This paper presents a comprehensive modeling approach for electrical machines with multi-phase systems, incorporating fundamental physical principles and accounting for saturation and cross-coupling effects. It begins with the model’s assumptions and derives a multi-phase winding representation in its orthogonal reference frame. The Clarke factor for multi-phase systems is derived, facilitating the calculation of cross-coupling factors of mutual inductances, especially between different winding systems. The model is further extended to multi-phase windings in an arbitrarily oriented (d, q)-reference frame. The electrical subsystem, which includes multiple multi-phase winding systems, is developed alongside machine power and torque equations. The model is validated through application to a real electrically excited synchronous machine (EESM) with a damper winding, modeled as a multi-phase system. Machine parameters, including nonlinear flux-linkage maps, are obtained through finite element analysis (FEA) to validate the cross-coupling factors of mutual inductances in the (d, q)-reference frame. Additionally, dynamic simulations in MATLAB/Simulink demonstrate the model’s effectiveness in nonlinear current control and dynamic simulation.

This study introduces an optimal reference voltage saturation (ORVS) strategy for nonlinear current control in electrical drives consisting of voltage source converters (VSCs) and electrically excited synchronous machines (EESMs). The ORVS is formulated as an analytically solvable optimization problem designed to maximize feasible current changes while considering both stator and exciter voltage constraints imposed by the limited dc-link voltages of the VSCs. The goal of ORVS is to minimize the difference between the desired and feasible current dynamics’ amplitude while maintaining their direction. The effectiveness of the proposed ORVS is illustrated and validated by high-fidelity simulations of a real nonlinear EESM, demonstrating its advantages over classical reference voltage saturation (CRVS) in achieving better current tracking accuracy and notably reduced cross-coupling effects.

This paper presents a constrained optimization-based neuro-adaptive control (CONAC) for nonlinear synchronous machines (SMs) under voltage constraints, which allows controlling the completely unknown electrical drive system, after a brief learning phase with very satisfactory control performance. The artificial neural network (ANN) in the proposed neuro-adaptive controller (NAC) learns online and empowers the controller to handle parameter uncertainties. Moreover, it solves a constrained optimization problem which allows considering the nonlinear voltage constraints as well, by deriving the adaptation laws of the ANN’s weights from the Lagrangian function. Boundedness of tracking error, convergence of the ANN weights, and satisfaction of the constraints are guaranteed by Lyapunov theory. Numerical simulations in combination with a realistic (nonlinear) synchronous machine drive demonstrate the effectiveness and robustness against parameter and modeling uncertainties of the proposed NAC and its very acceptable constraints handling.