【正文】 Winter Meeting, Columbus, OH, January 31 February 5, 1993. Manuscript submitted Aunsut 6. 1992: made available for printing November 10,1992. 2. NETWORK CHARACTERISTICS . General The general architecture of a feed forward neural work is shown in Figure 1. The most important characteristics of this work are: 1) processing units are grouped by layers, and 2) the processor interconnect is Figure 1. General architecture of a FFNN. organized such that all inputs to a layer e exclusively from outputs originating in some previous layer (the specific FFNN used does not have connections skipping layers). The basic equations that define the way this FFNN putes its output given an input vector x are presented in Appendix 1. The FFNN training process consists of determining the weights W(“) and the units’ biasing b(m),i n order to make the work respond in a given way. The training method used in this work was the well known backpropagation algorithm[l3,14,15,16]. Appendix 2 gives a basic description of the training process using backpropagation, and defines the training matrices. . Input Output The FFNN implementation used is constrained in part by the nature of the current classification problem and also in part by existing digital relay system organization. Based on this, the following criteria can be stated:z) Digital relays base their operation on samples of the measured quantity (current, in this case). The sampling rate and the data window varies depending on the application. For this particular case, since the NN must recognize wave shapes, it seems to be logical to use a one cycle length window. INRUSH DETECTION AS A PERMISSIVE FIGURE . INRUSH DETECTION RESTRAINING OPERATION Figure 2. Simplified block diagram of a protective relay using two possible implementations of the inrush detection function. zz) As shown in Figure 2, the function of recognizing inrush is accessory, ., it can be assumed that the digital relay has a different function to implement the power transformer protection (for example, primary overcurrent or differential principle), inrush detection can be used as permissive for the relay operation, or to restrain the relay operation. Independently of the way this bination is made, both functions (inrush detection and protection) may use the same sampling rate. A sampling rate of 12 samples per cycle (720 Hz), was chosen in view of reported experience on different digital relay designs iiz) The fact mentioned above bounds the problem as one of designing a FFNN that, given a sequence of samples of the transformer current, it can distinguish the two wave shapes. A good approach allows to have a work capable of determining if the input current is or is not an inrush, this means that the number of outputs of the neural work (number of units in the output layer) NN must be 1, necessary to indicate “true” and “false,” or “0” and “1”, as indicated in section . In this case it was chosen that the work’s output be 0 when the applied current is an inrush, and 1, when it is not an inrush . Basic Architecture A functional block representation of the scheme used to achieve the goals stated in the former sections is shown in Figure 3. This kind of work is sometimes called timedelay neural work [16] and has been used recently in another power system application [18]. Feed forward works have also been applied to the detection of high impedance faults with remarkable results [19,20]. Notice that the scheme given in Figure 3 is equivalent to the scheme of Figure 1, if the input xk is equal to the thk sample of input x(t). In other words, the work will receive the 12 samples of each window every sample period, and must make a decision based on these 12 samples (. one cycle), which implies the number of inputs must be 12. The number of layers and the number of units on each layer is determined by the heuristic process described in section (the only layer pletely defined at this point is the output layer) Figure 3. Timedelay work. 3. TRAINING STRATEGY . Training Examples Given that the work has to distinguish between two kind of signals, two sets of examples signals (cases) were prepared for that purpose: the inrush cases and the fault cases. The inrush cases were measured in the laboratory energizing at random a small power transformer of 50 VA, 1202040 V. The cases taken to train the work were chosen such that they represented an acceptable range of inrush current shapes (the six cases described sampling rate at which the inrush signal examples were measured was originally 84 samples per 60 Hz cycle, and then resampled (at a rate 7 times lower) to get the desired 12 samples/cycle. Figure 4 show some of the inrush training signals. The fault cases were generated by puter, some of these using an electromagic transients program [23], others by simple generation of faultlike signals (response of an RL circuit), and a third group of faultlike currents infected with second, third and fifth harmonics Figure 4. Four inrush training cases. Two special cases grouped with the inrush cases were the zero current (indicating the transformer is deenergized) and the load current (a simple sinusoidal wave with a magnitude equal to the transformer load current). For each case, signals were sampled at 12 samples per cycle (with a window length equal to one cycle) and the total of samples was limited to have about 100 windows (. seconds per case). . Data Windowing and Training Matrices The training matrices were built in such a way that the work was trained to produce a 0 output when the presented signal was an inrush, a zero current or a full load conditi