Introduction
Over the recent years, single-phase dynamic voltage restorer (DVR) has been used widely to deal with power quality issues for sensitive loads. Single-phase AC-AC converters are exploited as effective series compensators in the DVR systems to compensate voltage sags and swells. The most used AC-AC converters applicable in voltage conditioners are indirect AC-AC converters, direct and indirect matrix converters, and direct PWM AC-AC converters. However, all these converters suffer from some drawbacks. Indirect AC-AC converters require costly battery banks and huge super-capacitors to supply dc sources [1]. Matrix converters utilize a high number of semiconductors devices with complex commutation and provide bounded voltage gain with a maximum of 0.86 [2], [3]. Direct PWM AC-AC converters provide slight current distortion, simple control, simple structure, small parameters, high efficiency, and improved power factor [4], [5]. However, most of them are not able to operate in buck-boost mode simultaneously and suffer from discontinuous input current.
To overcome the aforementioned drawbacks, traditional single-phase Z-source AC-AC converters were proposed in [6], [7]. Although they can both boost and buck input voltage, they suffer from discrete input current, unshared ground between input and output. Quasi Z-source AC-AC converter is introduced in [8] to solve unshared ground, discontinuous input current issues. Also, voltage stress across capacitors decreased dramatically compared to traditional single-phase Z-source AC-AC converters. In [9], a safe commutation strategy has been applied to a family of quasi Z-source AC-AC converters to remove voltage overshoots across switches without requiring snubber circuits, which causes conduction losses reduction along with efficiency improvement. To reduce the number of passive components, a modified quasi Z-source AC-AC converter is proposed in [10]. It provides high-quality output voltage without utilizing output LC filters.
Recently, magnetically coupled inductors have been used in various types of impedance source topologies. In dc-dc impedance source converters, coupled inductors are applied into impedance networks to provide high voltage boost ability with the small duty cycle of converters [11]. Meanwhile, coupled inductors based impedance source inverters appeal to researchers more and more because of their high voltage boost ability with high modulation ratio and low stress across the semiconductors devices [12]–[19]. Single-phase Z-source AC-AC converters based on coupled inductors have been introduced to control ac voltage by adjusting their turn ratio besides the duty cycle of converters. In other words, coupled inductors give more options to impedance source AC-AC converters to regulate the ac output voltage. For instance, a transformer type of quasi Z-source AC-AC converter is presented in [20] to enhance voltage gain by increasing the turn ratio of the transformer along with the duty cycle changing. In order to reduce the size of the converter, an AC-AC impedance source converter based on
In this paper, a single-phase AC-AC converter based on coupled inductors is presented. The proposed converter has a lower number of passive components compared to similar counterparts. Its impedance source network structure produces high voltage gain with high-quality waveforms without input and output LC filter. Also, coupled inductors help the converter to attain desired voltage gain with small conducting pulses in a safe commutation strategy. Consequently, the proposed converter offers the turn ratio of coupled inductors as an extra control variable along with the converter’s duty cycle. Also, output voltage shares the same ground with input which can reverse and maintain phase angle well. Circuit analysis and operation theory are detailed in the rest of the paper, and experimental tests are performed on a laboratory prototype to verify the theoretical results. In addition, a dynamic voltage restorer based on the proposed converter is presented to compensate voltage sag and voltage swell. Simulation results are provided to show the ability of the proposed converter in voltage sag and swell compensation. Furthermore, the power loss analysis of the proposed converter is then presented and finally, the conclusion of the paper is included.
Proposed Magnetic Coupled Single-Phase AC-AC Converter
A. Circuit Description
The overview of the proposed AC-AC converter is shown in Fig. 1. The presented structure consists of ac input voltage, impedance network, and resistive load. Two bidirectional switches have been embedded in the impedance network. Impedance network includes input inductor (L), two capacitors (C1 and C2), two bidirectional switches (
B. Operation Principle
Due to dead time and overlap of switches and their speed limitation practically, inductors currents and capacitors voltages might be changed instantly and produce voltage and current spikes across the power switches, which can destroy them. As a result, a snubber circuit must be implemented to provide voltage and current laws of Kirchhoff and to prevent these destructive spikes. However, snubber circuits increase the cost and complexity of the converter and decrease its efficiency. Hence, a safe commutation strategy has been applied to the proposed converter to prevent voltage and current spikes.
Fig. 2 demonstrates the switching pattern of safe commutation strategy for the proposed converter in “boost/buck” “in phase/out of phase” modes. Accordingly, by considering the dead time situation in ideal switches, the switching pattern is formed by input voltage’s polarity:
is positive, and converter operates in “in-phase” mode,\text{V}_{\mathrm {i}} is fully turned on to provide the current path, and\text{S}_{\mathrm {1i}} is turned on for dead time issue.\text{S}_{\mathrm {2j}} is positive, and the converter performs in “in-phase” mode,\text{V}_{\mathrm {i}} and\text{S}_{\mathrm {2i}} are turned on to provide the current path, and\text{S}_{\mathrm {2j}} is fully turned on to prevent the commutation problem throughout the dead time duration.\text{S}_{\mathrm {1i}} is negative, and converter operates in “in-phase” mode,\text{V}_{\mathrm {i}} is conducting as the current path, and\text{S}_{\mathrm {1j}} is turned on because of dead time condition.\text{S}_{\mathrm {2i}} is negative, and converter performs in “in-phase” mode,\text{V}_{\mathrm {i}} and\text{S}_{\mathrm {2i}} is turned on to provide the current path and\text{S}_{\mathrm {2j}} is fully turned on for dead time situation.\text{S}_{\mathrm {1j}} is positive, and converter operates in “out-of-phase” mode,\text{V}_{\mathrm {i}} and\text{S}_{\mathrm {1i}} are switched on to provide the current path and\text{S}_{\mathrm {1j}} is turned on to prevent the commutation problem throughout the dead time.\text{S}_{\mathrm {2i}} is positive, and converter performs in “out-of-phase” mode.\text{V}_{\mathrm {i}} and\text{S}_{\mathrm {2i}} are switched on as the current path and\text{S}_{\mathrm {2j}} is turned on to prevent the commutation problem throughout the dead time.\text{S}_{\mathrm {1j}} is negative, and converter operates in “out-of-phase” mode,\text{V}_{\mathrm {i}} are conducting as the current path and\text{S}_{\mathrm {1i}}~\text{S}_{\mathrm {1j}} is switched on due to the dead time condition.\text{S}_{\mathrm {2j}} is negative, and converter operates in “out-of-phase” mode,\text{V}_{\mathrm {i}} and\text{S}_{\mathrm {2i}} are switched on as the current path and\text{S}_{\mathrm {2j}} is switched on to prevent commutation problem.\text{S}_{\mathrm {1i}}
Switching pattern of safe commutation strategy for boost/buck (a) in-phase mode, and (b) out-of-phase mode.
Fig. 3 illustrates the switching signals and key waveforms of the presented converter when it operates in “in-phase” mode when input voltage is positive. It can be seen that
Key waveforms of the proposed converter’s components in boost in-phase mode when Vi > 0.
Operation intervals of the proposed converter in boost in-phase mode when Vi > 0, (a): state I, (b): commutation mode when
Operation intervals of the proposed converter in buck out-of-phase mode when Vi > 0, (a): state I, (b): commutation mode when
Fig. 5 illustrates operating intervals of the proposed converter in buck out-of-phase mode when the input voltage and the output voltage are positive and negative, respectively. Fig. 5 (a) depicts state I when switch
C. Circuit Analysis
Following assumptions have been considered for the proposed circuit analysis: (1) It operates in continuous conduction mode (CCM). (2) The parasitic resistance of input inductor (
Equivalent circuits of the proposed converter in one switching period, (a). dT interval (state I), (b). (1-d) T interval (state II).
Also, Fig. 6 (b) shows the equivalent circuit of state II with the time interval of (1-d)T. In this mode, S2 is conducting while S1 turns off. The stored energy in the input and coupled-inductors are released to the capacitors as in equation (2), as shown at the bottom of the next page.
According to (1) and (2), the average equations in one switching period are obtained as:
In the steady-state, the average value of the voltage/current across the inductor and coupled inductors/capacitors is zero, so by considering zero for equations (3), as shown at the bottom of the next page,
the peak of


Fig. 7 illustrates output voltage gain versus duty cycle with the various turn ratios of coupled inductors. Clearly, the proposed converter follows a different characteristic curve compared to previous single-phase AC-AC impedance source converters. It can be seen that in boost in-phase mode, the proposed converter provides higher voltage gain with lower conducting pulse width by increasing transformer’s turn ratio. Furthermore, there are two operation regions based on the duty cycle range. For
Relationship between voltage gain and duty cycle of the introduced converter with various N.
Circuit Design of the Proposed Converter
Initially, the magnetic components of the proposed converter should be designed. Accordingly, the inductors parameters of the proposed converter are determined according to their maximum voltage and current ripple in dT interval. Regarding Fig. 5 (a), in the state I, the maximum voltage of L and \begin{align*} \begin{cases} \\ L=\frac {\left |{ V_{imax}-V_{C2max} }\right |dT}{\Delta I_{i}} \\ Lm=\frac {\left |{ \frac {V_{C1}max}{N+1} }\right |dT}{\Delta I_{L_{m}}} \\ \\ \end{cases}\tag{7}\end{align*}
Where \begin{align*} \begin{cases} \\ C_{1}=\frac {\left |{ \frac {1}{N+1}I_{L_{m}} }\right |dT}{\Delta v_{C1}} \\ C_{2}=\frac {\left |{ \mathrm {Ii-Io} }\right |dT}{\Delta v_{C2}} \\ \\ \end{cases}\tag{9}\end{align*}
If
Where, \begin{align*} \begin{cases} \\ V_{S1,max}=\frac {\sqrt {2} (N+1)}{N\left ({d-1 }\right)+2d-1}v_{i} \\ V_{S2,max}=\frac {\sqrt {2}}{N\left ({d-1 }\right)+2d-1}v_{i} \\ \\ \end{cases}\tag{11}\end{align*}
The peak and RMS current stress of the bidirectional switches can be obtained as (12) and (13), respectively.\begin{align*} \begin{cases} \\ I_{S1,max}=\frac {\sqrt {2}~P_{O}}{dv_{i}} \\ I_{S2,max}=\frac {\sqrt {2} (N+1)P_{O}}{dv_{i}} \\ \\ \end{cases} \tag{12}\\ \begin{cases} \\ I_{S1,rms}=\frac {\left ({\sqrt {1-d} }\right)P_{O}}{dv_{i}} \\ I_{S2,rms}=\frac {\sqrt {d} (N+1)P_{O}}{dv_{i}} \\ \\ \end{cases}\tag{13}\end{align*}
Application of the Proposed Converter as Dynamic Voltage Restorer
Fig. 8 depicts a dynamic voltage restorer based on the proposed single-phase ac-ac converter. The line voltage Vi is linked to the input of the proposed converter in shunt. Also, the output of the converter is connected in series with the line voltage and load by an injection transformer. Since the injection transformer ratio is 1:1, the compensation voltage
A. Bypass Mode
In this mode, the line voltage has the normal amount without voltage sag/swell faults. In this state, the proposed converter operates with the duty cycle of 1 and the output voltage of 0, when the bidirectional switch S1 is entirely switched off, while the bidirectional switch S2 conducts fully.
B. Boost In-Phase Mode
This state starts when the voltage sag happens and the line voltage is lower than the determined amount. In this mode the proposed topology performs in boost in-phase state. From (5) and Fig. 8, by applying KVL we can get \begin{equation*} v_{o}=v_{i}+v_{com}=v_{i}+\left({\frac {d}{N\left ({d-1 }\right)+2d-1}}\right)v_{i}\tag{14}\end{equation*}
C. Buck Out-of-Phase Mode
This mode starts when the voltage swell occurs and the line voltage is higher than the determined value. In this state the proposed converter operates in buck out—of-phase mode. Again from (5) and Fig. 8, by applying KVL we can obtain \begin{equation*} v_{o}=v_{i}-v_{com}=v_{i}-\left({\frac {d}{N\left ({1-d }\right)-2d+1}}\right)v_{i}\tag{15}\end{equation*}
By assuming N=2, the load voltage can be obtained as:\begin{equation*} v_{o}=\left({\frac {5d-3}{4d-3}}\right)v_{i}\tag{16}\end{equation*}
From (16), the load voltage gain versus the switching duty ratio is shown in Fig. 9. According to Fig. 9, the presented DVR can compensate up to over 50% voltage sag for D = (0.75, 1). Additionally, the proposed DVR can compensate voltage swell when D = [0, 0.6).
Comparative Study
Since the voltage characteristic of the proposed converter is different from other topologies, its voltage gain is compared to that in modified quasi Z-source single-phase AC-AC converters, which offer the same voltage characteristic curve. Fig. 10 shows that the proposed converter provides higher voltage gain with a lower conducting pulse width (higher d and lower 1-d) than the modified single-phase quasi Z-source AC-AC converter in the boost mode. Compared to the asymmetrical
Relationship between voltage gain and duty cycle of the modified single-phase qZS AC-AC converter and introduced converter with various N.
The proposed converter exploited a different structure of the windings compared with the converter in [27]. This diversity brings some advantages to the proposed converter. In [27], the voltage gain can be increased by lowering the transformer’s turn ratio. However, it can be a plus, especially in terms of the size; the converter suffers from the narrow range of the turn ratio. In other words, the practical range of the turn ratio for the high voltage requirement is 1.5 to 1.3, which can be a limitation for the design issue. Because by lowering the turn number in practice, distortion in output waveforms will occur. To solve this problem, the proposed converter attains high voltage boost/buck ability by increasing the turns from 1 to more than 6 in the design process according to the required voltage compensating in voltage sag/swell problems. Unlike conventional z-source and
In addition, the proposed converter exploits a reduced number of passive components compared to topologies in [20]–[24]. Likewise, the proposed converter utilizes a lower number of active components in comparison to the modified trans-Z-source AC-AC converter [23]. In this regard, a detailed comparison between the proposed topology and similar single-phase direct AC-AC converters is provided in Table 1 to 4. This investigation encompasses the operational, structural, and performance considerations of the proposed single-phase direct AC-AC converter as well as other similar ones. Accordingly, the number of active and passive components including inductors (
Evaluation and Results
To further investigate the correctness of the proposed topology, the circuit configuration was simulated in MATLAB environment. Then, the simulation results were compared to experimental ones obtained from a laboratory prototype presented in Fig.11. The setup specification is brought in table 5. Particularly, the safe-commutation strategy is performed by utilizing the digital signal processor (DSP-TMS320F28335). Two bidirectional switches have been used to implement the safe commutation strategy. Notably, each bidirectional switch consists of two back to back Power MOSFETs. High frequency coupled inductors have been designed with the turns number of ten and twenty for the primary and secondary sides, respectively. Also, each circuit component is chosen for the circuit design and its mathematical analyses described in previous sections. In addition, both of the simulations and experimentations were conducted in the same conditions. Accordingly, the experimental results of the proposed converter supplying a resistive load (
Boost operating mode behavior of the proposed converter includes: (a) input waveforms, (b) output waveforms, (c) input vs output, (d) S1, and (e) S2.
In this state, the duty cycle is assumed 0.9. The input voltage waveform is depicted in Fig.12.a. According to Table 5 and the obtained mathematical equations, the peak value of the output voltage, input current, and output current are approximately 150 V, 2.8 A, and 1.8 A, respectively verified by experimental waveforms in Fig. 12.a-c. This case (boost factor of 1.5) can be a suitable range for the 50% voltage sag compensation, applicable in dynamic voltage restorer. To achieve this boost factor by the modified single-phase AC-AC quasi Z-source converter, the duty cycle must be considered as d = 0.75. In other words, the pulse width of the
On the other hand, the operation of the proposed converter supplying a purely resistive load (
Buck mode results of the proposed converter include: (a) input and output voltage waveform, (b) input waveforms, and (c) output waveforms.
The output voltage and input current THD of the proposed converter in boost and buck operation modes are presented in Table 6. It is clear that in buck operation mode, the output voltage and input current THDs are about 2.67% and 45.85%. Also, in boost operation mode, the output voltage and input current THDs are about 2.37% and 3.20%. As a result, the proposed converter offers high-quality voltage and current waveforms without utilizing input and output filters. In addition, Table 7 compares the input current THD of the proposed topology versus the similar converters. From this table, it can be found that in the boost mode, the presented topology has a lower input current THD than the other converters, while providing it in the reasonable value in the buck mode.
Fig. 14 shows the simulation waveforms of the proposed converter with non-linear load for input frequency of 60 Hz, RMS input voltage of 73 V, duty cycle of 0.9, and transformer turn ratio of 2. A single-phase diode bridge rectifier with output capacitor of 470
Simulation waveforms of the proposed converter with non-linear load: (a) input and (b) output voltages, (c) input current.
Fig. 15 and Fig. 16 show the simulation results of the voltage sag and voltage swell compensation by utilizing the DVR based on the proposed converter. A proportional integral (PI) controller has been used to control the load voltage. According to Fig. 15, when 60% voltage sag occurs in line voltage at interval time of 0.2–0.3 sec, the load voltage is well compensated to a demanded value of 110
Simulation waveforms of the proposed DVR at 60% voltage sag compensation: (a) line voltage, (b) compensation voltage, (c) load voltage.
Simulation waveforms of the proposed DVR at 60% voltage swell compensation: (a) line voltage, (b) compensation voltage, (c) load voltage.
Power Loss Analysis
The main power losses of the proposed converter come from the magnetic losses, semiconductors losses, and ESR of the capacitors. The magnetic losses include copper and core losses. Based on [30], the copper losses of the inductor and coupled inductors can be calculated from (17) and (18), respectively.\begin{align*} P_{cu-L}=&\frac {\rho \left ({MLT }\right)I_{i}^{2}}{W_{A}K_{u}} \tag{17}\\ P_{cu-CI}=&\frac {\rho \left ({MLT }\right)n_{1}^{2}{(I_{Np}+{NI}_{Ns})}^{2}}{W_{A}K_{u}}\tag{18}\end{align*}
\begin{equation*} P_{fe}=K_{fe}B_{max}^{\beta }A_{c}l_{m}\tag{19}\end{equation*}
\begin{equation*} P_{M-tot}=P_{cu-L}+P_{cu-CI}+P_{fe}\tag{20}\end{equation*}
Moreover, semiconductor loss itself comprises switching and conduction loss, whereas the former is originated from the time delay in turning ON or OFF of the device and the latter is caused due to the parasitic resistance of the device [31]. Also, switching loss is caused by an inherent behavior of all switching devices that can be calculated by:\begin{align*} P_{s,on}=&\frac {1}{6}f_{s} V_{off-state} I_{on-state} t_{on} \tag{21}\\ P_{s,off}=&\frac {1}{6}f_{s} V_{off-state} I_{on-state} t_{off}\tag{22}\end{align*}
\begin{equation*} P_{sw} =\sum \limits _{j=1}^{N_{switch}} {\left ({{P_{sj,on} +P_{sj,off}} }\right)}\tag{23}\end{equation*}
In case of conduction loss, each switching device is modeled by a parasitic resistance and parasitic voltage source (acting against the current flow), then:\begin{align*} \begin{cases} P_{con-SW} =V_{on}^{sw}.i_{av-SW} +R_{on}^{sw}.i_{rms-SW}^{2} \\ P_{con-D} =V_{on}^{D}.i_{av-D} +R_{on}^{D}.i_{rms-D}^{2} \\ \end{cases}\tag{24}\end{align*}
\begin{equation*} P_{con}^{\,total} =\sum {(P_{con-SW} +P_{con-D})}\tag{25}\end{equation*}
Fig. 17 compares the efficiency of the proposed topology in various output power with similar AC-AC converters. For fair comparison, the same conditions are assumed for the converters. The parasitic resistance of the input inductor, coupled inductors, and equivalent series resistance of capacitors equal to
Fig. 18 (a) and (b) show the power loss distribution of the proposed converter at an output power of 300W. It can be found that the bidirectional switches have lower power losses than other components, which proves the low conducting and switching losses of the converter. While, in the previous AC-AC converters, the significant power loss comes from semiconductors.
Loss charts in the proposed topology at an output power of 300 W: (a) distribution and (b) circuit components losses.
Conclusion
A novel single-phase direct AC-AC converter has been presented in this paper. The proposed converter inherits all the advantages of the conventional single-phase impedance source AC-AC converters as follows: (1). It can operate in boost in-phase mode or buck-boost out of phase mode. (2). Output voltage shares the same ground with the input voltage; hence it can maintain or reverse-phase angle well with the input voltage. (3). It can be utilized as a dynamic voltage restorer to compensate voltage sags or voltage swells without using any dc storage such as battery or capacitor banks. A unique impedance network has been applied to the proposed converter to connect the ac source to the load directly. Thanks to the proposed impedance structure, it does not require passive components as input and output filters which leads to reducing in the size and cost of the converter. Magnetically coupled inductors have been employed in the proposed converter to provide high voltage boost ability with a small conducting duration of the switches by adjusting its turn ratio. As a result, the proposed converter offers high efficiency, low conducting losses and a high lifetime of semiconductors devices. A safe commutation strategy has been applied for the proposed converter to remove voltage or current spikes across the switches without needing any snubber circuits. Furthermore, the input current of the proposed converter is continuous, so it does not suffer from non-sinusoidal waveforms, high THD, high peak, and inrush current. Finally, the performance of the proposed converter has been testified within experimental results.