INTRODUCTION
In most power electronic equipment like SMPS, UPS, AC to DC converters are used as the interface with the utility voltage source. These equipments use diode rectifiers to convert the input AC into DC. Capacitive and inductive filters are used in the DC side to keep the output voltage ripple free. The uncontrolled rectifier with capacitive filter draws very large current near the peak of AC line voltage. The current does not flow continuously and it becomes zero for finite durations. Hence, these rectifiers draw distorted current from the AC line (Mohan et al., 1995).
In the recent years, massive use of power electronic equipments has increased the problem of power quality in electrical systems, the problem of line current harmonics also grows in its significance (Erickson and Maksimovic, 2001). The nonsinusoidal current which contains harmonics lead to distortion of the line voltage waveform, increased RMS current, electromagnetic interference etc. Several international standards are now available which limit the harmonic content due to line currents of equipment connected to electric utility. Passive filters are used to meet the standards such as IEC 61000, IEEE. But these filters increase the cost and occupies more space due to it’s size and weight. As a result, there is the need for a reduction in line current harmonics, or Active power Factor Correction (Rashid, 2007).
Many power electronic converters are used to shape the input current to nearly sinusoidal and also follow the supply voltage waveform closely (Singh et al., 2003). Among various power electronic converters boost converter is well suited for input current shaping and to obtain a controllable output voltage (Bashi et al., 2005; Lin and Tzou, 2009). The boost configuration reduces the noise at the input capacitor and the inductor present in the boost converter minimizes line current ripple and results in continuous current. There are two operating modes in boost converter based on current ripple. Discontinuous conduction mode results large current ripple and causes more stress on the switches. Therefore, it is preferred for low power applications. Continuous conduction mode operation reduces the current ripple and losses and it is the obvious choice for High power loads (Karaarslan, 2008).
The PFC of boost converter with CCM condition is possible with certain control strategy (Moon et al., 2011; Roggia et al., 2012). Among the various control methods, Hysteresis Current Control (HCC) is extensively used technique owing to its noncomplex implementation, enhanced system stability, fast response and less distortion in input current waveform (Zhou et al., 1990). In this study, HCC technique is used for wave shaping and regulating the output voltage. It also includes the design of boost converter and modelling of the converter using state space averaging. Finally, by using the MATLAB/SIMULINK model the simulation results are obtained.
BOOST CONVERTER OPERATION
The simplified configuration of boost converter with PFC controller is shown in Fig. 1. The boost converter has two distinct operating modes.
Mode 1: When the switch is in closed position (Fig. 2) the current is passing through the inductor L and the switch.

Fig. 1:  Boost converter with PFC controller 

Fig. 2: 
Switch is closed (TON) 

Fig. 3:  Switch is open (TOFF) 
During this time interval (TON), the current increases and inductor stores energy. At the same time the capacitor starts discharging through the load R.
Mode 2: When the switch is in open position as in Fig. 3, the current is flowing through the inductor L, diode D, the load R and the capacitor C. During this interval (TOFF), the current decreases and the energy that has been accumulated in the inductor get transferred to the capacitor. The mathematical equations are derived from the equivalent circuits of both the operating modes (Ramanarayanan, 2008). Then the state space averaging is used to obtain various matrices from which transfer function can be determined.

Fig. 4:  Closed loop boost converter using hysteresis control for PFC 
During first sub interval (0<t<DT_{S})
di_{L}/dt =V_{g}/L
dv_{c}/dt = v/RC
di_{L}/dt =V_{g}/L –(v/L)
During second sub interval (DT_{S}<t<T_{S})
dv_{c}/dt =I _{L}/C –(v/RC)
Where, D = Dutycycle = T_{ON}/T_{S}, T_{S }= T_{ON}+T_{OFF} , D’ = 1D
CURRENT MODE CONTROL FOR PFC
Different current control techniques are usually used for controlling the PFC converters (Fig. 4). For implementing the closed loop control, the supply voltage and the output voltage, input current of the boost converter are sensed. In outer voltage control loop, the boost converter output voltage is scaled down and compared with the reference value. The difference is given to the PI controller. The sine template obtained from the supply voltage is multiplied with the output of PI controller and the resulting signal sets the reference current. In Hysteresis current control, depending upon the maximum and minimum boundary limits of current, two sinusoidal current references are generated.

Fig. 6: 
Hysteresis current control for PFC 

Fig. 7: 
Output voltage of hysteresis current control boost converter for Vin = 35 V and R = 45 Ω 

Fig. 8: 
Supply voltage waveform and current waveform of hysteresis current control boost converter for Vin = 35 V and R = 45 Ω 
Table 1: 
Simulation parameters 

When the inductor current becomes less than the lower reference (IL, ref) the switch is turned ON and if it exceeds the upper reference (IU, ref) the switch is turned OFF. This results in variable frequency operation. A small Hysteresis band is selected in order to reduce the ripple in the boost inductor current (Fig. 5).
SIMULATION RESULTS
The boost converter with Hysteresis current control is implemented using MATLAB/SIMULINK program to improve the power factor. The values of various parameters used in the simulation circuit is given in Table 1.
Figure 6 shows the schematic diagram of Hysteresis current control for PFC in MATLAB/SIMULINK. The Fig. 7, 8 and 9 shows the waveforms for boost converter output voltage, supply voltage, source current and THD of source current.
The input voltage is varied from nominal value of 30 V (peak) to 40 V (peak) and the Load is varied from 35 45 Ω. The performance of the PFC converter is Analyzed with the help of THD, power factor for input voltage variation and load variation which is shown in Table 2 and Fig. 10.
CONCLUSION
This study concerns with modeling and simulation of boost converter with hysteresis current mode control. The duty ratio of the boost converter is varied by the control signal from the PFC controller. Hence, the output voltage regulation is good and the input current shape is nearly sinusoidal. Simulation studies were carried out for supply voltage variation as well as for load variation. The result of simulation shows that the THD of input current is less and there is no significant change in the powerfactor corresponding to input voltages variation and load variation.

Fig. 9:  FFT analysis of hysteresis current control boost converter for Vin = 35 V and R = 45 Ω 

Fig. 10: 
Variation of Power factor for various input voltages and loads 
Table 2: 
Vout (avg), THD and power factor for supply voltage variation and load variation 
