State Quadrant Modeling Approach: Simplifying High-Precision Modeling of DC-DC Converters for Model-Based Control Strategies

DC-DC converters switch from Continuous Conduction Mode (CCM) to Discontinuous Conduction Mode (DCM) when the inductor current drops to zero in scenarios such as load reduction and load pulse. CCM model-based control methods suffer from degraded performance under such conditions, whereas hybrid model-based control methods are limited by complex mathematical formulations of logical variables, piecewise structures, and inequalities and high computational costs. This paper proposes a state quadrant modeling approach which includes circuit state classification and state descriptor construction, offering high-precision and simplifying models for model-based control. The circuit state classification method identifies circuit states based on freewheeling conditions and current trends, ensuring comprehensive coverage of operating scenarios and enhancing modeling accuracy. Furthermore, the state descriptor construction method employs logical operations to derive one or two logical variables that uniformly represent different circuit states, eliminating the need for inequalities and piecewise structures. This method is highly scalable and applicable to single-inductor, dual-inductor, multi-phase, and isolated converters. It significantly enhances control performance, simplifies design, and improves computational efficiency when integrated into model-based control methods. Case studies demonstrate that the proposed models achieve 99.99% accuracy relative to simulink results and 98.99% accuracy relative to experimental results. They also reduce computation time by 36.85% in model predictive control and decrease voltage response time by 35.69%.