A unique rotary kite turbine designed with tensile rotary power transmission (TRPT) is introduced in this work. Power extraction, power transmission and the ground station are modelled in a modular framework. The TRPT system is the key component of power transmission, for which three models with different levels of complexity are proposed. The first representation is based on the stationary state of the system, in which the external and internal torques of a TRPT section are in equilibrium, referred to as the steady-state TRPT model. The second representation is a simplified spring-disc model for dynamic TRPT, and the third one is a multi-spring model with higher degrees of freedom and more flexibility in describing TRPT dynamics. To assess the torque loss on TRPT, a simple tether drag model is written for the steady-state TRPT, followed by an improved tether drag model for the dynamic TRPT. This modular framework allows for multiple versions of the rotor, tether aerodynamics and TRPT representations. The developed models are validated by laboratory and field-testing experimental data, simulated over a range of modelling options. Model-based analysis are performed on TRPT design, rotor design and tether drag to understand any limitations and crucial design drivers. Improved designs are explored through multi-parameter optimisation based on steady-state analysis.