Hybrid Switched-Capacitor Three-Phase Direct AC-AC Converter with Adjustable Output Voltage

Abstract

A switched-capacitor (SC) three-phase direct ac/ac converter is presented in this paper. It includes an additional inductor and two SC cells for each phase. Due to the introduction of the inductor, the output voltage can be adjusted. The proposed converter operates at a fixed switching frequency. One of the features of this topology is that the voltage stresses across the switches and capacitors equal half of the high-side voltage. In addition, the self-balancing capability of capacitor voltages and a simple modulation strategy are other characteristics. The main advantage of the proposed converter is the employment of unidirectional switches (a single MOSFET), which avoids the commutation problems in the bidirectional switches. A detailed description of the operation principle, quantitative analysis, and design considerations for the proposed converter is provided. Eventually, a prototype with 55 V/220 V and 3 kW is designed to demonstrate the feasibility and validity of the proposed converter.

1. Introduction

As the penetration of distributed renewable energy like photovoltaic and wind power expands, power quality concerns, including voltage swell/sag and voltage fluctuations, are attracting increasing attention [1]. Moreover, the growth, diversity, and sensitivity of loads also impose higher requirements on power quality [2]. Transformers, as commonly used devices in distribution networks, can achieve voltage adjustment between the power grid and equipment. If electrical isolation is not necessary, autotransformers are often employed to supply three-phase voltage to the loads. These devices have disadvantages such as high cost, large size, saturation, and high inrush current [3]. Furthermore, poor controllability and slow dynamic response fail to meet the voltage stability requirements of sensitive loads [4]. Therefore, as a key piece of equipment for renewable energy generation and utilization, the power electronic converter plays a vital role in resolving the above problems. The ac/ac converters, as an important branch of power electronic converters, are widely applied in industrial and commercial fields. The initial ac/ac conversion was performed by the employment of thyristor power converters, which can regulate the output voltage by implementing the phase angle control on the input voltage [5]. Nevertheless, these converters present some notable drawbacks, such as low voltage gain, poor harmonic performance and low efficiency [6,7]. In order to avoid these disadvantages of the thyristor power converters, a large number of PWM ac/ac converters have been proposed. These PWM ac/ac converters, as alternatives to transformers/autotransformers, can be generally divided into three categories: the indirect ac/ac converters [8,9,10,11], matrix converters [12,13,14,15] and the direct ac/ac converters [16,17,18,19]. The indirect ac/ac converter is a two-stage power converter, which requires a dc link to decouple the input and output. Therefore, this converter can adjust both the amplitude and frequency of the voltage. However, the dc link increases the volume and maintenance requirements of the converter. Consequently, in applications where only voltage amplitude adjustment is required, the benefits of the indirect converters are not significant. Matrix converters can regulate both the voltage amplitude and frequency simultaneously, but they usually exhibit obvious drawbacks such as complex modulation strategies, low voltage gain and input current THD [20,21,22]. Due to the absence of a dc link, the direct ac/ac converter is a single-stage conversion that has the advantages of compact size, low cost, high efficiency, and high power density. This makes it more attractive for applications that only require adjusting the voltage amplitude. The buck, buck-boost, and Cuk converters proposed in [18,19,23] have the characteristics of simple circuits and high efficiency. Nevertheless, due to the adoption of bidirectional switches, the components in the circuit may suffer from overvoltage stress, which can significantly degrade the reliability of these converters. Although the Z-source converters could achieve high voltage gain, they still have commutation issues owing to the employment of bidirectional switches [24,25,26].

The switched-capacitor converters (SCCs) were originally proposed for dc/dc conversion in low-voltage and low-power applications [27,28]. Subsequently, a variety of topologies have been applied in dc/dc, dc/ac and ac/dc. As most SCCs do not incorporate inductive components and only employ switches and capacitors, they present advantages such as simple structure, compact size, and high efficiency. Therefore, the SCCs have attracted widespread attention, and some applications have already benefited from them. The equivalent circuit models were developed in references [29,30,31] to facilitate the description and analysis of SCC behaviors. Furthermore, several publications have discussed the impact of circuit parameters on SCCs, which can help to improve the performance of SCCs [32,33,34]. Recently, the SC principle was introduced into the direct ac/ac converters. Reference [35] presents a single-phase direct ac/ac converter, which consists of two SC legs and can achieve a voltage conversion ratio of 1/2 or 2. It is characterized by the employment of unidirectional switches, differential connection and low-voltage stress across the components. Reference [36] proposes another non-differential bidirectional SC ac/ac converter composed of one SC and four bidirectional switches, which achieves the same voltage conversion ratio as reference [35]. The SCCs in the aforementioned references exhibit a fixed voltage conversion ratio. By introducing magnetic components, reference [37] develops a hybrid boost SCC that can adjust the output voltage by varying the duty cycle. A SC three-phase ac/ac converter was proposed in reference [38], which is derived from reference [36]. It consists of three modules, each containing 3 capacitors and 4 bidirectional switches. The modules can be connected in either a wye or delta configuration. Reference [39] presents another SC three-phase ac/ac converter with an open-delta configuration. Compared to reference [38], it achieves a one-third reduction in component count. According to reference [35], a reduced switch count SC three-phase ac/ac converter was reported in reference [40]. Due to the adoption of the differential structure, the introduced dc component enables the employment of unidirectional switches, which reduces the number of switches compared to references [38,39]. In summary, the results from references [35,36,37,38,39,40] are promising and demonstrate that the SC ac/ac converter can provide a new and effective solution for replacing traditional autotransformers, particularly in scenarios where only voltage amplitude regulation is required. However, the SC three-phase ac/ac converters with adjustable output voltage have not yet been reported.

This paper presents an SC three-phase direct ac/ac converter. An important characteristic of the proposed converter is the differential connection, which introduces dc components across all capacitors and switches. Due to no negative voltages across the capacitors and switches, unidirectional switches can be employed in the converter. Without bidirectional switches, the converter requires only a simple modulation strategy to avoid commutation issues. Furthermore, the switches and capacitors in this converter only withstand low voltage stresses. The capacitors can achieve self-balanced voltages. On account of the inclusion of a small magnetic component, the converter can realize a controllable output voltage by varying the duty cycle.

2. Description of the Proposed Three-Phase Direct AC-AC Converter

2.1. Topology Description and PWM Modulation Strategy

The proposed topology consists of three modules with a wye connection. The input voltages (v_A, v_B and v_C) are connected at points 2, 5, and 8, and the load voltages (v_R, v_S and v_T) are available at points 1, 4, and 7. Each phase is represented by one module. For instance, phase A is denoted by module A as illustrated in Figure 1a. Each module is composed of an input inductor (L_in) and two symmetrical switched capacitor cells (2 switched capacitors, 4 output capacitors and 8 switches). Therefore, the entire converter has 3 input inductors, 18 capacitors (C₁~C₁₈) and 24 switches (S₁~S₂₄). Owing to the lack of available paths for the current, direct ac/ac converters usually suffer from commutation problems, which will lead to voltage spikes across the components [41]. Hence, complex modulation strategies or snubber circuits are required to overcome this problem. Due to the absence of bidirectional switches in the proposed converter, this converter only needs a simple PWM modulation strategy to avoid the commutation problems. Consequently, the employed modulation strategy is shown in Figure 1b, in which switches S_even and S_odd are driven in a complementary manner during one switching period. Besides, a dead time is needed to prevent the shoot-through issue. Regardless of the direction of the current, there is always a current path in the converter, which can improve the reliability of this converter. Figure 1c shows the simplified symbol to denote a module.

2.2. Operation Principle

The proposed converter has the same three operational stages for each module in a switching period. Therefore, the analysis made here is only for module A during the positive half-cycle of the input voltage, which is shown in Figure 2. For thFFe negative half-cycle, module A presents the same operational stages except for the opposite current direction. The operational stages are described as follows.

Stage I (0 < t < DT_s) starts when S₂, S₄, S₆ and S₈ are in the on-state while S₁, S₃, S₅ and S₇ are in off-state. The input inductor L_in is directly connected to the input voltage v_A and stores the energy. The capacitor C₁ is in parallel connection with C₃. Similarly, the capacitor C₄ is connected in parallel with C₅. Capacitors C₂ and C₆ provide energy to the load during the whole DT_s interval. Switches S₂, S₄, S₆ and S₈ are turned-off by the end of stage I.

Stage II (DT_s < t < T_s) starts when S₁, S₃, S₅ and S₇ are in on-state while S₂, S₄, S₆ and S₈ are in off-state. The input inductor L releases the energy. The capacitor C₁ transfers the energy to C₂ and the load. The capacitor C₄ is charged by C₆. As capacitor C₃ has been discharging the energy in stage I, it will be charged during this stage. Likewise, capacitor C₅ will discharge the energy in this stage. Switches S₁, S₃, S₅ and S₇ are turned off at the end of stage II.

In order to prevent the shoot-through problem, it is crucial to add an appropriate dead time, denoted as stage III, between the above two stages. If the input inductor current is positive, the body diodes of S₁, S₃, and S₈ can provide the circulating path for the inductor current as shown in Figure 2c. In the same way, the body diodes of S₄, S₅, and S₇ can conduct the negative inductor current as well, which is illustrated in Figure 2d. One switching period consists of the above stages.

2.3. Operation Characteristic

By observing Figure 1a, it can be seen that the middle part of each module is a boost converter, connected with two SC cells. If parasitic parameters are ignored, the theoretical voltage gain of module A can be obtained by the combination of the voltage gains of the boost converter and two SC cells. The voltage gain of the boost converter is 1/(1 − D) and capacitors C₂ and C₆ are connected in series with C₃ and C₅ separately. Consequently, the voltage gain of module A is represented by (1). The other two modules have the same voltage gain.

$$G_A={\displaystyle \frac{v_{13}}{v_A}}={\displaystyle \frac{2}{1-D}}$$

(1)

Considering the duty cycle D = 0.5, the input and output voltages of each module are shown in Figure 3, where V_max is the maximum value of the output voltage v₁₃. For module A, the voltage v₁₃ is applied to capacitors C₂, C₃, C₅ and C₆. Therefore, Equations (2) and (3) can be achieved.

$$v_{c2}+v_{c3}-v_{c5}-v_{c6}=v_{13}$$

(2)

$$v_{c2}+v_{c3}+v_{c5}+v_{c6}=V_{\mathit{max}}$$

(3)

As mentioned previously, the capacitor C₁ will be connected to capacitors C₂ and C₃, respectively, within a switching period, and similarly, the capacitor C₄ will be connected to capacitors C₅ and C₆, respectively, during the same switching period. In other words, the switched capacitor C₁ can maintain the voltage balance across C₂ and C₃, while C₄ can keep the voltage balance across C₅ and C₆. Therefore, the total capacitor voltages C₁, C₂, and C₃ are equal, and the capacitor voltages C₄, C₅, and C₆ are equal too. The operation principle of module A can also apply to modules B and C. Adding Equations (2) and (3), Equation (4) can be obtained. Subtracting Equation (2) from (3), Equation (5) can be obtained.

$$v_{c1}=v_{c2}=v_{c3}={\displaystyle \frac{1}{4}}{V}_{\mathit{max}}+{\displaystyle \frac{1}{4}}{v}_{13}$$

(4)

$$v_{c4}=v_{c5}=v_{c6}={\displaystyle \frac{1}{4}}{V}_{\mathit{max}}-{\displaystyle \frac{1}{4}}{v}_{13}$$

(5)

As can be seen from Equation (4), each capacitor consists of an ac component v₁₃/4 and a dc component V_max/4. Moreover, capacitors C₁, C₂, and C₃ are in phase with the input voltage v_A. Their maximum values are equal to V_max/2, which is another advantage of the proposed converter. In the same way, capacitor voltages C₄, C₅, and C₆ have the same features, but they are out of phase with input voltage v_A as described in Equation (5). The capacitor voltages of modules B and C are the same as those of module A, except they are phase-shifted by −120° and +120° with respect to v_A, respectively, as shown in Figure 3c. All switches present the same shape as their corresponding capacitor voltages with the maximum value V_max/2, but they are high-frequency quantities. The voltage waveforms of the switches S₁, S₂, S₃ and S₄ in module A are illustrated in Figure 3d.

2.4. Module Configuration

In order to maintain the differential characteristic between the input and output, the three modules can only present a wye configuration. However, the three-phase load can be connected through a delta or wye connection. Therefore, there are two possible configurations (wye-delta and wye-wye) for the proposed converter. Different module-load connections lead to different voltage phasor configurations. Considering D = 0.5, the voltage gain and phase shift between the input and output voltages are analyzed for each configuration. The detailed results are listed in Figure 4.

3. Quantitative Analysis

3.1. Operational Modes of the Proposed Three-Phase Converter

According to the charging or discharging capacitor current, the SC cell can be categorized into three operational modes: no charge (NC), partial charge (PC), and complete charge (CC) [30,31]. The CC mode indicates that the capacitor will complete the entire charging or discharging process, which leads to a high current and thereby reduces the efficiency. Hence, the CC mode is not recommended. In contrast, there is a low constant capacitor current value in NC mode, which can help improve the efficiency. Nevertheless, a large capacitor or high switching frequency is required in this mode, which will increase the costs. Capacitors are only partially charged in the PC mode. Compared to the NC mode, the PC mode demonstrates similar advantages while requiring relatively lower capacitance and switching frequency. Therefore, the PC mode is a good choice for the SC cell [36]. The charging/discharging capacitor current will approach zero within a time interval of 5τ [36,42]. τ is the time constant of the SC cell, which is represented by Equation (8). To make the proposed converter operate in PC mode, the charging or discharging time interval must be less than 5τ, yielding.

$$D{T}_s\le 5\tau$$

(6)

$$(1-D)T_s\le 5\tau$$

(7)

$$\tau =(2R_{DS(on)}+R_{ESR})C$$

(8)

where R_DS(on) is the conduction resistance of one MOSFET switch, R_ESR is the equivalent series resistance (ESR) of a capacitor, and C is the capacitance for each capacitor utilized in the converter (all equal capacitors).

3.2. Equivalent Circuit

Under the condition of a balanced three-phase load, a three-phase equivalent circuit model seen by the load side with a wye-wye connection between the module and the load is established in Figure 5. This model includes the input equivalent inductors L_eq, the equivalent capacitances C_eq, the equivalent resistances R_eq and the output loads Z_o. For analytical convenience, the duty cycle D is set to 0.5. The input line-to-neutral voltage is denoted by three voltage sources v_ip in wye configuration, which is four times the input line-to-neutral voltage from the grid side. The resistances R_eq represent the conduction losses caused by SCs in each module during the charging and discharging processes [33]. Within each switching period, the voltage across the capacitor can be regarded as approximately constant.

Since the proposed converter shares the same operational process as the dc/dc SCC, its equivalent resistance R_eq is similar to that reported in previous studies [32,33]. As mentioned earlier, for module A, capacitor C₁ is connected in parallel with C₃ and C₂ during DT_s and (1 − D)T_s, respectively. Therefore, capacitor C₁ can be equivalent to the value of DC₁ and (1 − D)C₁ in parallel with capacitors C₃ and C₂, respectively [36]. Likewise, capacitor C₄ also has a value of DC₄ and (1 − D)C₄ to be connected to C₅ and C₆ separately. Considering D = 0.5 and all equal capacitors, the equivalent capacitance C_eq for each module can be obtained in this manner. The parameters of the three-phase equivalent circuit seen by the load side are listed as follows:

$$R_{eq}={\displaystyle \frac{1}{2f_{s}C}}{\displaystyle \frac{(e^{\frac{1}{f_s\tau }}-1)}{(1-e^{\frac{D}{f_s\tau }}-e^{\frac{1-D}{f_s\tau }}+e^{\frac{1}{f_s\tau }})}}$$

(9)

$$L_{eq}=16L_{in}$$

(10)

$$C_{eq}={\displaystyle \frac{3C}{8}}$$

(11)

where f_s is the switching frequency. To facilitate the analysis of different load connections, the proposed three-phase equivalent circuit can be simplified into a single-phase one as shown in Figure 6, where this single-phase circuit handles only one-third of the total output power. Its parameters can be calculated by using the equations mentioned above. The input voltage source is represented by v_is, the conduction losses are denoted by R_s, the reactive power in the circuit is represented by L_s and C_s, and the output resistance is denoted by Z_os. Their specific values are listed in

Table 1. Parameters for the single-phase equivalent circuit.

Connections (Module-Load)	vis	Ls	Cs	Rs	Zos
wye-wye	vip	Leq	Ceq	Req	Zo
wye-delta	vip	Leq	Ceq	Req	Zo/3

.

The analysis of the equivalent circuit illustrated in Figure 6 allows the derivation of key parameters, which are crucial for designing the proposed converter and will be discussed in the next section. These parameters also provide essential insights into the performance and characteristics of the proposed converter.

3.3. Comparisons with Other SC Three-Phase AC-AC Converters

Table 2. Comparisons between the proposed converter and other converters.

Topology	Proposed Converter	Ref. [38]	Ref. [39]	Ref. [40]
Inductor count	1	0	0	0
Adoption of bidirectional switches	No	Yes	Yes	No
Switch count	24	24	16	12
Frequency	Fixed	Fixed	Fixed	Fixed
Capacitor count	18	9	6	9
Voltage stresses	Vp/2	Vp/2	Vp/2	Vp
Voltage regulation	Yes	No	No	No
Voltage gain	2/(1 − D)	2 or 0.5	2 or 0.5	2 or 0.5
Complexity of modulation	Low	Low	Low	Low

lists some feature comparisons between the proposed converter and other converters. Due to the adoption of an additional inductor, the proposed converter can regulate the output voltage compared to other topologies. The voltage gain of each module in the proposed converter is twice that of those reported in [38,39] at the expense of more capacitors and switches (D = 0.5). The maximum voltage of the corresponding topology on the high-voltage side is represented by V_p. It can be observed from Table 2 that this paper shares the same advantage of low voltage stresses across the components with [38,39]. Moreover, another advantage of the proposed converter is the employment of unidirectional switches, which avoids the commutation problems of bidirectional switches and improves the reliability.

4. Design Considerations of the Proposed Converter

Based on the above analysis, the selection guidelines for the key parameters for the proposed converter are provided. The main specifications are as follows: output power P_o = 3 kW, input line-to-neutral voltage V_in = 55 V, output line-to-neutral voltage V_out = 220 V, line frequency f = 50 Hz, input power factor PF > 0.92, and duty cycle D = 0.5.

4.1. Input Inductor Selection

The input inductor is used to reduce the ripple of the input current. In each module, the voltage across the inductor is equal to the input voltage during stage I. Therefore, the inductance L_in can be expressed as follows:

$$L_{in}={\displaystyle \frac{D{V}_{in}}{\Delta i_{in}{f}_s}}$$

(12)

where Δi_in is the input current ripple. Considering D = 0.5, the minimum inductance can be represented by the following:

$$L_{in}\ge {\displaystyle \frac{3V_{in}^2}{2P_o{f}_s\Delta i_{in}\%}}$$

(13)

where Δi_in% is the ratio of Δi_in to the input current, which is taken the value of 0.2 in this paper.

4.2. Capacitance Calculation

Neglecting the conduction losses, the input reactive power of the proposed converter, as shown in Figure 6, can be expressed as follows:

$$Q_i=6\pi f{L}_s{I}_{is}^2-6\pi f{V}_{os}^2{C}_s$$

(14)

Furthermore, the input power factor PF is represented by the following:

$$P{F}_i={\displaystyle \frac{P_i}{\sqrt{P_i^2+Q_i^2}}}$$

(15)

Based on the above equations and the requirement of the power factor, the maximum capacitance C_s can be obtained by the following:

$$C_s=C_{eq}\le {\displaystyle \frac{1}{6\pi f{V}_{os}^2}}(6\pi f{L}_s{I}_{is}^2+P_o{\displaystyle \frac{\sqrt{1-P{F}_i^2}}{P{F}_i}})$$

(16)

Replacing Equation (11) into (16), the maximum value for capacitors C₁ to C₁₈ can be expressed as follows:

$$C={\displaystyle \frac{8}{3}}{C}_{eq}\le {\displaystyle \frac{4}{9\pi f{V}_{os}^2}}(6\pi f{L}_s{I}_{is}^2+P_o{\displaystyle \frac{\sqrt{1-P{F}_i^2}}{P{F}_i}})$$

(17)

In addition, the charging or discharging time interval must be less than 5τ to ensure that the SC cells can operate in PC mode, as mentioned earlier. Considering D = 0.5 and substituting Equation (8) into (6), the minimum capacitance can be represented by the following:

$$C\ge {\displaystyle \frac{0.1}{(2R_{DS(on)}+R_{ESR})f_s}}$$

(18)

4.3. Switches and Switching Frequency

In order to obtain a low conduction resistance, a MOSFET IPDD60R037CM8, which has an R_DS(on) value of 37 mΩ, was selected to implement the unidirectional switches. By substituting the values of R_DS(on), R_ESR and C into Equation (18), the minimum switching frequency that ensures the converter operates in PC mode can be obtained by the following:

$$f_{s\min }\ge {\displaystyle \frac{0.1}{(2R_{DS(on)}+R_{ESR})C}}$$

(19)

Furthermore, the feasibility of the switching frequency f_s in practical implementation should also be considered. Therefore, the switching frequency f_s was selected as 50 kHz.

5. Results and Discussion

To demonstrate the previous analysis and operation of the proposed converter, a 3 kW prototype is built as shown in Figure 7. The specific experimental parameters of the prototype, which are based on the methodology in Section 3, are summarized in

Table 3. Main specifications and components of the prototype.

Parameters	Quantity	Values
Input line-to-neutral voltage (vA, vB, vC)	-	55 Vrms
Line frequency f	-	50 Hz
Output power Po	-	3000 W
Output line-to-neutral voltage (vR, vS, vT)	-	220 Vrms
Switching frequency fS	-	50 kHz
Input inductor Lin	1	150 μH
Capacitors (C1~C18)	18	60 μF/4 mΩ
MOSFETs (S1~S24)	24	37 mΩ IPDD60R037CM8

.

The experiments were conducted with D close to 0.5, and the input was fed by three-phase ac power. Figure 8 shows waveforms of the three line-to-neutral input voltages (v_A, v_B, and v_C) and one output voltage (v_R) for the resistive load connected in a wye configuration. The output voltage v_R is in phase with the input voltage v_A. Furthermore, the amplitude of v_R is nearly four times that of v_A at D = 0.5, which validates the voltage phase analysis in Figure 4. The line-to-neutral input voltages (v_A, v_B, and v_C) and line-to-line output voltage (v_RS) waveforms for the resistive load with delta connection are illustrated in Figure 9. As described in Figure 4, there is a 30° phase-shift between the v_RS and v_A, and the amplitude of v_RS is $4\sqrt{3}$ times that of v_A.

The line-to-neutral output voltages v_R, v_S, and v_T for the resistive load with a wye connection (48 Ω per-phase) and line-to-neutral output current i_R are shown in Figure 10. It can be seen that i_R is in phase with v_R under the resistive load. Moreover, the output voltages v_R, v_S, and v_T are phase-shifted by 120° from each other.

Figure 11 illustrates the line-to-neutral output current i_R and line-to-neutral output voltages v_R, v_S, and v_T for the inductive load (0.61 power factor) with a wye connection. As expected, the current i_R under the inductive load lags behind the output voltage v_R. It has been proven that the proposed converter can also work normally under an inductive load.

The voltage waveforms for capacitors C₁, C₂ and C₃ in module A are shown in Figure 12. It can be observed that the capacitor voltages are approximately equal to half of the peak value of the output voltage v_R, which is one of the advantages of this converter. Figure 13 shows the capacitor voltages of C₁, C₇, and C₁₃. Since the capacitors are in different modules, their voltages have a phase shift of 120°. The voltages across S₁ and S₂ in module A are illustrated in Figure 14. Similarly, the voltage waveforms of switches exhibit the same characteristics as the corresponding capacitor voltages.

The line-to-neutral output current i_T and line-to-neutral output voltages v_R, v_S, and v_T for an unbalanced load are shown in Figure 15. Although one module handles more power than the other two (1 kW for two modules and 2 kW for one module), the line-to-neutral output voltages v_R, v_S, and v_T can still be maintained balanced. This is due to the self-balancing capability of capacitor voltages.

The efficiency of the proposed topology is shown in Figure 16. Figure 16 demonstrates that the peak efficiency is 90.42%. Additionally, when the converter reaches its rated power, the corresponding efficiency is 87.79%. It can be observed that the efficiency curves follow a parabolic-like trend, where the efficiency is lower at light loads, increases with the output power until it peaks, and then gradually decreases with a further increase in power.

The output voltage THD of v_R is measured under load variations as shown in Figure 17. As can be seen from Figure 17, the output voltage THD of v_R is less than 1% over a wide range. The output voltage THD is 0.86% at rated power, demonstrating that the proposed topology has a good output voltage waveform.

The experimental output voltage regulation curve under load variations can be seen in Figure 18. The voltage is 99.7% under no-load conditions. As the output power increases, the output voltage regulation shows a decreasing trend. The output voltage is 93.9% at rated power.

The input current THDi curve under resistive load is shown in Figure 19. As illustrated in Figure 19, at a power below 2.4 kW, the THDi is higher than 6%. At rated power, the THDi is 5.6%.

The above experimental results fully demonstrate the voltage regulation capability of this converter, and future research may explore the integration of this converter with traditional power equipment.

6. Conclusions

This paper proposes a three-phase ac/ac converter based on the SC principle. The main features of this converter are a simple modulation strategy, low voltage stresses across the components, and capacitor voltage self-balancing capability. Because of the adoption of an input inductor, this converter can adjust the output voltage. Furthermore, the employment of unidirectional switches overcomes the commutation issues of bidirectional switches. The operation principle of the converter is analyzed. Subsequently, the quantitative analysis and design considerations are conducted. At last, the experimental results verify the theoretical analysis and its advantages. The proposed converter is suitable as an alternative to the conventional three-phase autotransformer.