## 2 Methodology
### Upper and Lower Threshold of Penetration  
The lower and upper values of power and time of use presented in the Mexican scenario can be seen in Table 6. The values are taken from [35,36] and were estimated based upon the Mexican National Association of Manufacturers of Domestic Devices (in the case of the power) and on surveys made by the authors (in the case of the time of usage). It is worthy to state that these values might vary due to various factors such as the brand & model of the device, and the schedule of the users.  
It is important to mention that the conventional ranged power of air-conditioning is stated at 1000-4000 W, illumination & appliances at 100 W (incandescent lightbulb)-1700 W (microwave oven); and refrigeration at 150-400 W [40].  
In order to carry out the analysis upon a national scale, lower and upper values of the probable national percentage of the saving appliances saturation and the time-of-usage reduction have to be  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Activity** & **Lower Threshold** & **Upper Threshold** \\ \hline Power air-conditioning & 300 W & 1000 W \\ Power illumination \& appliances (aggregated) & 200 W & 585 W \\ Power refrigeration & 100 W & 190 W \\ Time air-conditioning & 1000 h/year & 1500 h/year \\ Time illumination \& appliances & 1200 h/year & 2200 h/year \\ Time refrigeration & 1000 h/year & 1850 h/year \\ \hline \hline \end{tabular}
\end{table}
Table 6: Lower and upper limits of power and time of use of the energy activities of the Mexican residential sector [35,36].  
Figure 4: Program code for calculating the annual electricity consumption of the Mexican residential sector.  
taken into account. These percentages represent the expected number of households that implement the efficient appliances and/or reduce their time of usage. For this, the governmental programs of energy efficiency were taken account of as well as their expectance of penetration amongst Mexican dwellings [41]. The values are displayed in Table 7.  
According to the two main programs of saving energy in the Mexican residential sector of the last two government administrations, i.e., the Program of Substitution of Electrical Devices for Energy Saving and the Program of Substitution of Incandescent Lightbulbs for Energy Saving Lightbulbs [33], it is expected to substitute between 300 thousand and 2 million old AC devices, the switch for efficient lightbulbs in 6 to 22 million dwellings, and the substitution of 2 to 14 million of inefficient refrigerators, all this in a period of 8 years [33]. With these figures, the lower and upper thresholds were set in Table 7 and in accordance to the goals of the existing programs.  
It is important to mention that the percentages are considered the same for both the appliance saturation and the households that reduce the time of usage of their devices. This is considering that the governmental programs which encourage users to purchase more efficient appliances and to reduce their time of use (including Daylight Saving Time) do not show a clear difference between the two approaches. It is considered that the remaining percentage of dwellings uses the averaged power and time of use, in this paper taken from Table 4.  
Finally, for a simplification purpose, it is considered that 100% of the dwellings have an electrical connection, electrical appliances and at least one refrigerator. In the realistic Mexican scenario, 97% of the residential stock is connected to the national grid [42]. Out of them, 99% have at least one appliance and/or electrical illumination device, and 89% have at least one refrigerator [42].