High-Bandwidth, Low-Computational Approach: Estimator-Based Control for Hybrid Flying Capacitor Multilevel Converters Using Multi-Cost Gradient Descent and State Feedforward

Abstract

This paper presents an estimator-based control framework for hybrid flying capacitor multilevel (FCML) converters, achieving high-bandwidth control and reduced computational complexity. Utilizing a hybrid estimation method that combines closed-loop and open-loop dynamics, the proposed approach enables accurate and fast flying capacitor voltage estimation without relying on isolated voltage sensors or high-cost computing hardware. The methodology employs multi-cost gradient descent and state feedforward algorithms, enhancing estimation performance while maintaining low computational overhead. A detailed analysis of stability, gain setting, and rank-deficiency issues is provided, ensuring robust operation across diverse converter levels and duty cycle conditions. Simulation results validate the effectiveness of the proposed estimator in achieving active voltage balancing and current control with 6-level AC-DC buck FCML, contributing to cost-effective solutions for FCML applications, such as data centers and electric aircraft.

Figures (18)

• Figure 1: Single swiching cell of flying capacitor converter with adjacent flying capacitors and $k$-th switch pair. $v_{c,k}$ is the voltage of $k$-th flying capacitor voltage. $S_{k}$ and $\bar{S}_{k}$ are the switching states of $k$-th upper switch and lower switch, respectively.
• Figure 2: Circuit diagram of grid-connected buck-type hybrid FCML converter with input filter. $v_{grid}$, $v_{in}$, $i_L$, and $v_{out}$ are grid voltage, input capacitor voltage, inductor current, and output capacitor voltage, respectively.
• Figure 3: Block diagram of the estimator-based controller for hybrid FCML converter. $v_{sw}$ represents the pole voltage, while $\mathbf{\hat{v}_{c}}$ denotes the estimated flying capacitor voltage. $\mathbf{\Delta d^{*}}$ is the output of the voltage balancing controller, $\mathbf{d^{*}}$ is the duty cycle reference, and $i^*_L$ refers to the current control reference. The controller structure is hierarchically organized based on the principle of time-scale separation.
• Figure 4: Block diagram of generalized proportional-integral-resonant (PIR) controller. $x$ is the target variable under control and $y$ is the output variable for controlling $x$. $\gamma$ is the variable to enable and disable some parts of the generalized PIR controller. $F(s)$ is the transfer function of the input filter.
• Figure 5: The figure of PSPWM carriers when $N = 5$ and $N = 4$. When $N$ is an odd number, the peak of one PWM carrier coincides with the valley of another. Conversely, when $N$ is an even number, no such overlap occurs, as the peaks and valleys are evenly distributed across the carriers.