## 2 Load Profile Development
### Transformer Thermal/Aging Model Description  
A transformer model based upon the IEEE Std. C57.91-2011 transient model (Annex G) was evaluated to assess how a transformer's solid dielectric (paper insulation) is aged by Load Profiles A and B with varying levels of harmonic distortion. Most substation transformers are balanced so that the voltage between phases does exceed a 3% difference. With smart grid monitoring and switching capabilities, ensuring system balance between phases is achieved easier when compared to past systems. The transformer model applied in the research assumes the substation transformer serves a balanced load, which nullifies the disadvantage of applying the IEEE method for derating [14]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Substation Transformer** & **Average THD\({}_{\text{V}}\) (\%)** & **Peak THD\({}_{\text{V}}\) (\%)** &
\begin{tabular}{c} **Average THD\({}_{\text{V}}\) during** \\ **Peak Load (\%)** \\ \end{tabular} \\ \hline XFMR 1 & 1.62 & 2.76 & 1.46 \\ XFMR 2 & 4.53 & 5.52 & 4.40 \\ XFMR 3 & 4.89 & 5.23 & 4.76 \\ XFMR 4 & 5.33 & 7.84 & 4.83 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Harmonic voltage monitoring results. Figure 4: Current harmonic spectrum for XFMR 4. Analysis of this model with varying load profiles identifies the peak demand that produces internal transformer temperatures that meet the limits set forth by IEEE Std. C57.91-2011 for normal and emergency capacity limits. In accordance with IEEE Std. C57.91-2011, this paper refers to transformer aging as the mechanical degradation of a unit's solid dielectric by means of thermal stress that is generated from the current flowing through the windings and leads [2]. Reducing the tensile and dielectric strengths of insulation reduces the material's ability to withstand short circuit stress and the associated mechanical movement, which increases the possibility of a failure during a downstream fault event. The models utilized in the analyses assume the transformer overall dielectric protection consists of TUK paper insulation submerged in mineral oil, which is consider the industry standard [2]. The IEEE Std. C57.91-2011 transient model calculates temperature of the transformer winding hottest spot, which is the area that experiences the most paper insulation aging and is considered the \"weak link\" of the unit regarding potential failure. The model calculates internal temperature variations in 30-second increments utilizing demand, ambient temperature, cooling system, winding properties, altitude, tap position, tank configuration, rated losses, and oil properties [2]. Because the research goal was to identify how a flattened load profile with a high harmonic content affects transformer temperatures, derating factors such as altitude adjustment and tap position were ignored so that a true measurement of the load profile effects could be identified. Unfortunately, the IEEE Std. C57.91-2011 model does not account for harmonic distortion, which is known to create additional internal heating [13]. To account for harmonics, the harmonic loss factors described in IEEE Std. C57.110-2008 were applied to the IEEE Std. 57.91-2011 transient model [13]. IEEE Std. 57.91-2011 categorizes transformer losses into three categories: (1) no-load losses (excitation losses), (2) load losses (impedance losses), and (3) total losses (sum of no-load losses and load losses) [10]. Load losses are comprised of \(I^{2}R\) losses and \"stray losses\", which are determined by subtracting \(I^{2}R\) losses from the measured load losses during testing. Stray losses are comprised of winding losses (conductor strand eddy current losses and circulating current between strands) and component losses (core, core clamps, magnetic shields, and tank). Testing has proven that winding losses (_Pec_) tend to be proportional to the square of the load current and approximately proportional to the square of the frequency [13].