## 3 Capacity Rating Procedure
### Derating--Long-Term Emergency Rating  
Long-term emergency loading is defined by IEEE Std. C57.91-2011 as a condition where a transformer must regularly support energy demands greater than its nameplate capacity ratings, which forces the winding hottest spot temperature to climb above the acceptable temperature of 130 \({}^{\circ}\)C These conditions are rare and are typically caused by failures occurring on others sections of the grid that require repair lead times consisting of weeks. The two most important factors when determining capacity limit loading are the (1) reduced lifespan of the unit and/or the (2) long-term physical damage to the unit and/or oil. In regards to aging, the approach defined in Section 3.1 is applicable to identifying acceptable loading limits. However, unlike application to normal operating conditions, the value of (4) will always be less than zero. The unit's owner should identify a new acceptable aging (\(A_{E}\)) value that represents potential dielectric damage that impacts the long-term investment. Recall that this determination is to support an abnormal loading condition, therefore higher than normal aging is expected. The new evaluation equation is illustrated in (13). \[A_{O}(l_{O},h_{O},\ c_{O},)-A_{N}(l_{N},h_{N},\ c_{N},)\geq-A_{E} \tag{13}\]  
Prevention of long-term equipment damage may be the most important aspect of determining an acceptable capacity rating for a unit under these conditions. IEEE identifies controlling winding hottest spot temperature and oil temperature as keys to preventing damage to the unit [2]. To prevent damage and/or catastrophic failure, IEEE limits the hottest spot temperature to 140 \({}^{\circ}\)C and the top-oil temperature to 110 \({}^{\circ}\)C. Due to the constant load above its nameplate rating, both hottest spot temperature and top-oil temperature have higher values given the same peak demands. Consider the 50 MVA SPX unit identified as the test unit for the analysis. If the unit serves the historical load profile (Profile B characteristics) with a peak demand ranging between 1.0 and 1.5 per unit, the metallic hottest spot temperature will reach a maximum value between 108 \({}^{\circ}\)C-150 \({}^{\circ}\)C depending upon THDI. With IEEE recommending a maximum value of 140 \({}^{\circ}\)C the maximum peak demand this unit can serve the cyclic load with a THDI = 10% is 1.47 per unit. Figure 7a illustrates the hottest spot temperatures induced by Profile B with peak demands varying between 1.0 and 1.5 per unit. Applying the same analysis with the flattened load profile (Profile A) revealed much higher temperatures. The transformer reaches 140 \({}^{\circ}\)C at a THDI = 10% for a peak demand equal to 1.18 per unit, which is 80.27% of the peak energy demand when Profile B is served. Figure 7b illustrates the hottest spot winding temperatures induced by Profile A for a peak demand ranging between 1.10 and 1.45 per unit. The top-oil temperature analysis reveals very similar results. IEEE limits the top-oil temperature to 110 \({}^{\circ}\)C [2]. The test unit reaches the IEEE limit when serving 1.46 per unit and \(\text{THD}_{\text{I}}=10\%\) when serving demands with Profile B characteristics. When the flatter Profile A is applied to the unit, the IEEE limit is achieved when the peak demand reaches 1.20 per unit with \(\text{THD}_{\text{I}}=10\%\). Figure 8 illustrates the top-oil temperature of the 50 MVA unit as a function of peak demand, load profile type, and \(\text{THD}_{\text{I}}\). One significant difference between applications of the two separate load profiles is the effects that harmonic distortion has on increased temperature for \(\text{THD}_{\text{I}}\) values less than 20%. For the 50 MVA test unit, harmonic distortion has a significant effect on the top-oil temperature. When serving Profile B, the top-oil temperature increases at a rate of 0.10 degrees per percentage change in \(\text{THD}_{\text{I}}\).