To quantitatively investigate the impact of interactions among control loops in a double-fed wind farm integrated with the grid via an MMC-HVDC system on sub-/super-synchronous oscillations, an analytical method combining modal analysis and relative gain array (RGA) is proposed. Firstly, a small-signal model of the double-fed wind farm integrated with the grid through MMC-HVDC is established, with its accuracy being verified by comparing its step response with that of an electromagnetic transient simulation model. Secondly, modal analysis is employed to identify the dominant sub-/super-synchronous oscillation modes affecting system stability, and the primary participating variables of these oscillation modes are determined through participation factor calculations, laying a foundation for subsequent analysis of the influence of interactions among different control loops. Thirdly, the RGA is introduced to confirm the existence of interactions, quantify and compare the strength of interactions among control loops associated with the primary variables of the dominant oscillation modes. This focuses subsequent research on the rotor-side converter (RSC) control loop of the wind farm and the fixed V/f control loop in the MMC-HVDC system. Finally, based on the variation of RGA values with influencing factors, the effects of the electrical distance of grid connection and the controller parameters on the degree of interaction among control loops are quantitatively evaluated and verified using time-domain simulation. The study reveals that, when the electrical distance increases or the proportional coefficient of the fixed V/f control on the MMC-HVDC side rises, the interaction between the RSC control loop on the double-fed wind turbine side and the fixed V/f control loop intensifies, leading to a decrease in system stability.