Open AccessArticle

Design of a Single-Stage Transformerless Buck–Boost Inverter for Electric Vehicle Chargers

Lixia Wang

Chenming Liu

and

Jingyang Fang

School of Control Science and Engineering, Shandong University, Jinan 250100, China

Author to whom correspondence should be addressed.

Appl. Sci. 2022, 12(13), 6705; https://doi.org/10.3390/app12136705

Submission received: 10 May 2022 / Revised: 15 June 2022 / Accepted: 16 June 2022 / Published: 1 July 2022

(This article belongs to the Special Issue Recent Developments in Electric Vehicles)

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Figure 1
Schematic diagram of the proposed single-stage transformerless buck–boost inverter system. "> Figure 2
Switching patterns for the positive half-wave of vc: (a) Inductor charged, (b) Inductor discharged. "> Figure 3
Switching patterns for the negative half-wave of vc: (a) Inductor charged, (b) Inductor discharged. "> Figure 4
Overall control block diagram of the proposed buck–boost inverter. "> Figure 5
Simplified control block diagram of the proposed buck–boost inverter. "> Figure 6
Simulation results of the proposed buck–boost inverter working as buck-type inverter. "> Figure 7
Simulation results of the proposed buck–boost inverter working as boost-type inverter. "> Figure 8
Pole-zero map of the closed-loop voltage control: (a) With damping controller (Gd(z) = 4), (b) Without damping controller (Gd(z) = 1). ">

Versions Notes

Abstract

This paper details the design and implementation of a single-stage transformerless buck–boost inverter for electric vehicle (EV) chargers. Being different from conventional H-bridge inverters, the proposed inverter operates like buck–boost dc/dc converters instead of buck dc/dc converters. As a consequence, the advantages of a buck–boost dc/dc converter, i.e., the arbitrary relationships between its input voltage and output voltage, are still applicable to the proposed inverter. Specifically, it remains in normal operation even when the peak ac output voltage is higher than the dc-link voltage. Simulation results are finally presented to illustrate its effectiveness.

Keywords:

electric vehicle (EV); buck–boost; inverter; power electronics; single-stage; transformerless

1. Introduction

Dc/ac power electronic converters, i.e., inverters, have found widespread applications in the areas of renewable generation [1,2,3,4,5], power conditioning [6,7,8,9], energy storage systems [10], and electric vehicles (EVs) [11,12]. Generally, buck-type inverters, such as the well-known H-bridge inverters, are employed to achieve the objective of dc to ac power conversion [1,2,3,4,5,6,7,8,9,10]. However, due to the inherent voltage step-down characteristic of buck converters [13], the peak ac output voltage for the buck-type inverter should always be lower than its input dc-link voltage. This requirement imposes several limitations on the design and operation of buck-type inverters. For example, in applications where the input dc voltage is equivalent to or lower than the output ac voltage, one additional stage of dc/dc power converter is necessary to boost up the dc-link voltage. Otherwise, the undesirable over modulation of buck-type inverters may occur, which will disrupt the system from normal operation [6].

Although the adoption of another dc/dc converter into the dc/ac power conversion system with low dc-link voltages, e.g., photovoltaic generation [1], is a feasible and widely used solution, this approach will inevitably increase the system cost and complexity. It is therefore highly desirable that the inverter can operate without any limitations on the relationships between its dc voltage and ac voltage. As an interesting attempt, Peng F. proposed a novel inverter, named the z-source inverter, which simultaneously achieves the objectives of dc to ac conversion and voltage boost [14]. Nevertheless, it necessitates extra filter components and complicated control algorithms.

As an alternative simple solution, a single-stage transformerless buck–boost inverter is proposed in this paper. By directly extending the operating principles of dc/dc buck–boost converter into dc/ac applications, the proposed inverter can be designed and operated in a straight-forward way, as will be discussed in the following sections.

2. System Schematic

Figure 1 shows a schematic diagram of the proposed single-stage transformerless buck–boost inverter system, where the dc-link voltage V_dc is maintained as a constant V_dc by a dc power supply. Through operating the semiconductor switches S₁–S₄, the inductor L_f can be charged from both directions, and then it will be discharged to supply the filter capacitor C_f and the load R_o so long as switch S₅ or S₆ are turned-on. In Figure 1, i_L, i_R, and v_c denote the inductor current, load current, and capacitor voltage, respectively.

3. Operation Principle

The operation principle of the proposed buck–boost inverter can be explained well by the switching patterns illustrated in Figure 2 and Figure 3. Assuming that the desirable waveform of the output voltage v_c is a sinusoid, which pulsates at fundamental frequency. Under this assumption, the operation of semiconductor devices will be dependent on the sign of v_c. For the case of a positive half-wave of v_c, S₁ and S₄ remain in the off-state, as shown in Figure 2. As it can be observed from Figure 2a, when S₂ and S₃ turn on, the dc power supply charges the inductor L_f, and hence, the inductor current i_L increases linearly. Meanwhile, S₆ remains in the off-state and the capacitor C_f releases its energy to supply the load R_o. In contrast, it is clear from Figure 2b that the inductor L_f transforms its energy to the capacitor C_f and load R_o when S₂ and S₃ turn-off, together with S₆ switched on. For the case of a negative v_c, the operations of S₂, S₃, and S₆ are replaced by S₄, S₁, and S₅, respectively. From the above analysis, the proposed buck–boost inverter operates very similar to the conventional dc/dc buck–boost inverter, except for its bipolar output voltage. As a consequence, it enables both the operation of voltage step-down and boost.

4. Mathematic Model

Let T_s denote the switching period, T_on represent the switching-on time of S₂ and S₃ or S₁ and S₄ in each switching cycle, T_off stand for the switching-on time of S₅ or S₆ in each switching cycle, and d_o = T_on/T_s designate the duty cycle. The state equation description of the proposed buck–boost inverter can be derived from Figure 2 as follows:

[\begin{matrix} \frac{d i_{L}}{d t} \\ \frac{d v_{C}}{d t} \end{matrix}] = [\begin{matrix} 0 & 0 \\ 0 & \frac{- 1}{R_{o} C_{f}} \end{matrix}] [\begin{matrix} i_{L} \\ v_{C} \end{matrix}] + [\begin{matrix} \frac{1}{L_{f}} \\ 0 \end{matrix}] v_{d c},

(1)

[\begin{matrix} \frac{d i_{L}}{d t} \\ \frac{d v_{C}}{d t} \end{matrix}] = [\begin{matrix} 0 & \frac{- 1}{L_{f}} \\ \frac{1}{C_{f}} & \frac{- 1}{R_{o} C_{f}} \end{matrix}] [\begin{matrix} i_{L} \\ v_{C} \end{matrix}] + [\begin{matrix} 0 \\ 0 \end{matrix}] v_{d c}

(2)

where (1) and (2) represent the equations for switching-on and switching-off, respectively. The state space average model of the proposed inverter can be further derived through adding (1) and (2) with their respective weighted coefficients of d_o and 1-d_o as follows:

[\begin{matrix} \frac{d i_{L}}{d t} \\ \frac{d v_{C}}{d t} \end{matrix}] = [\begin{matrix} 0 & \frac{- (1 - d_{o})}{L_{f}} \\ \frac{1 - d_{o}}{C_{f}} & \frac{- 1}{R_{o} C_{f}} \end{matrix}] [\begin{matrix} i_{L} \\ v_{C} \end{matrix}] + [\begin{matrix} \frac{d_{o}}{L_{f}} \\ 0 \end{matrix}] v_{d c} .

(3)

Based on (3), the transfer functions from the dc-link v_dc to the inductor current i_L and capacitor voltage v_c can be derived as:

\frac{i_{L} (s)}{v_{d c} (s)} = \frac{d_{o} (C_{f} R_{o} s + 1)}{C_{f} L_{f} R_{o} s^{2} + L_{f} s + R_{o} {(1 - d_{o})}^{2}},

(4)

\frac{v_{C} (s)}{v_{d c} (s)} = \frac{R_{o} d_{o} (1 - d_{o})}{C_{f} L_{f} R_{o} s^{2} + L_{f} s + R_{o} {(1 - d_{o})}^{2}} .

(5)

In steady-state, (4) and (5) can be reorganized as:

\frac{I_{L}}{V_{d c}} = \frac{d_{o}}{R_{o} {(1 - d_{o})}^{2}},

(6)

\frac{V_{C}}{V_{d c}} = \frac{d_{o}}{1 - d_{o}} .

(7)

It should be noted that (1)–(7) are only applicable to the case of positive output voltages (see Figure 2). In the case of negative output voltages, as shown in Figure 3, the v_dc in (1)–(7) should be replaced by −v_dc. This nonlinear behavior will bring in additional concerns to controller design. In order to address this problem, the absolute value of duty cycle do is used instead of its actual value. Furthermore, when the reference duty cycle crosses zero from a positive value to a negative value, the driving pulses of S₂ and S₃ are shifted to S₁ and S₄, and vice versa. Through this approach, the sign of the output voltage v_c can always be regulated to follow the sign of its reference, and (1)–(7) are applicable to |v_c|.

5. Controller Design

5.1. Open-Loop Control

It is obvious from (7) that the duty cycle for a desirable sinusoidal output voltage v_c = V_C_p sin(ωt) can be expressed as:

d_{o} = \frac{| V_{C p} \sin (ω t) |}{V_{d c} + | V_{C p} \sin (ω t) |} .

(8)

5.2. Closed-Loop Control

A typical double-loop controller, i.e., an outer voltage-loop and an inner current-loop controller [15,16], is incorporated to regulate the proposed buck–boost inverter. Its relevant control block diagram is shown in Figure 4, where K_pwm denotes the gain of the pulse-width modulator (PWM), z⁻¹ represents one sampling period time delay, and ZOH stands for the mathematical model of the zero-order-hold behavior of the pulse-width generator [7]. It should be mentioned that the proposed controller is implemented by a digital controller, and hence, the transfer functions of the controllers are expressed in the discrete z-domain. In contrast, the system plant model, which is described by (3), is represented in the continuous s-domain. Additionally, a control block denoted as G_d(z) is employed in the current controller to effectively dampen the resonant peak introduced by the LC-filter. Moreover, taking the varying loads into consideration, the load current i_R(s) is treated as a disturbance here.

The transfer function from the output of PWM generator to the inductor current i_L(s) can be derived from Figure 4 as follows:

T_{v i_i L} (s) = \frac{i_{L} (s)}{v_{i} (s)} = \frac{C_{f} s}{C_{f} L_{f} s^{2} + {(1 - d_{o})}^{2}} .

(9)

In addition, the transfer function from the output of PWM generator to the output voltage v_c (s) can be derived as:

T_{v i_v C} (s) = \frac{v_{C} (s)}{v_{i} (s)} = \frac{1 - d_{o}}{C_{f} L_{f} s^{2} + {(1 - d_{o})}^{2}} .

(10)

Applying the z-transformation with ZOH into (9) and (10), the relevant discrete expressions can be obtained as:

\begin{array}{l} T_{v i_i L} (z) = Ζ [(1 - z^{- 1}) \cdot \frac{T_{v i_i L} (s)}{s}] \\ = \frac{(z - 1) \cdot \sin [(1 - d_{o}) ω_{r} T_{s}]}{(1 - d_{o}) L_{f} ω_{r} \cdot {z^{2} - 2 z \cos [(1 - d_{o}) ω_{r} T_{s}] + 1}}, \end{array}

(11)

\begin{array}{l} T_{v i_v C} (z) = Ζ [(1 - z^{- 1}) \cdot \frac{T_{v i_v C} (s)}{s}] \\ = \frac{(z + 1) \cdot {1 - \cos [(1 - d_{o}) ω_{r} T_{s}]}}{(1 - d_{o}) \cdot {z^{2} - 2 z \cos [(1 - d_{o}) ω_{r} T_{s}] + 1}} \end{array}

(12)

where ω_r = 1/(L_fC_f)^1/2 denotes the resonance frequency of the LC-filter. After the derivation of (11) and (12), the simplified control block diagram of the proposed buck–boost inverter is illustrated in Figure 5, where all the transfer functions are expressed in the z-domain. The system and control parameter values are tabulated in TABLE I. It should be mentioned that the proportional gains G_i and G_d are used for the current controller, while a proportional-resonant (PR) controller with its proportional gain denoted as G_vp and resonant gain denoted as G_vr is employed as the voltage controller.

Based on Figure 5 and the system parameter values listed in Table 1, the pole-zero map of the closed-loop voltage control is illustrated in Figure 6, where the zeros are represented as circles while the poles are denoted as crosses. The effectiveness of the proposed damping control block G_d(z) can be clearly observed by comparing Figure 6a,b. As seen, the system poles are located much closer to the center of the unit circle after the carefully designed G_d(z) is enabled. It should be highlighted that the variation in the duty cycle will influence the stability of the proposed inverter, while the stability of conventional H-bridge inverters is independent of d_o. As a consequence, all the closed-loop poles should always stay within the unit cycle as the duty cycle varies. In order to ensure the system stability, the maximum value of the output voltage v_c should be given first, and then the maximum d_o can be derived according to (8). Next, the variation range of d_o can be obtained. Finally, the map of the closed-loop poles can be drawn to validate whether the system poles are always inside the unit cycle. As it can be seen from Figure 6a, the system can be stable even when the duty cycle is as high as 0.8, which corresponds to an output voltage of 400 V.

6. Simulation Results

Simulations models were built in Matlab/Simulink software based on the system parameter values listed in Table 1 and the schematic diagram shown in Figure 1. The simulation waveforms of capacitor voltage v_c and inductor current i_L under two cases, where the peak ac voltages (50 V and 150 V) are lower than and higher than the dc-link voltage, are demonstrated in Figure 7 and Figure 8. For these two cases, the dc-link voltage v_dc is maintained as a constant 100 V. As observed, the proposed inverter enables the operations of both buck-type and boost-type inverters. As mentioned, the switching patterns are changed while the system structure remains fixed. These results are consistent with the theoretical analysis.

7. Conclusions

In this paper, a single-stage transformerless buck–boost inverter has been proposed to directly achieve dc to ac conversion regardless of the relationships between its dc-link voltage and peak ac output voltage. The proposed inverter is an equivalent replacement of a conventional boost converter cascaded with an inverter, while the former features simpler circuit structure, lower cost, smaller volume, and straight-forward implementation. The analysis based on its state space average model indicates that the stability of the proposed inverter is dependent on the value of its duty cycle. Fortunately, this issue can be addressed by a well-designed outer voltage-loop plus inner current-loop controller. Simulation results are presented to validate its effectiveness.

Author Contributions

Conceptualization, J.F.; methodology, J.F.; software, J.F.; validation, L.W.; formal analysis, L.W.; data curation, L.W. and C.L.; writing—original draft preparation, L.W., C.L. and J.F.; writing—review and editing, L.W., C.L. and J.F.; visualization, L.W. and C.L.; project administration, J.F.; funding acquisition, J.F. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by Shandong University Distinguished Young Scholars Project, grant number: 31400082260522.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Schematic diagram of the proposed single-stage transformerless buck–boost inverter system.

Figure 2. Switching patterns for the positive half-wave of v_c: (a) Inductor charged, (b) Inductor discharged.

Figure 3. Switching patterns for the negative half-wave of v_c: (a) Inductor charged, (b) Inductor discharged.

Figure 4. Overall control block diagram of the proposed buck–boost inverter.

Figure 5. Simplified control block diagram of the proposed buck–boost inverter.

Figure 7. Simulation results of the proposed buck–boost inverter working as buck-type inverter.

Figure 8. Simulation results of the proposed buck–boost inverter working as boost-type inverter.

Figure 6. Pole-zero map of the closed-loop voltage control: (a) With damping controller (G_d(z) = 4), (b) Without damping controller (G_d(z) = 1).

Table 1. System and Control Parameter Values.

Description	Symbol	Value
Dc-link voltage	V_dc	100 V
Filter inductor	L_f	1 mH
Filter capacitor	C_f	50 µF
Load resistor	R_o	10 Ω
Output voltage	V_C	50–150 V
Current controller	G_i/G_d	1/4
Voltage controller	G_vp/G_vr	0.2/100
Fundamental frequency	f_o	50 Hz
Switching frequency	f_s	10 kHz
Sampling frequency	f_s	10 kHz
Rated power	P_o	1 kW

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Wang, L.; Liu, C.; Fang, J. Design of a Single-Stage Transformerless Buck–Boost Inverter for Electric Vehicle Chargers. Appl. Sci. 2022, 12, 6705. https://doi.org/10.3390/app12136705

AMA Style

Wang L, Liu C, Fang J. Design of a Single-Stage Transformerless Buck–Boost Inverter for Electric Vehicle Chargers. Applied Sciences. 2022; 12(13):6705. https://doi.org/10.3390/app12136705

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Wang, Lixia, Chenming Liu, and Jingyang Fang. 2022. "Design of a Single-Stage Transformerless Buck–Boost Inverter for Electric Vehicle Chargers" Applied Sciences 12, no. 13: 6705. https://doi.org/10.3390/app12136705

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