## 2 Methodology  
### Calculation Method  
According to Equation (1), the energy use of any electrical device can be estimated by multiplying its power by its time of use:  
\[\text{Energy}\ (\text{W}\!\cdot\!\text{h})=\text{Power}\ (\text{W})\!\cdot\! \text{Time}\ (\text{hours}) \tag{1}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Activity** & **Power (Watts)** & **Time of Use (Hours/Year)** \\ \hline \multirow{4}{*}{Air-conditioned} & Air-conditioning & 1000 & 1500 \\  & Illumination \& appliances & 585 & 2200 \\  & Refrigeration & 190 & 1850 \\  & Stove, water \& space heating & 1440 & 380 \\ \hline \multirow{2}{*}{Not air-conditioned} & Illumination \& appliances & 455 & 2200 \\  & Refrigeration & 190 & 1400 \\  & Stove, water \& space heating & 1150 & 380 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Averaged power and time of use of different activities in air-conditioned and not air-conditioned dwellings in Mexico [35; 36]. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Activity** & **Annual Use (TWh) a** & **Annual Use (TWh) b** \\ \hline \multirow{4}{*}{Air-conditioned} & Air-conditioning & 11.92 & 10.39 \\  & Illumination \& appliances & 8.94 & 8.92 \\  & Refrigeration & 2.43 & 2.43 \\  & Stove, water \& space heating & 3.81 & 3.79 \\ \hline \multirow{4}{*}{Not air-conditioned} & Illumination \& appliances & 24.44 & 24.46 \\  & Refrigeration & 6.59 & 6.50 \\  & Stove, water \& space heating & 10.51 & 10.68 \\ \hline \multicolumn{2}{c}{Total electrical} & 54.32 & 52.70 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Annual national use of the Mexican residential sector in 2015. a Study presented in this paper. Thereby, the calculation method is divided into two parts that might take stochastic values: The range of watts of the different devices, and the minimum and maximum time of usage of these devices. In order to calculate the total annual electricity use (TAEC) for Mexico in 2015, the activities within the air-conditioned dwellings (6.93 million) are broken down into air-conditioning, illumination & appliances, and refrigeration, whereas the activities within the free-running, i.e., not air-conditioned dwellings (24.44 million) are broken down into illumination & appliances, and refrigeration. Equation (2) shows the calculation with the respective number of air-conditioned and free-running households in the country:  
\[ \begin{split}\text{TAEC}=\sum\limits_{\text{n}=1}^{6.93\text{M}}& [(\text{PowerAC}\cdot\text{TimeAC})+(\text{PowerI& A}\cdot\text{TimeI& A})+(\text{PowerR}\cdot\text{TimeR})]\\ &+\sum\limits_{\text{n}=1}^{24.44\text{M}}[(\text{PowerI& A}\cdot\text{TimeI& A})+(\text{PowerR}\cdot\text{TimeR})].\end{split}  \tag{2}\]  
Equation (2) can be developed to Equation (3):  
\[ \begin{split}\text{TAEC}=\sum\limits_{\text{n}=1}^{6.93\text{M}}& (\text{PowerAC}\cdot\text{TimeAC})+\sum\limits_{\text{n}=1}^{6.93\text{M}}( \text{PowerI& A}\cdot\text{TimeI& A})+\sum\limits_{ \text{n}=1}^{6.93\text{M}}(\text{PowerR}\cdot\text{TimeR})\\ &+\sum\limits_{\text{n}=1}^{24.44\text{M}}(\text{PowerI& A}\cdot\text{TimeI& A})+\sum\limits_{\text{n}=1}^{24.44\text{M}}(\text{PowerR}\cdot\text{TimeR})\end{split}  \tag{3}\]  
Equation (3) shows the sum of the energy use for the 6.93 million air-conditioned households and the 24.44 million non-air-conditioned dwellings in Mexico in 2015 depending on the corresponding devices' power and time of usage. Furthermore, in Equation (3), PowerAC, PowerI&A, PowerR, TimeAC, Timel&A and TimerR have random values ranged between a respective lower and an upper threshold. These lower and upper thresholds depend on the minimal and maximum values of power for every devices and the minimal and maximum values of time of use for each activity (refrigeration, air-conditioning, and illumination & appliances).