New State-Space White-Box Transformer Model for the Calculation of Electromagnetic Transients

White-box models are detailed models for the investigation of the internal behavior of transformers during dielectric design. A new model of this type with significantly improved characteristics is presented in this paper. The model has been developed in state-space form, which is more flexible than an equivalent circuit and also makes it possible to optionally hide proprietary information on internal voltages. The proposed parameter determination methodology is very robust and allows the adequate representation of the damping. The methodology for determining inductive impedances and capacitances as a function of frequency using the Finite Element Method is described first. Then the fitting of the impedances obtained in the frequency domain by means of rational approximation functions is presented, which is based on the Vector Fitting algorithm in combination with Particle Swarm Optimization. The state-space model is obtained next, which is then used to perform time and frequency domain calculations. This new model has been successfully validated by comparison with measurements on a large power transformer used as case study during the activities of the JWG CIGRE A2/C4.52.