With presspack module of Insulated Gate Bipolar Transistor (IGBT) connected in series, Static Synchronous Compensator (STATCOM) can be connected to high voltage distribution system directly by a three-phase two/three level converter topology. However, the DC capacitor voltage in STATCOM can be disturbed by unbalance voltage in distribution system and began to be fluctuated at 100 Hz, which would bring great danger to the operation of equipment. According to conservation of energy, the mathematical models of STATCOM DC voltage fluctuations is established and simplified, and the relationship between DC voltage fluctuations with unbalance factor, capacity of DC capacitor and DC voltage amplitude is analyzed. Then, to realize the intuitive judgment of the device operation stability under unbalanced voltage, the method to determine the stable operating range of the DC voltage fluctuation of IGBT series-connected STATCOM with IGBT presspack modules is purposed. Finally, the correctness and effectiveness of proposed method is verified by simulations. This work is supported by the Science and Technology Project of State Grid Corporation of China (No. 5500-201913130A-0-0-00).