# Voltage Distribution on Transformer Windings Subjected to Lightning Strike Using State-Space Method
## 4 Application and Results
V\({}_{1}\) represents the winding voltage on the 1 st disc, while V\({}_{10}\) represents the winding voltage on the 10 th disc. Voltage waveforms V\({}_{1}\) and V\({}_{10}\) for different grounding resistances (\(R_{g}\)) are given in Figures 16 and 17. When the graphs are examined, the voltage difference between V\({}_{1}\) and V\({}_{10}\) of the neutral grounded high-voltage side of transformer is clearly seen. When the grounding resistance value increases, the voltage values V\({}_{1}\) and V\({}_{10}\) also increase. The change in grounding resistance caused an increase of approximately 118 kV in the peak voltage value of the first disc and the last disc. The voltage-time graphs for each disc of the power transformer with disc-type winding are presented in Figures 18 and 19. The simulation period for the state-space method is 6 ms. The discs were subjected to different voltage values. A rapid rise in voltage within the first 1 ms indicates the presence of high-frequency components generated when the lightning strike reaches the transformer. This lightning strike causes excessively high voltages in the transformer windings during the initial period (0-1 ms), a phenomenon attributed to  
Figure 13.0 Voltage waveforms of V\({}_{1}\) and V\({}_{10}\) for \(R_{g}\) = 1 \(\Omega\): (**a**) state-space method and (**b**) ATP-EMTP simulations. Figure 13.1 Voltage waveforms of V\({}_{1}\) and V\({}_{10}\) for \(R_{g}\) = 20 \(\Omega\): (**a**) state-space method and (**b**) ATP-EMTP simulations. Figure 13.2 Sending-end and receiving-end current waveforms of transmission line obtained by ATP-EMTP simulations. the short rise time of the lightning strike and wave propagation along the transmission line. Around 3 ms, a second significant voltage spike is observed, likely caused by reflection effects between the transmission line and the transformer, with reflected waves moving at a period of approximately 2 ms. The highest peak voltage (67 kV) is observed in the first disc, indicating that the majority of the lightning energy is absorbed by this disc. Voltages gradually decrease across the subsequent discs (e.g., V\({}_{2}\), V\({}_{3}\), V\({}_{4}\), etc.). The high-frequency oscillations observed in the graph, particularly during the first 1 ms, justify neglecting the magnetic core's influence. At such high frequencies, the inductance and capacitance of the windings dominate the system's behavior, while the magnetic properties of the core become less significant. The graphs presenting the peak voltage values on the discs of the neutral grounded high-voltage side of the power transformer are shown in Figure 20 for different \(R_{g}\) values. According to these graphs, the peak voltage values in the disc windings decrease linearly from the first disc to the last disc. Consequently, the windings in the first disc were subjected to the highest voltage, while those in the last disc were subjected to the lowest voltage. In addition, modeling a power transformer consisting of multiple discs in the ATP-EMTP can be time-consuming. This is because each disc must be drawn multiple times, or a drawn disc must be copied to the end of the circuit. However, the model used in this study does not require extensive drawings; instead, the matrices for a transformer with a large number of discs can be easily created, allowing the simulation to be completed by simply determining the value of \(N\) (the number of discs). Figure 13.3 Voltage distribution on transformer disc windings obtained using the state-space method.