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This study describes the power conversion and control solution used in the electrical power take-off of a 35 kW test rig developed to investigate a linear, direct drive, air-cored, tubular, permanent magnet generator for an offshore wave energy device. The solution proposed is to collect the power extracted directly from individual coils of the generator, which have different induced voltages and cannot easily be connected into a small number of phases. Local energy storage is integrated into the system to smooth the electrical output power and reduce the rating of the downstream inverter for grid interfacing. The solution is demonstrated by analysis, backed up by simulation and test results. This shows the potential and limitations of the proposed conversion technology solution.