1 Introduction

In most of the applications, for AC-DC power conversion it is necessary to havethe output dc voltage to be well regulated with good steady state and transient performance. The rectifier with filter capacitor is cost effective but it severely deteriorates the quality of the supply, [1] thereby disturbing the performance of other loads connected to it further causing other troubles. Power electronics engineers have been developing new approaches for better utility interface, to meet these imposed standards [2]. These new circuits are called as power factor correction circuits.

Three-phase AC-DC conversion of electric power is widely employed in adjustable speed drive (ASDs), uninterruptible power supplies (UPSs), HVDC systems, and utility interfaces with nonconventional energy sources such as solar photovoltaic systems (PVs) etc., [3–5] battery energy storage systems (BESSs), in process technology such as electroplating, welding units, etc., battery charging for electric vehicles and power supplies [6].

The current controller senses the input current and compares it with a sinusoidal current reference. To obtain the current reference, the phase information of the utility voltage or current is required. This information is obtained by employing a phase lock loop (PLL), which creates transients if the frequency ratio changes [7]. The single-switch rectifier has one of the simplest circuit structures. The two switch rectifier performs the same switching action as the single-switch rectifier but has the advantage of higher efficiency [8–10]. However, the scheme based on OCC exhibit instability in operation when magnitude of the load current falls below a certain level or when the converter is operating in the inverting mode of operation. To avoid it a modified OCC Bi-directional high power factor AC-to-DC converter is proposed in [11]. This scheme uses saw-tooth wave to generate PWM pulses which incorporate low frequency harmonics. OCC presents some drawbacks intrinsic with its physical realization: the controller and its parameters cannot be modified without hardware re-design; moreover they are influenced by temperature drifts, typical of analog systems. To overcome these limitations the OCC technique is implemented digitally using Field-programmable gate array (FPGA) [12]. This system uses PLL to find phase information of utility voltage and current. Another drawback of this system is that controller takes integer numbers only. The split operation is limited only to dividing number by a power of two.

A new single-phase multilevel flying capacitor active rectifier using hysteresis-based control is reported in [13], the power factor and output voltage regulation is achieved by controlling the input current. PLL is used to find the phase information of input voltage which creates the transients as the frequency ratio changes. Smart charger for electrical vehicle using three wire distribution feeders is proposed in [14]. To achieve bi-directional flow six active switches are used, which increases switching losses, hardware, and complexity. A simple control technique for a single-phase bridgeless active rectifier with high power factor and voltage stabilization using partial digital implementation is implemented in [15].

This paper not only presents the comparative study between two cases but addresses the aforementioned drawbacks. The used converter is bridgeless, transformer-less, and output DC current sensor less. All the above mentioned schemes are implemented digitally to incorporate the advantages of digital implementation. The detail simulation is carried out using MATLAB/Simulink and to validate it experimental setup is develop using DSPic33FJ64MC802 digital controller for 1 KW system.

2 System Modeling

For controlling and digital implementation of most of the part of the system author preferred DSPic33FJ64mc802 controller, which having all the features of digital signal processor (DSP). The detail simulation is carried out in Simulink of MatLab. The Sim-Power tool of MatLab is used to implement the block schematic of single-phase bi-directional converter. Figure 1 shows the single-phase representation of the converter. VIN is the AC line voltage of 140 V and 50 Hz. ‘L’ represents the line inductor carrying current Iin (t). Controlled Switches S1–S4 are arranged in a bridge. ‘C’ is the DC side capacitor of 440 F and ‘R’ is the variable resistive load. Io and IL are output and load currents respectively.

Fig. 1
figure 1

Single-phase full bridge converter

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2.1 Digital Implementation of SPWM Technique

For implementation of sinusoidal PWM technique SPic33FJ64MC802 digital controller is used. This controller operates on 3.3 VDC supply voltage. It has 10-bit (Analog to Digital conversion) ADC, hence its total full scale count is 210 = 1024. It means that for analog input 3.3 V to ADC controller pin gives 1024 count. For the implementation we consider this value as 2.5 V. The conversion of output AC voltage to its linear DC value is made using series connection of step-down transformer and precision rectifier shown in Fig. 2.

Fig. 2
figure 2

Conversion of output AC voltage to its linear DC value

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This sinusoidal PWM scheme, in this section is used for inversion operation; hence its output is 230 VAC as per the design. To implement it digitally, an array of percentage duty cycle is developed and filled it into the look-up table. The look-up table consists of totally 200 values based on the line frequency and switching frequency.

For implementation of sinusoidal PWM technique DSPic33FJ64MC802 digital controller is used. The ADC count value for the 2.5 V operating voltage is same as mentioned in above section. To implement it digitally, an array of percentage duty cycle is developed and filled it into the look-up table. The look-up table consists of total 200 values of duty cycles, based on the line frequency and switching frequency. When power is on, initially Kfactor value is less for soft start mechanism. Slowly, it increases with the increment value 0.01 to achieve desired AC voltage that is 160 V. It is represented in terms of embedded C code and it is updated after every 1 ms, and duty cycle value is updated after every 50 s. For the analysis purpose, author takes 160 V as input AC RMS voltage to boost it up to 380 VDC link voltages.

2.2 Digital Implementation of SPWM Technique

This scheme is used for the rectification operation. Soft start mechanism is used in which when power is ON duty cycle increases from 0 % till to achieve desired voltage. For implementation of continuous switching PWM technique DSPic33FJ64MC802 digital controller is used. This controller operates on 3.3 VDC supply voltage. It has 10 bit (Analog to Digital conversion) ADC, hence its total full scale count is 210 = 1024. It means that for analog input 3.3 V to ADC controller pin gives 1024 count. For the implementation we consider this value as 2.5 V. The conversion of feedback DC voltage to its equivalent step-down value is done using voltage divider circuit. The desired boosted DC voltage is 380 V for line voltage 230 VAC. For digital implementation the feedback voltage is converted to its equivalent step down voltage as described and shown in above paragraph. We convert the 380 VDCFB into 2.5 V desirable for the digital controller. The band is provided of 10 VDC as an upper threshold (390 VDC its equivalent step-down voltage is 2.58 V) and lower threshold (370 VDC its equivalent step-down voltage is 2.45 V). It is shown in Fig. 3.

Fig. 3
figure 3

Band of 10 V provided as upper and lower threshold

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Advantage of this technique is that the input current flowing similar to input voltage due to continuous fast switching, hence power factor value is nearer to unity and the regulation of output DC voltage is better. The control block for presented converter is shown in Fig. 4.

Fig. 4
figure 4

a Control block for single-phase converter and b input side representation of the single-phase converter circuit

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3 Simulated and Experimental Results

In order to check the performance of converter using CSPWM and SPWM techniques for rectification and inversion using SPWM technique detail simulation is carried out on MATLAB/Simulink platform and the DSPic33FJ64MC802 digital controller is used for the implementation.

3.1 Simulated and Experimental Results of Rectification Using CSPWM

Simulated and experimental result waveforms for rectifying mode of operation are shown in Fig. 5. Trace 1 of Fig. 5a shows the simulated waveform of line current following the line voltage to indicate the unity power factor. The experimental result for the same is shown in Trace 2 of Fig. 5a. This shows the exactly similar result like simulated waveform. The channel 1 is at 50 V/Div and channel 3 is at 5 A/Div.

Fig. 5
figure 5

a Simulated and experimental results of line current and line voltage to show high power factor. b Simulated and experimental results of line voltage, line current, and DC link voltage when load changes from 80 to 5 % periodically to show voltage stabilization period. c Line current harmonic pattern to show third harmonics discarded and reduction in fifth and seventh harmonics

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The DC side load is changed from 5 to 80 % periodically to show the output voltage regulation which is shown in Fig. 5b. Trace 1 of Fig. 5b shows simulated result, it can be seen that as load changes from 80 to 5 % and from 5 to 80 % the DC link voltage remains regulated. Trace 2 shows experimental result for the same. It can be observed that the DC link voltage regulated within very small period which is negligible when load change occurred. Channel 2 and 4 are at 50 V/Div and channel 3 is at 2 A/Div. Trace 3 visualizes the step change and period of DC link voltage regulation after load change occurred. When load changes from 5 to 80 %, time/division knob is at 250 ms which shows the voltage regulated within the period of 40 ms, the line current increases and line voltage remains constant. The line current harmonics pattern is show in Fig. 5c. It can be observed that all the lower order harmonics and third harmonics are totally discarded while fifth and seventh harmonics are reduced up to negligible level.

3.2 Simulated and Experimental Results of Rectification Using SPWM

Simulated and experimental result waveforms for rectifying mode of operation are shown in Fig. 6. Trace 1 of Fig. 6a shows the simulated waveform of line current flowing maximum at the peak of line voltage and almost zero at the starting to indicate the degradation in power factor. The experimental result for the same is shown in Trace 2 of Fig. 6a. This shows the exactly similar result like simulated waveform. The channel 1 is at 50 V/Div and channel 3 is at 5 A/Div.

Fig. 6
figure 6

a Simulated and experimental results of line current and line voltage to show degraded power factor. b Simulated and experimental results of line voltage, line current and DC link voltage when load changes from 80 to 5 % periodically to show distortions during voltage stabilization and stabilization period. c Line current harmonics pattern to show third, fifth, and seventh harmonics are present

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The DC side load is changed from 5 to 80 % periodically to show the output voltage regulation which is shown in Fig. 6b. Trace 1 of Fig. 6b shows simulated result, it can be seen that as load changes from 80 to 5 % and from 5 to 80 % the DC link voltage becomes unregulated. Trace 2 shows experimental result for the same. It can be observed that the DC link voltage regulation take more period when load change occurred. Channel 2 and 4 are at 50 V/Div, channel 3 is at 2 A/Div and time/division knob is at 500 ms. Trace 3 visualizes the step change and period of DC link voltage regulation after load change occurred. It shows that when load changes from 5 to 80 % the voltage regulated within the period of 100 ms, also the line current and line voltage disturbance increases. The line current harmonics pattern is show in Fig. 6c. It can be observed that thirrd, fifth, and seventh harmonics are present which shows that total harmonic distortion (THD) increases.

3.3 Simulated and Experimental Results of Inversion Using SPWM

To show the bi-directional operation using the same converter the inversion operation is shown in Fig. 7. The simulated result in Fig. 7a shows the inverted current is exactly 180° of inverted voltage. The experimental results are taken for pure resistive load shown in Fig. 7b.

Fig. 7
figure 7

a Simulated results of inverted line current and line voltage at exactly 180° phase shifted to show inversion action, b experimental results

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3.4 Comparative Study Between Proposed CASES

The comparisons between the two CASES are made for various loads ranging from 90 to 250 Ω. The parameters observed during the comparison are power factor, THD, and DC load current. The detailed comparison is shown in Fig. 8a and b. Figure 8a shows the parameters for the CASE-I (rectification using CSPWM and inversion using SPWM). It can be observed that full load power factor is 97.8 % and THD is 6.3 % only. The parameters for the CASE-II (rectification and inversion both using SPWM) are shown in Fig. 8b. It is shown that power factor is 80.3 % and THD is 19.8 %.

Fig. 8
figure 8

a Variation in power factor and THD with change in load and DC load current for case-I. b Variation in power factor and THD with change in load and DC load current for case-II

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4 Conclusion

Two schemes CSPWM and SPWM are reported for the same converter for rectification and inversion operation. The scheme using rectification with CSPWM and inversion with SPWM exhibit remarkable advantages such as high power factor, less DC link voltage stabilization period, and low THDs. Compared to this scheme second scheme (rectification and inversion both using SPWM) is less efficient. The detail simulation studies are carried out to show the comparison and effectiveness of the schemes.