[INSIGHT] Determining Catastrophic Days in Electric Power Distribution Utilities

 By Engr. Edward Joseph Maguindayao & Engr. John Paul P. Manzano    -  

Reliability Indices

One way of evaluating the performance of power systems is through reliability indices. Reliability indices account for the power supply interruption or the availability of power supply to end-users. These indices can either be customer-oriented where the number of interruptions experienced by customers is counted, or load-oriented where the load of the affected customers is considered. Customer-oriented indices include the system average interruption duration index (SAIDI) [1–9], system average interruption frequency index (SAIFI) [1–8, 10], momentary average interruption frequency index (MAIFI) [1–3, 10], and customer average interruption duration index (CAIDI) among others [1–2, 4].

The reliability of a distribution system is a random process, and the reliability indices are the random variables. These indices consider the duration and frequency of power outages, number of customers served, and customers affected by the interruption. This means that the reliability indices can have a wide scatter of values. Moreover, the values of these indices can be relatively high, indicating the presence of major event days (MEDs) [11].

Normalization thus becomes necessary to remove outlier values to better evaluate the performance of a distribution utility (DU).

The need for a new method

Because the Philippines experiences many calamities such as typhoons, earthquakes, and volcanic eruptions, long and widespread power interruptions can be expected. High reliability index values due to major events affect the performance assessment of a DU.

As a result, there will be days with unusually high reliability indices [16–17]. Therefore, a new classification known as catastrophic days (CDs) was recommended for adoption and further study [11]. This new category has a higher threshold than MEDs which needs to be quantified in order to better gauge the system performance. In determining CDs objectively, the extreme values on top of the MEDs are removed so that the reliability indices will better reflect the performance of the DU [18].

Although only SAIDI is considered in identifying CDs, all indices on the identified day are removed when computing the adjusted reliability indices [11–12].

The Energy Regulatory Commission (ERC) in 2013 has set standing guidelines for monitoring the reliability indices and conducted a number of assessments to determine the reasonable values of SAIFI and SAIDI for identifying reward and penalty levels of on-grid DUs [19–20]. The maximum values in which the penalty level for a DU is zero are 25 interruptions/customer-year and 56.25 hours/customer-year for SAIFI and SAIDI, respectively.

System Average Interruption Frequency Index (SAIFI)

SAIFI refers to the ratio of the number of affected customers to the total number of end-consumers served. A value of unity means that all the customers experienced one interruption over a particular time duration, while a value exceeding unity means that some customers experienced more than one interruption event. SAIFI may be computed over different periods of time such as per day or for a whole year.

System Average Interruption Duration Index (SAIDI)

SAIDI is the ratio of the total duration of interruption experienced by the customers to the total number of customers served. The usual unit of duration used is in minutes, which is then multiplied by the number of consumers who experienced the interruption [1]. It can also be expressed in hours.

Beta Method

The standard method for MED identification is the beta method [11], which is illustrated in Figure 1. It requires obtaining the TMED from the average, α, and the standard deviation, β, of the natural logarithmic (ln) values of SAIDI. For its implementation, the zero SAIDI and SAIFI days are first removed from the five-year interruption data. The remaining values in the dataset are then arranged from least to greatest SAIDI value, after which, the SAIDI values are expressed as natural logarithms. The average value and the standard deviation of the converted SAIDI values are then computed.

Heuristic Method

The heuristic method is essentially a modified beta method, the flowchart of which is shown in Figure 1. This method essentially follows the same process flow as that of the beta method implementation except for the part in finding a suitable β multiplier, which should be greater than 2.5 [25].

Figure 1. Flowchart of the heuristic method and the box and whisker method [21, 25, 26].

Box and Whisker Method

The box and whisker method follows the same process flow, up to the computation of ln SAIDI values as shown in Figure. 1.

The statistical variables median, first quartile (Q1), and third quartile (Q3) value are computed. The interquartile range (IQR) is the difference between Q3 and Q1 values. The resulting IQR value is multiplied by 3, which is then added and subtracted from Q3 and Q1, respectively, to obtain the upper and lower values, respectively. The required statistical variables for this method are illustrated in Figure 2.

Figure 2. Variables for box and whisker method [21, 26].

All days with ln SAIDI value exceeding the upper value are considered as CDs [21]. Meanwhile, days that exceeded the lower value are ignored as it is desirable to have lower reliability index values.

All reliability indices in the identified MEDs or CDs are removed from the computation of the adjusted reliability indices. The adjusted annual SAIDI and SAIFI values are obtained by adding up the remaining daily SAIFI and SAIDI values.

Summary of Interruption Data

The daily SAIFI and SAIDI values were obtained by aggregating the number of customers affected by interruptions and the corresponding duration for a single day over different feeders within the franchise area of an electric cooperative. Meanwhile, days with no interruption or with interruption that extended from the previous day were noted with zero SAIFI and SAIDI (for days covered by an extended interruption, the values were added to the day when the interruption started).

The data were tabulated from January 1, 2010 to December 31, 2014 for a total duration of five years. Lastly, the annual SAIFI and SAIDI values were determined from the aggregated daily values for each corresponding year.

Table 1 summarizes the number of zero SAIFI and SAIDI days per year, as well as the corresponding annual SAIFI and SAIDI values.

Table 1.  Number of zero SAIFI and SAIDI days and annual SAIFI and SAIDI 

Natural Logarithm of SAIDI Values

After arranging the non-zero daily SAIDI values from least to greatest, each entry was converted to its natural logarithmic form. Figure 3 shows the plot of ln SAIDI values and their corresponding frequency of occurrence.

For the beta method to be applicable in the data set, the ln SAIDI values must closely resemble a Gaussian distribution. Based on the histogram presented in Figure 3, it can be assumed that the distribution of the ln of SAIDI values follows a bell-curve pattern (Gaussian).

On top of verifying that normalization is indeed applicable for the considered data set, presenting the SAIDI values in their natural logarithmic form made it easier for data handling and ensured that the values were close to each other without compromising extreme values.

Figure 3. Frequency distribution of the natural logarithm of SAIDI values.

Beta Method Implementation

Days with SAIDI value greater than 1.48 hours/customer-day were considered MEDs. Using this criterion, the identified MEDs are tabulated in Table 2. The corresponding SAIFI value for each day was included since it provides information on the number of customers who experienced interruptions relative to the number of customers served [11].

Table 2. Identified MEDs from 2010 to 2014.

 

Heuristic Method and Box and Whisker Methods Implementation

The only difference between the implementation of the beta method and the heuristic method is the choice of a suitable β multiplier for the computation of the threshold value. Due to the subjective nature of choosing a single β multiplier to determine the CD threshold, certain values of the β multipliers were investigated and the results are shown in Table 3.

The chosen multipliers were from 2.50 and higher. This is the logical approach since a CD must be a part of the MED subset [25]. The chosen multipliers were the transition point wherein the identified CD is reduced by one as illustrated in Table 3.

Table 3. Effect of increasing β to the threshold and the removed days.

Meanwhile, the computed values of the variables needed for the box and whisker method implementation are shown in Table 4.

Table 4.  Box and whisker method variables and corresponding values.

 

Adjusted Annual Reliability Indices                        

From the implementation of the box and whisker method, only one CD was identified. In contrast, the number of identified CDs using the heuristic method was found to be highly dependent on the chosen β multiplier. 

It shall be assumed in this section that the chosen β multiplier for the heuristic method implementation is between 2.82 and 4.91 so that the two methods identify July 16, 2014 as the lone CD.

After identifying the MEDs and CDs, they were removed from the computation of the new annual SAIDI and SAIFI. The results and comparisons are summarized in Table 5.

Table 5. Unadjusted and adjusted annual reliability indices [26].

Conclusion

The methodology outlined in this article can serve as an initial step in crafting a revised policy guideline for distribution utilities to identify CDs, instead of subjectively removing days which have high reliability indices. Along with the standard set for determining MEDs, the study could potentially save distribution utility operators from unnecessary penalties due to poor reliability indicators brought about by frequent natural calamities in the country.

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Edward Joseph H. Maguindayao obtained his engineering degree from UP Los Baños and is currently taking up his graduate studies at UP Diliman. 

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John Paul P. Manzano obtained his undergraduate degree from UP Los Baños and his graduate degree from UP Diliman.

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