## 2 Estimation of Interruption Costs Arising from Transmission System Originated Failures
### Sector Periodic Demand Model  
The interruption costs in VBRI assessment are expressed as demand-normalized costs (DNC), and therefore, the proposed method utilizes a periodic demand model to estimate the demand-normalized interruption costs for the bulk system customer sectors. Figure 3 shows the steps involved to obtain the sector periodic demand (SPD) model for a bulk system. The proposed model is designated as the SPD model in this paper. The first step of the methodology is to identify the major customer sectors in a bulk system. Electricity consumers are classified into various customer sectors depending on their end-use applications. Typically, customers within a specific sector share similar needs for electricity and are affected similarly by power outages. Residential, commercial, and industrial sectors are a significant part of a bulk system load. However, specific customer sectors, such as farm or oil sectors, may exist in bulk systems based on the region they operate. The next step is to obtain the historical load data for each customer sector identified in the previous step. The acquisition of customer sector load data is a part of utility load research [39; 40], which is used to analyze cost-of-service, load forecasting, load management technologies, and other system planning-related activities. In recent years, customer sector load data can be obtained from the advanced metering infrastructure (AMI) in various time intervals. As the proposed methodology is aimed at emerging power systems transitioning to meet low-emission environmental targets, the intermittent renewable generation and electric vehicle loads are incorporated in the load profile of the customer sector that owns them. The proposed methodology in this paper utilizes the hourly interval load data expressed in kilowatts (kW) as given by (1). \[D_{i}=\left\{H_{i,h}\mid i=1,2,\ldots d\text{ and }h=1,2,\ldots,24\right\} \tag{1}\]  
where the daily load profile \(D\) is a set of 24-hourly loads \(H\), and \(d\) is the total number of days of historical data used in the analysis. Adequacy assessment in system planning utilizes annual reliability indices, and therefore, the evaluation period is typically one year. The sector load data obtained are then grouped into \(N\) periods such that the diurnal loads with identical profiles are grouped into one period as described in (2). \[\left\{D_{i,p=1,2,\ldots N}\right\}\in\left\{D_{i}\right\}\left|\mu\left(D_{i =j}\right)\approx\mu\left(D_{i\
eq j}\right)\text{ and }med\left(D_{i=j}\right)\approx med\left(D_{i\
eq j}\right) \text{ for j}=1,2,\ldots,d \tag{2}\]  
Figure 3: Development of a sector periodic demand model. (**a**) Methodology steps, (**b**) Sub-division of the evaluation period. where functions \(\mu()\) and \(med()\) evaluate the mean and median of \(D_{i}\). The proposed methodology then determines a representative load profile for each of the \(N\) periods. It should be noted that increasing the number of periods will improve the accuracy of the SPD model. This will, however, reduce the accuracy of the survey results due to the increased complexity in outage cost estimation by the customers at increasing time resolutions. A trade-off is therefore required. The bulk system reliability indices are highly sensitive to the peak load since the system is vulnerable to customer outages due to generation failures during minimum reserve conditions and transmission failures during line congestion. The load profiles in a period are therefore represented by one load profile \(RD_{p}\) with the highest peak load as shown in (3). The representative load profile is then sorted in descending order. \[RD_{p}=D_{i=k,p}\left|max\big{(}\{H_{k,h}\}\big{)}>max\big{(}\{H_{i\
eq k,h}\} \big{)}\right. \tag{3}\]  
The contribution of transmission system failures to customer outages is highly dependent on the network structure and configuration, and such outages can occur during off-peak hours as well.