# Decoupled MPC Power Balancing Strategy for Coupled Inductor Flying Capacitor DC-DC Converter
###### Abstract  
A decoupled model predictive control (MPC) power balancing strategy for a coupled inductor-based flying capacitor DC-DC converter (FCDC) is a proposed to solve the power imbalance caused by the parameter differences in the coupled inductor. The decoupled mathematical model of coupled inductor FCDC is firstly derived by analyzing the converter operation state under various modes. On this basis, the control relationship between inductor current and flying capacitor (FC) voltage is redefined and an MPC power balance strategy based on the inductor current with single-step optimization is proposed. The proposed MPC strategy not only achieves decoupled power balancing control but also solves multi-objective dynamic optimization control of the inductor current and FC voltage, greatly reducing the computation load. A detailed theoretical analysis of the proposed strategy is presented and the balancing performance is effectively verified through the experiments.  
volume was not effectively optimized. Through the above analysis, although the coupled inductor helps to improve the system's power density, the phase-to-phase power imbalance caused by the difference in the coupled parameters is still a key issue that needs to be addressed.  
For FC topology, in addition to current control, it is also necessary to control the voltage of the FC to ensure it is half of the port-side voltage. Ref. [18] studied FC voltage self-balancing characteristics with small perturbations. Ref. [19] proposed an FC voltage control strategy based on an RLC circuit, which showed acceptable reliability. However, the auxiliary circuit weakens system reliability and increases system cost. Based on the average state equation, refs. [20; 21] proposed the decoupled control strategy of output voltage and FC voltage sharing control using a PI algorithm for three-level and five-level FC topology. However, with the dynamic response speed of the linear regulator, it is hard to satisfy abrupt load changes. To address this issue, ref. [22] proposed a FC topology control method based on MPC. However, the multi-objective control brings a heavy computational load to the MPC strategy. Therefore, refs. [23; 24; 25] use mean square error, dynamic optimization, and artificial neural network methods, respectively, to estimate the optimal cost function, but these algorithms are complex to apply. Ref. [26] proposed an improved MPC algorithm for a bidirectional four-quadrant flying capacitor bi-directional DC-DC converter and derived a decoupled control model for the dual-side capacitor and inductor current, and achieved desired control performance. However, the three control objectives still impose a large computational load on system control.  
Coupled inductor FCDC effectively improves the power density of an ESS, but the power imbalance issue caused by the parameter differences in the coupled inductor has not been solved. In this paper, a decoupled MPC power balancing strategy with single-step optimization for a two-phase coupled inductor FCDC is proposed. The proposed strategy not only achieves decoupled power balancing control but also solves the multi-objective dynamic optimization control issue of inductance current and FC voltage and greatly reduces the computational load. The proposed strategy has favorable power, balancing performance and dynamic performance, and has been effectively verified through experimental results.