A Single-Phase AC-AC Power Electronic Transformer Without Bulky Energy Storage Elements

Abstract

Compared with the line-frequency transformer (LFT), the emerging power electronic transformers (PETs) have gained wide concerns due to the significant merits of higher power density, higher reliability, more flexibility, and multiple functions. However, the need for bulky energy storage elements, multi-stage power conversion and reduced conversion efficiency, and the intrinsic twice-frequency pulsating power issue are the main disadvantages of the conventional single-phase PETs. To overcome the above shortcomings of conventional single-phase PETs, this paper develops a matrix-type single-phase AC-AC PET without bulky energy storage elements. The proposed PET consists of a line-frequency commutated rectifier, a half-bridge LLC resonant converter with a fixed switching frequency, a boost converter, and a line-frequency commutated inverter. The LLC operates efficiently with unity voltage gain and acts as a high-frequency isolated DC transformer (DCX). The boost converter provides AC output voltage regulation function and the line-frequency commutated inverter unfolds the output voltage of the boost converter to generate the sinusoidal AC output voltage. As a result, high power density, reduced power conversion stages, direct AC-AC power conversion without twice-frequency pulsating power, high conversion efficiency, and high reliability are achieved. The experimental results on a 1kW PET prototype show that sinusoidal input current and output voltage, ZVS of the LLC stage, and output voltage regulation capability are realized. The experimental results verify the correctness and feasibility of the presented methods.

1. Introduction

Traditional line-frequency transformers (LFT), valued for their simple, reliable design, have long been responsible for voltage transformation and isolation in power grids. However, their bulkiness, limited controllability, and fault/harmonic propagation issues now critically influence modern grid advancements [1,2]. With the development of power electronics technology, the power electronic transformer (PET), which employs power electronic converters and high-frequency transformers (HFTs) to achieve power transmission and electrical isolation, has garnered significant research attention [3,4,5]. The product of the core cross-section area A_e and winding window area A_w, which represents the physical size of the transformer, satisfies the following relationship:

$$A_w{A}_e\propto {\displaystyle \frac{P}{J_{rms}{B}_{m}f}}$$

(1)

where f denotes the operating frequency, and P represents the rated power of the transformer. Without increasing the winding current density J_rms and maximum core flux density B_m (and therefore degrading the efficiency), a higher operating frequency can significantly reduce the size of the transformer. The comparison of volume and weight between an LFT and an HFT with the same rated power is shown in

Table 1. Comparison between single-phase LFT and HFT.

Parameters	LF Transformer	HF Transformer
Power rating	1 kW	1 kW
Operating frequency	50 Hz	65 kHz
Magnetic Core	silicon steel	PC95 ferrite
Volume	160 × 150 × 150 mm	50 × 42 × 50 mm
Weight	12.5 kg	0.7 kg

.

It is clear that the use of high-frequency transformers has significantly reduced its volume and weight, and has great potential for application where there are strict requirements on power density. Meanwhile, the use of fully controllable semiconductor devices such as IGBT and MOSFET realizes multifunctionality. As a smart power distribution device integrating voltage transformation, power quality control, and power flow management, PETs demonstrate adaptability across different power generation, distribution, and consumption scenarios, with applications in electric traction, renewable energy microgrids, smart distribution grids, and other fields [6,7,8].

Generally, PET employs AC-DC rectifiers, isolated DC-DC converters, and DC-AC inverter stages to achieve AC-AC conversion. The stages are decoupled by one or more DC-links with large-capacity energy storage components. These topologies offer enhanced controllability and a DC bus port [9,10]. However, multi-stage power conversion leads to reduced efficiency, while bulky energy storage elements on the DC-link limit power density. Additionally, electrolytic capacitors have a short lifespan and worsen when working at high temperatures [11]. This issue constrains the PET lifespan and reliability. In single-phase applications, the DC-link capacitor also suffers from twice-frequency power pulsation issues [12]. To achieve high conversion efficiency, high power density, and high reliability in PETs, matrix-type PET topologies utilizing direct AC-AC conversion have gained increasing research interest. These topologies feature single-stage power conversion, offering higher efficiency compared to multi-stage conversion; eliminate large DC-link capacitors, enhancing power density; and replace electrolytic capacitors with film capacitors, while the latter has a longer lifespan and better temperature resistance so the reliability and lifespan of the system improved [13,14].

To enhance conversion efficiency, soft switching isolated converters, such as dual active bridge (DAB) converters [15] and resonant converters [16], have been applied to the PETs. In [17], a series resonant converter (SRC) was implemented in a single-stage AC-AC PET, achieving high efficiency. In [18], the authors proposed a single-stage PET based on DAB, demonstrating improved output voltage regulation than the SRC-base PET. To reduce the switch count and enhance the power density, a hybrid DAB converter, combining a full-bridge and a half-bridge, was introduced in [19]. In [20], a current-source SRC-based single-stage PET achieved zero-voltage switching (ZVS) for primary-side switches across a wide input voltage range. However, the use of an uncontrolled diode rectifier on the secondary side limited the bidirectional power flow. In [21], the authors applied an SRC operating near its resonance frequency in an AC-DC converter, achieving ZVS in both the HV side and LV side, and obtaining a stable gain independent of the load.

This paper proposes a single-phase matrix-type AC-AC PET without bulky energy storage elements. Unlike a multi-level single-phase PET, the input full-bridge rectifier and the output full-bridge inverter operate under the line frequency, the switching losses are reduced, and it is possible to replace these semiconductor devices with a smaller capacity, resulting in a smaller total chip area. Furthermore, replacing the electrolytic capacitors with film capacitors in the DC-link, to enhance the power density and reliability, avoids the problem of twice the line frequency. The LLC operates near the resonant frequency with a unit voltage gain, functioning as a high-frequency isolated DC transformer (DCX) [22]. The DCX-LLC converter in the proposed topology could achieve ZVS, reducing switching losses, and allowing a higher switching frequency and a smaller volume of the heat sink. The increased switching frequency is conducive to reducing the size of passive components such as transformers and filters, and further improving the power density. The boost converter regulates the AC output voltage, providing flexible voltage regulation capability.

The rest of this paper is organized as follows. Section 2 details the topology and operational principles of the proposed single-phase PET. Section 3 presents the ZVS analysis and control strategy. Experimental results validating the proposed method and topology are provided in Section 4. Finally, the conclusion of this paper is drawn in Section 5.

2. Topology and Operating Principles of the Proposed PET

2.1. Proposed Topology

As illustrated in Figure 1, the proposed PET topology comprises a grid-side full-bridge rectifier, a half-bridge LLC resonant converter, a boost converter, and a load-side full-bridge inverter. The grid-side full-bridge rectifier (S1–S4) and load-side full-bridge inverter (S11–S14) operate at a line frequency, while the switches of the traditional AC-DC rectifiers and DC-AC inverters operate at high frequencies, resulting in high losses. L_i represents the input filter inductor, which improves the input current quality. C_r denotes the resonant capacitor, while L_m and L_r correspond to the magnetizing inductance and resonant inductance, respectively. T represents the high-frequency transformer with a turn ratio of n:1. The filter capacitor of the input rectifier is shared as the primary-side half-bridge capacitor of the resonant converter. Similarly, the filter capacitor of the output inverter serves dual functions as the boost converter’s filter capacitor. Both the leakage inductance L_r and magnetizing inductance L_m are integrated into the transformer T.

Due to the adoption of the matrix-type structure, the DC-link voltage is a fold sinusoidal voltage rather than a consent DC voltage and avoids the use of large-capacity electrolytic capacitors in the topology structure. C₁, C₂, C₃, C₄, and C_o serve as the filter capacitors for the HB-LLC and the Boost converter, respectively, and also functions as the input/output filter capacitor for the PET. All capacitors in the topology are film capacitors renowned for their long lifespan and small volume. Therefore, the electrolytic capacitor-free structure can enhance the potential reliability and power density of the system. Without large-capacity energy storage elements in the topology, the phase of the DC-link voltage on the primary side and the secondary side is almost the same, achieving transient energy balance between the power source and the load, and avoiding ripple power with the twice line frequency.

2.2. Operating Principles

Figure 2 shows the key waveforms of the proposed PET at line frequency timescale. The full bridges on the grid and load sides commutate according to the polarity of the input voltage. S1~S4 and S11~S14 operate with line frequency. When v_g > 0, S1, S4, S11, and S14 are conducting while S2, S3, S12, and S13 are turned off. When v_g < 0, the switch states reverse. The rectifier generates a half-cycle sinusoidal voltage for the primary DC-link, while the load side inverts the secondary DC-link’s half-cycle sinusoidal voltage into a sinusoidal output. The LLC resonant converter (S5, S7 and S6, S8) operates near the resonant frequency with a 50% duty cycle, producing an AC square-wave voltage with a sinusoidal envelope in the series resonant tank and generating a resonant current with a sinusoidal envelope. The converter achieves unity voltage gain at the primary sides and secondary sides. In the Boost* converter, S9 and S10 alternate conduction with specific duty cycles D_b (with S9), to control the secondary DC-link voltage and thereby regulate the output voltage. In a steady state, the PET approximately satisfy:

$$\left|v_g(t)\right|=v_{dc1}(t)=k{v}_{dc2}(t)=k{D}_b\left|v_o(t)\right|$$

(2)

where k is related to the transformer ratio n and the LLC resonant converter unity gain. The equivalent circuit of the proposed PET topology under unity gain is shown in Figure 3. From (2) and Figure 3, this topology enables transient energy balance between the source and load. Although large capacitance helps suppress voltage ripple, it introduces excessive input reactive power and reduces power density. Thus, the filter capacitor selection requires consideration between the DC-link voltage ripple, input power factor, and power density.

The LLC resonant converter exhibits two resonant frequencies. f_r (formed by L_r, C_r, and load) and f_m (determined by the transformer’s magnetizing inductance L_m) can be expressed as:

$$f_r={\displaystyle \frac{1}{2\pi \sqrt{L_r{C}_r}}}$$

(3)

$$f_m={\displaystyle \frac{1}{2\pi \sqrt{(L_r+L_m)C_r}}}$$

(4)

The LLC resonant converter in this PET operates at a switching frequency f_s slightly below f_r but above f_m. The key waveforms are shown in Figure 4. Different dead times between the primary and secondary bridge gate signals introduce phase shifts in resonant tank voltages, generating a small resonant current peak at the high-frequency transformer’s primary and secondary sides.

The half-cycle operational states of the resonant converter are illustrated in Figure 5a–j. At t0, energy transfers forward with C_r charging (Figure 5a). At t1, the secondary current i_p reverses the polarity, while the primary current reversal occurs later at t2 due to the magnetizing inductance current (Figure 5b,c). Turning off S1 and S3 enables body diode conduction through secondary MOSFET drain-to-source capacitance C_ds charging (Figure 5d,e). During t4–t5, a reverse voltage spans across to L_r, creating a current resonance peak (Figure 5f), causing primary current reversal and S6 body diode conduction after primary MOSFET capacitance charging (Figure 5g,h). ZVS is achieved when turning on S8 and S6 at t6 and t7, respectively (Figure 5i,j). And then enter the next cycle.

3. ZVS Analysis and Control Scheme of the Proposed PET

3.1. ZVS Analysis

Improving the overall efficiency of the system is one of the key research concerns for power electronic transformers. In the topology proposed in this paper, most of the losses come from the conduction losses of the MOSFETs and the switching losses of the high-frequency switches. Therefore, it is necessary to achieve soft switching for all devices on both the primary and secondary sides of the LLC converter as much as possible to enhance the efficiency of the power electronic transformer.

Typically, the LLC converter utilizes the magnetizing inductance current i_m to achieve soft switching of the switches. For instance, in the state shown in Figure 5b, turn off the S1 and S4 and turn on the S2 and S3. To achieve ZVS, the magnetizing inductance current should fully charge the drain-to-source capacitance C_oss of the MOSFET with Q_ossp within the dead time. Considering the DC-link voltage as:

$$v_g=V_{im}\left|\sin \left({\omega }_{i}t\right)\right|$$

(5)

Since f_s is much larger than f_m, let us assume that the magnetizing inductance is charged and discharged linearly within half a cycle. When the switch is switched, the magnetizing inductance current reaches its peak I_mp.

$$I_{mp}=V_{im}\left|\sin \left({\omega }_{i}t\right)\right|/8Lm{f}_s$$

(6)

At this moment, the ZVS condition of the switch is:

$$I_{mp}{T}_{dp}=(V_{im}{T}_{dp}|\sin ({\omega }_{i}t)|/8Lm{f}_s)>2Q_{ossp}=2C_{oss}{V}_{im}|\sin ({\omega }_{i}t)|$$

(7)

However, the capacitance C_ds of MOSFET is a nonlinear function of the voltage across its source and drain terminals:

$$C_{oss}=a/\sqrt{U_{im}|\sin ({\omega }_{i}t)|}+b$$

(8)

In the equation, a and b are specific parameters related to the MOSFET. Therefore, for determinate system parameters, the soft-switching condition varies with the DC-link. The lower the primary and secondary voltages, the larger the value of C_oss is (8), and therefore the more difficult it is to achieve the ZVS condition (7). In this case, to ensure that the ZVS condition is still met at a certain voltage, L_m is usually designed to be smaller. However, an overly small L_m will increase the reactive current on the resonant tank, increasing the conduction loss of the system. Thus, in this topology, by controlling the timing when the switch is turned on and off, the negative resonant current charges the drain-source capacitance, achieving a wider range of ZVS. As can be seen in Figure 3, compared to i_m, the resonant current peak near the switching point can provide a larger Q to charge the C_ds, making the ZVS condition (7) easier to achieve. Through the design of the resonant converter’s switching frequency, magnetizing inductance, and dead time_, the proposed control method can achieve a wider range of ZVS.

3.2. Control Scheme

In power electronic transformers, in order to accurately control the voltage and current waveforms of the system, it is necessary to dynamically obtain the phase information of the grid voltage. Therefore, a phase-locked loop (PLL) is used in this paper. As shown in Figure 6, the phase detector (PD) based on SOGI [23] compares the output phase θ with the input signal v_g in terms of the phase, generating an error voltage v_q corresponding to the phase difference between the two signals. The error voltage is through a PI controller (as a low-pass filter, LPF) to produce the frequency for the integrator (as a voltage-controlled oscillator, VCO). When there is a phase difference between the output and input signal, for example, the output phase leads to the input phase, the PD outputs a negative error v_q. Then, the frequency output by the PI controller is reduced, thereby reducing the leading phase. And a positive error v_q occurs when there is a phase lag until the phase difference is adjusted to 0. After obtaining the phase information of vg, the input rectifier S1, S2, S3, and S4 and the output inverter S11, S12, S13, and S14 will switch their states at the zero-crossing point, as shown in Figure 6.

The gain of power electronic transformers is determined by the resonant converter and the boost converter as shown in (2). The controller regulates the output v_o by adjusting the duty cycle of the Boost converter. The transfer function of the v_o the duty cycle D_b can be expressed as:

$${\left.{\displaystyle \frac{{\widehat{v}}_o}{{\widehat{D}}_b}}\right|}_{V_{dc2}}={\displaystyle \frac{D_b{V}_{dc2}(1-\frac{s{L}_b}{D_b^2{R}_L}) }{s^2{L}_b{C}_o+s{L}_b/R_L+D_b^2}}$$

(9)

Due to the presence of zero points on the right side of the plane in (9), the existence of non-minimum phase links will cause a reversal overshoot during control. In order to ensure that the controller bandwidth is sufficient to track the sinusoidal voltage and guarantee the stability of the control loop, additional compensation networks are always required. However, the DC-link voltage V_dc2 of the boost converter is time-varying during operation, which brings difficulties to the design. Thanks to the characteristic that the gain of the resonant converter and the boost converter is almost unaffected by the load condition, the system bandwidth can be reduced. As shown in Figure 6, the cut-off frequency of the feedback closed-loop for the RMS of the output voltage is very low. Therefore, the effect of the right-half-plane zero is weakened, and, for the purpose of enhancing the response to the input voltage and reference output voltage, a feedforward is added. When the input voltage or reference voltage changes, the feedforward will quickly calculate a D_b. Meanwhile, the feedback closed-loop will adjust the D_b within a few line frequency cycles, so that the RMS of the output voltage follows the given voltage. If the load changes, for example when the load becomes heavier, the RMS of the output voltage will decrease. The PI controller will reduce D_b to keep the output constant.

S9 and S10 alternate conduction with D_b. The LLC resonant converter (S5, S7 and S6, S8) operates with a constant frequency and a 50% duty cycle, and the primary and secondary sides use fixed different dead-time Tdp and Tds. The switched gate waveform modulation is shown in Figure 6.

4. Experimental Results

In this section, a 1kW PET prototype was developed and tested. The switching frequency of the LLC converter is 65 kHz, while 20 kHz is the Boost converter, achieving a balance between the smaller-sized passive components and the greater losses at a high switching frequency. Then, the resonant inductance (6.4 μH) and resonant capacitance (0.9 μF) are designed with (2). The filter is designed according to the ripple requirements, and the magnetizing inductance is set at 320 μH for the ZVS condition (7). In the 1kW PET prototype, a PQ5050 Core is used, as shown in Table 1. The prototype of the proposed PET is shown in Figure 7, and the system experimental parameters are presented in

Table 2. Parameters of the proposed PET.

Parameters	Value	Parameters	Value
Input voltage vg	220 Vrms 50 Hz	Inductance Li	220 μH
Output voltage vo	220 Vrms 50 Hz	Inductance Lr	6.4 μH
Turns ratio n	1.2	Inductance Lm	320 μH
Capacitance C1 C2	2 × 2.7 μF	Inductance Lb	470 μH
Capacitance C3 C4	2 × 2.7 μF	LLC frequency fs	65 kHz
Capacitance Co	3.3 μF	BOOST frequency fb	20 kHz
Capacitance Cr	0.9 μF	Power rating	1 kW

.

Figure 8 shows the input and output waveforms of the PET under the rated load and half-load conditions. The input and output voltages and currents are all smooth sinusoidal waves. Due to the filter capacitors on the bus of the system, the input current is slightly ahead of the input voltage, which is mainly caused by the capacitive reactive power of the bus capacitors. The power factor of the PET under-rated load was measured to be 0.99, with 3.52% THD of the input current and 1.56% of the output voltage. In summary, the proposed PET can generate a sinusoidal input current and a controllable output voltage.

Figure 9 shows the steady-state working waveforms of the LLC resonant converter under rated load and half-load conditions. As shown in Figure 9a,b, the primary rectifier and the secondary inverter operate according to the polarity of the input voltage and generate fold sine waves with the same phase on the DC-link. The high-frequency transformer and the primary current present a sinusoidal envelope in the fold sine wave voltage. Figure 9c,d are magnified views near the peak of the bus voltage. The resonant current is approximately sinusoidal, and its amplitude is related to the load. At the same time, there is a small negative resonant peak near the zero-crossing point, consistent with the previous statement in Figure 4.

The ZVS waveforms of the resonant converter are tested as shown in Figure 10. Figure 10a,b gives the overall waveforms of the gate-source voltage and drain-source voltage of the switch. Figure 10c,d are enlarged views near the peak of the drain-source voltage. The drain-source voltage u_ds of the MOSFET drops to 0 before the arrival of the switching signal u_gs. All switches achieve ZVS.

The dynamic performance test waveforms of the PET are shown in Figure 11. Each group of experiments tests three waveforms of the primary-side current, output voltage, and current of the PET. In Figure 11a, the load changes from half-load to rated load, the primary side current of the transformer decreases and remains stable, and the output voltage can be maintained stable. In Figure 11b, the load changes from rated load to half-load, the output current increases and remains stable, and the output voltage can be maintained stable, too. This indicates that the system responds quickly to the load, the controller is stable, and it has a very small steady-state error. Therefore, the system has good output performance and stability.

The efficiency of the system is measured by the HIOKI 3390 power analyzer, and the results are shown in Figure 12. Under rated load conditions, the peak efficiency reaches 94.2%.

The proposed PET was evaluated against other converters discussed in the existing literature, with the comparison results presented in

Table 3. Performance comparison with the AC-AC converters in the literature.

Parameters	Proposed Topology	[19]	[24]	[25]
Switches	8 in LF 6 in HF	6 in LF 6 in HF	12 in HF	8 in HF
Input filter inductor	220 μH	350 μH	500 μH	2 × 645 μH
Output filter inductor	/	385 μH	500 μH	2 × 645 μH
Output filter capacitor	3.3 μF	1.3 μF	N/A	220 nF
DC-link capacitor	Film capacitor (2 × 2.7 μF)	Film capacitor (2 × 2 μF)	Electrolytic Capacitor	Electrolytic Capacitor (3 × 680 μF)
Resonant inductor	6.4 μH	6.16 μH	80 μH	108 μH
Efficiency	94.2%	92.1%	92.8%	91.3%
MOSFETs	FCH072N60F, 600 V, 52 A, 72 mΩ	FCH072N60F, 600 V, 52 A, 72 mΩ	C2M0040120D, 1200 V, 36 A, 80 mΩ	SCT3120AL, 650 V, 21 A, 120 mΩ
Transformer frequency	65 kHz	100 kHz	100 kHz	30 kHz
Power rating	1 kW	2 kW	1 kW	500 W
Peak voltage (per unit)	1	1	2.25	2.57
RMS current (per unit)	2	2	1.6	1

. There are fewer switches operating at high frequencies, and also a reduced quantity and size of passive filter inductors and DC-link capacitors (replaced with small film capacitors) compared with [24,25]. This improvement enhances the stability and power density of the system. At the same time, it avoids the issue of twice-frequency power pulsation of the DC-link, which leads to the loss of electrolytic capacitors, accounting for 24.15% of the total loss in [25]. The resonant inductance and the magnetizing inductance of the LLC converter are both integrated into the transformer, without an additional inductor. Reduction of passive components is conducive to enhancing the power density and can also reduce system costs. The proposed PET can achieve ZVS on all high-frequency switches of the resonant converter, achieving higher efficiency. In contrast, ref. [19,24] having one or two high-frequency switches that cannot achieve ZVS during the positive or negative half-cycle of the line frequency reduces the conversion efficiency. As the DAB-based PET, ref. [19] faces the problem of matching input and output voltages, and thus has a limited voltage regulation range. In comparison, the proposed topology adopts DCX-LLC and post-stage voltage regulation has a more effective power regulation.

5. Conclusions

This paper presents a single-phase matrix-type AC-AC power electronic transformer without bulky energy storage elements. By sharing the input and output filter capacitors with HB-LLC and Boost converter, respectively, and adopting a half-bridge configuration, the proposed PET reduces the number of components and enhances the power density. Additionally, through dead-time control, all switches in the resonant converter operating at resonant frequency achieve ZVS under time-varying DC-link voltage, and both the rectifier and the inverter operate at the line frequency. Therefore, the system is highly efficient. Moreover, the matrix-type topology inherently eliminates twice-frequency power pulsation, while employing film capacitors improves system reliability and lifespan. Through simple and reliable control strategies, the Boost converter enables effective power regulation and AC output control. Finally, the input and output waveforms without distortion can achieve power factor correction (PFC) without the need for additional control loops. Overall, the PET proposed in this paper adopts direct AC-AC conversion with a compact structure and high efficiency. Potential deployments include smart grids and microgrids that require flexible control, as well as places where volume and weight requirements are critical, such as aerospace and transportation. Future research directions will adopt a Modular Multilevel Converter (MMC) and wide bandgap semiconductors, such as SiC/GaN, to improve the operating voltage level of the PET, increasing the working frequency and further enhancing the power density.