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Generally, for existing Insulation co-ordination studies the power system has been modeled either by deterministic mathematical techniques or by statistical methods. The shortcoming of the existing conventional mathematical technique of Insulation co-ordination analysis is that it assumes that the power system dynamics is linear. This makes analysis of over voltage response of the system under transients less optimal for determining over voltage withstand of system elements. Thus, this work seeks to model a lightning induced over voltage transient in a High voltage power system substation(132/33KV) used as a case study) using Hidden Markov Model, to determine the maximum likelihood lightning surge signalThe stationdata and configuration was modeled/simulated (in a MATLAB environment), which implements the algorithms used in the work. The Hidden Markov algorithm(which makes use of observable parameters to study what is happening at the hidden states), was used to formulate the problem, while the Baum-welch and Viterbi algorithm were used to find/identify the maximum likelihood lightning overvoltage waveform. These hidden states are represented with different scenarios introduced in the work and the waveform identified, is used to determine the Basic Insulation level(BIL), which is used to determine other parameters accurately, which in turn helps to ensure an optimal/novel Insulation coordination procedure for power system equipment in the station.
The results showed that the minimum required margin(15%) exceeded by a little value(i.e. about 1.08) and the evaluation carried out to raise the protection margin to 18% meant the relocation of the arrester to within 5.56m of the transformer.

1.0 Background of the Study
The demand for the generation and transmission of large amounts of electric power today, necessitates its transmission at extra-high voltages. In modern times, high voltages are used for a wide variety of applications covering the power systems, Industry and research Laboratories. Such applications have become essential to sustain modern civilization[1].
The diverse conditions under which a high voltage apparatus is used necessitate careful design of its insulation and the electrostatic field profiles[2]. This entails the analysis of the electrical power system to determine the probability of post insulation flashovers. For instance, analysis must be carried out to determine that the insulation contained within power system components like transformers has the acceptable margin of protection. Since the internal insulation is not self-restoring, a failure is completely unacceptable. An insulation co-ordination study of a substation will present all the probabilities and margins for all transients entering the station.
Over voltages are phenomena which occur in power system networks either externally or internally. The selection of certain level of over voltages which are based on equipment strength for operation is known as Insulation co-ordination[3]. It is essential for electrical power engineers to reduce the number of outages and preserve the continuity of service and electric supply. In another perspective, Insulation co-ordination is a discipline aiming at achieving the best possible techno-economic compromise for protection of persons and equipment against over voltages, whether caused by the network or lightning.

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