# A Multinomial DGA Classifier for Incipient Fault Detection in Oil-Impregnated Power Transformers
## 3 Methods and Modeling
### Analysis of Dissolved Gases  
One of the most prevalent technique for detecting progressing faults in transformers immersed in oil is gas analysis. DGA became an established art following the discovery in 1928 by [PERSON] [32] that by extracting and studying dissolved gases generated during a progressively deteriorating condition in oil-filled transformers, one is be able to detect the problem with adequate precision. Since the gases formed in the course of a slow evolution of faults are dissolved in oil, extracting and analyzing these dissolved gases can foretell the onset of incipient fault condition [7; 8; 19]. Faults that are identifiable through DGA include corona discharge, heating of the core, arcing, and partial discharge. This early detection of emergent faults not only results in appreciable cost savings but also in intangible benefits such the timely decommissioning of faulty transformer units whose continued use may be risky. Additionally, early detection of emergent faults allows personnel to create a maintenance outage schedule for units in a precautionary state and document anomalies for newly purchased units under warranty. Cost saving is attained by preventing or alleviating damage to the transformer [12]. DGA, which discriminates against normal and abnormal conditions, is founded on the premise that an oil-immersed transformer in proper working conditions generates little or no fault gases. The DGA process begins with the collection oil samples from the transformer. The samples are then subjected to tests and procedures to determine the identity and quantity of liquefied gases [8]. Gases of interest for DGA analysis that are typically found dissolved in oil comprise ethane (C\({}_{2}\)H\({}_{6}\)), ethylene (C\({}_{2}\)H\({}_{4}\)), oxygen (O\({}_{2}\)), methane (CH\({}_{4}\)), acetylene (C\({}_{2}\)H\({}_{2}\)), nitrogen (N\({}_{2}\)) and hydrogen (H\({}_{2}\)). Fault gases can be categorized into three [7; 8; 33; 34; 35; 36; 37; 38] namely;  
1. Hydrogen gas and hydrocarbons: H\({}_{2}\), CH\({}_{4}\), C\({}_{2}\)H\({}_{2}\), C\({}_{2}\)H\({}_{4}\)
2. Carbon oxides: CO\({}_{2}\) and CO
3. Non-fault gases: N\({}_{2}\) and O\({}_{2}\)  
The quantity and ratios of these gases will vary depending on whether a fault is developing in the transformer or not. A critical evaluation of the variation of gases present can precisely determine the underlying condition and the extent to which internal damages have been occasioned [39]. The leading causes of gas formation within an inservice transformer are either of thermal or electrical origins. DGA not only detects and identifies possible faults, but also improves the safety and reliability of the equipment while minimizing maintenance cost [23]. Typical faults that manifest in in-service transformers have been identified in [12; 40; 41] as follows;  
1. Partial Discharge (PD)--A partial discharge occurs when a confined section of a solid or fluid insulation material under high voltage stress experiences a partial collapse but does not entirely seal the space in between two conducting materials. In our context, the term PD refers only to corona PDs occurring in gas bubbles or voids as explained in [40]. 2. Energy Discharges--Energy discharge is the creation of a local conducting path or short circuit between capacitive stress grading foils that creates sparking around loose connections. 3. Thermal Faults--refers to the circulation of electric current in insulating paper that result from excessive dielectric losses. These losses are themselves associated with moisture or an improperly selected insulating material that result in excessive dielectric temperatures. The faults described above may manifest themselves in different ways as described in Table 2.  
When mineral oil heats up to between 150-500 \({}^{\circ}\)C, methane, ethane, ethylene, and hydrogen are formed in varying quantities. As the temperature rises to exceed 500 \({}^{\circ}\)C, acetylene is generated in large quantities [16; 17].