A Single-Phase Buck-Boost Matrix Converter with Low Switching Stresses

Ashraf, Naveed; Izhar, Tahir; Abbas, Ghulam

doi:https://doi.org/10.1155/2019/6893546

Mathematical Problems in Engineering

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Abstract Introduction Conclusion Data Availability Conflicts of Interest References Copyright Related Articles

Research Article | Open Access

Volume 2019 | Article ID 6893546 | https://doi.org/10.1155/2019/6893546

A Single-Phase Buck-Boost Matrix Converter with Low Switching Stresses

Naveed Ashraf,¹Tahir Izhar,¹and Ghulam Abbas²

Academic Editor: Luis M. López-Ochoa

Received17 Jul 2018

Revised09 Jan 2019

Accepted20 Jan 2019

Published20 Feb 2019

Abstract

The suggested single-phase ac-to-ac matrix converter operated with inverting and noninverting characteristics may solve the grid voltage swell and sag problem in power distribution system, respectively. It is also employed as a direct frequency changer for domestic induction heating. The output voltage is regulated through duty cycle control of high frequency direct PWM (DPWM) and indirect PWM (IDPWM) switching devices. The DPWM control switches control the switching states of IDPWM switching devices. The inverting and noninverting characteristics are achieved with low voltage stresses and hence low dv/dt across the high and low frequency-controlled switches. This reduces their voltage rating and losses. The high voltage overshoot problem in frequency step-up operation is also analyzed. The sliding mode (SM) controller is employed to solve this problem. Pulse selective approach determines the power quality of load voltage. The validity of the mathematically computed values is carried out by modelling the proposed topology in MATLAB/Simulink environment and through hardware results.

1. Introduction

Single-phase direct ac-to-ac converters with bipolar voltage gain are widely employed as radio frequency induction heating, induction motor driver, and voltage sag and swell compensator. Traditionally, ac voltage and frequency regulation is achieved through indirect dual ac-to-ac converters [1–4]. They have high losses, poor conversation efficiency, and low reliability. Direct ac-to-ac converters [5–7] have simple circuit arrangement, small size, low cost, and high conversion efficiency and are easy to control due to single stage power conversion.

The power quality supplied at consumer ends is becoming poor day by day due to rapid, uneven spreading of loads and transient generated by heavy loads [8, 9]. Buck-boost ac voltage controllers regulate the dynamic variation of the load voltage. Voltage sags and swells degrade the load performance and power quality. They are normally analyzed in terms of their phase jump, depth, and duration. The research in [10] shows their existence and impact in power system. The end users have to use power conditioning units for their better power quality, safety, and performance. Dynamic voltage restorers (DVR) as discussed in [11, 12] are used to solve the problem of voltage sags in power distribution system. The DVR based on FACTS devices as in [13–15] stabilizes the disturbances in grid voltage without considering the problems of generated harmonic and power quality.

Various direct ac-to-ac voltage regulation techniques through PWM control are discussed in [16]. They are implemented by replacing the unidirectional switching devices with bidirectional devices. They can only operate as buck regulator [17] or boost regulator [18] but not both. The ac-to-ac voltage controller in [19, 20] only solves the voltage sag or swell disturbance but not both due to unipolar voltage gain. The ac power converters with z-source arrangements having buck-boost characteristics are introduced in [21–23]. They only solve the voltage sag problem up to 25% without power storage device. An ac-to-ac power conversion technique based on interphase conversion is developed in [24] to improve the power system disturbances. The solution of voltage sag problem is accomplished by getting ac power from other healthy phases. The analysis in [25] solves the problem of unidirectional voltage gain at the cost of hybrid three-phase transformer. The problems of poor power quality are solved with z-source [26] and quasi-z-source [27] topologies. The current rating of power switches has to be increased due to conduction of high current during short-through period. The current and voltage surges are generated due to short circuiting of source or filtering capacitor through switching action that can damage the switching devices. The coupled inductors as in [28] solve the problems of voltage and current surges, but it increases the size and cost of the switching converters. An ac-to-ac converter with common grounding and bipolar voltage gain is proposed in [29]. It operates in noninverting buck and inverting buck-boost mode to compensate the grid voltage sag and swell problem. It cannot be operated as noninverting boost operation. Its high frequency switches operate at high voltage stresses. It is implemented with eight IGBTs having high switching and conduction losses. It cannot be used as a direct frequency changer (DFC) to control the load frequency.

The body diode of MOSFET limits its operating speed as it has poor reverse characteristics. This problem is solved in [30, 31] with series connection of fast recovery diode that prevents its forward biasing. In its inverting mode, two high frequency switches are operated with the voltage stresses of + . Its low frequency switches operate at and . A buck-boost matrix converter (MC) with common input and output ground is proposed in [32]. Its noninverting operation is implemented with four high frequency switches with the voltage stresses of + resulting in high dv/dt. Its low frequency switches operate at and . High voltage and current surges are generated in the frequency boost operation as they depend upon the voltage stresses. The reverse voltage is developed across the fast recovery diode as MOSFET is on in IDPWM control, and across MOSFET as fast recovery diode is forward biased in DPWM control. The high voltage stresses increase the voltage rating of the diode and MOSFETs. This increases the forward voltage, on-state resistance of diode and MOSFET that result in high conduction losses. The total harmonic distortion (THD) of the output voltage is very high due to nonsinusoidal nature of the output voltage.

In this proposed research, a single-phase MC is implemented with both noninverting and inverting characteristics with low voltage stresses across the switching devices, thus having low losses. SM controller is developed to solve the problem of high voltage overshoot and poor power quality in frequency step-up operation. Pulse selected approach is used to find out the harmonics contents of the load voltage. The analysis of the proposed research is validated through the MATLAB/Simulink environment and hardware results.

2. Operating Modes of the Proposed Converter

The proposed converter in [33] can also be implemented with noninverting and inverting buck-boost characteristics having low voltage stresses and losses. Each switch is the series combination of a MOSFET “M” and diode “”. Its operation in noninverting and inverting modes with positive and negative input voltage is detailed below.

2.1. Noninverting Buck-Boost Mode with Positive Input

In this operating mode, the buck-boost of the output voltage is accomplished by varying the duty cycle via the control of switching devices , and , as DPWM and IDPWM control, respectively. The switch is switched at the low output frequency. The remaining switches , , and remain off in this operating mode, thus offering no conduction and switching losses. The current conduction paths for the turn on and turn off period of high frequency switching devices are highlighted in Figures 1(a) and 1(b), respectively. PWM average switching model with duty cycle “d” for positive input voltage based on the analysis in [29] is obtained as follows.All state variables of (1) in steady state condition are distributed at fundamental frequency (low frequency); their derivative terms can be ignored to find their voltage and current transfer ratios. That is to say,

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

2.2. Noninverting Buck-Boost Mode with Negative Input

The direct high frequency PWM switching of and with indirect switching of switches and controls the output voltage for negative input voltage. Inductor is charged and its stored energy is released to load during turn on and turn off intervals, respectively. In this operating mode, the low frequency switch remains in conduction state. The three remaining switches , , and are not required to be turned on. The current paths through which the inductor is charged and power is transferred to load are highlighted in Figures 1(c) and 1(d), respectively. Noninverting averaging PWM model with duty ratio “d” for negative input voltage is realized as follows.

The voltage and currents gains are computed by solving (4) as their derivative terms are ignored in steady state condition.

2.3. Inverting Buck-Boost Mode with Positive Input

The inverting output with buck-boost characteristics is accomplished via the PWM switching of switches as direct and , as indirect control. Such switching stores energy in inductor and then transfers it to load through the current conduction paths as shown in Figures 1(e) and 1(f), respectively. From the remaining four switches, switch is switched at low load frequency and there is no role of switches , , and in this mode of operation. Inverting averaging PWM model with duty ratio “d” for positive input voltage can be realized as follows.

The variable of the right-hand sides of (7) can be ignored in steady state due to their low variation to determine the voltage and current transfer ratios or gains. That is to say,

2.4. Inverting Buck-Boost Mode with Negative Input

The negative input is converted into positive output via the switching action of one low frequency switch and four high frequency switches , and , as direct and indirect PWM control, respectively. The remaining switches , , and maintain their off state throughout the operation of this mode. Figures 1(g) and 1(h) show the charging and discharging path of inductor current. Inverting averaging PWM model with duty ratio “d” for negative input voltage is realized as follows.

Equation (10) in steady state is realized to find the voltage and current gains. That is to say,

The operating modes from “A” to “D” can be used to operate the proposed converter as an ac voltage controller and a direct frequency changer with noninverting and inverting buck-boost characteristics. Next section explores the operation of the proposed converter as an ac voltage controller and direct frequency changer in detail.

3. Operation as a Voltage and Frequency Controller

The operation of the proposed converter can be realized as a voltage controller and direct frequency changer by operating it in noninverting and inverting modes. The detail of operation as ac voltage controller and direct frequency changer is explored below with the help of their corresponding switching sequences.

3.1. Matrix Converter as a Noninverting and Inverting AC Voltage Controller

The noninverting operation of proposed converter as an ac voltage controller is obtained by switching the proposed converter in mode “A” and “B” alternatively. Its inverting operation requires the alternative operation of mode “C” and “D”. The situation is depicted in Figures 2(a) and 2(b) indicating the gating sequence of noninverting and inverting buck-boost characteristics with two direct and two indirect PWM control switches.

(a)

(b)

3.2. Matrix Converter as a Frequency Changer

The proposed converter can also be implemented for step change of the load frequency. The frequency buck and boost operation are discussed separately with the help of switching waveforms.

(1) Frequency Buck Operation. In frequency buck operation, the output frequency is considered to be one-half of the input frequency. So, it operates in mode “A” to “D”, respectively, as the required output is noninverted and inverted for first and second cycles of the input voltage as shown in Figure 3.

(2) Frequency Boost Operation. In frequency boost operation, the output frequency is considered two times as that of input frequency. The required output is obtained with the operation of the proposed converter in modes “A”, “C”, “D”, and “B”, respectively, as shown in Figure 4.

The analysis from Figures 2–4 shows that the low frequency switches have less control effort as compared to high frequency switches. So RMS and average currents through low frequency switches are low than that of high frequency switching devices. Section 4 compares the performance parameters of the proposed converter with the existing converters in detail.

4. Performance Evaluation of the Proposed Converter

The performance of the proposed converter is evaluated and compared with the existing matrix converters in terms of voltage stresses and power losses.

4.1. Voltage Stresses

Voltages are developed across the series connected diode once a high frequency switch is controlled in IDPWM manners as diode is reverse biased. Reverse voltage is developed across the MOSFET in DPWM control as diodes is forward biased. The instantaneous voltage stresses across the low and high frequency-controlled switches are computed in (13), where and are the input and output voltage, respectively.The instantaneous voltage across the switching devices of converters in [30, 31] for inverting and in [32] for noninverting modes is computed in (14) and (15), respectively.

So, the voltage stresses across the MOSFET and series diode in the proposed converter are low and hence they have low dv/dt problem.

4.2. Power Losses

The losses of switching devices come from switching and conduction losses.

(1) Switching Losses. The controlled switch is a series combination of MOSFET and fast recovery diode. The switching loss of MOSFET depends on switched voltage, current, switching frequency, output capacitance, and rise and fall time. The switching losses of diodes depend on their reverse recovery characteristics. There are no switching losses of diode in a DPWM controlled switch as diode cathode has negative voltage [32]. In the same way, there is no switching loss of MOSFET of IDPWM controlled switch as it is always in conduction state to ensure the continuous inductor current. The switching losses of proposed converter and converters in [31, 32] are the same and computed in (16) and (17), respectively. (2) Conduction Losses. The conduction losses of low switching frequency devices depend on forward bias voltage of fast recovery diode (), its on-state resistance (), on-state resistance of MOSFET (), and magnitude of conducted current () as current conducted by each switch is the same as the inductor. The conduction losses are computed by considering the sinusoidal output current [29] in the form . The conduction losses of the proposed converter and the converter in [31] are computed in (18) and (19), respectively. where , , and represent the forward voltage, forward resistance of high voltage diode, and forward resistance of MOSFET, respectively.

The conduction losses of the proposed converter are low as on-state voltage drops, and resistances of low voltage rating devices are lower than that of high voltage rating devices as evident from (18) and (19).

5. Parameter Design of the Proposed Converter

This section involves the design of inductor, semiconductor switching devices, and input and output capacitors on the basis of the maximum voltage and current stresses as discussed in [29]. The maximum inductor current ignoring ripple during buck-boost operation for constant output power and input voltage can be realized as follows.

The peak-to-peak allowable ripples of the state variables of (1) can be expressed by (21) and (22) where is the switching period. The required value of inductor to hold the above peak-to-peak ripple in inductor current is computed as follows.

The maximum inductor current including ripple component is computed as follows.

Similarly, the required value of output capacitance to hold the peak-to-peak ripple of output voltage is realized as follows.

The values of inductor and capacitors are designed by knowing the values of the input voltage, switching frequency, maximum voltage gain, load impedance, peak-to-peak value of inductor current () and output ripple ().

The input capacitance is based on the discontinuous duration of the input current and is computed as follows.

Output capacitance depends on the output ripples and is realized as follows.

6. Harmonic Analysis

The output voltage waveform in variable frequency operation is nonsinusoidal due to generated harmonics. A pulse selective approach as discussed in [34, 35] is employed to compute the harmonic contents analytically by decomposing a complex nonsinusoidal to its parent sinusoidal waveforms. As the frequency of the output voltage is changed in discrete steps, a step change of 25 Hz is taken for harmonic analysis. The resulted computed harmonics coefficients are summarized in Tables 1 and 2. Through the analysis of Table 1, a generalized close form is developed in (33).

7. Sliding Mode Controller

The sliding mode (SM) control is a more suitable feedback approach in direct ac-to-ac converters having inherent variable structure. The buck-boost system is a nonminimum phase system with respect to output voltage regulation [36]. The output voltage is indirectly controlled through the control of inductor current. The output voltage regulation through inductor current control based on sliding control theory, ensures the fast and dynamic response. The basic key is to design a SM control law that ensures the arrival of the system’s states at equilibrium point. The instantaneous inductor current in the proposed converter is unidirectional for positive and negative input voltage. The error signal is generated by comparing it with the reference current; i.e.,

The error and its derivative are selected as state variables and , which are rewritten as follows.

7.1. Sliding Surface

The following switching function is selected to govern the switching states of the proposed converter:where “S” is the trajectory of the state variable. The error signal is selected as sliding surface to generate the desire control (gating) signals for high frequency switching devices of the proposed converter.

The existence of the SM control requires the test of transversality, reachability, and equivalent control condition.

(1) Transversality Condition. It describes the controllability of the system ensuring that system dynamics are affected from the SM control [37]. It means that control variable should be in the derivative form of the sliding surface. That is to say,

(2) Reachability Condition. It describes the ability of the system to reach the sliding surface [37].

(3) Equivalent Control Condition. It determines the local stability of the system and ensures that system remains in the sliding surface once it enters the sliding surface [37]; i.e.,

The required conditions to test the existence of the SM control are tested for all operating modes of the proposed converter and are tabulated in Table 3, ensuring the transversality, reachability, and equivalent control condition.

8. Simulation Results

The proposed converter is simulated in MATLAB/Simulink environment to find the voltage stresses across the high and low frequency-controlled switches. The noninverting and inverting modes are simulated as a frequency controller with the duty ratio of 0.5. Typical circuit parameter values used in simulation circuit as tabulated in Table 4 are computed by using (29), (31), and (32) and by considering their reactive power rating.

8.1. Frequency Buck Operation

The frequency step-down operation with output frequency of 25 Hz is accomplished by operating the proposed converter in noninverting and inverting mode in consecutive cycles of the input voltage waveform. Figure 5 shows the voltage stresses across the high and low frequency switching devices in noninverting and inverting mode.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

It is evident from Figure 5 that voltage stresses across the high frequency switches (D_S2), (D_S3) and (D_S5), (D_S6) are restricted to and , respectively. The voltage stresses across the low frequency switches , , , and are . But the voltage stresses in inverting mode of [29–31] are raised to a high value of .

8.2. Frequency Boost Operation

In frequency step-up operation, the output is forced to be changed from inverting to noninverting and vice versa to get the required output. This action generates the high voltage surges in the output voltage that can cause the high voltage stresses and high dv/dt across the switching devices. Figures 6 and 7 explore these problems for proposed and converter in [31], respectively.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(a)

(b)

(c)

(d)

(e)

(f)

It is clear from the Figures 6 and 7 that maximum voltage stresses of high frequency switching devices in proposed converter are and . But in [31], they are increased to and hence they have the problem of high dv/dt.

The nonsinusoidal nature of the output voltage degrades power quality of the output voltage. SM feedback controller is designed to improve the power quality and to reduce the voltage overshoot problem across the switching devices as shown in Figures 8 and 9, respectively.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

9. Experimental Setup

An experimental setup is constructed to validate the simulation results (see Figure 10). The hardware consists of eight MOSFETs (IRF840) as power electronic switches along with RHG3040 fast recovery diodes. The filter capacitor at the input side and the output side is 1 μF and 4.7 μF, respectively, while the coil has an inductance of 1 mH. Low frequency switching signals are generated by using STM microcontroller. The synchronization of the low frequency control signals with input voltage is accomplished with zero-crossing detection of the input voltage. Two complementary high frequency PWM switching signals are generated with SM controller. The gate driving circuits are implemented with hybrid chips (EXB840) with isolated dc supplies. All the experimental results are recorded using Rigol (DS1052E) oscilloscope in which red color represents inputs and blue color represents outputs.

As already remarked, the proposed converter may be employed as an ac voltage controller. Figure 11 shows the output of the proposed converter in noninverting and inverting operating modes with a voltage gain of 0.5.

(a)

(b)

Similarly, the proposed converter may be employed as a direct frequency changer (DFC). Figure 12 shows the conversion of 50 Hz input frequency to 25 Hz and 100 Hz output frequency, respectively. High surges in output voltage result in high surges in input current (see Figure 13).

(a)

(b)

As can be observed from Figures 12 and 13, in open-loop, once the output is changed from noninverting to inverting and vice versa, it generates the surges in output voltage and input current. This problem may result in failure of the switching devices. The surges in output voltage and input current can be eliminated by introducing SM controller into the loop. Figure 14 shows the output voltage and input current of the closed loop system in frequency boost operation of 100 Hz. The experimental results indicate that the generated surges have been successfully eliminated by the controller with regulated output voltages. The total harmonic distortion in the input current is found to be less than 3%.

(a)

(b)

10. Conclusion

This research is focused on a direct ac-to-ac buck-boost matrix converter having bipolar voltage gain to cope with the power system disturbances such as voltage sag and swell by ensuring low voltage stresses and hence low dv/dt across low and high frequency-controlled switches This results in low conduction losses due to their low forward voltage and low on-state resistance. The proposed converter can also change the load frequency in variable frequency drive system and radio frequency induction heating. The power quality of the output voltage in variable frequency mode is analyzed by finding the harmonic contents through pulse selective approach. The problem of generated voltage and current surges in frequency boost operation is analyzed. A robust sliding mode controller is designed to suppress these high surges of output voltage and input current. This also improves the power quality of the output voltage with reduced THD and improved power factor. The dynamic stability including transversality, reachability, and equivalent control condition of the proposed converter is verified for its all operating modes. The detailed simulation and experimental results validate the performance of the proposed controlled converter.

Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

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Copyright © 2019 Naveed Ashraf et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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