In general, the power system has been studied using either deterministic mathematical methodologies or statistical methods for existing Insulation co-ordination research. The existing traditional mathematical technique for insulation co-ordination analysis has a flaw in that it assumes linear power system dynamics. As a result, establishing the over voltage withstand of system elements requires a less ideal examination of the system’s over voltage reaction under transients. Thus, the goal of this research is to employ a Hidden Markov Model to model a lightning-induced overvoltage transient in a high-voltage power system substation (132/33KV as a case study) in order to find the most likely lightning surge signal. The data and configuration of the station were modeled and simulated (in a MATLAB environment), which implemented the algorithms used in the study. The problem was formulated using the Hidden Markov algorithm (which uses observable parameters to investigate what happens at hidden states), and the Baum-welch and Viterbi algorithms were used to find/identify the highest likelihood lightning overvoltage waveform. These hidden states are represented in the work by various scenarios, and the waveform identified is used to determine the Basic Insulation Level (BIL), which is then used to accurately determine other parameters, resulting in an optimal/novel Insulation coordination procedure for power system equipment in the station.
The results showed that the minimum needed margin (15%) was exceeded by a small amount (i.e. around 1.08) and that increasing the protection margin to 18% entailed moving the arrester to within a few feet.

Background of the Study
Today’s requirement for large-scale electric power generation and transmission necessitates transmission at extremely high voltages. High voltages are employed in a wide range of applications nowadays, including power systems, industry, and research laboratories. Such applications are now required to keep contemporary civilisation alive[1].
Because of the many settings in which a high voltage device is operated, rigorous insulation and electrostatic field profiles must be designed[2]. This requires a thorough examination of the electrical power system in order to assess the likelihood of post-insulation flashovers. For example, an examination must be performed to evaluate whether the insulation within power system components such as transformers has a sufficient margin of safety. A failure is entirely unacceptable because the interior insulation is not self-restoring. All of the probabilities and margins for all transients entering the station will be presented in an insulation co-ordination analysis of a substation.
Overvoltages are a phenomenon that can occur either externally or internally in power system networks. Insulation co-ordination is defined as the selection of a specific level of over voltages for operation based on equipment strength. It is critical for electrical power engineers to limit the amount of outages and maintain service and power supply continuity. Insulation coordination, on the other hand, is a discipline aimed at reaching the best feasible techno-economic compromise for protecting people and equipment from overvoltages induced by the network or lightning.

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