# A Review of Health Assessment Techniques for Distribution Transformers in Smart Distribution Grids
## 3 Transformer Health Assessment Techniques
### Fuzzy Logic  
To overcome the limitations of the health index calculation method, fuzzy logic has been proposed as a suitable approach. Fuzzy logic is supposed to be used for representing vague concepts and uncertain information, especially in cases in which conventional logic techniques couldn't be applied effectively [35; 36]. The structure of a complete fuzzy control system includes three steps: fuzzification, inference and defuzzification. At the first step, fuzzification calculates fuzzy values from exact values at the input. The fuzzy inference applies all applicable fuzzy rules to calculate the fuzzy value for the output. The defuzzification determines the exact output value from the fuzzy result obtained in the fuzzy inference step [37]. The basic structure of fuzzy control system is shown in Figure 3.  
Figure 2: The structure of the health index calculation method.  
In recent years, the advantages of fuzzy logic and its related applications such as optimization, decision making and diagnosis have been put into evidence. In diagnostic applications, fuzzy systems are typically used. In [38], Fuzzy logic is applied to evaluate the possible effects of the health condition on the oil-immersed transformer. The five considered health indices are dissolved gas analysis (DGA), furans, load history, aging and humidity. The transformer's statement is assessed based on three cascade connection fuzzy subsystems including risk, maintenance and decision. This cascade model helps to evaluate the probabilities of an error occurring and its corresponding consequences. The maintenance subsystem model helps to estimate the level of the maintenance recommendations based on the output of the risk model, health index and failure rate. The overall decision model outputs the level of required maintenance actions. The proposed method is deployed on a 35 years-old transformer. The results show the estimation of the date in which the transformer may need a maintenance action, and the required actions to extend the transformer lifetime. Paper [39] uses a fuzzy knowledge-based expert system to assess the transformer's health. All the parameters can be analyzed individually. Because of the variation in operational and the effect of many factors controlling the transformer variables, the policies applied to manage transformers may differ even with the transformers that have the same rating and calendar age. Due to the inexact information and the complexity of the asset management model. The article pointed out that Fuzzy logic is an effective tool that can give a highly reliable assessment for solving this kind of problem.  
Fuzzy logic is also applied for analyzing transformer data in paper [40] to diagnose the transformer faults. This method uses a multi-band infrared imager sensor and a discharge circuit detection sensor to set up the eight sensors detection platform. The fault diagnosis model is given based on the consistency of sensors and sensor's trust degree. The fuzzy model with a multi-sensors system can help to get accurate results and enhance the system operation. Through experiment and analysis, this fault diagnosis model can improve the fusion precision and diagnostic accuracy more effectively than the  
Figure 3: The basic structure of the fuzzy control system.  
general fusion algorithm and arithmetic mean value algorithm and can scientifically diagnose the transformer equipment of power grid from multi-angles. Thereby, the feasibility and effectiveness of the method are verified. In [41], fuzzy logic was applied to predict the health index values. In this article, oil quality, furan and dissolved gas were used as assessment parameters. However, it is obvious that this assessment method has some limitations, the scoring and ranking values still depend on the opinion of operators in the utilities. The values of the health index will be inconsistent even if they use the same equation because of using different weighting factors and scoring methods.