Pontifical Catholic University of the Rio Grande do Sul Brazil Applying Artificial Neural Networks to Energy Quality Measurement Fernando Soares dos Reis

Pontifical Catholic University of the Rio Grande do SulPontifical Catholic University of the Rio Grande do Sul

BrazilBrazil

Applying Artificial Neural NetworksApplying Artificial Neural Networks to Energy Quality Measurement to Energy Quality Measurement

Fernando Soares dos ReisFernando Soares dos ReisFernando César Comparsi de CastroFernando César Comparsi de CastroMaria Cristina Felippetto de CastroMaria Cristina Felippetto de Castro

Luciano Chedid LorenzoniLuciano Chedid LorenzoniUiraçaba Abaetê Solano SarmanhoUiraçaba Abaetê Solano Sarmanho

Table of Contents

INTRODUCTION INTRODUCTION

OBJECTIVES OBJECTIVES

TERMS AND DEFINITIONSTERMS AND DEFINITIONS

GENERATION OF THE ENTRANCE VECTORGENERATION OF THE ENTRANCE VECTOR

PARAMETERS OF THE NEURAL NETWORKPARAMETERS OF THE NEURAL NETWORK

SIMULATION ANALYSISSIMULATION ANALYSIS

CONCLUSIONSCONCLUSIONS

INTRODUCTIONINTRODUCTION

Market-optimized solution for electric Market-optimized solution for electric power distribution involves energy power distribution involves energy quality control.quality control.

In recent years the consumer market In recent years the consumer market has demanded higher quality has demanded higher quality standards, aiming efficiency standards, aiming efficiency improvement in the domestic as well improvement in the domestic as well industrial uses of the electric power.industrial uses of the electric power.


Electric power quality can be assessed byElectric power quality can be assessed by

a set of parametersa set of parameters : :

Total Harmonic Distortion (THD)Total Harmonic Distortion (THD);; Displacement FactorDisplacement Factor;; Power FactorPower Factor;;

These parameters areThese parameters are

obtained byobtained by ......


MMeasuring the easuring the voltage and voltage and current in thecurrent in the electric mains.electric mains.

Most measurement systems employs Most measurement systems employs some filtering in order to improve the some filtering in order to improve the measured parametersmeasured parameters..

IIs crucial for the measurement s crucial for the measurement performance that the filter does not performance that the filter does not introduce any phase lag in the measured introduce any phase lag in the measured voltage or current.voltage or current.

OBJECTIVESOBJECTIVES

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

TERMS AND TERMS AND DEFINITIONSDEFINITIONS

Artificial neural networks are Artificial neural networks are collections of mathematical models that collections of mathematical models that emulate some of the observed emulate some of the observed properties of biological nervous properties of biological nervous systems and draw on the analogies of systems and draw on the analogies of adaptive biological learning.adaptive biological learning.


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


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


A linear ANN which uses the GHA as A linear ANN which uses the GHA as learning rule performs the Subspace learning rule performs the Subspace Decomposition of the training vector Decomposition of the training vector set ;set ;

Each subspace into which the training Each subspace into which the training set is decomposed, contains highly set is decomposed, contains highly correlated information;correlated information;

Therefore, since the auto-correlation of Therefore, since the auto-correlation of the noise component is nearly zero, the noise component is nearly zero, upon reconstructing the original vector upon reconstructing the original vector set from its subspaces, the noise set from its subspaces, the noise component is implicitly filtered out.component is implicitly filtered out.


The older rule of learning is the The older rule of learning is the postulate of Hebb´s learning. postulate of Hebb´s learning.

If neurons on both sides of a If neurons on both sides of a synapse are activated synchronous synapse are activated synchronous and repeatedly, the force of the and repeatedly, the force of the synapse is increased selectivity. synapse is increased selectivity.

This simplifies in a significant way This simplifies in a significant way the complexity of the learning circuitthe complexity of the learning circuit.

GENERATION OF THE GENERATION OF THE ENTRANCE VECTORENTRANCE VECTOR

Through the Through the simulation in simulation in Mathcad software Mathcad software sinusoidal signs sinusoidal signs of noisy positive of noisy positive semicycle (with semicycle (with harmonic harmonic components) components) were generated, were generated, divided in one divided in one hundred sixty hundred sixty seven points each seven points each one of the ten one of the ten samples.samples.

PARAMETERS OF THE ARTIFICIAL PARAMETERS OF THE ARTIFICIAL NEURAL NETWORK (ANN)NEURAL NETWORK (ANN)

The subject was treated through a The subject was treated through a entrance-exit mapping associating entrance-exit mapping associating data and results obtained with the data and results obtained with the model developed in Mathcad model developed in Mathcad software, using the associated data software, using the associated data and results as entrances of the ANNand results as entrances of the ANN

PARAMETERS OF THE PARAMETERS OF THE ARTIFICIAL NEURAL ARTIFICIAL NEURAL NETWORK (ANN)NETWORK (ANN)

The net was parameterized The net was parameterized considering only three sub-spaces of considering only three sub-spaces of the initially presented the initially presented one hundred one hundred sixty sevensixty seven..

The core of the problem was that the The core of the problem was that the eigenvalues were adjusted in the eigenvalues were adjusted in the direction of the eigenvectors in order direction of the eigenvectors in order to be considered just the fundamental to be considered just the fundamental components of the sinusoidal waves, components of the sinusoidal waves, disrespecting the other noise signs.disrespecting the other noise signs.


The Vector of Entrance: HThe Vector of Entrance: Has the size as the size of ten samples (ten positive of ten samples (ten positive semicycles with different noises) in semicycles with different noises) in RR167167 (hundred sixtyth seventh order), (hundred sixtyth seventh order), due to the one hundred sixty seven due to the one hundred sixty seven points belonging of the sampled points belonging of the sampled sinusoidal wavessinusoidal waves. .

These are the parameters of the net:These are the parameters of the net:

Sub-spaces: Sub-spaces: The number of The number of considered sub-spaces was three, considered sub-spaces was three, because in this application the because in this application the objective was to extract the objective was to extract the fundamental fundamental sinusoidal wavesinusoidal wave..

These are the parameters of the net:These are the parameters of the net:


Initial Learning Tax: Initial Learning Tax: The learning tax The learning tax (the speed in which the neural (the speed in which the neural network learns) used was of 1x 10network learns) used was of 1x 10-20-20, , what is considered to be a slow tax, what is considered to be a slow tax, due to the dimension of the entrance due to the dimension of the entrance vector. vector.


Training Season: Training Season: The maximum The maximum number of training seasons (in which number of training seasons (in which the entrance vector was presented to the entrance vector was presented to the neural network) was of one the neural network) was of one thousand.thousand.


Initial Synapses Interval (R): Initial Synapses Interval (R): The The used interval was [–7,5; 7,5], where R used interval was [–7,5; 7,5], where R is calculated starting from the average is calculated starting from the average of the synapses number by neuron of the synapses number by neuron (the entrance and exit connections (the entrance and exit connections that allow the a neuron to interact with that allow the a neuron to interact with the others).the others).



The results were shown satisfactory, The results were shown satisfactory, because the Neural Network got to because the Neural Network got to filter the signs with harmonic filter the signs with harmonic content. In some cases the filtering content. In some cases the filtering was not of extreme effectiveness, but was not of extreme effectiveness, but it presented purest waveforms than it presented purest waveforms than the originally presented to the net.the originally presented to the net.


In the graphs are indicated the In the graphs are indicated the Entrance (E),Entrance (E), the the Exit (S)Exit (S) and the and the Difference (D)Difference (D) that consists of the that consists of the Noise (D = E-S)Noise (D = E-S). The . The Entrances(E)Entrances(E) curves were moved, not representing curves were moved, not representing a DC gain.a DC gain.


0 20 40 60 80 100 120 140 160 18050

0

50

100

150

200192.017

22.608

Ei

Si

Di

1660 i


0 20 40 60 80 100 120 140 160 18050

0

50

100

150

200181.624

20.795

Ei

Si

Di

1660 i


0 20 40 60 80 100 120 140 160 18050

0

50

100

150

200185.558

20.582

Ei

Si

Di

1660 i


The results obtained in this work The results obtained in this work demonstrate the capacity of NNs demonstrate the capacity of NNs through the Hebbian Algorithm in through the Hebbian Algorithm in accomplishing with success the accomplishing with success the filtering of harmonic content and noise filtering of harmonic content and noise in the power line. in the power line.


With the obtained results, it fits to With the obtained results, it fits to propose new studies of the NN in propose new studies of the NN in order to optimize such results. The order to optimize such results. The practical implementation of the same practical implementation of the same would be the object of a next stage.would be the object of a next stage.

OBRIGADO!OBRIGADO!

Gracias!Gracias!

Thank You!Thank You!

Documents

Pontifical Catholic University of the Rio Grande do Sul Brazil Applying Artificial Neural Networks to Energy Quality Measurement Fernando Soares dos Reis