Comparison of transient time-domain and harmonic quasi-static solution of electrical and thermal coupled numerical stress grading calculations for large rotating machines

In terms of future development of stress grading systems for large rotating machines it is required to calculate the electric surface field strength distribution as well as the temperature profile along the stress grading surface with sufficient accuracy. Due to high nonlinear material characteristics the design and optimization of such systems are a very time consuming process. In order to accelerate this process a finite element model with implemented numerical optimization algorithm was developed in the past. The model takes the nonlinear electrical and thermal coupled material properties into account. In terms of a short design time an optimization is needed to design a typical multi-layer stress grading configuration for large rotating machines, i.e. turbo-generator with a rated voltage higher than 16.5 kV and an output higher than 400 MVA, a harmonic quasistatic approximation is performed to solve the FEM-model. The advantage of this procedure is a decrease of the calculation time by a factor of about 25-100 compared to a full transient time-domain solution. Caused by the nonlinear specific resistive behaviour of the stress grading material it is usually necessary to perform a time-domain solution to consider the development of harmonic content. In case of a quasi-static harmonic calculation with an applied sinusoidal voltage this effect is neglected. This paper shows the results on a real stator bar geometry with stress grading systems by means of two different numerical models based on FEM. The first model allows calculating the time-domain behavior of the stress grading system and takes the harmonic content caused by the stress grading material into account (transient model). Introduction of electrical and thermal time constants is presented as well as the electrical potential and field strength distribution along the insulation surface over time. Finally electrical and thermal results in case of a steady state condition are compared qualitatively as well - s quantitatively with results obtained by a quasi-static harmonic calculation.