The method used to calculate insertion indexes plays an important role in determining the overall performance of the modular multilevel converter. Direct voltage control, which is the simplest option, results in a large circulating current ripple because this modulation technique does not account for the arm voltage ripples. This led to the development of compensated modulation techniques that compensate for the arm voltage ripples thereby eliminating the circulating current ripple. There are two variants of compensated modulation-closed loop and open loop. The closed-loop version requires measurement of the arm voltages without distortion and delay, which is difficult to achieve in practice. The open-loop method overcomes this challenge by using estimated arm voltages. However, accurate knowledge of the system parameters is needed for effective removal of the circulating current ripples. This is a limitation because the parameters change with time and operating conditions. This paper presents a modified version of the open-loop method, which includes a scheme for correcting parameter errors online. The method estimates the parameters, arm capacitances, and time delay, by using feedback controllers acting on the circulating current ripples. Mathematical derivation of the method, together with its validation using simulation and experimental tests, is presented in detail.