# Study of Partial Discharge Inception Voltage in Inverter Fed Electric Motor Insulation Systems
## 6 Conclusions  
In this paper, a thorough analysis of different electrical waveform factors and environmental conditions affecting PDIV was performed. In addition, different PDIV estimation models from the literature were reviewed identifying the pros and cons. Given the importance of temperature on the PDIV and the high temperature of the winding during operation (180 \({}^{\circ}\)C), several models were studied at high temperature. For that, the experiments were performed at the range of 20-260 \({}^{\circ}\)C. The advantages and disavantages of the Dakin, parallel-plate, Lusuard,i and FEM and Paschen's models were identified in comparison to the experiments. Based on the drawback of these models, a new model avoiding experiments and computational simulations is proposed. The proposed model is based on the parallel-plate model, where Dunbar correction was implemented in order to consider the effect of the temperature on air properties. The proposed model showed the best compromise between computational requirements and estimation accuracy at different temperature levels. Furthermore, the effect of permittivity was also considered.  
Even though there is a general agreement regarding how variables such as pressure, temperature, waveform, and polarity or frequency affect the PDIV, further studies are necessary in terms of humidity, rise time, and pulse width. Independent analysis of the pulse width in the literature does not provide consistent results. Therefore, a multifactorial analysis of the rise time, pulse width, and duty is recommended, with and without overshoot waveforms.  
Additionally, a model that is able to consider the overshoot and ringing resulting from WBG-based converters, where environmental conditions are also considered, is still necessary. The extended volume-time theory seems to be a good basis to consider different waveform characteristics, but the effect of environmental conditions should be added.  
The present article can form a basis to continue developing the PDIV estimation models for turn-to-turn insulation systems. It provides an overview of the different factors affecting the PDIV, together with different models to estimate it. It also offers a simple PDIV estimation model considering the temperature evolution.  
Conceptualization, L.E.A., G.A. and A.E.; methodology, L.E.A., G.A. and A.E.; validation, L.E.A., G.A. and A.E.; formal analysis, L.E.A., G.A., A.E. and X.B.; investigation, L.E.A., G.A., A.E., G.U. and X.B.; data curation, L.E.A.; writing--original draft preparation, L.E.; writing--review and editing, L.E.A., G.A., A.E., G.U. and X.B.; supervision, G.A., A.E. and G.U.; project administration, G.A., A.E. and G.U.; funding acquisition, G.A., A.E. and G.U. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the ELKARTEK program of the Department of Economic development, Sustainability and Environment of the Basque Government grant number KK-2021/00044 and KK-2022/00073.  
Not applicable.  
The data presented in this study are available on request from the corresponding author.  
The authors declare no conflict of interest.