# Research on Bidirectional Isolated Charging System Based on Resonant Converter

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Bidirectional Isolation Type Charging System and Characterization

_{dc}. Power switches Q

_{1}~Q

_{4}obtain drive signals to invert the DC voltage V

_{dc}, Q

_{5}~Q

_{8}pulse blocking, and body diodes D

_{q5}~D

_{q8}conduct work to rectify the high-frequency signal on the secondary side of the transformer.

_{5}~Q

_{8}inverts the DC power into a high-frequency AC signal, Q

_{1}~Q

_{4}pulse blocking, and the body diode D

_{q1}~D

_{q4}completes the rectification function. Then the bidirectional totem pole converter achieves the inverter supply AC load power.

#### 2.1. Modeling Analysis of Bidirectional Totem Pole Converter

_{ac}(t) is the AC current; v

_{dc}(t) is the DC bus voltage; R is the equivalent resistance of the rear stage converter; C

_{dc}is the DC bus capacitance; L is the AC inductance; v

_{in}(t) is the grid voltage.

**A**,

_{0,}B_{0}**A**,

_{1}**B**are state coefficients.

_{1}_{ac}(t) v

_{dc}(t)]

^{T}and the input vector u(t) = [v

_{in}(t)], the steady-state expressions of the state vector and the input vector for the whole switching period T can be obtained by combining Equations (1)–(4) as follows:

**X**,

**U**, and

**D**are the steady-state values of the state vector, input vector, and duty cycle, respectively.

**I**is the unit matrix.

_{id}(s) for input current versus duty cycle and G

_{vd}(s) for bus voltage versus duty cycle are:

_{id}(s) is the commonly used control object, where R, L, and C

_{dc}are constants in the transfer function. At the same time, duty cycle D, AC input current I

_{ac}, and output voltage V

_{o}are the quantities that keep changing with normal operation. According to Equation (20), the factors affecting the duty cycle are the input voltage and the output voltage; when the input power is specific, the factor affecting the size of the AC input current is also the input voltage. There is a large filter capacitor at the output of the bidirectional totem pole converter circuit, so the output voltage does not vary much and can be neglected [26]. Therefore, the factor affecting G

_{id}(s) is the magnitude of the input voltage. To analyze the effect of the input voltage on the transfer function, the Byrd diagram is drawn for different input voltage levels, as shown in Figure 4.

_{id}(s) are different for different input voltages, whereas the high-frequency characteristics are the same. The current loop deals with the high-frequency signal, so the influence of the low-frequency band can be ignored in the analysis, and then the control system can be designed.

#### 2.2. Bidirectional CLLLC Resonant Converter Modeling

#### 2.2.1. Equivalent Circuit Model

_{1}to Q

_{4}makes the input voltage v

_{ab}of the resonant network a square wave signal with amplitude varying from −V

_{dc}to V

_{dc}, for which the Fourier expansion is carried out to obtain the following expression:

_{s}is the switching frequency.

_{ab}and their RMS values are:

_{cd}, the fundamental component of the output voltage v

_{cd_FHA,}and its RMS value V

_{cd_FHA}are obtained as follows:

_{ab}and v

_{cd}.

_{o}, the expression of the output current of the resonant network is:

_{Ls}is the RMS value of the output current of the resonant network.

_{cd_FHA}is in phase with i

_{Ls}, the rectifier network, as well as the output load, can be equated to a purely resistive load, i.e.,

_{eq}is the resistance converted to the primary side; C

_{s}

^{′}is the capacitance converted to the primary side; L

_{s}

^{′}is the inductance converted to the primary side; n is the transformer ratio.

_{ab_FHA}(t), and the voltages between points c and d on the secondary side are converted to nv

_{cd_FHA}(t) on the primary side, while the capacitance inductance on the secondary side is converted to the primary side, resulting in the equivalent circuit model of the rear stage converter, as shown in Figure 5.

#### 2.2.2. Characteristic Analysis

- Voltage Gain Characteristics

_{n}is the normalized frequency, k is the inductance factor, and Q is the quality factor. The expressions are:

_{r1}is the resonant frequency of the resonant inductor and resonant capacitor of the transformer, i.e., the resonant frequency of L

_{p}, C

_{p}, or L

_{s}, C

_{s}; f

_{s}is the switching frequency.

_{n}change at different Q values are shown in Figure 7.

- 2.
- Impedance Characteristics Analysis

_{1}is the primary series resonant impedance; Z

_{2}is the equivalent secondary series resonant impedance; Z

_{m}is the excitation inductance impedance; ω

_{s}= 2πf

_{s}is the switching angle frequency.

_{in})> 0 when f

_{n}> 1, we can get the resistive divider of the bidirectional CLLLC resonant converter as shown in Figure 8.

_{n}= (k + 1)

^{−1/2}is the inductive region. The inductive region in the region where f

_{n}> 1 can realize the ZVS of the switching transistor, and in the process of designing k and Q it is essential to ensure that the curve falls within these two regions.

- 3.
- Design Conditions for the Inductance Factor K and Quality Factor Q

_{min}satisfies:

_{n}> 1, the voltage gain curve is located in the inductive region and monotonically decreasing; in the area of 1/(k + 1)

^{1/2}< f

_{n}< 1, the voltage gain curve may be located outside the inductive area and may not appear monotonically, to meet the requirements, Q needs to meet certain conditions, thus the following focus on this operating frequency range. To meet the ZVS condition of the switching transistor, Im(Z

_{in}) > 0 should be satisfied. Then:

_{1}

^{′}(f

_{n}) = 0; then there is a unique solution in the range of 1/(k + 1)

^{1/2}< f

_{n}< 1; that is, f

_{n1}= 1/(2k + 1)

^{1/4}, which is a minimal value, and which is substituted into the equation F

_{1}(f

_{n}) to get:

^{1/2}< f

_{n}< 1, A(f

_{n}) > 0, B(f

_{n}) < 0, and C(f

_{n}) there exists a zero point for:

_{n2}< f

_{n1}and C(f

_{n}) > 0 in the range f

_{n1}< f

_{n}< 1. To make M′(f

_{n}) less than 0, it follows that:

## 3. Control Strategy of the Charging System

_{dc}is compared with the reference voltage v

_{dc_ref}to obtain the error v

_{err}; the error v

_{err}is first passed through the transfer function G

_{v}(s) of the voltage loop PI controller, and then multiplied by the v

_{shape}obtained through the phase-locked loop PLL to get further the current reference which is consistent with the phase of the ac input voltage i

_{ac_ref}, and then make a difference with the sampled input current i

_{ac}, the result i

_{err}after the current loop PI controller transfer function G

_{i}(s) for Sinusoidal Pulse Width Modulation (SPWM), the output signal through the drive circuit to control the switching transistor on and off.

_{o}and the given voltage V

_{o_ref}make a difference through the PI regulator and for limiting, and then through the pulse frequency modulation (PFM) and the driver module to control the switch transistor Q

_{1}~Q

_{4}on and off; at this time the secondary side switch transistor is only renewed by the body diode. The control in the reverse operation is similar to that in the forward movement and will not be described in detail here.

#### 3.1. Current Internal Loop Controller Design

_{id}(s) is the transfer function of the input current versus the duty cycle.

_{i}(s) is:

_{ip}is the proportionality factor; k

_{ii}is the integration factor.

_{c}= 2πf

_{s}= 3.14 × 10

^{4}rad/s, while keeping the phase margin as γ

_{i}= 45°. Substituting the design conditions to Equation (49) to obtain:

_{ip}= 0.2137 and k

_{ii}= 6710. The open-loop Bode diagram of the current loop before and after correction of the system is shown in Figure 11; the cut-off frequency of the system after modification is 5 kHz, and the phase margin is 45°, so the system can reach the steady state to meet the design requirements.

#### 3.2. Voltage Outer Loop Controller Design

_{vp}is the proportionality factor; k

_{vi}is the integration factor.

_{iv}(s) is the transfer function that represents the relationship between input current and output voltage, which can be obtained from Equations (18) and (19):

_{vc}= 62.8 rad/s, and the phase margin is set to 45°. Substitute s = jω into Equation (55) to obtain the corresponding amplitude and phase frequency characteristics as:

_{vp}= 0.0242 and k

_{vi}= 1.822. The open-loop Bode diagram of the voltage loop before and after correction of the system is shown in Figure 13. The cutoff frequency of the system before correction is 290 Hz, which becomes 10.1 Hz after correction, and the phase margin also becomes 46°, which shows that the PI controller meets the expected design requirements.

#### 3.3. Control of Soft Start

_{max}began to decline at a uniform rate, and the end of the start-up the frequency is equal to the circuit operating frequency. Frequency reduction method 2 is improved on the basis of the former circuit to establish the initial stage of resonant network energy with a faster rate of frequency reduction, to complete and then to reduce the relatively slower switching frequency to complete the process of establishing the output voltage until the start-up is completed. Frequency reduction method 3 uses the exponential function to calculate the switching frequency at each moment, but its decreasing speed is faster than the linear downscaling speed, which generates a larger current overshoot when the CLLLC resonant converter does not reach the steady state [30]. Therefore, the first frequency reduction method is used in this paper.

## 4. Parameter Design of Charging System

#### 4.1. Parameter Design of Bidirectional Totem Pole Changer

- AC Inductance

_{in}is:

_{o}is the output power; η is the efficiency.

_{in(min)_rms}= 176 V, the input current maximum RMS value I

_{rms(max)}is:

_{peak}is:

_{in(min)peak}is the peak voltage of the minimum input voltage; f

_{s}is the switching frequency.

- 2.
- DC Bus Capacitance

_{dc}is the output voltage; V

_{dc(min)}is the minimum capacitance-voltage value allowed after the energy cutoff at the input.

_{cpp}is the peak-to-peak value of the ripple.

- 3.
- Power Switching Transistor Selection

#### 4.2. Parameter Design of Bidirectional CLLLC Resonant Changer

- Transformer Turns Ratio

- 2.
- The Maximum and Minimum Voltage Gain of the Transformer

- 3.
- Inductance Factor K and Quality Factor Q

- 4.
- Resonant Inductance and Capacitance

- 5.
- The Selection of Power Switching

## 5. Simulation Analysis

#### 5.1. Simulation of the Forward Operating State

_{1}are shown in Figure 19. Through the detection of the voltage at the terminal of the primary-side switching transistor Q

_{1}and the current flowing through Q

_{1}, it can be seen that when the voltage at Q

_{1}drops from V

_{dc}to zero, the current flows positively through the switching transistor Q

_{1}only from the anti-parallel body diode of Q

_{1}, so the primary-side switching transistor in this state can realize ZVS. The waveforms of the resonant current and the excitation current are shown in Figure 20. When the excitation current is equal to the resonant current, the excitation current increases rapidly in the reverse operation, which shows that the operation is near the quasi-resonant point at this time. Due to the fluctuation of the DC bus voltage, the switching frequency of the resonant converter fluctuates between 95 kHz and 102 kHz.

_{q5}and D

_{q7}with the post-stage output voltages are shown in Figure 21 and Figure 22. The detection of the secondary sidelobe diodes D

_{q5}and D

_{q7}shows that D

_{q5}and D

_{q7}just achieve ZCS, i.e., the secondary sidelobe diodes can achieve ZCS, the output voltage fluctuates between 47.9 V and 48.1 V when stable, and the output voltage ripple is about 0.4%

#### 5.2. Simulation of Reverse Operating State

_{5}are shown in Figure 23. The DC bus voltage fluctuation makes the resonant converter’s switching frequency fluctuate between 110 kHz and 115 kHz. The Q

_{5}current flows positively to the switching transistor only after the voltage at Q

_{5}is zero, so the secondary side switching transistor can realize ZVS.

_{q1}and D

_{q3}can just achieve ZCS, and the waveform approximates a sinusoidal waveform. The current waveforms of diodes D

_{q1}and D

_{q3}are shown in Figure 25.

## 6. Experimental Verification

#### 6.1. Forward Operation

_{gs_2}and drain-source voltage V

_{ds_2}of the primary-side switch transistor Q

_{2}in the forward operation of the rear stage CLLLC resonant converter are shown in Figure 32. When V

_{ds_2}drops to zero potential, V

_{gs_2}starts to increase, indicating that all switch transistors on the primary side in the forward operation mode can achieve ZVS, thus reducing the turn-on loss of the switch transistors.

#### 6.2. Reverse Operation

_{gs_5}and drain-source voltage V

_{ds_5}of the rear stage CLLLC resonant converter at the secondary side switch transistor Q

_{5}during reverse operation are shown in Figure 35, and V

_{gs_5}starts to increase when V

_{ds_5}drops to zero potential, thus realizing ZVS. The current waveforms of the body diodes D

_{q1}and D

_{q3}and the resonant current waveforms are shown in Figure 36. It can be seen that the body diodes can achieve zero-current shutdown and that the resonant current approximates a sinusoidal waveform, which is the highest efficiency.

## 7. Conclusions

- Mathematical modeling of bidirectional totem pole converter using small signal analysis can obtain the transfer function of input current transformation with a duty cycle; an equivalent model of a bidirectional CLLLC resonant converter is obtained by fundamental wave analysis for characterization, and the parameters of the design are reasonable.
- The front stage adopts voltage and current double closed-loop control to keep the DC bus voltage stable, and the rear stage adopts frequency conversion and a high-frequency soft start to control the constant output voltage. The simulation model results of the control system show that the control strategy designed in this paper is reasonable.
- The experimental results prove that the bidirectional charging system can achieve power factor correction and has soft switching characteristics across the full load range.

## Author Contributions

## Funding

## Conflicts of Interest

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Symbol | Description | Value |
---|---|---|

V_{in} | AC input voltage range | 176–264 V |

V_{in_rated} | Rated AC side input voltage | 220 V |

V_{dc} | DC bus voltage range | 380–420 V |

V_{dc_rated} | Rated DC bus voltage | 400 V |

V_{o} | DC output voltage range | 44–56 V |

V_{o_rated} | Rated DC output voltage | 48 V |

P_{o} | Rated power | 300 W |

f_{s} | Switching frequency | 50–150 kHz |

f_{r1} | Resonant frequency | 100 kHz |

η | Efficiency | 95% |

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**MDPI and ACS Style**

Zhou, K.; Sun, Y.
Research on Bidirectional Isolated Charging System Based on Resonant Converter. *Electronics* **2022**, *11*, 3625.
https://doi.org/10.3390/electronics11213625

**AMA Style**

Zhou K, Sun Y.
Research on Bidirectional Isolated Charging System Based on Resonant Converter. *Electronics*. 2022; 11(21):3625.
https://doi.org/10.3390/electronics11213625

**Chicago/Turabian Style**

Zhou, Kai, and Yue Sun.
2022. "Research on Bidirectional Isolated Charging System Based on Resonant Converter" *Electronics* 11, no. 21: 3625.
https://doi.org/10.3390/electronics11213625