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Star-connected cascaded H-bridge (SCHB) STATCOM is being widely used at medium and high voltages to support the grid by injecting positive and negative sequence current. Under balanced conditions, the rated reactive power is usually utilized to calculate the required reactive current reference based on instantaneous power theory. However, under grid voltage sag, the rated reactive power changes due to the introduced negative sequence current and extra zero sequence voltage for cluster voltage balancing, which may increase overcurrent and overmodulation risk. Therefore, determining how to derive the maximum compensable reactive power is required for SCHB STATCOM under the grid voltage sag. In this article, the quantitative relationship between the imbalanced degree of grid voltages and reactive power reference is fully explored. On this basis, the maximum reactive power is calculated under voltage sags by considering current and voltage limitations. In this calculation, a new geometrical analysis method is proposed, which makes the calculation speed faster for online calculations. Therefore, a new grid support control strategy is proposed for the SCHB STATCOM under grid voltage sag, which can effectively support the grid with the maximum output reactive power. Finally, the proposed method is verified by experimental results on a 400 V/7.5 kVar SCHB STATCOM prototype.