## 3 Capacity Rating Procedure
### Existing Unit Derating--Normal Operations  
The goal of establishing a normal operation capacity limit is to ensure a transformer will deliver power effectively for its entire life expectancy, which is defined by IEEE Std. C57.91-2011 as approximately 180,000 h at full nameplate rating or 25 years given off-peak periods [2]. Given the same peak demand, a transformer serving Profile A (flattened profile) experiences higher internal temperatures for longer periods of time when compared to the effects of Profile B [6]. Units that are currently installed on the grid were sized utilizing the typical historical cyclic load profile. Therefore, it may be unlikely that the unit can deliver the same amount of peak demand without experiencing higher than expected internal temperatures and ergo increased loss of life. The best approach for preventing excessive aging of a unit is to derate the existing capacity limits [35; 36; 37; 38; 39; 40; 41; 42; 43]. Derating is established by reducing the peak energy demand of the unit to a level that maintains the hottest spot temperature (\(\Theta_{\text{H}}\)) below acceptable levels according to IEEE Std. C57.91-2011 [2]. Aging is affected by the ambient temperature surrounding the transformer unit; therefore, varying weather conditions throughout the year may dictate seasonal capacity limits [14]. If a single limit is satisfactory, analysis is performed to identify the time of year when daily average ambient temperatures and load requirements produce the most extreme transformer aging and/or internal temperatures. Derating the capacity limits for normal operating conditions consists of identifying a multiplier that represents a \"per unit\" reduction in the existing acceptable peak demand, which could equal the nameplate rating of the unit. A peak demand derating multiplier is identified by comparing the original transformer aging [\(A_{O}\)] to the new transformer aging [\(A_{N}\)] induced by a flattened load profile. With all environmental conditions the same (weather, season, etc. ), the only variance between existing \(A_{O}\) and \(A_{N}\) is the load factor, harmonic demand, and peak demand. The original aging (\(A_{O}\)) is a function of the original load factor (\(l_{O}\)), harmonic demand (\(h_{O}\)), and peak demand (\(c_{O}\)). Aging (\(A_{N}\)) due to the new load requirements is a function of the new load factor (\(l_{N}\)), harmonic demand (\(h_{N}\)), and peak demand (\(c_{N}\)). New aging should be equal to or less than the original aging (\(A_{O}\)), which is illustrated in (4). The aging can be for a 24 h period, 1 week, or a month depending upon the desires of the utility. \[A_{O}(l_{O},h_{O},c_{O})-A_{N}(l_{N},h_{N},c_{N})\geq 0 \tag{4}\]  
The dielectric insulation aging methods described previously were applied to the 50 MVA SPX test unit to identify aging associated with Profiles A (\(A_{N}\)) and B (\(A_{O}\)). Although variations in the new load factor (\(l_{N}\)) and new harmonic distortion levels (\(h_{N}\)) may not be controlled by the utility, the new peak demand \(c_{N}\) can be controlled by establishing operational capacity limits. Applying the procedure to the 50 MVA SPX test unit results in the following; for the SPX test unit to age at a rate equivalent to the one induced by Profile B (\(A_{O}\)) with a peak demand equal to 1.0 per unit, the peak demand of Profile A must be limited to 0.72 per unit. At this peak, the new loadfactor for the transformer demand is 0.881, which is much higher than Profile B at \(LF\) = 0.682. Table 3 summarizes the results of applying both Profiles. Figure 5 illustrates a comparison between Profile B with 1.0 per unit peak demand and Profile A with varying peak demands ranging between 0.70-1.2 per unit. The figure utilizes the aging associated with Profile B as the benchmark for aging that all other conditions are compared with.