## 3 CDL-Based DR Scheme
### Cdl  
First, CDL is defined. From the LSE's view, there exists a desired total load curve, which supports some of its goals. It is necessary to take into account LSE's own constraints but to consider customers as sufficiently flexible. For example, from the social public view, decreasing coal consumption of conventional generation and consuming as many RESs as possible is the goal. Therefore, the CDL can be defined as a desired load curve that ensures no abandonment of RES. In other words, CDL is a guidance directrix for customers in DR. Additionally, the contribution that each customer makes to promote the total load curve approaching CDL can be quantified to measure its DR performance. According to its definition, CDL is calculated by the LSE, which ensure the uniqueness and fairness of CDL.  
This paper studies CDL from the social public viewpoint, that is, the promotion of RES integration. If it comes to other viewpoints, for example, maximizing LSE's welfare, a corresponding CDL can be calculated and it will be studied in the future. In high proportion RES integration power systems, DR resources and conventional generations are controllable resources, while RES and inflexible loads are uncontrollable resources if the abandonment of RES is not considered. The basic goal for controllable resources is to balance uncontrollable resources, which requires that:  
\[P_{c}(t)=-\sum_{i\in\mathcal{I}}D_{i}(t)=P_{d}(t)-P_{r}(t)\quad\forall t\in \mathcal{T} \tag{1}\]  
where \(P_{c}(t)\) represents power output of conventional generators at time slot \(t\); \(P_{d}(t)\) represents the inflexible load at time slot \(t\); \(P_{r}(t)\) represents power of RES at time slot \(t\); \(D_{i}(t)\) represents the \(i\)th DR customer's load at time slot \(t\); and \(\mathcal{T}=(1,2,\cdots,T)\) represents the time set and \(\mathcal{I}=\{1,2,\cdots,l\}\) represents DR customer set. Let \(\Delta(t)=P_{d}(t)-P_{r}(t)-P_{c}(t-1)\). \(\Delta(t)+\sum_{i\in\mathcal{I}}D_{i}(t)\) represents the difference of the demand for conventional generators in two successive time slots. Traditionally, this difference is suitable for load changing only. However, in power systems with RES, there has to be a balance between the superposition of the load and RES, which is known as pure load. In practice, too much regulation of conventional generators is not efficient and is even unfeasible because of constraints of generations, e.g., the ramp rate limit [45]. As a result, LSE requires the difference of the demand for conventional generators in two successive time slots to be limited in a certain range, and if it is likely to exceed the threshold, the DR event will be implemented. According to the definition of  
Figure 1: Timeline of the proposed DR scheme.  
CDL, DR customers take responsibility for the total exceeded regulation part; thus, the CDL for DR customers is:  
\[P_{CDL}(t)=\left\{\begin{array}{ll}\Delta P_{\text{up.max}}-\Delta(t)&D^{*}(t )+\Delta(t)>\Delta P_{\text{up.max}}\\ \Delta P_{\text{down.max}}-\Delta(t)&D^{*}(t)+\Delta(t)<\Delta P_{\text{down.max }}\end{array}\right. \tag{2}\]  
where \(P_{CDL}(t)\) is the calculated CDL at time slot \(t\); \(D^{*}(t)\) is the forecasted flexible load at time slot \(t\); and \(\Delta P_{\text{up.max}}\) and \(\Delta P_{\text{down.max}}\) represent the maximal increasing and decreasing capacity of the total conventional generation, respectively.  
In fact, LSE requires DR customers to regulate their load from time slot \(t\)-1 to \(t\) to approach the CDL. The ideal regulation value \(P_{\Delta CDL}(t)\) is:  
\[P_{\Delta CDL}(t)=P_{CDL}(t)-\sum{{}_{i\in\mathcal{I}}D_{i}(t-1)} \tag{3}\]