THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

Transformer design is a challenging engineering task, where the different physical fields have to be harmonized together to fulfill the implied specifications. Due to the difficulty of this task, it can be separated into several subproblems. The first subproblem, in the pre-concept phase, during the transformer design is the calculation of the cost optimal key-design parameters, where not only the technical but also the economical parameters have to be considered, as well. This subproblem belongs to the most general branch of the non-linear mathematical optimization problems. This paper presents the main directions of the evolution and trends in the power transformer design. Main directions of the considered research and the future trends in the field of preliminary design transformer optimization methods are summarized.

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Evolution and Modern Approaches of the Power Transformer Cost Optimization Methods

This article presents an algorithm for modelling an Adaptive Neuro Fuzzy Inference System (ANFIS) for power transformer paper conditions in order to estimate the transformer’s expected life. The dielectric characteristics, dissolved gasses, and furfural of 108 running transformers were collected, which were divided into 76 training datasets and another 32 testing datasets. The degree of polymerization (DP) of the transformer paper was predicted using the ANFIS model based on using the dielectric characteristics and dissolved gases as input. These inputs were analyzed, and the best combination was selected, whereas CO + CO2, acidity, interfacial tension, and color were correlated with the paper’s deterioration condition and were chosen as the input variables. The best combination of input variables and membership function was selected to build the optimal ANFIS model, which was then compared and evaluated. The proposed ANFIS model has 89.07% training accuracy and 85.75% testing accuracy and was applied to a transformer paper insulation assessment and an estimation of the expected life of four Indonesian transformers for which furfural data is unavailable. This proposed algorithm can be used as a furfural alternative for the general assessment of transformer paper conditions and the estimation of expected life and provides a helpful assistance for experts in transformer condition assessment.

Transformer Paper Expected Life Estimation Using ANFIS Based on Oil Characteristics and Dissolved Gases (Case Study: Indonesian Transformers)

The presented paper aims to establish a strong basis for utilizing machine learning (ML) towards the prediction of the overall insulation health condition of medium voltage distribution transformers based on their oil test results. To validate the presented approach, the ML algorithms were tested on two databases of more than 1000 medium voltage transformer oil samples of ratings in the order of tens of MVA. The oil test results were acquired from in-service transformers (during oil sampling time) of two different utility companies in the gulf region. The illustrated procedure aimed to mimic a realistic scenario of how the utility would benefit from the use of different ML tools towards understanding the insulation health index of their transformers. This objective was achieved using two procedural steps. In the first step, three different data training and testing scenarios were used with several pattern recognition tools for classifying the transformer health condition based on the full set of input test features. In the second step, the same pattern recognition tools were used along with the three training/testing scenarios for a reduced number of test features. Also, a previously developed reduced model was the basis to reduce the needed number of tests for transformer health index calculations. It was found that reducing the number of tests did not influence the accuracy of the ML prediction models, which is considered as a significant advantage in terms of transformer asset management (TAM) cost reduction.

Application of Machine Learning in Transformer Health Index Prediction

Interpretation of oil test data for transformer insulation condition is essential towards justifying asset management practices. Traditionally, an empirical formula (EF) is used by asset managers. This study introduces principal component analysis (PCA) and analytic hierarchy process (AHP) as two alternatives. Through the use of an oil test dataset consisting of 39 in-service UK transmission transformers measured for multiple ageing related parameters, PCA demonstrated its potential in working directly with data to explore parameter relations as well as ranking transformers according to their conditions. AHP on the other hand presented a way to coherently aggregate criteria in a flexible hierarchical setup for identifying the weightages of the oil test parameters before interpretation of measurements. The interpreted conditions based on PCA and AHP, along with a track-record proven EF are similar, particularly for transformers at extreme ends of the insulation condition.

Insulation condition ranking of transformers through principal component analysis and analytic hierarchy process

Aging of power transformers is one of the biggest challenges electrical utilities face. As transformers are commissioned, their insulation system composed of liquid (oil) and solid (paper and pressboard) insulations will deteriorate over time, jeopardizing longevity and reliability of transformers. As a means for optimizing capital expenditure without undermining the reliability of electricity supply, transformer aging or condition assessment has been a key practice for utilities. In most cases, it stems from interpreting the measurements of different parameters that can be tested from transformer oil. One such parameter is moisture in oil, which is one of the most commonly measured parameter by the UK utilities [1].

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Seasonal influence on moisture interpretation for transformer aging assessment

Ageing of large transformer fleets is a challenge for utilities. To assess the condition of existing transformer fleets, transformer oil is commonly tested for multiple parameters and the data are recorded in large databases for subsequent interpretation. Through analysing multiple databases including oil test results and individual transformer details pertaining to UK in-service transformers operating at primary voltage levels of 33, 132, 275 and 400 kV, population analyses revealed a generic early degradation phenomenon as indicated by an early peak in acidity and 2-FAL trends with in-service age. By exploring the phenomenon from manufacturer, loading and oil chemistry change perspectives, results suggested that the early degradation was most likely due to an oil chemistry change resulting from hydrotreatment oil refining method introduced in the late 1980s. Judging from the faster degradation trend of the affected transformers, a separate asset management strategy may be needed.

An early degradation phenomenon identified through transformer oil database analysis

Ageing Assessment of Transformers through Oil Test Database Analyses and Alternative Diagnostic Techniques

Transformer ageing assessment is an essential step towards facilitating asset management decisions and it involves the interpretation of oil test results normally recorded in a huge database for a large population of in-service transformers. In addition to the need for analysing individual transformer data, this study aims to demonstrate and illustrate some typical challenges that asset managers could face in analysing oil test databases pertaining to large transformer populations. Through analysing multiple oil test databases of in-service transformers, potential challenges are found to be the change in measurement procedure, oil treatment practice, oil temperature and oil contamination. It is hoped that the recognition and the consideration of these challenges could serve as a foothold towards more confident and reliable ageing assessment of in-service transformers for justifying asset management decisions.

Sheng Ji Tee

Papers

Insulation condition ranking of transformers through principal component analysis and analytic hierarchy process

Seasonal influence on moisture interpretation for transformer aging assessment

An early degradation phenomenon identified through transformer oil database analysis

Ageing Assessment of Transformers through Oil Test Database Analyses and Alternative Diagnostic Techniques

Challenges in oil test database analysis for ageing assessment of in-service transformers