The role of high/medium power bidirectional DC-DC converters in the next generation of multi-terminal high voltage DC transmission networks is to enable intercontinental bulk power transfer. This is encouraged by increased DC-DC converter functionalities such as DC voltage stepping/matching, DC line tapping, power flow regulation, bidirectional power flow control, and DC fault isolation. In this work, a bidirectional dual active bridge (DAB) DC-DC converter is selected to pursue such functionalities, due to its desirable features for use in high power applications. This includes galvanic isolation, fast power reversal, high power density, buck/boost operation, possibility of high stepping ratio of conversion and its inherent fault isolation capability without a need for a very fast controller. However, increased reactive power and reduced soft switching range are the main limitations of DAB for applications involving high voltage conversion ratios. Reactive power circulation increases the converter RMS current leading to an increase in conduction losses especially in high power applications. Therefore, a novel triple phase shift (TPS) control algorithm that minimises the total reactive power is proposed to enhance the performance of the DC-DC converter. The algorithm iteratively searches for TPS control variables that satisfy the desired active power flow while selecting the operating mode(s) with minimum reactive power consumption. In addition, a complete DAB converter behaviour under TPS control which has not been studied in the literature before is performed for both power flow directions. Steady state analysis is undertaken for each mode by computing exact expressions for modes power transfer and range (to characterise mode boundary) without fundamental frequency assumption. A new definition of reactive power consumption based on converter total inductance is proposed and a detailed constraint for zero voltage switching (ZVS) is also presented. Moreover, it is shown that all known DAB phase shift modulation techniques including conventional, dual and extended phase shift, represent special cases of TPS, therefore the presented analysis provides a generalised theory for all phase shift based modulation techniques. To scale the converter to higher power level, a modular DAB converter is implemented with a development of power sharing controllers that utilise TPS modulation scheme. The focus is to ensure stable operation of the DAB modules in both power flow directions in the presence parametric mismatches. The reactive power minimisation algorithm and a new DC fault management mechanism are embedded within the proposed controllers. Detailed simulation and experimentation are used to validate the proposed algorithm and power sharing controllers.