# A Multinomial DGA Classifier for Incipient Fault Detection in Oil-Impregnated Power Transformers
## 1 Introduction  
The transformer is an indispensable piece of equipment in generating, transmitting, and distributing electricity [1]. They are also expensive and account for massive capital expenditure in the contemporary electrical network. Not only do they require huge fiscal investments but the reliability and dependability of the entire electricity grid depends primarily on their operational stability [2, 3, 4, 5]. It is, therefore, imperative that utility companies give priority to failure prevention and the substance of optimal operational status of their electrical network. Maintaining these assets in an optimal and efficient state is a key priority of many electric utilities globally. In fact, a huge portion of the annual budget of these utility companies is allocated to condition monitoring and maintenance of these assets [6, 7, 8]. Condition monitoring and asset management is therefore a key concern in all electric utility providers. With a typical electrical network deploying transformers in their thousands, condition monitoring easily becomes a labor-intensive and time-consuming exercise. The basic principle upon which a transformer works is that of mutually induced magnetic flux that links the primary with the secondary windings. When an alternating current flows through the primary windings, it induces a voltage that is greater than or less than that across the secondary windings depending on whether the unit is a stepdown or step-up transformer [1, 9]. The frequency of the induced and inducing voltages however remain unchanged. Figure 1 illustrates the basic manner of construction of a transformer. The transformer comprises of an intricate arrangement of a pair of coils wound on an iron core. To prevent the iron core from acting as a conductor, it is assembled using thin layers of varnish coated steel [10]. During normal operation, an alternating current on the primary windings produces a changing flux within the core. The flux in turn induces an electromotive force (emf) within the core that in turn sets up the circulating currents called Eddy Currents. Eddy currents produces losses, which manifest as heat. The magnitude of this loss can be calculated by Equation (1) [11]. \[P_{e}=K_{e}\ B_{m}^{2}t^{2}f^{2}V\ \text{Watts} \tag{1}\]  
where \(P_{e}\) is the hysteresis loss in Watts, \(K_{e}\) is the stein Metz hysteresis coefficient; \(t\) is the material thickness; \(B_{m}\) is the flux;\(f\) the rate of magnetic oscillations and \(V\) volume of in m\({}^{3}\). As is seen from Equation (1), the heating up of a transformer during operation is anticipated. The concern therefore is how to prevent and manage the excessive build-up of heat to destructive levels. Several techniques have been used to accomplish this. One of these being to immerse the transformer core and winding in mineral oil. Oil not only acts as a coolant but also is itself also an insulating material [12]. Recent studies suggest that many transformers do not live up to their expected lifetime of between 25-35 years [2]. In Kenya for instance, as many as 10-12% of the population of distribution transformers are prematurely retired against an international annually rate of between 1 and 2% in the more industrialized countries [2]. The failure of a single transformer disrupts economic activities for both the consumers and utility company [13]. For continued reliability and availability there must be continuous monitoring and maintenance of the transformer. However, with the huge number of transformers deployed in an electrical network, monitoring, and maintenance is a daunting task that requires massive labor and time. Kenya Power has reported that it owns about 70,000 transformers countrywide deployed at various locations scattered all around the country [14]. Dissolved and free gas analysis is a widely used and highly regarded means of detecting incipient faults in oil-immersed transformers. DGA reliably gauges a transformer's operational status and is extensively used in routine maintenance [15; 16].