Rule Extraction from Artificial Neural Networks for Voltage Security Analysis P. J. Abrão 1,2 A. P. Alves da Silva 2 A. C. Zambroni de Souza 2 abrao@iee.efei.br alex@iee.efei.br zambroni@iee.efei.br 1 Federal Center of Technology Education at Goiás, Brazil 2 Federal Engineering School at Itajubá–Eng. System Group GESis, Brazil Abstract – This work presents a methodology based on production rules extracted from Artificial Neural Networks. The aim is assessing Voltage Security under a new point of view. This methodology is compared with Decision Trees, and the results obtained render this technique as a viable alternative. The IEEE-14 bus system is used. I. INTRODUCTION One of the most challenging problems in real time operation of power systems is associated with voltage stability assessment (VSA). The problem of voltage stability is related to the ability of the power system to maintain an appropriate voltage profile on all its buses. Being directly associated with the available reactive power reserve, the voltage instability phenomenon is characterized by a progressive reduction on the voltage magnitudes. Voltage instability begins locally, and it can spread allover the interconnected system, causing total voltage collapse. The instability process can have different causes, depending on the nature of the electric loads and the dynamics of the voltage control equipment. With the goal of understanding and solving the voltage stability problem, several methodologies have been proposed during the last few years [1]. However, most of them require a high computational burden. Analytical techniques for solving the VSA problem do not allow the operators to implement preventive or corrective control actions in due time. One possible solution to overcome this drawback is the application of automatic learning techniques associated with an efficient methodology for generating training patterns [2]. Decision trees have been applied for on-line VSA. Nevertheless, decision trees are among the machine learning techniques with the highest variance. On the other hand, artificial neural networks (NNs) have shown outstanding precision for classification and regression tasks. The major shortcoming of the NN approach is its opacity, i.e., its low degree of human comprehensibility regarding its inference process and encoded knowledge (represented by the values of synaptic weights). It is common to use the symbolic knowledge provided by decision trees in combination with the highly efficient NN numerical inference process. However, this hybrid approach does not guarantee consistency between the results provided by the decision tree and the corresponding NN. Reference [3] shows the first attempt to explain the NN inference process in a power system problem (fault diagnosis). In reference [3], each inference process of linear associative memories are interpreted, separately, through the extraction of symbolic rules, i.e., no interpretation is provided for the NN knowledge base as a whole. This paper tackles the mentioned above drawback of the NN approach for VSA. An algorithm for qualitatively interpreting the knowledge base of a nonlinear feedforward NN is employed [4]. The paper also proposes the application of a very fast training algorithm [5], which is fully compatible with the algorithm for rule extraction [4], and suitable for dealing with very large databases. The main motivation for the proposed approach is to give the power system operator a symbolic knowledge base, which is consistent with the NN inference process. II. RULE EXTRACTION FROM NNs An easy way to visualize rule extraction from NNs is through the following example with only one processing unit. The idea is to generate a finite set of production rules so as to describe the NN inference process by a symbolic mapping. The rules represent the NN output for any possible input. In Figure 1, X={x 1 ,x 2 ,x 3 } represents the input vector, W={w 1 , w 2 ,w 3 } are the synaptic weight values, f(⋅) is the activation function, and 2 is the bias (assumed zero). x 1 w 1 = 2 ƒ ( Σ w i x i + θ ) y x 2 w 2 = - 1 w 3 = - 0.5 θ = 0.0 x 3 Figure 1 – Knowledge extraction from simple processing unit. Considering f(⋅) as a step function, a decision rule can be established based on the activation function input, i.e, A if >0 y= B if <0 Unkwown (U) if =0      ∑ ∑ ∑ Table 1 shows the mapping from the binary inputs to the output y. TABLE 1 – BINARY VARIABLES MAPPING. x1 1 1 1 1 0 0 0 0 x2 1 1 0 0 1 1 0 0 x3 1 0 1 0 1 0 1 0 Σ 0.5 1.0 1.5 2.0 -1.5 -1.0 -0.5 0 y A A A A B B B U A set of rules representing the NN input-output mapping can be formed by observing the resulting classification for each case. That is, 0-7803-7278-6/02/$10.00 ©2002 IEEE