The paper deals with a modeling approach for a hybrid excitation synchronous machine using equivalent reluctance networks. From a finite element modeling (used as a reference model), it aims to define a computationally efficient model suitable for integration with optimization algorithms. Therefore, it propose to perform a parameter design model of the electrical machine. One of the main ideas is to have a model enabling the machine design with or without permanent magnet. Firstly, the paper depicts the geometric parameterization of the machine. Then, it presents the development of a reluctance network model. This approach offers a compromise between accuracy and computational efficiency, making it suitable for future optimization tasks in the design and control of synchronous machines.