In traditional power system state estimation (PS-SE), the iterative step size of state correction equation is generally fixed. But considering the low data quality and the complex network condition in practice, it is difficult that the convergency, estimation quality, and computation efficiency can reach the satisfactory state simultaneously by adopting fixed step iteration strategy. To solve this problem, we find a variant of classical logistic function (we call it as the generating function) which can intrinsically match the iteration demand of PS-SE, it is adopted as the step size adjusting factor. By “installing” some control parameters on the generating function and adjusting part of them by the feedback of the iteration performance in real time, generating function can be auto-adjusted in the iteration process to satisfy PS-SE’s demand. In addition, a weight factor function is introduced to auto-adjust the state variables’ weights in iteration period, it has good performance on suppressing bad data. The proposed step adjusting mechanism is directly controlled by the iteration performance, this means it couples loosen with the network mathematical model, so it is a model low-dependent PS-SE algorism with good portability. Based on IEEE30 node system, it is found that the proposed algorithm is superior to the one of adopting fixed step strategy in terms of convergence, computation efficiency and estimated quality when the measurement has bad data and the power system is under quasi ill-conditioned and ill-conditioned.