## 4 Results and Discussion
### PEMD Scenarios Analysis  
The day-ahead DR model was applied to all the PEMD case scenarios discussed in Table 12, assuming the maximum peak prices \(spp_{c,h,Max}\) for the period of each distribution company to be set at 200%, 250%, and 300% of their initial values. The three different price scenarios were applied to the profit maximization model presented in Equation (1) by maximizing the daily profit from the three distribution companies without considering the monthly capacity charge. Figure 19 shows the impact of applying the proposed DR model on Sunday, 8 December 2019, considering all case scenarios. The profit maximization model always selects the maximum peak price for the given price scenarios. It can be observed that, the PEMD cases scenarios [C1-C4] show a lower peak drop in the peak period due to having lower price elasticity in comparison to [C5-C8], indicating the higher the peak period price, the higher the peak drops in the peak period. The periods after and before the peak period, especially from 2-4 PM and 9-11 PM, are extremely important. This is because the demand removed from the peak period is rescheduled towards them. Therefore, the new peaks might form, especially in case scenarios with high self-elasticities [C5-C8], indicating the more demand is reduced in the peak period, the higher the new peaks' demand is. C6 represents the worst-case scenario, especially at higher peak prices, representing a lossless-PEMD with double the weight for the closest two hours outside the peak period. C2 represents the highest new peak formed among the cases [C1-C4], although since it has half the self-elasticity of C6, the new peak was not as severe. Figure 18: Applied Day-ahead DR Model for a selected day. There is a clear trade-off between the demand reduced from the peak period and newly formed peaks. Figure 20 shows the peak reduction percentage for the whole day for each case scenario. C6 shows an increase in the peak by \(-1.46\%\) at 300% peak price. It is noted that, in the case scenarios with low self-elasticity [C1-C4], a price increase leads to a steady decrease in the day's peak demand. In contrast, in the cases scenarios with high self-elasticity [C5-C8], higher prices can lead to a lower day's peak reduction due to the newly formed peaks. More than 5%-day peak reduction can be achieved in most cases except for C2 and C6, which are the worst cases among all case scenarios. C6 was the only scenario to show an increase in peak demand at 300% peak price, which is due to two main reasons: first, C6 depicts the high self-elasticity scenario where consumers are highly responsive to the price change, leading to more demand being shifted to hours outside of the peak period. Secondly, C6 depicts the scenario with both the lossless case where all demand removed from any hour will be allocated to other hours and the case where the weight of demand shifted to the closest two hours is doubled. Hence, the higher the price increase, the more demand is re-allocated with a higher concentration on the hours outside the peak period being 15:00 and 21:00, as seen in Figure 19. Other cases such as C5 had a slightly less bad case at 300% peak pick as there was an even redistribution of demand reallocated to the surrounding 4 h of the peak period, making the newly formed peak less than C6, while in C8, there was 25% less demand shifted, making the new peaks also less than C6. Although the peak price is low enough in high elasticity scenarios, even with more demand shifted to closer hours, a high peak reduction can still be achieved. Figure 19: Hourly demand impact of DR-model under different case scenarios. Figure 20: Day peak demand reduction percentage. The load factor is calculated by dividing the mean demand for the whole day by the maximum demand. Figure 21 represents the comparison between the load factor for each scenario with the original demand. The results show that, the load factor can be improved around 5%, by setting high prices in low self-elasticity cases and lower prices in high self-elasticity cases.