## 3 Capacity Rating Procedure
### New Unit Design Changes  
Utilities frequently provide design specifications to transformer manufacturers for large units designated for utilization in power substations. Adjusting design requirements can negate the long-term aging effects induced by Profile A with high harmonic content. Design changes to minimize aging due to Profile A must focus on minimizing the internal heat produced by a unit through normal operation. The aging model defined in the previous section relies upon calculating internal temperatures of the unit, which is a function of ambient temperatures, energy demand, unit efficiency (losses: winding, core, and stray), thermal dielectric properties, cooling system, and tank construction [2]. The aging model converts the transformer electrical and physical components into a thermal circuit that is utilized to evaluate how rapidly heat due to current flow is dissipated through the windings, paper insulation, oil, and physical components of the tank. The complete thermal circuit consists of deriving the solution to thirty seven separate equations that represent temperatures at multiple internal locations of the transformer. The goal of the thermal is circuit to calculate the transformer's winding hottest spot temperature (\(\Theta_{H}\)), which is considered the location most susceptible to insulation failure due to heat. The thermal circuit determines the temperature of the unit's hottest spot for a given evaluation period (\(\Delta t\) = 0.5 min) by calculating winding temperature based upon current flow, unit construction, and oil temperatures within the tank (top and bottom). The calculations also account for ambient temperature, rated ambient temperature, and the applied cooling system affects. The magnitude of \(\Theta_{H}\) is applied to (5), which calculates the per unit transformer insulation aging (\(F_{AA}\)) for \(\Delta t\). To determine the equivalent aging  
Figure 5: Comparison of aging induced by Profile B with peak energy demand = 1.0 per unit and Profile A with energy demand ranging between 0.7 and 1.2 per unit. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Profile** & **A** & **B** \\ \hline Load Factor & 0.881 & 0.682 \\ Capacity Limit & 0.72 per unit & 1.0 per unit \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Capacity Rating (% Nameplate) for Profile A & B. (\(F_{EQA}\)) for a 24 h period, the calculated aging for each \(\Delta t\) is summed and normalized by the total time, as illustrated in (6), where \(N\) represents the total number of evaluation periods. \[F_{AA}=e^{i\frac{[15000]}{383}-\frac{15000}{\alpha_{H}^{2}-273}]} \tag{5}\]  
\[F_{EQA}=\frac{\sum_{n=1}^{N}F_{AA,n}\Delta t}{\sum_{n=1}^{N}\Delta t} \tag{6}\]  
To identify which design attributes possess the most impact in reducing aging due to a flattened load profile, the authors applied Profile A with a 1.0 per unit peak demand to the SPX 50 MVA unit while varying the design attributes listed below by percentages (90%, 80%, 70%, etc.) of their original design. Without any design changes, the accrued aging for a 24 h period was calculated at 37.43 h by (5) and (6). Figure 6 illustrates the aging for a 24 h period if each design attribute is varied exclusively. * Stray Losses (construction variation)
* \(I^{2}R\) Losses (winding conductor variation)
* Core Losses (core construction variation)
* Hottest spot rise over ambient temperature (solid dielectric variation)
* Average winding temperature rise over ambient (solid dielectric variation)
* Litres/US gallons of fluid (tank size variation)  
Design changes that impacted internal operating temperatures the most were (1) reducing the rated hottest spot rise over ambient (HRA) temperature and (2) minimizing the amount of heat produced by stray and \(I^{2}R\) losses. Figure 6 illustrates transformer aging as calculated by (5) and (6) for each attribute as a function of original design variation in size or quantity (20-200%). HRA has a significant impact upon solid insulation aging.