In this study, decision trees were compared with (direct and hybrid) artificial neural networks.
Table 4 summarizes the obtained results : in its upper part, those corresponding to the first list of candidate attributes (i.e. excluding the pre-disturbance load power margin), and, in its lower part, those corresponding to the second list of candidate attributes (i.e. including the pre-disturbance active and reactive power margins). It reports on accuracy and computational performances of decision trees and four different types of artificial neural networks. The ``direct'' and ``margin direct'' MLPs use all candidate attributs as inputs, whereas the ``hybrid'' and ``margin hybrid'' ones use only the test attributes identified by the corresponding decision tree. The classification MLPs (``direct'' and ``hybrid'') use two output neurons, corresponding respectively to the secure and the insecure class, while the ``margin'' MLPs use a single output neuron, the desired value of which corresponds to a normalized and truncated version of the post-contingency load-power margin. Note that for the artificial neural networks, the table reports only the best results obtained, in terms of accuracy, among various trials.
Table 4: Preventive security assessment of the Brittany system
The results are quite coherent with the preceding ones. The various neural networks provide better accuracy than the corresponding decision trees, though at the expense of very high computational requirements.
In any case, the use of the post-contingency load power margin at the
learning step allows to improve the accuracy of the neural networks by
about 1%, at least. In addition, it appears that the corresponding
neural networks behave more smoothly nearby the classification
threshold, and thus make it easier to tradeoff false alarms vs non
detections of insecure states. For example, in the case of the
``hybrid margin'' MLP of last line of the table, it is possible to
eliminate almost all non-detections of insecure states while only very
slightly increasing the overall error rate, from 4.5% to 5.0%. Since
the output of the MLP approximates the post-contingency load power,
nearby the classification threshold, this may indeed be achieved very
straightforwardly, by merely shifting by about 35MW the classification
threshold at the MLP output. Remembering that the numerical margin
computation error is itself about 15MW large
, we conclude that the hybrid MLP has
reached a very satisfactory level of accuracy.
Finally, in both parts of the table we observe that the direct MLPs are more accurate than the corresponding hybrid ones, although at the expense of significantly longer training times. However, the difference appears to be much smaller (below the statistical significance level) in the lower part of the table, i.e. when the pre-contingency load-power margin is included in the list of candidate attributes. In other words, provided that among the candidate attributes there is a reduced number (say, less than 20) containing most of the security information, the decision trees will be able to indentify them and thus the hybrid MLPs approaches will yield the best accuracy vs efficiency compromize. On the other hand, if the security information is diffused among a larger number of candidate attributes, the direct MLPs may outperform the hybrid ones in terms of accuracy, and, their difference in accuracy is a measure of the information shared by the attributes which were not selected by the tree.