## 3 Capacity Rating Procedure
### New Unit Design Changes
With 10% and 20% reductions in this value, the aging, as identified by (6), is reduced by 15.44% and 41.33% for the 50 MVA unit when Profile A is applied. Quantifying the trend line of (6) as a function of HRA as illustrated in Figure 6 results in the polynomial illustrated in (7), where \(p_{h}\) is the percentage variation of HRA. To calculate the percent decrease in aging as compared to the existing HRA design value with Profile B (\(p_{h}=1.0\) per unit), (8) is applied to identify the aging reduction \(R(p_{h})\) as a function of HRA variation. \[F_{EQA}(p_{h})=11204{p_{h}}^{4}-47040{p_{h}}^{3}-64558{p_{h}}^{2}+26747p_{h}- 4493 \tag{7}\]  
\[R(p_{h})=\frac{F_{EQA(1.0)}-F_{EQA(p_{h})}}{F_{EQA(1.0)}}\times 100\% \tag{8}\]  
Figure 6: Aging induced by Profile A on the 50 MVA SPX unit as a function of design attributes. As defined IEEE Std. C57.91-2011, HRA is a function of the load current, the temperature rise of fluid at the top of the duct over bottom fluid, and the bottom fluid rise over ambient temperature. Improving the thermal insulation properties of the transformer would reduce these internal operating temperatures. Thermal properties are improved by reducing the thermal conductivity of the unit's liquid and solid dielectrics. The two most common types of solid dielectrics (paper insulation) for liquid immersed transformers are TUK and variations of Dupont's Nomex (910 or 410), which are documented as having at least 10 \({}^{\circ}\)C better thermal performance than the former [46; 47; 48; 49]. Nomex, which is classified as a high temperature dielectric, has historically been utilized in mobile transformers due to its light weight and strong thermal properties. However, in recent years utilities have begun applying the solid dielectric to substation units to improve thermal performance. Utilizing Nomex can increase a unit's thermal rating, which allows for the winding hottest spot temperature to exceed 110 \({}^{\circ}\)C without considerable aging [49]. Because the cost of Nomex can be twenty times greater than TUK, completely upgrading the unit's solid dielectric may be infeasible. However, a hybrid insulation system composed of both TUK and Nomex may be sufficient to increase the thermal rating and regulate costs [49]. Utilizing alternative liquid dielectrics instead of mineral oil can also negate the additional heating effects, which essentially reduces the standard HRA. Since 2016, many researchers have identified better thermal performance utilizing mineral oil alternatives, such as natural ester and silicon [49; 50]. The typical thermal class of TUK is 105 \({}^{\circ}\)C in mineral oil. Based upon IEEE C57.154-2012, Nomex 910 has a thermal rating of 130 \({}^{\circ}\)C in mineral oil and 140 \({}^{\circ}\)C in natural ester. For older units that were designed with higher safety margins, improving HRA during a rewind might be accomplished by improving the amount and type of paper insulation. For newer units with smaller design safety margins, improving HRA during a rewind may be impossible due to the limited space and already the possible application of high temperature dielectrics. Reducing losses (\(l^{2}R\) and stray) also contributes to mitigating the aging effects induced by Profile A. Losses manifest as heat within the conductor windings, which thereby increases the hottest spot temperature and ergo aging. The generated heat is absorbed by the bulk oil in the tank and radiator and eventually transferred through conduction to the external environment. Stray losses are due to stray electromagnetic flux in the core, core clamps, windings, magnetic shields, and enclosure or tank walls. Therefore, reducing stray losses consists of minimizing the flux flowing through these components. If the original transformer unit design was created to produce minimal stray losses, increasing aging through these means may be impossible.