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This study presents a new scheme for a continuously variable (CV) series braking resistor (SBR) with independent per phase controller. The CV-SBR is a CV and not stepwise. A novelty of the work presented is that the CV-SBR operates on the whole range of wind speeds. The proposed scheme is applicable to fault ride-through (FRT) of fixed speed wind turbines (FSWTs). The CV-SBR scheme is compared to the single-step (SS) and multi-steps (MS) SBRs. The CV-SBR scheme is modelled and simulated in PSCAD/EMTDC™. The performance of the wind turbine is studied for balanced and unbalanced fault scenarios. The CV-SBR scheme is advantageous over the other two candidates with its ability to limit the fault current and reduce the turbine speed deviation at any wind speed. The CV-SBR is employed with a static synchronous compensator (STATCOM) to allow FRT of FSWT connected to weak grid during nearby faults and to deliver the reactive current required by some grid codes. The CV-SBR scheme is successful in reducing voltage disturbance's consequences on the generator's mechanical system. Simulation results show that the CV-SBR allows FRT of FSWT connected to weak grid where the STATCOM alone is not able to sufficiently enhance the FRT of FSWT during nearby faults.