# Design and Analysis of a Three-Phase Single-Stage AC-DC Converter with Series Resonant Tank for Electric Vehicle Charging Stations

Mohammad Ramezani, Majid Pahlevani, Praveen Jain

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Mohammad Ramezani, Majid Pahlevani, Praveen Jain. Design and Analysis of a Three-Phase Single-Stage AC-DC Converter with Series Resonant Tank for Electric Vehicle Charging Stations. The 26th European Conference on Power Electronics and Applications, GDR SEEDS France & EPE Association, Mar 2025, Paris, France. 10.34746/epe2025-0281. hal-05082296

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# Design and Analysis of a Three-Phase Single-Stage AC-DC Converter with Series Resonant Tank for Electric Vehicle Charging Stations

Mohammad Ramezani, Majid Pahlevani, and Praveen Jain

Queen's Centre for Energy and Power Electronics Research (ePOWER)

Department of Electrical and Computer Engineering, Queen's University
Kingston, Canada

E-Mail: m.ramezani@queensu.ca, majid.pahlevani@queensu.ca, praveen.jain@queensu.ca

**Index Terms**—Single-stage, Battery charger, Electric Vehicle (EV), AC-DC converter, Three-phase system.

**Abstract**—This paper presents an analysis and design of a three-phase single-stage ac-dc converter with an LC resonant tank for use in the charging infrastructure for electric vehicles (EVs). The analyzed converter simplifies the power conversion process by reducing the number of components, enhancing both the system reliability and the efficiency. The operation of the converter is modeled and different modes of operation are presented. The introduced single-stage converter achieves zero voltage switching (ZVS), to minimize power losses and to optimize system performance. A prototype is designed and implemented, achieving 95.9% efficiency with low input current total harmonic distortion (THD) and output voltage ripple utilizing small non-electrolyte capacitors. The simulation and experimental results validate the design and control scheme, showing the effectiveness of the proposed approach for modern EV charging stations.

## I. INTRODUCTION

Along with the growing utilization of EVs, reliable and efficient charging infrastructure is becoming more important. Conventional EV charging technologies, still have potential for enhancement in terms of charging speed, minimizing energy losses, and reducing component count [1]–[3]. The three-phase ac supply provides an improved and faster energy supply compared to a single-phase system. Single-stage implementation of the three-phase chargers, simplifies the process of power conversion, which in turn reduces the number of components used and hence increases the system reliability and efficiency.

In the literature, several methods for achieving single-stage power conversion have been introduced.

Modified single-stage flyback and forward-based converters are viable [4] but induce high voltage stress on the components [5]. Boost-type bridgeless ac-dc converters offer efficient single-stage power conversion [6], while they have a high dc link voltage and a double line frequency issue at the output [7]. Non-boost-based bridgeless ac-dc converters, utilizing topologies such as buck, buck-boost, single-ended primary-inductor converter (SEPIC), and Cuk address some of the challenges found in boost-based bridgeless converters, at the cost of additional components [8].

Full-bridge and half-bridge ac-dc converters deliver low input current ripple in current-fed configurations [9], [10], and address the double-frequency issue effectively in voltage-fed configurations [11]. They offer soft-switching, making them ideal for high-power applications [12]. DAB-based ac-dc converters are known for their high efficiency and power density and soft-switching [13], but come with a higher cost due to the number of switches involved. Matrix ac-dc converters excel in reducing THD and ripple at very high frequencies, while the increased operational frequency makes safe switching more demanding and reduces reliability [14]. Matrix converters are advantageous in high-power applications, offering high efficiency and power density by eliminating energy storage elements in their design [15], despite the significant cost due to the use of many switches. When resonant tanks are integrated into single-stage converters, resonant ac-dc converters are created. These converters enable soft-switching conditions and impact the converter gain, making them adaptable for a wide range of applications, from low to high power [16]. However, the addition of components can lead to higher costs and increased control complexity [17]. In
conclusion, the spectrum of single-stage ac-dc converters is broad and diverse, serving various applications at varying power levels. Each converter type offers unique benefits and challenges, efficiency curve, component stress, cost, and control complexity.

Three-phase power systems present numerous advantages over single-phase power systems, making them a more favorable choice for various applications. Devices that operate on three-phase power can deliver the same power output while being smaller and lighter than their single-phase counterparts. In the domain of single-stage converters, several approaches have been devised to implement three-phase single-stage converters, with the goal of maximizing the power density. These converters can be constructed by stacking single-phase modules, with multiple configurations documented in the literature. The isolated stacked Cuk converters were explored by [18]–[20]. In [21] stacked H-bridges were implemented, while in [22] three-phase diode bridge rectifiers with H-bridge modules are combined. In [5] a flyback stacked design is introduced, and in [23], stacked boost-based modules are used. In [24] stacked single-stage interleaved totem pole modules are used. These modular structures share characteristics related to voltage stress, discontinuous conduction mode (DCM) or continuous conduction mode (CCM) operation modes, and THD, reflecting their constituent modules. In the existing literature, non-modular single-stage converters have been studied which include DAB-Based and matrix-based three-phase single-stage converters, as well as configurations that integrate a single-stage boost rectifier with a switching stage. A three-phase diode rectifier is combined with a T-type inverter in [25], with a half-bridge LLC resonant circuit in [26], with an interleaved half-bridge in [27], and a full-bridge converter in [28]. Non-modular single-stage ac-dc converters generally provide a lower number of switches compared to modular ones.

An approach to improve efficiency and performance in dc-dc converters across various operating conditions has been introduced in [29]. The converter features a quasi-rectangular waveform for the input current and soft-switching, leading to reduced conduction losses in magnetics and power semiconductors. In [30] a new isolated bridgeless single-stage light emitting diode (LED) driver is presented, featuring high power factor and soft-switching performance. This topology integrates a bridgeless boost power factor corrector (PFC) with an isolated current-driven half-bridge dc-dc converter, resulting in a bridgeless single-stage PFC structure. A direct power transfer path using coupled inductors reduces

<figure><img src="image_2.png" /><figcaption>Fig. 1: Three-phase single-stage charger with LC resonant tank.</figcaption></figure>

conduction losses by transferring power from the input source to the output [31].

Building upon the insights from earlier discussions, the converter used in this work is set to combine all of these capabilities. single-stage ac-dc conversion with a non-modular three-phase approach and resonant tank can lead to a very compact and efficient design. The result is a more streamlined, cost-effective, and reliable charging solution.

## II. THREE-PHASE SINGLE-STAGE CHARGER WITH LC RESONANT TANK AND ITS CONTROL SCHEME

The structure of the three-phase single-stage charger with an LC resonant tank is shown in Fig. 1. The three-phase input voltage is connected to the midpoint of the three-phase bridge legs with series inductors $L_{g1a}$, $L_{g1b}$, and $L_{g1c}$. The leg midpoints are also connected to the primary winding of the transformer through a series LC resonant circuit, which includes components of $C_{sa}$, $C_{sb}$, $C_{sc}$, $L_{sa}$, $L_{sb}$, and $L_{sc}$. Following this, the high-frequency ac signal is transmitted through a Y-Y isolated transformer, after which it is rectified by a three-phase diode bridge on the secondary side, with dc voltage at the output for battery charging.

The modeling of the converter starts with the derivation of time-domain equations, as shown in equation (1). Starting with the phase a variables, $L_{g1a}$ specifies the self-inductance of the input inductor. $V_{Lg1a}$ represent the voltage across the input inductor while $i_{sa}$ denote the currents going through it.

$$V_{Lg1a} = L_{g1a} \frac{di_{sa}}{dt} \qquad (1)$$

Similar equations for phases b and c can be derived considering $L_{g1a} = L_{g1b} = L_{g1c} = L_{g1}$. Neglecting the terms associated with the initial conditions, equation (2) is derived where $i_{s(n)}$ is the input inductor current and n donates phase a, b, or c:

$$i_{s(n)} = \frac{1}{L_{g1(n)}} V_{Lg1(n)} \cdot t \qquad (2)$$
Next, the equations governing currents and voltages in the resonant part of the circuit can be determined. The general form of these equations is derived from the following set of differential equations. In this series resonant section, the inductors and capacitors are assumed to have equal values for all phases, such that $L_{sa} = L_{sb} = L_{sc} = L_s$ and $C_{sa} = C_{sb} = C_{sc} = C_s$. The series current for phase a is denoted as $i_{pa}$, the voltage across the capacitor as $V_{csa}$, and the voltage across the entire series resonant tank, including inductor $L_{sa}$ and capacitor $C_{sa}$, is represented by $V_{sera}$. The differential equations for phase a are provided in equations (3) and (4).

$$L_{sa} \frac{di_{pa}}{dt} + V_{csa} = V_{sera} \quad (3)$$

$$C_{sa} \frac{dV_{ca}}{dt} = i_{pa} \quad (4)$$

Solving for the differential equations above, the series current for each phase can be determined as follows in equation (5) where n donates phase a, b, or c:

$$i_{p(n)} = Y \sin(\omega t)V_{ser(n)} + \cos(\omega t)I_{p0(n)} - Y \sin(\omega t)V_{cs0(n)} \quad (5)$$

$I_{p0(n)}$ and $V_{cs0(n)}$ denote the initial inductor current and initial capacitor voltage, respectively. Term Y represents the characteristic admittance of the series path, as defined in equation (6). Term $\omega$ corresponds to the resonant frequency of series resonant path, as defined in equation (7).

$$Y = \sqrt{\frac{C_s}{L_s}} \quad (6)$$

$$\omega = \frac{1}{\sqrt{C_s L_s}} \quad (7)$$

In equations (2) and (5), the terms $V_{Lg1(n)}$ and $V_{ser(n)}$ depend on the state of the switches and diodes. To properly model the system, $S(t)$ and $D(t)$ functions are defined in (8) and (9).

$$S(t) = \begin{cases} -2/3, & \text{S100 (V1)} \\ -1/3, & \text{S110 and S101 (V2 and V6)} \\ 0, & \text{S000 and S111 (V0 and V7)} \\ 1/3, & \text{S010 and S001 (V3 and V5)} \\ 2/3, & \text{S011 (V4)} \end{cases} \quad (8)$$

$$D(t) = \begin{cases} -2/3, & \text{D100 (D1)} \\ -1/3, & \text{D110 and D101 (D2 and D6)} \\ 1/3, & \text{D010 and D001 (D3 and D5)} \\ 2/3, & \text{D011 (D4)} \end{cases} \quad (9)$$

State S100 shows the switching configuration where upper switch of phase a is active while lower switches for phases b and c are active. Other combinations can be explained similarly. Various switch configurations can produce eight distinct voltage vectors, as illustrated in Fig. 2. By neglecting the terms associated with the initial conditions, equations (2) and (5) can be rewritten as in equations (10) and (11). $E_n$ donates the input voltage of phase n and $V_{dc}$ represents the dc link voltage. Furthermore, $S(t)$ and $D(t)$ are defined in the same manner as in equations (8) and (9), but considering specific timing characteristics.

$$i_{s(n)} = \frac{1}{L_{g1}} (E_n - S(t)V_{dc}) \cdot t \quad (10)$$

$$i_{p(n)} = Y_2 \sin(\omega_2 t) (D(t)V_o + S(t)V_{dc}) \quad (11)$$

The timing of each switching state is found on the basis of the sector in which they reside and the amplitude of the voltages of each phase. In Fig. 3, six segments are defined based on magnitude of the voltage in each phase, showing what switch states are present in each segment. Referring to Fig. 2 and Fig. 3, in the $V_6 - V_1$ sector, dwell times for the active vectors (i.e., S100 and S101) and zero vectors (i.e., S000 and S111) can be calculated based on the instantaneous values of the three-phase voltages and the dc link voltage at each time. These dwell times are calculated to ensure that the average voltage over one switching period $T_s$ matches the reference voltage vector $V_{ref}$. $V_{ref}$ is set based on the control objectives, which are determined to maintain a constant dc link voltage $V_{dc}$ and achieve a sinusoidal input current. In the control system, $V_{ref}$ shown in Fig 2 consists of two components, which are $V_{ref-d}$ and $V_{ref-q}$, as described in equations (12) and (13). $\theta$ represents the angle of the rotating reference frame. $K_I$ and $K_P$ are the proportional and integral gains of the used proportional integral (PI) controller. The values of $I_{d-ref}$ are determined by another PI controller that is fed from the error between $V_{dc}$ and $V_{dc-ref}$. $I_{q-ref}$ is set to zero, implying that the rectifier draws its current in phase with the voltage of the grid.

$$V_{\text{ref-d}} = K_P \cdot (I_{\text{d-ref}} - I_d) + K_I \cdot \int (I_{\text{d-ref}} - I_d) dt \quad (12)$$

$$V_{\text{ref-q}} = K_P \cdot (I_{\text{q-ref}} - I_q) + K_I \cdot \int (I_{\text{q-ref}} - I_q) dt \quad (13)$$

After obtaining the reference values, they are employed to compute the dwell times for the active and zero vectors. Using the feedback loops in the dq frame, the regulation of the dc link voltage and the assurance of a sinusoidal input current are achieved. Let $T_1$ represent
<figure><img src="image_3.png" /><figcaption>Fig. 2: A reference vector in segment $V_6-V_1$ generated by combination of active vectors (i.e., S100 and S101) and zero vectors (i.e., S000 and S111).</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Fig. 3: Six segments defined by the magnitude of each phase, each including four vectors with different active time.</figcaption></figure>

the dwell time for switching state S100, and let $T_2$ denote the dwell time for switching state S101, as given by equations (14) and (15).

$$T_1 = T_s \cdot \frac{V_1}{V_{dc}} \qquad (14)$$

$$T_2 = T_s \cdot \frac{V_2}{V_{dc}} \qquad (15)$$

The control system is illustrated in Fig. 4. The main control variable is the switching frequency and it is regulated to control the flow of power. The outermost control loop uses a PI controller to stabilize the dc link voltage at a predetermined value. The inner layer of control regulates amplitude of the input current with respect to the load. In this part of the control framework, the three-phase input current is converted into the dq domain, placing it in a stationary reference frame so it can be controlled with a PI controller. The required angle for doing the transformation is extracted from sensing the three-phase input voltage. The transformed values are adjusted by another PI controller to maintain a high-quality sinusoidal input current. Once the reference input

<figure><img src="image_5.png" /><figcaption>Fig. 4: The control system for three-phase single-stage charger.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 5: Six modes of operation and their sub-modes in section V6-V1.</figcaption></figure>

current waveforms are established, a PI controller regulates the frequency of the triangular waveform used in the pulse width modulation (PWM) stage. This is achieved by comparing the output current against the desired reference value. By doing so, this control mechanism ensures sinusoidal input current for all three phases as well as regulating the needed current for battery charging application.

### III. SIMULATION RESULTS

The calculations are subjected to validation and further exploration in this section through comprehensive simulations conducted using PSIM. Different modes of operation with their respective sub-modes are identified.

The currents flowing through the input inductors and the series resonant tank for phase n are represented by $i_s(n)$, and $i_p(n)$, respectively and are described by equations (10) and (11). The operation of the converter in each segment is divided into six modes, each corresponding to a specific set of switch states. Fig. 5 illustrates the six primary modes of operation and their respective sub-modes within segment $(V_6-V_1)$. For other segments introduced in Fig. 3, the modes and sub-modes are similarly analyzed.
<figure><img src="image_7.png" /><figcaption>Fig. 6: The implemented three-phase single-stage charger.</figcaption></figure>

Within the ($V_6 – V_1$) segment, only the switching configurations $S000$, $S100$, $S101$, and $S111$ are active as shown in Fig. 5. The order of occurrence of these configurations results in six distinct modes. Each of these modes include several sub-modes, dependent on the configuration of active diodes on the secondary side. Once all six modes have cycled, the converter returns to mode 1, and this cycle continues until the segment ends at the positive peak of $E_a$. Subsequently, the ($V_1 – V_2$) segment starts where combinations of $S000$, $S111$, $S100$, and $S110$ are present in it.

## IV. EXPERIMENTAL RESULTS

To validate the performance of the introduced converter and control method, a prototype three-phase single-stage charger was built. The setup shown in Fig. 6 shows the implemented converter that is connected to the three-phase source at the input terminals and to the dc load at the output terminal. Inductors, switches, and diodes are mounted on the bottom of the board and command signals and sensor readings are performed using a field programmable gate array (FPGA) board.

Fig. 7 shows the three-phase input voltage and current waveforms from the sensors, received from the FPGA signal tap. At 70 V line-to-line ac voltage, each phase draws 5.53 A of root mean square (RMS) current. As can be seen, the current and voltage for the individual phases are in phase. The calculated current THD for this power level is 7.45%, which is acceptable considering the power level. According to the readings from the input

<figure><img src="image_8.png" /><figcaption>Fig. 7: Three-phase input voltage and current waveforms.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 8: Gate-source and drain source signal of one switch showing ZVS</figcaption></figure>

source and output power calculations, the input power is read at 374.6 W and the output power is 359.1 W. The readings yield an efficiency of 95.9%. High efficiency is expected because ZVS is present in all switches. Fig. 8 shows the gate-source and drain-source signals of lower switch of phase a during a switching cycle. As can be seen, ZVS is achieved, which helps increase the efficiency.

The dc link and the output voltages are shown in Fig. 10. As can be seen, the output voltage is set to an average of 133.4 V volts with a ripple of 3.7%. Considering only 9 µF capacitance is used at the dc link, the ripple is relatively small. Similarly, the output voltage of 56.2 V is archived with the designed gain in the resonant section. The ripple in the output voltage is calculated to be 4.7% of the output voltage considering
<figure><img src="image_10.png" /><figcaption>Fig. 9: Voltage of phase A and three-phase current.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Fig. 10: Output rectified voltage</figcaption></figure>

9 μF output capacitance.

## V. CONCLUSION

In this paper, a three-phase single-stage ac-dc converter with an LC resonant tank presented which offers a highly efficient, compact, and reliable solution for EV charging stations. The converter improves system efficiency while maintaining low THD and output voltage ripple by simplifying the power conversion process and reducing the component count compared to multi-stage alternatives. Ensuring ZVS, as demonstrated in the experimental results, contributes to achieving high efficiency. For a prototype that was tested at 359 W output power, an efficiency of 95.9% is obtained, with minimal current ripple and voltage fluctuations. The compact and efficient design of the converter makes it well-suited for modern EV charging applications.

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