# Voltage Distribution on Transformer Windings Subjected to Lightning Strike Using State-Space Method
## 5 Conclusions  
In this paper, we investigated the voltage distributions in the windings of the discs on the neutral grounded high-voltage side of a disc-structured power transformer, as well as the voltage-current waveforms generated on the transmission line by a lightning strike on a single-phase distributed-parameter transmission line, using the state-space method. Inductor currents and capacitor voltages are selected as state variables. At the sending end of the line, there was a sudden voltage spike at megavolt levels due to a lightning strike. The arrival time of the lightning strike at the transformer windings depends on the characteristic impedance of the line, causing the current-voltage waves to reach the transformer windings with a delay of approximately 1 ms. Therefore, this study also includes the effect of the transmission line on the voltage distributions in the windings due to lightning strikes. Peak voltage values at the transformer discs and current-voltage  
Figure 19: Voltage distribution on transformer disc windings obtained using the ATP-EMTP. Figure 20: Peak voltage values of disc windings: (**a**) for \(R_{g}=1\ \Omega\), (**b**) \(R_{g}=20\ \Omega\). values at the sending and receiving ends of the transmission line are recorded. The peak voltage values of the first disc, the fifth disc, and the last disc are 67 kV, 40 kV, and 6.5 kV, respectively, for a grounding resistance of 1 \(\Omega\). The voltage difference between the interconnected discs is approximately 6.5 kV, while the voltage difference between the first and last discs is 60.5 kV. It was also observed that the peak voltage values on the discs increased as the grounding resistance value increased. Although the peak voltage values increased, the voltage difference between the discs remained constant at approximately 6.5 kV, while the voltage distribution decreased linearly from the first disc to the last. This indicates that insulation in the first discs is more critical than in the last discs. Since the peak voltage level varies in each disc, the winding insulation in the discs may also differ. The windings must be designed to withstand excessive voltages. The first disc, which was subjected to the highest voltage, should be reinforced with additional insulation materials. When transformer windings are subjected to overvoltage conditions, several critical issues can arise, including insulation breakdown, thermal stress, dielectric failure, mechanical stresses, and spark or arc formation. Any deformation that may occur in the windings, or any short-circuit faults that may arise between the discs, between the windings, or between the disc and the transformer tank under operating voltage, can also be analyzed using this method. Additionally, the effect of a lightning strike on one phase and its impact on other phases can be examined with this approach. These issues underscore the critical need for robust overvoltage protection systems to ensure the reliability and longevity of transformers. The results obtained using the state-space method were compared with those from the ATP-EMTP. It was determined that the results from both methods are nearly identical and compatible. The state-space method can be used as an alternative approach for transient-state analysis of the transformer model, also known as a high-frequency power transformer, which is utilized in frequency response analysis. It can be applied to power transformers with varying numbers of discs. This method facilitates the design of transmission lines and transformer protection equipment. Thanks to the state-space method, transient analysis can be performed on transmission lines and transformers without requiring a transient simulation program; a math solver is sufficient. Conceptualization, M.S.M. and I.A. ; methodology, M.S.M. ; software, I.A. ; validation, M.S.M. and I.A. ; formal analysis, I.A. ; investigation, I.A. ; resources, I.A. ; data curation, I.A. ; writing--original draft preparation, I.A. ; writing--review and editing, I.A. ; visualization, I.A.