# Residential Demand Response Scheduling with Consideration of Consumer Preferences
## 3 Use of Real-World Data  
For the proposed model, our goal is to explore its potential for real-world application; because of this, we generate test instances based on the measured data. More precisely, the consumer behavior and preferences are based on the data collected in a survey conducted by the Department of Energy & Climate Change, UK [21]. The survey data were collected from 251 households in England over the period from May 2010-July 2011. For each of the households, the electrical power demand and energy consumption were monitored. The participating households were selected on the basis of the life-stage of the occupants. During the course of the survey period, the occupants also completed diaries of use for some of the products they used. They were also requested to complete survey questions about their environmental attitudes. There were no special incentives to influence the behavior of participants. The households were divided into five groups: family with (FWC) and without children (FNC), multiple pensioners (MP), single pensioner (SP) and single non-pensioned (SNP). For each household and individual appliance, energy consumption has been monitored every 10 min. An illustration of aggregated data can bee seen in Figure 2.  
It is well known that some appliances, like lighting, audio/visual, computers, _etc._, cannot be controlled without a significant impact on consumer comfort. Because of this fact, in the generated problem instances, we assume that only cooking and washing appliances could be scheduled. The energy consumption of the other appliances is used as a base load. It is important to point out that water heating appliances are also excluded from scheduling because the vast majority of surveyed households used natural gas instead of electricity (see Figure 2). Although the monitored data show the energy consumption, they also give information on the time periods when householdshave used such appliances. To be more precise, a high level of energy consumption corresponded to a high number of working appliances at some time. In the generation of problem instances, the energy consumption for each group of households is treated separately. It is understandable that there could be a high demand to use appliances of Type A at some time period \(t\), which indicates that many household have a preference for using \(\tilde{A}\) at \(t\). This simple logic is used to generate preferences (variables \(c_{hat}\)) in the following way. The first step is to convert the hourly energy consumption curve \(f_{\tilde{A}\tilde{H}}(t)\), for appliance type \(\tilde{A}\) and household type \(\tilde{H}\), into a probability distribution. This can be done using the following formula:  
\[prob_{\tilde{A}\tilde{H}}(t)=\frac{f_{\tilde{A}\tilde{H}}(t)}{\sum_{i=1.24}f_{ \tilde{A}\tilde{H}}(i)},\qquad t\in\hat{T} \tag{16}\]  
In Figure 3, we show the distribution of oven working periods for 250 FWC using the corresponding probability distribution. The procedure for generating preference levels \(c_{hat}\) for a specific household \(h\) and appliance \(a\) is done in the following way. Let us say that \(h\) is of type \(\tilde{H}\) and \(a\) is of type \(\tilde{A}\). For simplicity, let us assume that operating time \(t_{a}=1\). Initially, all of the values of \(c_{hat}=0\). Using the probability distribution \(prob_{\tilde{A}\tilde{H}}\), we would, one by one, select time periods for which the preference values would be set from 1-6. This is done iteratively, in an ascending order of \(i\), by selecting a time period \(\hat{t}_{i}\) based on the probability distribution \(prob_{\tilde{A}\tilde{H}}\) and setting \(c_{hat}=i\), with the constraint \(\hat{t}_{i}\
eq\hat{t}_{j}\). The procedure in case of \(t_{a}>0\) is the same, except that the constraints forbid the overlapping of selected time intervals. Figure 2: Illustration of the hourly energy consumption of different appliances (per household) from survey data. The image corresponds to average energy consumption of all participating household for working days.