4. Solution of Coupled Electromagnetic and Thermal Fields

The objective of this chapter is to discuss the electromagnetic and thermal simulation requirements when designing large power transformers; in particular, the focus will be on the study of overheat problems in the transformer tank due to the leakage flux and the induced eddy currents. There are a number of requirements for the model specification, the field solution, and the evaluation of the results, related to the electromagnetic performance, as there are a number of requirements for the model specification, the field solution and the evaluation of results, related to the thermal performance, of a power transformer. The model specification covers the geometric description, material properties of the components used in the device, current and voltage sources, as well as the numerical parameters, such as those related to the finite element method (FEM) (Silvester and Ferrari in finite elements for electrical engineers, Cambridge University Press, 1996 [1]). The coupled electromagnetic–thermal simulation requires the solution of two sets of equations. Since, in the overwhelming majority of cases, the time constants between the electromagnetic and thermal response are very different, the two sets of field equations can be solved separately; in other words, they are loosely coupled. The electromagnetic field equations may require a static, time-harmonic, or transient field solver, whereas the thermal field equations may require a static (steady-state) or transient field solver. The coupled electromagnetic–thermal simulation addresses both aspects of physics, i.e., electromagnetic and thermal, and the way the effect of one on the other is taken into account, by considering the temperature rise due to electromagnetic losses, and the effect on the material properties due to the change in temperature. Material property modeling plays a key role in the accurate simulation of the device. Since the magnetic properties of steel are nonlinear and hysteretic, and anisotropic for the grain-oriented steel used in transformers, advanced material models are needed for an accurate representation of the material, under the different operating conditions of a transformer. Simcenter™ MAGNET™ software is a general-purpose simulation tool on which the content of this chapter is based. This tool can be used for the design and analysis of many devices. More in-depth information on its general capabilities can be found at (Simcenter MAGNET knowledge base articles [2]).