We carried out similar investigations on the emergency state detection problem corresponding to the Brittany system of the EDF EHV system.
A decision tree grown on the basis of 1156 learning states is represented in Fig. 5. Its 9 test attributes, automatically selected among the 154 candidate ones, correspond to reactive reserves of various combinations of plants, HV and EHV voltages as well as active and reactive power flows. Its error rate, determined on the basis of 1156 test states, different from the learning states, is 8.5%; it corresponds to 3.8% false alarms and 4.7% non-detections, among which only 0.2% are actually dangerous errors, i.e. states which lead to a straightforward voltage collapse, while the others are states whose load-power margin is below a fixed threshold but which do not lead to voltage collapse.
Figure 5: Emergency detection tree for the Brittany system
Further, direct and hybrid MLPs as well as direct and hybrid 
classifiers were constructed for the same problem. Let us provide
computational figures of the various approaches applied to this
realistic power system security problem. As concerns the decision
tree, the total CPU time required for its building and testing is less
than 10 minutes on a SUN Sparc2 workstation. On the other hand, the
learning and testing of the direct MLP takes about 36 hours on the
same hardware
; note that the
MLP structure complexity is kept to a minimum and the number of
learning states remains moderate. Finally, the direct takes
about 30 minutes to train, in order to determine an appropriate value
of 
. On the other hand, at the prediction stage, the decision tree
needs about 0.1ms, the direct MLP about 1ms and the direct
about 100ms to classify one state.
As concerns accuracy, the obtained results are summarized in Table 3. They appear to be quite consistent with those found earlier. In particular, hybrid approaches allow us to improve the error rates of a tree by about 1.5%, while being about ten times faster at the learning and prediction stage than the corresponding direct approaches, thanks to the reduced number of attributes.
Table 3: Emergency state detection of the Brittany system.
Focusing on the hybrid MLPs, Table 3 provides three different results : (i) the pure hybrid classification MLP derived by translating the tree structure; (ii) the hybrid MLP using the 9 test attributes identified by the tree, but which uses an a priori given structure; (iii) the margin hybrid MLP, which adapts its weights during the back-propagation procedure so as to reproduce the continuous margin rather than the discrete class. Concerning accuracy, the two first obtain very similar results, suggesting that the MLP's accuracy is not very sensitive to its structure (the speed of convergence is however affected rather strongly). The last method is significantly more accurate, suggesting that exploitation of a continuously varying margin may improve significantly results obtained by the MLP models which provide intrinsically a continuous input/output mapping.
As for the pure MLP, we note again that it is significantly more accurate (by about 1.5%) than the best hybrid approach, which allows us to appraise the price we pay by using only the information provided by 9 DT test attributes rather than all 154 candidate ones.
As concerns the methods, for the present system the direct
version performs significantly better than the hybrid one, while the
latter improves with respect to the original tree. Our interpretation
is that the attribute weighting of the direct version is ``by chance''
superior to the hybrid one. This shows again the high sensitivity of
the method to the distance chosen.