysteresis controlled Shunt Hybrid filter the reactive power and current
harmonics becomes scanty. The Least mean square algorithm is used for extracting
the fundamental reference current for hysteresis current control. By balancing
the active filter dc voltage using the PI controller reduces the losses of SAF.
The proposed filter achieves 0.99 power factor and current harmonics are reduced
to less than 5%. The dominant harmonic of the supply current is five. So passive
filter is tuned for the fifth order harmonics and SAF balances the reactive
power and other harmonics. The burden of the SAF is very much diminished.