Closed-Form Optimal Current-Limiting Curve-Based Variable Duty-Cycle Soft Start-Up Strategy for the LLC DC Transformer

The LLC converter-based dc transformer is popular for its stiff voltage gain, very high efficiency, and simple control. To avoid excessive start-up inrush current and hardware overdesign, the fixed-frequency variable duty-cycle soft start-up strategy is often adopted. However, in this conventional strategy, the optimal current-limiting curve (OCC) is derived by the challenging numerical model iterative algorithm, which is difficult to model, calculate online, and adapt to different operating conditions. To solve this problem, a closed-form OCC (COCC)-based soft start-up strategy is proposed. The COCC is derived by state-trajectory analysis and can be quickly calculated through the simple closed-form equation, providing greater practicality and flexibility while accurately maximizing the utilization of the allowable peak current. Furthermore, the closed-form equation makes it possible to estimate the start-up capability under the variable duty-cycle strategy. The calculation method of the maximum allowable start-up load is proposed, offering an important basis for the design of distribution system restoration schemes. Finally, a 50-kW dc transformer is built to verify the effectiveness of the proposed strategy under various conditions.