Speed–Time Modeling of Induction Machines During Direct‐On‐Line Starting Using Analytical and Iterative Special Trans Function Theory Frameworks

The direct‐on‐line starting of induction machines (IMs) is a highly nonlinear electromechanical process, typically modeled in the literature using torque expressions based on the Kloss equation and the Thevenin equivalent circuit, combined with the Lambert W function. Although these Lambert‐based models are well‐established, there is a need for alternative analytical approaches that offer greater flexibility in modeling. This work develops new closed‐form and iterative analytical models for predicting the no‐load speed profile during direct starting, employing Perovich's Special Trans Function Theory (STFT). The proposed formulations contribute to a more robust mathematical interpretation of the complex nonlinear processes during starting. Exact STFT solutions and an optimized iterative STFT algorithm are derived, providing a balanced trade‐off between computational efficiency and prediction accuracy. The models are validated through numerical simulations and experimentally tested on a 300 W laboratory prototype, demonstrating excellent agreement with simulation results and practical measurements. The proposed formulations focus on single‐cage IMs; extension to double‐cage or deep‐bar designs requires further investigation. Complete MATLAB and Mathematica implementations are provided to support reproducibility and further development. The results confirm that STFT‐based analytical modeling offers a powerful and useful framework for characterizing the dynamic behavior of IMs under the most demanding operating conditions—direct‐on‐line starting.