# Analysis of a single phase resistive bridgeless rectifier for SMPS and UPS applications.

INTRODUCTIONPower supplies with active power factor correction (PFC) techniques are becoming necessary for many types of electronic equipment to meet harmonic regulations and standards such as the IEC 61000-3-2 and IEEE 519. Most of the PFC rectifiers utilize a boost converter at their front end. However, a conventional PFC scheme has lower efficiency due to significant losses in the diode bridge. Also the input operating power factor is lagging in nature. Operation under unity power factor is an important feature in AC to DC Boost power converters. In this regard, the previous researchers have used only sinusoidal input voltage and currents with known input frequencies for power line applications (Liu and Chang, 2009). The conventional methods of converting AC to DC are not sufficient to meet the requirements in high efficiency power applications. So, various topologies of switch-mode boost converters are developed for efficient power conversion. In (Kazerani et al., 1991; Vazquez et al.,2005) the PFC method with active current wave shaping was presented. A boost converter topology was introduced in (Louganski and Lai, 2007) to eliminate the leading phase distortion. One more boost converter topology was presented in (Kwon et al., 2008) to reduce the reverse recovery losses of the diode. Various solutions to reducing the reverse recovery losses were mentioned in (Zhao et al., 2001; Lu et al., 2003; Su and Lu, 2010). In (Crebier et al., 2005), the merits and demerits of various boost converter topologies were discussed. In (Martinez and Enjeti, 1996), the demerits of conventional boost type PFC circuit were eliminated. The advantages of using boost converters were discussed in (Huber et al., 2008). Classification of single stage converters with respect to the AC source frequency and the absence of large bulk capacitor in the DC link was discussed in (Moschopoulos and Jain, 2005). The safety isolation in an isolated boost converters were presented in (Mi et al., 2003; Chow et al., 2000; Zhu et al., 2003). Mixed mode operation of a boost rectifier for a wide range of load variations was presented in (Tripathi et al., 2002). A theoretical study of switching power converters with PFC were discussed in (Tse and Chow, 2000; Tse, 2003) in which the resistive behaviour were elaborated in an open loop.

The above works have mainly focussed on the boost power converters using sinusoidal input with known input frequencies. In wind energy conversion systems the input voltage amplitude and input frequency are time varying in nature and also in SMPS and UPS applications constant regulated voltage is required. To achieve maximum power absorption and to reduce the total harmonic distortion we should enforce the resistive input behaviour at the input of the boost converters that is independent of the input characteristics. In this paper the proposed switching controller provides the desired resistive input behaviour.

MATERIALS AND METHODS

PFC Circuit:

The general schematic of a PFC circuit is shown in Figure 01. The controlled rectifier may be a conventional diode rectifier with boost converter circuit or bridgeless boost rectifier circuit.

Conventional Boost Converter:

The basic topology of the conventional AC-DC PFC boost converter is shown in Figure 02. A great deal of research has been conducted on this converter to minimise the power losses. Generally, bridgeless PFC topologies may reduce the conduction losses by reducing the number of semi conductor components in the line current path. Compared to conventional PFC boost converter (Figure. 02) one diode is eliminated from the line current path, so that the line current simultaneously flows through only two semiconductors, resulting in a reduced conduction losses.

Bridgeless Boost Converter:

The basic topology of the Bridgeless AC-DC PFC boost converter is shown in Figure 03. The Schottky Diodes and MOSFETs are used to achieve the lower conduction losses. To decrease the conduction losses, MOSFET 2 is kept on when the time varying input voltage Vac is positive. Similarly, MOSFET 1 is kept on when the time varying input voltage is negative.

Operating Principle:

Mode 1 Operation:

When Vac > 0 and MOSFET1 is turned on, the current starts flowing from Vac towards L,MOSFET1,MOSFET2 and back to Vac, Thus energy starts building in the inductor and inductor stores energy in the electromagnetic fields. We denote this as a Mode 1 of operation. Refer the Figure 04 (a).

Mode 2 Operation:

When MOSFET1 is turned off, the potential across the inductor is gets added to the source voltage and this net potential charges the battery. Thus current starts flowing from Vac towards L,D1,Battery,MOSFET2 and back to Vac. We denote this as a Mode 2 of operation. Refer the Figure 04 (b).

Transient Analysis:

In Mode 1 operation the inductor current can be written as

iL(t) = iL(t1) + [i/L][[integral].sup.t.sub.t1]Vac(t)dt, t1 [less than or equal to] t [less than or equal to] kTs (1)

Where k--Sampling Time, Ts--Switching period of MOSFET1 and t1--starting time of switching cycle

When time t = t1, MOSFET 1 is turned on and the total inductor current is the sum of initial inductor current due to previous switching cycle and the inductor charging current between the instants t1 to kTs. The MOSFET voltage drop is ignored when it is on.

In Mode 2 operation the inductor current equation can be written as

iL(t) = iL(kTs) + [i/L][[integral].sup.t.sub.kTs](Vac(t) - VB - VD)dt, kTs [less than or equal to] t [less than or equal to] t 2 (2)

Where VB--Battery Voltage and VD--Voltage drop across the diode

When time t = kTs, MOSFET 1 is turned off and the total inductor current is the sum of initial inductor current during charging and the inductor discharging current between the instants kTs to t2.

By using averaging technique the inductor current can be written as

iL(t) = [DELTA]Q/Ts = [1/2LTs] Vac ton (1 - Vac/[Vac - VB - VD]) (3)

Where Q--Total charge passing through the inductor and ton--On time

From the above equation, there is a non-linear resistance exists between the input terminals.

After some algebraic manipulations, the input resistance can be written as

Rin = 2LTs/[ton.sup.2] (1 - Vac/[VB + VD]) (4)

From the above equation it is very clear that the input resistance is proportional to L, Ts and inversely proportional to [ton.sup.2].

Condition for Resistive Input Behaviour:

We know that, from the Figure 05, t0 [less than or equal to] toff

To find t0, we set iL (t2) = 0.Hence,

to = Vac ton/(VB + VD - Vac) (5)

The on time and off time can be written in terms of duty cycles are as follows

ton = dTs

toff = (1-d) Ts (6)

Using (5) and (6) and after performing some algebraic manipulations

d(VB+VD) [less than or equal to] VB+VD-Vac (7)

Therefore the condition to achieve resistive input behaviour is as follows

d [less than or equal to] (1 - Vac/(VB+VD)) (8)

Thus the duty cycle is depends only on the input voltage, Battery Voltage and Voltage drop across the diode. That is the circuit can be activated in to a pure resistive mode only when the duty cycle satisfies the above equation.

Proposed Control System Methodology:

From (4), Rin depends on Switching Time, on time and Inductance. Since switching frequency is fixed, hence switching period Ts is generally cannot be a proper control variable, inductor is also fixed and then the only parameter which changes and affects the value of input resistance is on time. Thus we can select ton as a control variable and also it is depends on duty cycle d.

Now Let us consider,

Let b = VB+VD, Rin = Vac/iL, c = 2LTs/[ton.sup.2], Vac = v (9)

Using (9) in (4)

Rin = c(b-v/b) (10)

Now Let us define,

c = Rd + [DELTA]R (11)

Where Rd--Desired resistance of the input circuit

Using (11) in (10)

Rin = (Rd + [DELTA]R)((b-v/b)) (12)

By defining

Error [delta]e = Rd - Rin (13)

Using (12) in (13)

[delta]e = Rd - [(Rd + [DELTA]R)((b-v/b))] (14)

If [DELTA]R is defined as

[DELTA]R = [(1 - (v/b)).sup.-1](z + (v/b) Rd) (15)

By using (15) in (14)

[delta]e = - z (16)

If z is the output of the PI Controller

Then z =Kp[delta]e + Ki [integral] [delta]e dt (17)

Using (17) in (16)

(1+Kp) [delta]e + Ki [integral] [delta]e dt (18)

Using (15) in (11) and after some mathematical manipulations c = b/(b - v) (Rd + z) (19)

The value of duty cycle d is calculated using (9) and c is given by (19).

The above Figure 06 illustrates the block diagram of proposed control system methodology in which PWM signals are generated by the controller and duty cycle is adjusted by the controller to obtain the resistive input behaviour.

RESULTS AND DISCUSSION

Simulation Results:

A Simulink model of the resistive bridgeless rectifier and its proposed controller were developed using MATLAB with the following parameters: Vac (Peak) = 6 V, C = 100[micro]F, R = 1k[ohm], L = 0.1H, [f.sub.i] = 50Hz and [f.sub.s] = 1 kHz; Where [f.sub.i] and [f.sub.s] are the input signal and switching frequencies respectively. The Simulink model of the bridgeless rectifier with proposed controller is shown in the Figure 07.

The resistive bridgeless rectifier circuit is simulated. For different loads, it has been observed that the source currents are exactly in phase with the voltages. The input power factor is 0.99, nearly unity. This is achieved by tuning the duty cycle of the PWM signals. The source voltage and source current waveforms are exactly in phase with each other as shown in Figure 08 and Figure 09 respectively. Figures 08 and 09 stretches the results obtained for a desired input resistance of Rd = 5 k[ohm] and a duty cycle of d = 0.20.

The above Figure 10 illustrates the harmonic current pattern and the THD is 4.82% which is less than the guidelines given in the IEC 61000-3-2 and IEEE 519 standards. The PWM signals of the MOSFETs are shown in the Figure 11 and Figure 12.

When the duty cycle is less than the bound given by (8) (ie., d [less than or equal to] 0.7561); hence the circuit operates in the pure resistive mode. The proposed controller is used to achieve the desired resistance by adjusting the duty cycle of PWM signals. The duty cycle oscillation at 36% is shown in the Figure 13. Since b/(b - v) is very close to unity, this term is assumed to be one in controller implementation. Considering (4) and ignoring the term Vac/[VB+VD] which is typically small for a boost rectifier, which yields the resultant Rin = 5k[ohm], when the duty cycle of the PWM signal is 20%. The duty cycle oscillation at 20% is shown in Figure 14.

The load resistance has been changed in the steps of 100 ohms and the corresponding variations in power factor has been obtained. It has been observed that irrespective of load variations, the power factor is always unity. The power factor variation with respect to load resistance is shown in the Figure 17.

The source voltage has been changed in the steps of 1 Volts and the corresponding variations in power factor has been obtained. It has been observed that irrespective of source voltage variations, the power factor is always unity. The power factor variation with respect to source voltage is shown in the Figure 18.

In order to vary the duty cycle the desired resistance Rd has been adjusted and the corresponding changes in power factor has been obtained. From the above Figure 19, it is very clear that when d [less than or equal to] 0.7561, the power factor is unity and the bridgeless converter is operated in pure resistive mode and when d [greater than or equal to] 0.7561, the power factor immediately decreases which indicates the inductive nature of the converter circuit. Hence when the duty cycle is more than the bound given by (8), then the bridgeless converter enters in to inductive mode.

Hardware Results:

To evaluate the performance of the resistive bridgeless rectifier circuit experimentally, a three phase version was developed as shown in Figure 20. The controller is implemented and tested for one phase initially and the results are reported here. The following components were used: IGBTs, 600V, 16A(IXGP16N60C2D1); Diodes, 600V, 30A (RHRP3060); Electrolytic capacitor, 100[micro]F, 25 V; L = 0.1 H.

The PFC circuit and its Driver circuit assembly are shown in Figure 21. The input inductors and PIC Microcontroller assembly are shown in Figure 22.

The current through the inductor and the input voltage were measured using Agilent 320 DSO and these two signals are in phase with each other as shown in Figure 23. The PWM signals are generated by using PIC16F628A Microcontroller and the PWM Signals are shown in Figure 24.

The output voltage along with source voltage waveforms are shown in Figure 25.

The output current waveform is shown in Figure 26.

Conclusion:

A single phase resistive bridgeless rectifier has been designed and its performance was analyzed. The switching controller has been implemented using MATLAB Simulink. The duty cycle of the PWM signals was controlled to get a resistive input behaviour (When (d [less than or equal to] 0.7561)). When the duty cycle is more than 0.7561, then the circuit enters in to inductive mode; that is the input current vector lags the input voltage vector. The bridgeless rectifier with proposed switching controller circuit provides the unity power factor. The THD also has been controlled to a tolerable limit. For dynamic load variations as well as for dynamic source variations, the input power factor is always unity.

ARTICLE INFO

Article history:

Received 3 September 2014

Received in revised form 30 October 2014

Accepted 4 November 2014

REFERENCES

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(1) Tamizhselvan Annamalai and (2) Dr. V. Rajini

(1) Research Scholar, Department of Electrical and Electronics Engineering, SSN College of Engineering, OMR Salai, Kalavakkam, Chennai, Tamilnadu, India.

(2) Professor, Department of Electrical and Electronics Engineering, SSN College of Engineering, OMR Salai, Kalavakkam, Chennai, Tamilnadu, India.

Corresponding Author: Tamizhselvan Annamalai, Department of Electrical and Electronics Engineering, Sri Venkateswara College of Engineering, Post Bag #3, Pennalur, Sriperumbudur Taluk, Postal Code--602 117, Chennai, Tamilnadu, India

E-mail: tamizh@svce.ac.in, tamizhselvan.annamalai@gmail.com, Phone:+919500717990.

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Author: | Annamalai, Tamizhselvan; Rajini, V. |
---|---|

Publication: | Advances in Natural and Applied Sciences |

Article Type: | Report |

Geographic Code: | 9INDI |

Date: | Nov 15, 2014 |

Words: | 2924 |

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