3.4.1. Variance Error Correction

The traditional K-means algorithm is a vector quantization method that partitions observation into distinctive clusters. Each cluster centroid represents all members in the cluster. However, the centroid representation can lead to a high variance since each demand load profile of the cluster is represented by the same centroid, as shown in Figures 6 and 7. To compensate for such anomalies in the prediction, we defined a correction model, part of the ECM, as described in Algorithm 2, called the variance correction model. With this, the forecasted load profile was adjusted with the mean error of the recent seven-day actual demand load profile forecast. This process alters the forecasted cluster centroid with the deviations with the latest forecast to compensate for maximum variations with each cluster centroid.


**Figure 6.** 22 June 2017 demand load profile.

**Figure 7.** 30 June 2017 demand load profile.

#### 3.4.2. Permanent Bias Error Correction

The demand load profile varies with time, even with a similar set of predictors, as shown in Table 2. The prediction gap can be significant, as depicted in Figure 8. These changes are mainly due to the addition of power equipment or changes in the number of users. As mentioned earlier, the information on the feature state characteristics is not accounted for by the K-means model.

**Table 2.** A set of similar load predictors.


**Figure 8.** Comparing two demand load profiles.

A permanent bias error correction model is, therefore, devised to compensate for the variations in the demand load profile. With an intermittent short-term (i.e., 15 min) forecast interval, the correction model uses an estimated error rate of the actual data of the previous seven days to retard the forecast deviation, as shown in Figure 9. The algorithm for this process is described in Algorithm 3. The variance error correction precedes the permanent bias error correction.


**Figure 9.** Permanent bias error correction effect.
