Voltage tracking of bridgeless PFC Cuk converter using PI controller

W. M. Utomo1, N. A. A. Isa2, A. A. Bakar3, A. F. H. A. Gani4, B. E. Prasetyo5, H. Elmunsyah5, Y. M. Y Buswig7 1,2,3,4 Department of Electrical Power Engineering (JEK), Faculty of Electrical and Electronics Engineering (FKEE), Universiti Tun Hussein Onn Malaysia, Malaysia 5 Department of Electrical Engineering, Politeknik Negeri Malang, Indonesia. 6 Department of Electrical Engineering, Universitas Negeri Malang, Indonesia. 7 Department Electrical and Electronic Engineering, Faculty of Engineering, Universiti Malaysia Sarawak, Malaysia


INTRODUCTION
Power electronic equipment with an active power factor correction (PFC) for telecom, datacom, and automotive electrical system are becoming necessary nowadays [1][2][3][4][5]. There are several types of DC-DC BPFC converters were developed for PFC applications such as boost, buck, buck-boost, SEPIC and Cuk converters [6]. However, for low power application, BPFC Cuk converter is the most reliable converter because it offers low THD of input current, good power factor, easy to implement in transformer isolation, and natural protection against inrush current from start-up or overload current [7][8][9][10][11]. This converter acts similar to the buck-boost converter since it able to step up and step-down the output voltage by controlling the duty cycle [11,12] Basically, the DC-DC converter used power semiconductor devices that operated as the electronic switches which are refer as switched mode power supply [SMPS] [13,14]. The operation of this switching devices may cause inherently nonlinear characteristic of the BPFC Cuk converter [15]. Pulse width modulation (PWM) is the most popular method for the various switching technique [15,16]. Switch-mode PWM dc-dc converters used to provide a constant output voltage [17]. Proportional-Integral (PI) controller often to use as the control method for PWM switching due to the simple design and easy to implement [18,19].
The proposed system bridgeless PFC Cuk converter is shown in Figure 1 where, a single MOSFET switch replacing the two MOSFETs, which helps to reduce high conduction loss and size of the structure [20,21]. In this case, the structure proposed to reduce the complexity of controller circuit. Basically, bridgeless PFC structure suffer from the difficulty of implementation of control circuit because of two switches. Nevertheless, this structure can reduce conduction losses form bridgeless. In this paper, the output voltage was selected to -42 and -54 V for the electric vehicle application [22][23][24]. Meanwhile -48 V is used in telecommunication application [7,25].
The remainder of this study is organized as follows: operation of BPFC Cuk converter will be shown in section II. Then the parameter design for PFC converter is presented in section III. Section IV describe about the P.I controller for BPFC Cuk converter. Simulation result and analysis in section V, followed by conclusion in section VI.

OPERATION OF BPFC CUK CONVERTER
The proposed BPFC Cuk structure as shown in Figure 1. When the MOSFET M is turned-on during positive cycle, Dp, D1 are on-state and Dout is off-state as shown in Figure 2. There are two modes for this operation. For the first mode, the inductors L1 and L2 are charging. Meanwhile, the capacitor C1 and capacitor C2 are discharging. Then output inductor Lo is charging and capacitor Cout is discharging. In mode 2 condition, capacitor C1 and capacitor C2 are charging through inductors L1 and L1. Then, the inductor Lout recharges the capacitor Cout.
When the MOSFET M is turned-on during negative cycle, Dn, D2 operate in on-state and Dout is offstate as shown in Figure 3. There are two modes for this operation. First, the inductors L1 and L2 are charging, the capacitor C1 and capacitor C2 are discharging, the output inductor Lo is charging and capacitor Cout is discharging. For the next condition, capacitor C1 and capacitor C2 are charging through inductors L1 and L1. Then, the inductor Lout recharges the capacitor Cout and power supplied to the load.
When the MOSFET M is turned-off, Dp, D1 are off-state and Dout is on-state as shown in Figure 4. There are four conditions for this mode. In the first condition, capacitor C1 and capacitor C2 are charging. Inductors L1 and L2 are discharging. Then, the output inductor Lout is discharging while, capacitor Co is charging and the power is supplied to the load. For the second condition, inductor L1, inductor L2 and capacitor C2 are discharging. Then, inductor L1, inductor L2 and capacitor C2 are discharging, while capacitor C1 is charging. Output inductor Lout is discharging and capacitor Cout is charging and the power is supplied to the load. For the third condition, inductor L1, inductor L2 and capacitor C2 are discharging. Meanwhile capacitor C1 is charging. Then, capacitor Cout is discharging through output inductor Lout and the power is supplied to the load. For the fourth condition, capacitor C1 and capacitor C2 are discharging through inductors L1. Then, L2 are charging and output inductor Lout recharges capacitor Cout. Then, the power is supplied to the load.
When the MOSFET M is turned-off, Dn, D2 are in off-state while Dout is on-state as shown in Figure 5. There are four modes at this condition. First, capacitor C1 and capacitor C2 are charging, at the same time inductors L1 and L2 are discharging. Then, the output inductor Lout is discharging, capacitor Co is charging and the power is supplied to the load. In the second mode, inductor L1, inductor L2 and capacitor C2 are discharging. Then, inductor L1, inductor L2 and capacitor C2 are discharging while capacitor C1 is charging. Output inductor Lout is discharging. Capacitor Cout is charging and power is supplied to the load. For the third mode, inductor L1, inductor L2 and capacitor C2 are discharging, but capacitor C1 is charging. Meanwhile, capacitor Cout is discharging through output inductor Lout and the power is supplied to the load. In the fourth mode, capacitor C1 and capacitor C2 are discharging through inductors L1. Then, L2 is in charging mode. However, inductor Lout recharges the capacitor Cout. and the power is supplied to the load.
The average AC supply current is given as (2), Where the Re is defined as the effective input resistance of the converter and given by (3) ⋅ ⋅ The Dton is the summation of D1Ts and D2Ts. On the other hand, the average output current of diode during one-line cycle is equal to the average current, Io through to the load, R Thus, it can be simplified by evaluating (2) by using (3) and applying the power-balancing between the AC supply and DC output, the voltage conversion ratio is equal to:

Gain ratio as function of duty cycle, D
DCM operation mode requires that the sum of duty cycle and the normalized MOSFET-off time length to be less than one. Following inequality must be satisfied:

Design of input inductor L1 and L2
The input inductance is calculated by using inductor current ripple: The maximum inductor current ripple calculated from the peak input current is given by (9) , ⋅ √ ⋅ , By substituting (9) into (10), the input inductance L1 can be calculated. Noted that, the L1 is equal to L2, thus the same formula can be used. The value of input inductance can be found as:

Design of output inductor, Lo
From (1), the average output current of diode, IDo during one line-cycle of the AC supply can be determined by (11) , Ke is dimensionless parameter are defined and can be expressed by (12) ⋅ The average output current is the average diode current, Le from can be found by (13) ⋅ ⋅ (13) Therefore, the output inductor can be determined by applying (10) and (13):

Design of input capacitor, C1 and C2
The input capacitor, C1 is an important component in the Cuk topology since it may distort the quality of AC supply current. The C1 must be designed properly by considering resonant frequency, fr not close to line frequency fL and switching frequency fsw. Hence, the energy transfer to capacitor C1 is determined based on inductors L1, L2, and Lo values. In addition, a better initial estimation for choosing the resonant frequency, fr is given by (15). Noted that, the C1 is equal to C2 which the same formula can be used, thus the design C1 (16) is:

Design of output capacitor, Co
Since the input of converter is AC supply, the output capacitor must be large enough to reduce the output voltage ripple. Thus, the output ripple frequency of the converter is two times of the input frequency, given in (15). In the worst case, the output current during half-period of the ripple frequency is provided by the output capacitor. Therefore, the output voltage ripple must be selected based on the application requirement and Co can be obtained as follows: Figure 6 illustrate the simulation diagram of proposed design of P.I controller for BPFC Cuk converter by using Maltab software. The reference voltage for P.I controller is set to -48V with 2/50 gain value. The value of P is 1.0 while the value of I is 3.34. The output of the P.I control is a power value and in order to convert it to a quantity that is comparable to that of the control signal, it goes through a power to PWM signal converter.  Figure 7 show the characteristic of BPFC Cuk converter output voltage with P.I controller when the reference voltage is set up to -42V output voltage. The result shows the P.I controller functional well since the BPFC Cuk converter produce -42 V output voltage by following the reference voltage command. The overshoot voltage is -56 V. At 0.6 seconds, the system achieved steady state condition. When the reference voltage for P.I controller is set to -48 V, the BPFC Cuk converter will produce -48 V output voltage as shown in Figure 8. The overshoot voltage is -59 V. The steady state condition achieved at 0.5 seconds. Figure 9 illustrate the -54 V output voltage with P.I controller. The overshoot voltage is -63 V. For -54 V output voltage, the system starts to achieve stability at 0.41 seconds ( Figure 10). Figure 1 show the result for the output voltage ripple value with P.I controller. As increase the output voltage, the ripple will be increase too. P.I control is functioning well in order to reduce the output voltage ripples.

CONCLUSION
In this paper, a proportional-integral control for bridgeless PFC Cuk converter is discussed. Various output voltage was set up to observe the characteristic of output voltage during steady state and step response. The proposed design of P.I controller able to control the output voltage of BPFC Cuk converter. As increase the output voltage value, the overshoot voltage will increase too but the steady state time will be faster. Furthermore, the performance of BPFC Cuk converter become better since the output voltage able to achieve fast steady state condition. The output voltage ripples are affected toward the output voltage value. However, the P.I controller able to reduce the output voltage ripples.