A modified hysteresis current controller to achieve nearly constant switching frequency operation for a cascaded H bridge inverter based STATCOM is the focus of this article. The varying switching frequency characteristics of conventional hysteresis current controller for grid connected systems is a threat to the other loads, despite of the fast transient response offered. A constant switching frequency operation imparts a proper current filtering action and quick current tracking in grid connected systems. The modified hysteresis controller using variable hysteresis boundary proposed in this article contributes constant switching frequency characteristics without compromising the dynamic performance of the system. The variable hysteresis boundary is determined from the computed values of current error, and this computation is based on the sampled values of reference voltage vector. The boundary computation is embedded in the space vector modulation of inverter to ensure optimal switching vector selection. When compared to the conventional two-level voltage source inverters, multilevel inverters have enhanced power capability and quality. The hysteresis current controller described in this article is designed for a cascaded H-bridge inverter based STATCOM to achieve a voltage fast fourier transform (FFT) profile similar to that of a space vector modulated cascaded H-bridge inverter. The three-level cascaded H-bridge inverter based STATCOM with proposed current control strategy has better steady-state performance, faster dynamic performance, and constant switching frequency characteristics as compared to a voltage controlled space vector modulated three-level cascaded H-bridge inverter based STATCOM, which is experimentally substantiated. The hardware implementation of the controller for the STATCOM of rating 5 kVA is carried out on OPAL-RT real-time simulator platform and is validated experimentally for a three-phase balanced load.