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Coupling Thermo Electric Fields

Bruce Klimpke, Technical Director
Integrated Engineering Software

As computer power continues to increase, and software algorithms advance, the demand for more complex simulations continues to grow. The need to improve product reliability and reduce manufacturing costs is driving the demand for accurate and complex simulations. One of the most notable demands is the requirement to couple physics from different disciplines, or as it has recently been called, multi-physics. In reality, all electromagnetic phenomena will change the thermal distribution and properties within a device. For many applications the effect is negligible, or so small it can be ignored. In other cases, neglecting the coupling will significantly reduce the realism of the solution or render the final product useless. Thus for the simulation of chips, or the design of electrical bushings, the combining of thermal and electrical analysis is essential.

For every electrical system, the flow of electric current through a conductor generates heat. For many applications, the heat produced can be a significant factor in the design of the product and in some cases the dominant factor. Solving this problem requires first the solution of the electrical conduction problem. Once the current paths are known, then the volume heat density can be calculated directly by the ohmic losses.

The volume heat density is then the required heat source for a thermal analysis. The thermal analysis performed by the Kelvin (2D) or Celsius (3D) INTEGRATED simulation systems require all the thermal material properties as well as the appropriate boundary conditions, such as the applied temperature, to be known. Celsius and Kelvin serve the same purpose, except that Kelvin approximates the full 3D world by reducing the problem to 2 dimensions. These programs are general thermal analysis programs and can be used to model everything from chips and motors to high voltage equipment. The programs’ key features are their ease of use and unique ability to be combined seamlessly with electrical analysis software. Thus the designer can focus on achieving the best possible design rather than trying to contend with the nuances of the software program.

There are two distinct levels of difficulty involved in solving the combined electrical and thermal problems with a design. The first level is where the temperature distribution within the device has a negligible effect on the electrical solution. For this case, we simply solve the electrical problem once and use subsequent ohmic losses as an input for the thermal analysis. The thermal or temperature distribution within the device is readily calculated. So, when designing a chip, the electrical properties may not be significantly changed by the temperature. In this case only one electrical and thermal analysis is required.

The second level, which refers to more advanced simulations, requires many solutions to be generated from the electrical and thermal programs. For example, if the electrical conductivity of the materials is strongly dependent on the temperature, a further electrical analysis would be required after the thermal analysis. This again would change the heat distribution from the original analysis. Thus, an iterative procedure occurs between the electrical and thermal analysis, until the electrical and thermal parameters converge. This is typically what is required in a high voltage bushing.

Solving electrical and thermal problems are mathematically the same for static problems. However, the practical implementations are quite different. For most practical thermal analysis, radiative effects and forced convective heat transfer are introduced into an equivalent heat transfer coefficient. This is used on the surface of the part being analysed. Therefore most heat or temperature modeling is undertaken by analysing the temperature within the part of interest and the effects on the nearby volumes are simply neglected.

However, when solving electrical problems the situation is quite different. Not only is the designer interested in the electric field within the part, but also the field in the air space that surrounds the part. Even if the electric field calculation is only required within or on the part, the entire volume about the part has to be modeled. This is illustrated in the example below.

combined-analysis

Figure 1: Temperature contours. Figure 2: Voltage contours on the transformer bushing.
Courtesy of HSP Hochspannungsgeräte GmbH
As we can see the electric field extends far beyond the bushing boundaries (theoretically to infinity), whereas the thermal field is only modeled within the bushing.

Two distinct methods can be used to model both the electric and thermal field. One is called the Finite Element Method (FEM) and the other is the Boundary Element Method (BEM). The FEM method is by far the most commonly used. This method is almost exclusively used for thermal analysis, as there is no need to model the thermal field outside the bushing. The same method can be used for the electrical analysis, but this introduces some major drawbacks, particularly when modeling the space exterior to the bushing. To calculate the electric field, the BEM is far superior as it can model the exterior volume trivially. Therefore, ideally the FEM is used for the thermal analysis and the BEM for electrical analysis.

To conclude, more advanced solutions requiring multi-physics to reach an accurate calculation can be best obtained by simulation software using both finite and boundary element software. These require seamless coupling so the designer can focus on design and not on long learning curves to get the simulation results. In addition, the advent of 64 bit personal computers with memory of 32 GB is now common. This radical change in computer memory allows the solutions of coupled electrical and thermal analysis that would have been impractical for full 3D simulation on a 32 bit machine. To enhance this further, multiple quad core processors are now available. Software advances making use of many processors (parallelization) will enhance the level of realism of coupled field analysis due to the radical speed improvements.

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