# A Thermal Discomfort Index for Demand Response Control in Residential Water Heaters
## 7 Conclusions and Future Work  
This article presented an approach to evaluate the impact on the thermal comfort of direct demand response control using electric water heaters. An index associated with the thermal discomfort was defined according to the following procedure. First, a water utilization forecasting model was built using real power data from a set of electric water heaters and applying an ensemble learning technique. Then, a linear model was developed to estimate the temperature of the water in the electric water heater tank. Finally, the TDI associated with an intervention on the electric water heater was defined stochastically, and calculated via Monte Carlo simulation. A specific water heater simulator was developed for the evaluation of the proposed TDI.  
The computational models and the reliability of the proposed index were evaluated in three real case studies. The first case considered two electric water heaters from different users with different average historical utilization. The TDI values were analyzed for both electric water heaters for different penalization factors \(\rho\). Results confirmed that the proposed index correctly models discomfort since higher TDI values were computed for the electric water heater with the higher average historical utilization. The difference in TDI values increased when considering larger penalty values. The second case analyzed the use of TDI for sorting water heaters according to the discomfort caused by their intervention. Two sets of ten households were generated and simulated, considering two different utilization patterns and two interruptions (in the morning and the evening). Results confirmed that in the ranking generated with the TDI computed for the morning interruption, households with high probability of water utilization in the morning were in the last ten positions of the ranking. A similar result was obtained for the afternoon interruption, as expected. The third case study explored the use of parameter \(\rho\) to tune the interruption priority, considering an additional special household and two values of \(\rho\). Results demonstrated that the new special household was in eleventh position in both rankings when \(\rho=1\) and changed to the last position in both rankings when \(\rho=1000\), properly modeling a non-interruptible appliance (e.g., for sanitary reasons). The main lines of future work are related to estimating an economic value of the TDI index (in USD/MWh), useful to characterize the profit of reducing the energy demanded by a set of electric water heaters by applying the interruption action in order to compare this strategy with other demand response techniques (e.g., using fuel generators or batteries). Expanding the developed simulator to consider all generators in the system is another line for future work to fairly compare demand response strategies by using TDI values and the economic impact of an interruption.  
R.P.: research conceptualization, data analysis, code development, manuscript writing, manuscript revision and correction. J.C.: data analysis, data cleansing, manuscript writing, manuscript revision and correction. S.N.: research conceptualization, data analysis, manuscript writing, manuscript revision and correction. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The work of [PERSON] was partly supported by ANII and PEDECIBA, Uruguay.  
The authors declare no conflicts of interest.