3.4.3. Temporary Bias Error Correction

Special event bias may occur with persistent multiple error events even after the application of the error correction models mentioned above, as shown in Figure 10. Special event bias is defined as a sudden change in the amount of power over a quarter of the maximum load happening in a two-or-more-hour period. The evidence of such occurrences is significant in most demand load data. A classic example is the Korean research institute (KEPRI) building demand load data used in our case study analysis. In the dataset, the total number of such occurrences was 91 over a 553-day period.

**Figure 10.** Special event bias.

Although it is sudden, the occurrence of special event bias is significant in a given period. From Figure 11, the duration of the sudden bias is logarithmic in time. The highest magnitude of the bias lasts for the first few hours and monotonically decreases with time to the nominal value. In this study, we compensated for these sudden changes in the demand load forecast with a temporal bias error correction model. The procedure for the error compensation is similar to the permanent bias error correction, except for the required input data and error correction formula. The occurrence distribution and occurrence duration distribution are shown in Figures 12 and 13, respectively.

**Figure 11.** Special event occurrence.

**Figure 12.** Special event load fluctuation distribution.

**Figure 13.** Special duration distribution.

Actual data for the previous3h(*T*) was utilized to estimate the error for compensation. The formulation of the correction model, as defined in Equation (17), is to correct the average quantum of the special event, learned for one hour until the power remains zero. An initial correction value, α, is an average of the event values that occurred in the past. With the KEPRI demand dataset, α was estimated as 312.6 KW. Considering that temporary bias error correction is a model for accident events, the average elapsed period, *T*, was set to be 3.5 h, which is the average time required to identify an event.

$$
\hat{y}\_t = \alpha (1 - e^{-\frac{T-t}{\delta^5}}) \tag{17}
$$
