*3.3. Internal Evaluation of the Clustering Method*

After performing customer segmentation via clustering, the accuracy the clustering result should be assessed. Evaluation methods are commonly divided into external and internal processes [28]. In external evaluation, the result is assessed by a comparison with the actual value. Internal evaluation is normally used when the data does not contain actual values; thus, the assessment is based on the idea that good results have minimum distance within clusters and maximum distance between clusters (i.e., high intracluster similarity and low intercluster similarity). Although there are many evaluation methods available, we consider only internal evaluations, since they are used to measure the goodness of clustering evaluation structure without respect to external information (i.e., labels or actual results). Among these, we use the Davies–Bouldin index (DBI) and Dunn index (DI). The DBI is an internal evaluation method to quantify clustering quality. It evaluates customer segmentation based on the similarity between clusters and is calculated as follows:

$$DBI = \frac{1}{n} \sum\_{i=1}^{n} \max\_{j \neq i} \frac{\sigma\_i - \sigma\_j}{d(\mu\_i, \mu\_j)} \tag{5}$$

where *n*, μ*i*, σ*i*, and *d*(μ*i*, μ*j*) are the number of clusters, the centroid of cluster*i*, average distance between μ*<sup>i</sup>* and all objects in cluster *i*, and the Euclidean distance between μ*<sup>i</sup>* and μ*j*, respectively. Its output is a single number, and clustering algorithms with lower output values indicate better performance.

The DI is another internal evaluation method to quantify clustering quality. The indicator measures how well clusters are separated and how dense they are. It can be formulated as follows:

$$DI = \frac{\min\_{1 \le i < j \le n} d(i, j)}{\max\_{1 \le k \le n} d'(k)} \tag{6}$$

where *d*(*i*, *j*) and *d* (*k*) are the distances between centroids of cluster *i* and *j* and between objects within cluster *k*, respectively. Its output is a single number, and clustering algorithms with larger output values indicate improving performance.

#### *3.4. Cost-e*ff*ective Analysis*

From the perspective of operation research (OR), cost-effective analysis is an important component. The effectiveness of customer targeting through load profile segmentation in DR operation is operation cost reduction. Thus, we need to identify the amount of cost variation compared with opt-in and targeting recruitment. We confirmed it by using the cost-effectiveness test which is one of the economic analysis methods usually performed before public project investment [29]. It is divided into Total Resource Cost (TRC), Program Administrator Cost (PAC), Ratepayer Impact Measure (RIM), and Participant Cost Test (PCT). We considered the PAC test to recognize the cost effect according to DR customer targeting in perspective of DR operator (i.e., utility or ISO). The cost and benefits list should be defined before economic effectiveness estimation. The list for analysis from the perspective of DR operators can be specified in Table 2.

To identify whether the utility project is appropriate for investment, each cost/benefit item should be calculated. If the cost-effectiveness test result has a positive value, it represents that the project has profit. The project is a nonprofitable business in the opposite case.

Avoided energy costs is the benefit of decreasing the amount of power purchased in accordance with electricity consumption reduction. It can be formulated as follows:

$$AEB = ER \times ARLI \tag{7}$$

where *ER* and *ARU* are the amount of power reduction and the unit cost of energy avoidance (i.e., average system marginal price (SMP) during DR event), respectively.


**Table 2.** Benefits and cost list for cost-effectiveness analysis in DR operation.

Avoided transmission and distribution cost is the benefit reducing demand for transmission and distribution construction as a result of decreasing annual peak demand. It can be formulated as follows:

$$ATDB = PR \times (ATU + ADUI) \tag{8}$$

where *PR*, *ATU*, and *ADU* are peak reduction capacity in power system, unit cost of transmission construction avoidance, and unit cost of distribution construction avoidance, respectively.

In the case of the cost list, it contains the cost of revenue loss from changes in sales, incentives, DR system operation, measure, evaluation, marketing, and education. Revenue loss from changes in sales is a cost as the utility company cannot provide power to customers as an amount of DR reduction. Incentive paid cost is cost for utility companies to provide incentives to DR participants as a result of demand reduction. Measurement, evaluation, marketing, and education cost are included in DR operation cost and we assume that these costs are calculated proportionate to the number of DR customers.

#### **4. Load Profile Segmentation for E**ff**ective DR Program Operation in Korea**

DR options in Korea have mostly been unavailable to residential customers and have been implemented only for commercial and industrial customers. However, utility companies have recently attempted to attract residential customers by changing their policies and opening DR programs to them. The Korea Electric Power Corporation (KEPCO) which is a utility in Korea also conducted a peak-time rebate (PTR) pilot program from November 2017 to February 2018 in 10 events to develop an appropriate residential DR program in Korea [30]. It was performed with about 800 residential customers living in Seoul, Korea. The PTR program was designed based on incentive-based DR to mitigate peak demand by reducing participant demand in accordance with the utility's notification. After the DR event, the PTR provides incentives based on the amount of demand reduction achieved after participants receive a notification to reduce their demand. It does not have any penalty in the case of the PTR program and can make customers who pay a flat electricity price realize that the electricity price has a time-varying rate system.

Although this PTR program is designed for opt-in customers, targeted enrollment to select residential customers with high DR potential is necessary to improve the benefits of the DR program. Therefore, we analyze residential customer demand data from the PTR pilot program and apply the two-stage clustering methodology discussed in the previous section. From this study, we obtain customer clusters according to load pattern and consumption and select suitable groups for efficient DR operation through an analysis of group characteristics. Finally, we identify the actual demand reduction effect in the case of opt-in operation and targeted enrollment operation by applying residential customer data during an actual PTR event.
