To achieve continuous and real-time stress optimization control of the dual active bridge converter under power transmission or voltage fluctuations, it is crucial to study the patterns between modes and among optimization control variables in modes. However, current research needs depth, and functional expressions of stress optimization control variables are complex.

This paper employs genetic algorithms for stress optimization. The intrinsic laws among the optimization variables in each mode are elucidated through the optimization results. An innovative trigonometric function polar coordinate method is adopted to derive the corresponding optimization control variable function expressions.

Firstly, based on waveform equivalence simplification and the principle of waveform and energy transmission, the four locally optimal modes are identified from the twelve working modes, which exhibit low stress or effective values in different power ranges. It reduces the number of modes that require optimization, which reduces the optimization burden.

Secondly, the stress of the four modes is optimized, and the optimization results are compared to determine the laws governing the optimization variables in different power ranges with different k values. Through systematic analysis, the laws of four local optimal operating modes in the low/high power section can be obtained.

Thirdly, the expressions with optimization variables are obtained by substituting these laws into the corresponding power transfer expression. The optimized variables are converted into trigonometric polar coordinate forms through the trigonometric function polar coordinate method. The expressions for the minimum current stress function and its optimization control variables are obtained by substituting optimized variables into the stress expression to obtain the minimum stress value.

Compared with the current stress in the full power range for four local operating modes, the optimal mode and optimal control variables for each power segment across the entire power range are selected, thereby achieving global optimization control. The innovations in this study are presented.

(1) Analyze and contrast the current stress optimization results for different voltage adjustment rates k to discern the laws among the optimized variables across the four local optimal modes in various power ranges.

(2) The power constraint and trigonometric polar coordinate methods are utilized to derive a precise expression for the optimal stress control variables. The globally optimal control variables are selected by comparing the current stress of four local optimal modes.

The following conclusions can be drawn. (1) Under the buck operation conditions of stress optimization for both forward and reverse power transfer across the entire power range, mode 1.1 is globally optimal during low forward transmission power when 0<P<k²(1-k); mode 1.4 becomes globally optimal during high forward transmission power in the range k²(1-k)<P<k/2. Similarly, for low reverse transmission power, mode 2.1 is globally optimal in the range k²(k-1)<P<0, and mode 2.3 becomes globally optimal during high reverse transmission power when -k/2<P<k²(k-1). (2) The stress optimization control under TPS modulation improves the efficiency of the DAB converter compared to other modulation strategies. Notably, it exhibits a significant enhancement under the low-power segment and high-voltage mismatch scenarios.