For some newly-developed large coal-fueled power plants in China， the multi-mode SSR problem caused by the relatively high compensation level of fixed series capacitor in long-distance high-capacity plant-to-grid transmissions， poses a realistic threat to the safety of the turbine-generators and the stability of the grid. Taking the Shangdu series-compensated transmission project（2nd phase） as an example， this paper discusses the mechanism of multi-mode SSR occurrence. Basic principles of supplementary excitation damping control（SEDC）to improve multi-mode torsional damping are studied. Furthermore， several key issues on SEDC and the solutions are discussed. That provides useful guidance of further research and application of SEDC to solve the SSR problems in the power systems in China.