We have illustrated the application of various methods to emergency and preventive voltage security assessment to derive criteria able to anticipate a possible risk of voltage collapse in real-time and trigger appropriate (emergency or preventive) control actions if necessary.
In the emergency state detection problem, the investigation has been based on usual operating parameters (e.g. power flows, voltages) obtained from system snapshots made ``just after the occurrence of a disturbance''. On the other hand, it is possible to use more sophisticated ``features'' so as to improve accuracy; this was illustrated in the preventive security example by the pre-disturbance load power margin, which allowed to improve significantly the accuracy of all the tested methods. We believe, however, that available non-parametric computer based learning methods are sufficiently powerful to exploit standard ``operating parameters''. A main advantage is that this leads to a more systematic, and mostly automatic approach, and that the resulting criteria are expressed in terms of variables easily appraised by operators and engineers in charge of security studies. Admittedly, to reach better accuracy, larger learning sets may be needed; but these may be easily obtained via random sampling and parallel simulations, where the price to pay is mainly in terms of cheap computing power. This is also illustrated by the larger training set size used in the preventive security assessment example, which allows, despite the more stringent conditions, to reach a very high level of accuracy.
The major tendencies which emerge from our comparative experiments are the following.
The multi-layer perceptrons together with second order optimization methods are a very flexible and easy to apply approach. It provides generally very good results in terms of accuracy, although at the expense of very slow learning, which may prevent easy interactive experimentation; actually, for problem sizes of the order of those encountered in large scale power system security applications a reduction of at least two orders of magnitude in learning times would be required. On the other hand, the MLPs are able to exploit very effectively continuous security margins or indices, in particular to improve accuracy. This is a main advantage shared with other continuous regression methods like SMART, for example. However, at the current stage of advancement the main drawback of these methods is the ``black-box'' nature of the provided security criteria, which are unable to tell their physical meaning. This is a significant shortcoming, for without the ability to produce understandable decisions, it is hard to be confident in the reliability of methods that address real-world problems [30].
Decision trees appear to be by far the fastest method both at the learning and at the prediction step. Together with their good interpretability this efficiency enables us to ``play'' with them in order to analyze a data base and acquire new physical insights. From this respect they are rather unique. In particular, they are able to explicitly identify among many candidate attributes those which significantly influence the security status of the system. Further, their step by step approach to decision making is quite close to the reasoning of human experts; they are therefore easier to appraise, criticize and accept by the latter. On the other hand, as concerns accuracy many interesting sophistications have been proposed in the literature, such as ``linear combination splits'' and ``regression trees'' which are able to further improve them [32][31]. However, the elementary trees we used appear to be already of good accuracy while often easier to interpret than more sophisticated ones.
The nearest neighbor method shows a rather erratic behavior in terms of accuracy. Most often its performance in high dimensional attribute spaces is very deceiving, but occasionally it may be very good. This is because we use as attributes standard ``operating parameters'' and because we have still no systematic methodology to choose a proper distance or similarity measure in this attribute space. Nevertheless, the results obtained so far are promising and we believe that research should proceed in order to develop systematic approaches to adapt distances to problem specifics. The nearest neighbor method may be used in many ways, once an appropriate distance has been found. For example, the distance of the nearest neighbor to the current state may be used as a measure of the degree of confidence one may attach to the diagnostic provided on the basis of the data base. If the latter distance is too large, it would be concluded that for the current state no reliable security information may be derived. If, on the contrary, the nearest neighbors are sufficiently close to the current state, various kinds of detailed and specific security information may be extrapolated from these states to the current situation, and shown to the operator. After all, the nearest neighbor method replicates the way operators approach problems, by recalling similar situations seen in the past.
Finally, the hybrid approaches show to be effective in ``rounding off'' corners of the ``box-type'' security regions defined by decision trees. In particular the ``margin hybrid'' DT-ANN approach is very promising in conciliating the simplicity of the trees and the accuracy of multi-layer perceptrons.
As concerns accuracy, it is worth mentioning that for security
assessment problems it is in practice necessary to distinguish among
``false alarms'' and ``non-detections'' of insecurity. In the context
of our comparative study of learning methods we did not make this
distinction, which would render the interpretation of results more
complex, without affecting the main conclusions. Let us mention,
however, that there exist several alternative techniques which enable
us to reduce the risk of non-detections. For example, the most
straightforward approach may be used by any of the computer based
learning techniques; it consists merely of increasing slightly
the classification threshold of the load-power margin at the time of
learning the model, so as to introduce a sufficient bias in the
classification. On the other hand, in the context of regression
techniques (MLPs, SMART, 
...) allowing us to approximate security margins of unseen states,
we could as well increase the classification threshold at the time of
using the model. Both techniques show to be quite efficient in
practice, although the latter is more flexible than the former. Thus,
in the context of our preventive voltage security assessment example,
shifting the load-power margin threshold by about 35 MW enables us to
eliminate almost completely non-detections while increasing only
moderately the number of false alarms (
decreases from 2.25%
to 0.6 % while 
increases from 2.25% to 4.4%).