This work proposes a new scheme for the solution of the Synthetic Dynamics Power Flow (SDPF) method. The integration of the SDPF equations requires an implicit technique, hence, the mixed Adams-BDF algorithm was chosen. As the original version of SDPF presented some problems to solve some well-and ill-conditioned cases and diverged for unsolvable cases, a modification based on the polar form of the optimal multiplier (OM) from the Load Flow with Step Size optimization (LFSSO) was proposed and tested. The choice of the OM was supported by its reported ability to solve ill-conditioned cases and capability to indicate the unsolvability of a power system. The new modified SDPF was tested with some IEEE benchmark cases, four practical cases as well as three reported ill-conditioned networks.