Many recent large-scale power system breakdowns have been the consequence of instabilities characterized by sudden voltage collapse phenomena.
One of the main reasons for this is that transient stability limits of power flows have increased, consequently to the improvements of protections as well as static var compensators and generator speed and voltage regulators. Thereby more power may be transferred over longer distances and systems which used to be transient stability limited become voltage stability limited. This situation has been observed in North-American and European power systems and has been a major incentive to research on voltage stability. Although recent advances are impressive there are still open questions, in particular as concerning the definition of widely accepted models and security criteria. We refer the reader to [3][2][1] for an overview of the concepts and industry experience in this field.
Voltage security concerns mainly the ability of a system to control its EHV voltage while submitted to various contingencies, in particular to outages and rapid load build up. In power system operation a useful concept is the load power margin (LPM); this is a security margin expressed in terms of the amount of additional load (P and Q) which may be supplied by the system under acceptable conditions. Various ``exact'' or ``approximate'' approaches have been proposed in the literature to compute this kind of margin [7][6][5][4], with computing times of the order of several power flow computations. The direct physical interpretation of the LPM makes it an easily accepted tool by operators. Note also that in practice there is often a good correlation among LPMs obtained by different ways, which suggests that they may be interpreted as a distance to insecurity.
For a given power system, the available LPM depends on its topology, load level, and available reactive generation and compensation resources, while the amount of margin required depends on the actual load trend. Thus, the system will be considered as secure if it is able to withstand all credible contingencies with sufficient post-contingency LPM. While many factors may influence the pre- and post-contingency LPM, we conjecture that for a given contingency in most circumstances only a rather small number of system parameters will actually influence its severity, i.e. the difference of its pre- and post-contingency LPMs. In other words, voltage security assessment should be decomposed into (i) the computation of the pre-contingency LPM once per operating state, using any of the above computational techniques, and (ii) the evaluation of contingency severities, where simplified approximate models may be used. We shall discuss and illustrate this conjecture and propose a systematic approach to derive a simple but reliable assessment of the contingency severity.
In particular, to obtain a prediction of the impact of a contingency on the LPM, without requiring on-line the recomputation of the post-contingency margin, we propose to use statistical regression techniques. These techniques exploit large random samples of operating conditions simulated off-line (to precompute pre- and post-contingency LPMs) in order to identify the main factors which influence the severity of a contingency and to build approximate simplified models of its post-contingency LPM. These approximate models are easy to exploit on-line and may thus be used for contingency ranking and evaluation, and for determining dangerous combinations of contingencies and even control actions for security enhancement.
The remainder of the paper is organized as follows. In section 2 we introduce the overall regression based framework to voltage security assessment, and briefly describe the complementary regression tree and multilayer perceptron techniques. Section 3 provides an overview of a case study carried out on the Brittany region of the EHV system of Electricité de France, so as to assess the approach in the context of three typical contingencies. Before concluding, we discuss in section 4 the various possible uses of the approach for off-line studies and on-line operation.