# Residential Demand Response Scheduling with Consideration of Consumer Preferences
## 3 Use of Real-World Data
In our model, we take the operating times and the energy consumption of appliances from data provided by [23; 24], and the values can be seen in Table 1. For simplicity, in the model, we only use a single appliance for washing and drying machines having energy consumption equal to their average. The generated problem instances represent a time period of 24 h. One time period is equal to one full hour. At each time instance, the number of households \(N\) and the number of them in each group (FWC, FWN, MP, SP and NSP) is proportional to the same values in the monitored data. These values are given in Table 2. Furthermore, the probability of an individual household submitting a request for using an appliance is proportional to the frequency of appliance utilization. Approximate operating \begin{table}
\begin{tabular}{c c c} \hline \hline
**Type** & **Time** & **kW** \\ \hline Stove & 1 & 1.5 \\ Oven & 1 & 2.4 \\ Washer dryer & 2 & 2.0 \\ Dishwasher & 1 & 1.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Energy use and operating time for different appliances. Figure 3: Illustration of converting the average energy consumption of cooking appliances (per household) to the appliance use distribution. frequencies, for each group, in the case of washer/dryers and dishwashers could be derived from the survey data. In the case of cooking appliances, no precise data are given. For them, these values are specified based on experience. Further, the operation periods are slightly adjusted to have a ration close to one-to-one for total energy consumption between cooking and washing appliances, since this property exists in the monitored data [25]. In the generated problem instances, all users submit a request for at least one appliance. The base demand (all other appliances) has the shape of the equivalent demand curve of the one in the monitored data, but scaled down proportionally. The scaling is used to have the energy use of washing and cooking appliances equivalent to 20% of total energy consumption, as in the monitored data. The values for the hourly pricing scheme are taken from [26], and the exact used values can be seen in Figure 4. This is one of the standard sources for such data and is also used in [27]. Instead of a convex cost function, we use a linear piece-wise approximation, which is also commonly used in the literature. The exact values can be seen in Figure 5. The maximal allowed load \(L\) was equivalent to 1.1-times the scaled value (to correspond to the number of households in test instance) of the monitored data. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Household** & **Percentage** & \multicolumn{4}{c}{**Frequency (Days)**} \\ \cline{3-6}
**Type** & **(\%)** & **Dish Washer** & **Washing Macine/Dryer** & **Oven** & **Stove** \\ \hline FWC & 31.2 & 0.26 & 0.24 & 0.33 & 0.77 \\ FNC & 29.6 & 0.26 & 0.28 & 0.33 & 0.56 \\ SP & 13.6 & 0.20 & 0.21 & 0.25 & 0.45 \\ MP & 11.6 & 0.20 & 0.21 & 0.25 & 0.50 \\ SNP & 14.0 & 0.22 & 0.25 & 0.17 & 0.40 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Data for appliance use for different types of households. FWC, family with children; FNC, family without children; SP, single pensioner; MP, multiple pensioners; SNP, single non-pensioned. Figure 4: Hourly pricing program used for evaluating the proposed model. The data are taken from ComEd [26].