*3.3. Fleet Analysis*

The vehicle analysis presented in the previous section was of value in assessing the viability of individual vehicles for V2G; however, in order to participate in grid services, the pooled available capacity is likely to be of principal concern to an aggregator. One key requirement for predicting this capacity is predicting the total number of vehicles available at a future time, i.e., it may not be necessary to predict the availability of individual vehicles if the total number available can be predicted. Two approaches were used to make this prediction: a sum of individual vehicle's predicted binary availability (SoV) and a sum of individual vehicle's probability of availability (SoP).

To calculate SoV, the binary availability of each vehicle (*av*) predicted by the model (*m*) for a unique half-hour period (*hhu*) in the test dataset was summed, i.e., *totalav* (*m*, *hhu*) = *<sup>n</sup> <sup>v</sup>*=<sup>1</sup> *av*(*m*, *hhu*). The actual number of available vehicles for a period *hhu* in the test set was also determined. An error score, *error*(*m*), was then calculated for the model *m* by averaging the percentage error between actual and predicted total availability over all 2736 (57 days \* 48) unique half-hour periods in the test dataset. The accuracy of the model was defined as *accuracy*(*m*) = 1 − *error*(*m*).

The SoP approach was identical to the SoV approach with the exception that the total availability predicted by the model *m* for half-hour period *hhu* was calculated by summing the predicted probability of each vehicle being available, i.e., a threshold was not used to make a binary prediction for each vehicle before summing. For example, given four vehicles, each with a probability of 0.25 that would individually be predicted to be unavailable, this method would predict one vehicle of the group to be available. In this way, vehicles always contributed to the predicted total in correlation with their likelihood of availability.

These calculations were performed for the CMAh and AutoML models. The results, shown in Figure 9, revealed that the accuracy for both models was relatively low using the SoV approach, and no significant difference was found between the two models using a Welch's t-test (*p* > 0.05). However, the use of the SoP approach improved accuracy by 8.2% for CMAh and 9.5% for AutoML, both of which were found to be highly statistically significant improvements (*p* < 0.001). The accuracy of AutoML-SoV was 1.7% higher than that of CMAh-SoV, a result that was also highly statistically significant (*p* < 0.001).

**Figure 9.** Accuracy of the predicted total number of vehicles over the test period using 2 different approaches (SoV and SoP) for the CMAh and AutoML models (see text for details). Error bars show +1 standard deviation. SoV, the sum of individual vehicle's predicted binary availability; SoP, the sum of individual vehicle's probability of availability.
