1. Pontifical Catholic University of the Rio Grande do Sul Brazil Applying Artificial Neural Networks to Energy Quality Measurement Fernando Soares dos Reis Fernando César Comparsi de Castro Maria Cristina Felippetto de Castro Luciano Chedid Lorenzoni Uiraçaba Abaetê Solano Sarmanho

2. Table of Contents  INTRODUCTION  OBJECTIVES  TERMS AND DEFINITIONS  GENERATION OF THE INPUT VECTOR  PARAMETERS OF THE NEURAL NETWORK  SIMULATION ANALYSIS  CONCLUSIONS

3. INTRODUCTION  Market-optimized solution for electric power distribution involves energy quality control.  In recent years the consumer market has demanded higher quality standards, aiming efficiency improvement in the domestic as well in the industrial environment.

4. INTRODUCTION Electric power quality can be assessed by a set of parameters :  Total Harmonic Distortion (THD);  Displacement Factor;  Power Factor; These parameters are obtained by... obtained by...

5. INTRODUCTION Measuring the voltage and current in the electric mains. electric mains.  Most measurement systems employs some filtering in order to improve the measured parameters.  It is crucial for the measurement performance that the filter does not introduce any phase lag in the measured voltage or current.

6. OBJECTIVES In this work, a linear Artificial Neural Network (ANN) trained by the Generalized Hebbian Algorithm (GHA) is used as an eigenfilter, so that a measured noisy sinusoidal signal is cleaned, improving the measurement precision.

7. TERMS AND DEFINITIONS An artificial neural network is a mathematical model that emulate some of the observed properties of biological neural systems.

8. TERMS AND DEFINITIONS The key element of the ANN paradigm is the structure of the information processing system. It is composed of a large number of highly interconnected processing elements that are analogous to neurons and are tied together with weighted connections that are analogous to synapses.

9. TERMS AND DEFINITIONS A linear Artificial Neural Network (ANN) trained by the Generalized Hebbian Algorithm (GHA) is used as an eigenfilter, so that a measured noisy sinusoidal signal is cleaned, improving the measurement precision.

10. TERMS AND DEFINITIONS  A linear ANN which uses the GHA as learning rule performs the Subspace Decomposition of the training vector set ;  Each subspace into which the training set is decomposed, contains highly correlated information;  Therefore, since the auto-correlation of the noise component is nearly zero, upon reconstructing the original vector set from its subspaces, the noise component is implicitly filtered out.

11. TERMS AND DEFINITIONS  The adopted learning rule is the postulate of Hebb´s learning.  If neurons on both sides of a synapse are activated synchronous and repeatedly, the strenght of the synapse is increased selectively.  This simplifies in a significant way the complexity of the learning system  This simplifies in a significant way the complexity of the learning system.

12. GENERATION OF THE INPUT VECTOR  The input vector set comprises ten vectors (ten positive semicycles with different harmonic noises), each vector of size R 167. This is due to the fact that the sinusoidal signals were sampled with 167 samples.

13. PARAMETERS OF THE ARTIFICIAL NEURAL NETWORK (ANN) The net was parameterized considering only three sub-spaces of the initially presented one hundred sixty seven.  The net was parameterized considering only three sub-spaces of the initially presented one hundred sixty seven.  The core of the problem was that the eigenvalues were adjusted in the direction of the eigenvectors in order to be considered just the fundamental components of the sinusoidal waves, disregarding the other noise signals.

14.  Sub-spaces: The number of considered sub-spaces was three, because in this application the goal was to extract the fundamental sinusoidal wave. These are the parameters of the net: PARAMETERS OF THE ARTIFICIAL NEURAL NETWORK (ANN)

15.  Initial Learning Rate: The learning rate (the speed in which the neural network learns) used was of 1x 10 -20, which is considered to be a slow rate, due to the dimension of the input vector. PARAMETERS OF THE ARTIFICIAL NEURAL NETWORK (ANN)

16.  All synapses are randomly initialized with values in the interval [–7,5; 7,5]. PARAMETERS OF THE ARTIFICIAL NEURAL NETWORK (ANN)

17. SIMULATION ANALYSIS  Next we show some of the obtained results. In the graphs are indicated the Input Signal (E), the Output Signal (S) and the Difference Signal (D). The Difference Signal consists of the Harmonic Noise (D = E-S). For the best visualization the Input Signal (E) curves were offset, so, there is no DC gain involved in the process.

18. SIMULATION ANALYSIS

21. CONCLUSIONS  The results obtained in this work demonstrate the potential ability of linear Artificial Neural Networks trained by the Hebbian Learning Algorithm in the filtering of the harmonic noise in the power bus. Although in some cases the filtering was not perfectly effective, the output waveform presented lesser harmonic content than the originally one presented to the Neural Network.

22. CONCLUSIONS  In all cases, no phase lag was observed, which is a quite desired feature. The obtained results suggest that further Neural Network architectures should be assessed.

23. OBRIGADO!Gracias! Thank You!