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This paper studies the effectiveness of reactive power compensation using a multilevel, hexagram-converter-based STATic COMpensator (STATCOM) with one-cycle control (OCC) for a wind farm with fixed-speed turbines, and the interaction with the power system network. Comparison is made with several common types of multilevel voltage source converters used for STATCOM applications. A new voltage control method based on OCC principles for hexagram-based STATCOMs is proposed and proven by a wind farm power system simulation showing the improvement of voltage variations caused by wind speed changes. The experimental results from tests of a small-scale hexagram converter prototype have verified the proposed converter and control method.