Dynamic neural networks (DNNs) are widely used in data‐driven modeling of nonlinear control systems. Due to the complexity of the actual operating nonlinear power systems, rigorous dynamic models are always unknown. DNNs can focus on methods that only use input and output information to establish accurate dynamic models and reduce noise in measured data, which is called data‐driven modeling. The core of the DNN is the feedback with memory function. This paper analyzes the traditional Elman neural network (ENN) and nonlinear auto‐regression with exogenous input (NARX) neural network with different structure feedback structures, and proposes a full feedback dynamic neural network (FF‐DNN) with exogenous input. Eight different kinds of neural networks (including ENN, NARX, etc.) are compared and analyzed. The eight kinds of neural networks are applied on the experimental data of the DC‐AC inverter and the power system of Zhejiang Juchuang Smart Technology Company Park in Wenzhou. The experimental results are used to compare the performance of the data‐driven models established by eight different kinds of neural networks under different noise conditions, verify the robustness and generalization performance of dynamic data‐driven modeling based on FF‐DNN, and demonstrate the feasibility and effectiveness of FF‐DNN in actual power systems. © 2023 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.