This paper presents a study to estimate future Health Index (HI) of transformer population based on Hidden Markov Model (HMM). In this paper, HI was represented as hidden state and the condition parameter factors in the HI algorithm namely Dissolved Gas Analysis Factor (DGAF), Oil Quality Analysis Factor (OQAF) and Furfural Analysis Factor (FAF) were represented as the observable states. A case study of 1130 oil samples from 373 oiltyped distribution transformers (33/11 kV and 30 MVA) were examined. First, the mean for HI in each year was computed and the transition probabilities for the condition data were obtained based on non-linear optimization technique. Next, the emission probabilities for each of the condition parameter factors were derived based on frequency of occurrence method. Subsequently, the future states probability distribution was computed based on the HMM prediction model and viterbi algorithm was applied to find the best optimal path sequence of HI for the respective observable condition. Finally, the predicted and computed HI were compared to the hypothesized distribution. Majority of the predicted HI agrees with computed HI. Predicted HI based on OQAF records the most accurate estimation throughout the sampling years. Inconsistencies are observed in year 2 and between year 7 and 10 for the predicted HI based on FAF. The predicted HI based on DGAF is in line with the computed HI during the first 2 years and deviates at the later stage of the sampling period.

This paper presents a study to estimate individual condition parameters of the transformer population based on Markov Model (MM). The condition parameters under study were hydrogen (H2), methane (CH4), acetylene (C2H2), ethylene (C2H4), ethane (C2H6), carbon monoxide (CO), carbon dioxide (CO2), dielectric breakdown voltage, interfacial tension, colour, acidity, water content, and 2-furfuraldehyde (2-FAL). First, the individual condition parameter of the transformer population was ranked and sorted based on recommended limits as per IEEE Std. C57. 104-2008 and IEEE Std. C57.106-2015. Next, the mean for each of the condition parameters was computed and the transition probabilities for each condition parameters were obtained based on non-linear optimization technique. Next, the future states probability distribution was computed based on the MM prediction model. Chi-square test and percentage of absolute error analysis were carried out to find the goodness-of-fit between predicted and computed condition parameters. It is found that estimation for majority of the individual condition parameter of the transformer population can be carried out by MM. The Chi-square test reveals that apart from CH4 and C2H4, the condition parameters are outside the rejection region that indicates agreement between predicted and computed values. It is also observed that the lowest and highest percentages of differences between predicted and computed values of all the condition parameters are 81.46% and 98.52%, respectively.

This paper presents an investigation of the condition state distribution and performance condition curve of the transformer population under different pre-determined maintenance repair rates based on the Markov Prediction Model (MPM). In total, 3195 oil samples from 373 transformers with an age between one and 25 years were tested. The previously computed Health Index (HI) prediction model of the transformer population based on MPM utilizing the nonlinear minimization technique was employed in this study. The transition probabilities for each of the states were updated based on 10%, 20% and 30% pre-determined maintenance repair rates for the sensitivity study. Next, the HI state distribution and performance condition curve were analyzed based on the Markov chain algorithm. Based on the case study, it is found that the pre-determined maintenance repair rates can affect the HI state distribution and improve the performance condition curve. The 30% pre-determined maintenance repair rate gives the highest impact, especially for the transformer population at state 4 (poor). Overall, the average percentage of change for all HI state distributions is 16.48%. A clear improvement of HI state distribution is found at state 4 (poor) where the highest percentage can be up to 63.25%.

In this paper, a maintenance cost study of transformers based on the Markov Model (MM) utilizing the Health Index (HI) is presented. In total, 120 distribution transformers of oil type (33/11 kV and 30 MVA) are examined. The HI is computed based on condition assessment data. Based on the HI, the transformers are arranged according to its corresponding states, and the transition probabilities are determined based on frequency of a transition approach utilizing the transformer transition states for the year 2013/2014 and 2012/2013. The future states of transformers are determined based on the MM chain algorithm. Finally, the maintenance costs are estimated based on future-state distribution probabilities according to the proposed maintenance policy model. The study shows that the deterioration states of the transformer population for the year 2015 can be predicted by MM based on the transformer transition states for the year 2013/2014 and 2012/2013. Analysis on the relationship between the predicted and actual computed numbers of transformers reveals that all transformer states are still within the 95% prediction interval. There is a 90% probability that the transformer population will reach State 1 after 76 years and 69 years based on the transformer transition states for the year 2013/2014 and 2012/2013. Based on the probability-state distributions, it is found that the total maintenance cost increases gradually from Ringgit Malaysia (RM) 5.94 million to RM 39.09 million based on transformer transition states for the year 2013/2014 and RM 37.56 million for the year 2012/2013 within the 20 years prediction interval, respectively.

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This work examines the failure rate of the transformer population through the application of the Markov Model (MM) and Health Index (HI). Overall, the condition parameters data extracted from 3,192 oil samples were analysed in this study. The samples were from 370 transformers with the age range between 1 and 25 years. First, both HIs and failure rates of transformers were determined based on the condition parameters data of the oil samples known as Oil Quality Analysis (OQA), Dissolved Gas Analysis (DGA), Furanic Compounds Analysis (FCA) and age. A two-parameter exponential function model was applied to represent the relationship between the HI and failure rate. Once the failure rate state was obtained, the non-linear optimisation was used to determine the transition probability for each age band. Next, the future failure rate of the transformer population was computed through the MM prediction model. The goodness-of-fit test and Mean Absolute Percentage Error (MAPE) were utilised to determine the performance of the predicted failure rate. The current study reveals that the future state of the transformer population and failure rate could be predicted through MM based on updated transition probabilities. It is observed that the MAPE between predicted and computed failure rates is 7.3%.

In this study, statistical distribution model (SDM) is used to predict the health index (HI) of transformers by utilizing the condition parameters data from dissolved gas analysis (DGA), oil quality analysis (OQA), and furanic compound analysis (FCA), respectively. First, the individual condition parameters data were categorized based on transformer age from year 1 to 15. Next, the individual condition parameters data for every age were fitted while using a probability plot to find the representative distribution models. The distribution parameters were calculated based on 95% confidence level and extrapolated from year 16 to 25 through representative fitting models. The individual condition parameters data within the period were later calculated based on the estimated distribution parameters through the inverse cumulative distribution function (ICDF) of the selected distribution models. The predicted HI was then determined based on the conventional scoring method. The Chi-square test for statistical hypothesis reveals that the predicted HI for the transformer data is quite close to the calculated HI. The average percentage of absolute error is 2.7%. The HI that is predicted based on SDM yields 97.83% accuracy for the transformer data.

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