The rapid development of electric vehicles (EVs) has increased the demand for efficient and reliable EV charging stations. The DC/DC converter is a critical component in EV charging stations, responsible for providing appropriate charging voltage to the EV battery pack. However, these converters often face challenges such as significant output voltage fluctuations and slow dynamic response when subjected to load disturbances. To address these issues, this study focuses on the CLLC resonant DC/DC converter, known for its soft-switching characteristics, high efficiency, and high power density. Traditional control strategies like proportional-integral (PI) control are commonly used but exhibit limitations in handling dynamic disturbances. This paper proposes a fuzzy active disturbance rejection control (FADRC) strategy to enhance the dynamic performance and robustness of the DC/DC converter in EV charging stations.
The CLLC resonant converter topology consists of primary and secondary full-bridge circuits, resonant inductors (Lr1 and Lr2), resonant capacitors (Cr1 and Cr2), and a magnetizing inductor (Lm). The converter operates at two resonant frequencies: fr1 when only Lr1 and Cr1 participate in resonance, and fr2 when Lm joins the resonance. The resonant frequencies are given by:
$$ f_{r1} = \frac{1}{2\pi\sqrt{L_{r1}C_{r1}}} $$
$$ f_{r2} = \frac{1}{2\pi\sqrt{(L_{r1} + L_m)C_{r1}}} $$
To design an effective controller, a small-signal model of the CLLC resonant converter is developed using the extended describing function (EDF) method. This approach linearizes the nonlinear system by considering only the fundamental components of the state variables, such as resonant currents and capacitor voltages. The state-space representation of the small-signal model is:
$$ \frac{d\mathbf{x}}{dt} = \mathbf{A}\mathbf{x} + \mathbf{B}u $$
$$ y = \mathbf{C}\mathbf{x} $$
where $\mathbf{x}$ is the state vector, $u$ is the control input (switching frequency), and $y$ is the output voltage. The transfer function relating the switching frequency perturbation to the output voltage is derived as:
$$ G(s) = \mathbf{C}(s\mathbf{I} – \mathbf{A})^{-1}\mathbf{B} $$
However, the full-order model is complex, with a high order due to multiple energy storage elements. To simplify controller design, a reduced-order model is obtained using the frequency sweep method. The second-order equivalent transfer function is:
$$ G_p(s) = \frac{c_1 s + c_0}{s^2 + a_1 s + a_0} $$
where $a_0 = 2.538 \times 10^9$, $a_1 = 10990$, $c_0 = -6.638 \times 10^5$, and $c_1 = 1.668$. This model accurately captures the dynamic behavior of the converter in the low-to-medium frequency range, making it suitable for control system design in EV charging stations.
The proposed control strategy employs a dual-loop structure: an inner current loop with PI control and an outer voltage loop with FADRC. The voltage loop takes the output voltage $V_0$ and reference voltage $V_{\text{ref}}$ as inputs, producing the reference current $I_{\text{ref}}$ for the inner loop. The FADRC combines linear active disturbance rejection control (LADRC) with fuzzy logic to adaptively tune parameters. LADRC consists of a linear extended state observer (LESO) and a linear state error feedback (LSEF) law. For a second-order system, the general form is:
$$ \ddot{y} = -a_1 \dot{y} – a_0 y + b u + \omega $$
where $\omega$ represents external disturbances. By defining the total disturbance $f = (b – b_0)u + \omega – a_1 \dot{y} – a_0 y$, the system is rewritten as:
$$ \ddot{y} = b_0 u + f $$
The state variables are chosen as $x_1 = y$, $x_2 = \dot{y}$, and $x_3 = f$. The state-space model is:
$$ \dot{\mathbf{x}} = \mathbf{A}\mathbf{x} + \mathbf{B}u + \mathbf{E}\dot{f} $$
$$ y = \mathbf{C}\mathbf{x} $$
with matrices:
$$ \mathbf{A} = \begin{bmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{bmatrix}, \quad \mathbf{B} = \begin{bmatrix} 0 \\ b_0 \\ 0 \end{bmatrix}, \quad \mathbf{E} = \begin{bmatrix} 0 \\ 0 \\ 1 \end{bmatrix}, \quad \mathbf{C} = \begin{bmatrix} 1 & 0 & 0 \end{bmatrix} $$
The LESO is designed as:
$$ \dot{\mathbf{z}} = (\mathbf{A} – \mathbf{L}\mathbf{C})\mathbf{z} + \mathbf{B}u + \mathbf{L}y $$
where $\mathbf{z} = [z_1, z_2, z_3]^T$ estimates $[y, \dot{y}, f]^T$, and $\mathbf{L} = [\beta_1, \beta_2, \beta_3]^T$ is the observer gain matrix. Using pole placement, the observer bandwidth $\omega_o$ is set, and gains are calculated as $\beta_1 = 3\omega_o$, $\beta_2 = 3\omega_o^2$, $\beta_3 = \omega_o^3$. The LSEF law is a PD controller:
$$ u_0 = k_p (V_{\text{ref}} – z_1) – k_d z_2 $$
and the control law is:
$$ u = \frac{u_0 – z_3}{b_0} $$
The controller bandwidth $\omega_c$ determines $k_p = \omega_c^2$ and $k_d = 2\omega_c$. To enhance adaptability, fuzzy logic is integrated to adjust $k_p$ and $k_d$ online. The fuzzy controller inputs are the error $e = V_{\text{ref}} – y$ and its derivative $\Delta e$, with outputs $\Delta k_p$ and $\Delta k_d$. The fuzzy sets are {NB, NM, NS, ZO, PS, PM, PB}, and membership functions are Gaussian. The fuzzy rules for $\Delta k_p$ and $\Delta k_d$ are summarized in the following tables:
| e / Δe | NB | NM | NS | ZO | PS | PM | PB |
|---|---|---|---|---|---|---|---|
| NB | PB | PB | PM | PM | PS | ZO | ZO |
| NM | PB | PB | PM | PS | PS | ZO | NS |
| NS | PM | PM | PM | PS | ZO | NS | NS |
| ZO | PM | PM | PS | ZO | NS | NS | NM |
| PS | PS | PS | ZO | NS | NS | NM | NM |
| PM | PS | ZO | NS | NM | NM | NM | NB |
| PB | ZO | ZO | NM | NM | NM | NB | NB |
| e / Δe | NB | NM | NS | ZO | PS | PM | PB |
|---|---|---|---|---|---|---|---|
| NB | PS | PS | ZO | ZO | PB | PB | PB |
| NM | NS | NS | NS | NS | ZO | NS | PM |
| NS | NB | NS | NS | NS | ZO | PS | PM |
| ZO | NB | NM | NM | NS | ZO | PS | PM |
| PS | NB | NM | NS | NS | ZO | PS | PS |
| PM | NM | NS | NS | NS | ZO | ZO | PS |
| PB | PS | ZO | ZO | ZO | PB | PB | PB |
The adjusted parameters are:
$$ k_p’ = k_p + \Delta k_p, \quad k_d’ = k_d + \Delta k_d $$
Stability analysis of the FADRC involves proving the boundedness of the observer estimation error and the tracking error. The observer error dynamics are:
$$ \dot{\mathbf{e}} = (\mathbf{A} – \mathbf{L}\mathbf{C})\mathbf{e} + \mathbf{E}\dot{f} $$
where $\mathbf{e} = [e_1, e_2, e_3]^T = [x_1 – z_1, x_2 – z_2, x_3 – z_3]^T$. By assuming the disturbance derivative $\dot{f}$ is bounded, the error remains bounded. For the closed-loop system, the tracking error converges to zero with properly chosen $k_p$ and $k_d$, ensuring stability in EV charging station applications.
Simulation results validate the effectiveness of the FADRC strategy. The CLLC resonant converter parameters are: input voltage $V_{\text{in}} = 350\,V$, output voltage $V_0 = 60\,V$, resonant capacitors $C_{r1} = 9.722\,nF$ and $C_{r2} = 327\,nF$, resonant inductors $L_{r1} = 260\,\mu H$ and $L_{r2} = 7.752\,\mu H$, magnetizing inductor $L_m = 1300\,\mu H$, transformer turns ratio $n = 5.8$, and resonant frequency $f_r = 100\,kHz$. Under load step changes, the FADRC-based converter exhibits superior performance compared to PI control. For a load step-down from 100% to 50%, the FADRC reduces the output voltage peak to 60.91 V and the recovery time to 10.554 ms, whereas PI control results in a peak of 62.56 V and a recovery time of 10.58 ms. Similarly, for a load step-up from 50% to 100%, FADRC achieves a peak of 62.95 V and recovery in 30.873 ms, outperforming PI control (63.68 V peak, 31.757 ms recovery). These results demonstrate that FADRC enhances dynamic response and robustness in EV charging stations.
In conclusion, the fuzzy active disturbance rejection control strategy effectively addresses the challenges of output voltage fluctuations and slow dynamic response in DC/DC converters for EV charging stations. By integrating fuzzy logic with linear active disturbance rejection control, the system achieves improved anti-disturbance capability and voltage stability. This approach ensures reliable and efficient operation of EV charging stations, contributing to the advancement of electric vehicle technology.