## 4 Results and Discussion
### PEMD Analysis  
#### 4.2.1 Residential PEMD Analysis  
Pre-implementation of DR requires a well-established estimation of the PEMD to analyze the impact of price ranges on demand. The short-term price elasticity is the best estimation for self-elasticity (\(\epsilon_{h}\)) as it shows the negative relationship between price and demand change in short periods. Based on an analysis of residential tariffs for the periods between 1984 to 2014, the short-term price elasticity of electrical demand for the residential sector in Jordan was estimated at \(-\)0.0575 [47]. Although, since price responsiveness of demand varies at different hours of the day, two scenarios are assumed: (1) \(\epsilon_{h}\) is assumed constant for every hour, (2) \(\epsilon_{h}\) is assumed to be double in peak periods. Hourly cross-elasticity represents the amount of energy  
Figure 14: Absolute percentage error of the forecasted results in December 2019 and related weather conditions. shifted from one hour to other hours of the day both backwards and forwards in time. To estimate the amount of potential shiftable energy in peak load hours, as well as its time horizon, a detailed analysis of the different loads impacting DR and their penetration in the residential sector is conducted, which is represented in Table 9.  
The data in Table 9 was used to estimate the normalized weight of each appliance's energy consumption relative to other appliances, which is shown in Figure 15. The figure depicts an estimation of the weight of each appliance's share of the residential electrical demand for the loads discussed in this study, where it is more probable that it holds in the evening load period when consumers return from work and need to use both water and space heating. Residential loads can be classified into different types according to their flexibility and DR characteristics: Thermostatically controlled loads (TCLs), deferrable loads, uninterruptible loads [66]. TCLs are highly correlated to temperature and environmental factors, where due to their thermal storage properties, their demand can be more flexible with a lower impact on consumer comfort. Deferrable loads refer to appliances that are flexible to  
Figure 15: Daily load weights of electrical appliances in Jordan’s residential sector. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Appliance** & **Penetration Rate (\%) 1** & **Watts 4** & **H/Day** \\ \hline
**Vacuum cleaner** & 68\% & 1200 & 0.5 \\
**Dishwasher** & 7\% & 1800 & 1 \\
**Washing machine** & 97\% 2 & 1800 & 1.5 \\
**Water heater (Electrical/Gas)** & 79\% 0.5 2, 3 & 4000 & 3 \\
**AC** & 32\% & 1800 & 12 \\
**Freezer** & 16\% & 200 & 12 \\
**Refrigerator** & 98\% & 200 & 12 \\
**Microwave** & 54\% & 1500 & 0.5 \\
**Laptop/PC** & 31\% & 120 & 3 \\
**TV** & 98\% & 200 & 3 \\
**Lighting** & 100\% & 420 & 6 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Power consumption and penetration rates of different electrical appliances in Jordan’s residential sector. use and can also be shifted with low impact on consumer comfort. Finally, uninterruptible loads refer to the appliances that require continuous energy demand while being used and are highly correlated to consumer comforts where they usually have little DR potential. Both TCLs and deferrable loads are estimated to represent 82.9% of the residential sector which amounts to a significant potential for DR in Jordan's residential sector. Water heating and deferrable appliances can be easily shifted in peak demand periods resulting in peak shaving. According to the previous discussion, cross-elasticity is estimated under two scenarios related to the amount of energy re-allocated in peak time:  
1. **A lossless-case scenario**: Reduced energy at a certain hour is re-allocated into other hours of the day without a loss in total energy consumption. Hence, the summation of all cross elasticities in every column in the PEMD is equal in magnitude to the self-elasticity at that hour. 2.