High power dual active bridge (DAB) converters are widely adopted in DC and hybrid AC/DC micro-grids, for which <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">fast start-up dynamics</i> of DAB converters is a key requirement. Conventional start-up methods usually require complex operation stages, and a time-consuming parameter-tuning process, resulting in slow dynamics. In this work, we propose a new simple and optimal start-up method for DAB converters. Major contributions lie in <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">three-folds</i> . (i) We theoretically analyze the transmission power and the peak inductor current of extended phase-shift modulation. (ii) A new Lagrange Multiplier method is proposed to solve the optimal phase-shift ratios of the underlying control problem, resulting in very fast control dynamics at maximum power transmission, fully respecting the system permissible current limit. (iii) An effective and simple strategy by <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">solely</i> manipulating the gate signals in the first switching period is newly proposed to eliminate the magnetic bias. The proposed method avoids complex parameter-tuning procedures. Experimental results demonstrate the effectiveness of the proposed method. Results confirm that with the proposed solution a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">much faster</i> start-up process with a controllable inductor current <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">without</i> DC bias is achieved, in comparison with the recently reported start-up methods.