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PREDIÇÃO DE SÉRIES TEMPORAIS DO RESERVATÓRIO DA USINA HIDRELÉTRICA DE SOBRADINHO ATRAVÉS DE REDES NEURAIS RECORRENTES NARX

Sérgio Paulo Melo de SouzaJosé Maria Pires de Menezes Júnior

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Introduction

Brazil's electricity generation system is a large hydro-thermo-eolic system;

The National Interconnected System (SIN) consists of the interconnection of the

electrical systems;

The Brazilian Electricity Sector (SEB) consists of three fundamental pillars: expansion

planning, operation planning and scheduling, and the accounting and settlement

process of energy transactions in the short-term market (Souza et al, 2014);

Currently, the National Electric System Operator (ONS) uses the NEWAVE model to

carry out the medium and long-term planning of the electric system (Souza et al, 2014);

The development of methodologies to assist both prediction of reservoir level and

prediction of a plant's affluent flows is very important, given the importance of

determining the volume of water available for electricity generation.

Predição de séries temporais do reservatório da Usina Hidrelétrica de Sobradinho através de redes neurais recorrentes Narx| Sérgio P. M. Souza, José M. P. De Menezes Jr

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Introduction

Forecasting future information is a very complex but necessary task in many sectors of

the economy;

The prediction of time series consists of defining the next point in a series of data, from

a historical memory of data previously occurred in a given context, through non-linear

models;

In this context, Machine Learning, through the Artificial Neural Networks (RNA),

becomes a great ally in the studies referring to reservoir data;

RNAs are tools that compute data in a manner similar to that performed by networks of

biological neurons (Haykin, 2009).

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3 / 19Predição de séries temporais do reservatório da Usina Hidrelétrica de Sobradinho através de redes neurais recorrentes Narx| Sérgio P. M. Souza, José M. P. De Menezes Jr

Introduction

These systems offer an alternative in solving complex problems because they are able

to learn from examples, deal with incomplete data, deal with non-linear problems, and

these, once trained, can carry out predictions and generalizations almost

instantaneously;

A new paradigm of neural network design has been proposed under the name of

Automatic Machine Learning (AutoML), where the idea is to solve problems without

human intervention (Thornton et al, 2012);

AutoML has been applied in this work to find the hyperparameters automatically;

In this sense, this work aims to implement and compare the performance of the neural

networks FTDNN (Focused Time Delay Neural Network) and NARX (Nonlinear

AutoRegressive model with eXogenous inputs) in the prediction of the time series of

useful volumes and natural flows related to the Hydroelectric Power Plant Sobradinho.

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Dynamic Neural Networks

Dynamic artificial neural networks are extensions of

the MLP network (Multi Layer Perceptron) capable

of modeling the dynamics of a process, from a time

series (Souza et al, 2014);

An MLP network can be transformed into a dynamic

network by the inclusion of time delays or feedback

loops (Souza et al, 2014);

We call the FTDNN (Focused Time Delay Neural

Network) the dynamic neural network built with the

inclusion of input delay (Takens, 1981):

𝑥 𝑛 is the sample of the time series in time 𝑛,

𝑑𝑒 is called the embedding dimension and 𝜏 is

called the embedding delay,

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Recurrent Neural Networks (NARX)

It is possible to represent a non-linear discrete time system

through several models, among them we have the NARX

(Nonlinear AutoRegressive model with eXogenous inputs)

models;

This model uses a feedback loop to model the process

dynamics and is mathematically represented by:

𝑦 𝑛 + 1 = 𝑓 𝑦 𝑛 ,… , 𝑦 𝑛 − 𝑑𝑦 + 1 ; 𝑢 𝑛 ,… , 𝑢 𝑛 − 𝑑𝑢 + 1

where y(n) ∈ ℝ and 𝑢 𝑛 ∈ ℝ represent, respectively, the input

and output of the model at time n, whereas 𝑑𝑦 ≥ 1 and 𝑑𝑢 ≥ 1,

where 𝑑𝑢 ≤ 𝑑𝑦, are called the immersion dimension and context

dimension, respectively (Chen, 2013).UFPI


Multi-step ahead Prediction (MPA)

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When we are interested in a long-term prediction, we use a

multi-step ahead prediction (MPA):

Recursive prediction

More complex

Prediction tends to infinity becomes a dynamic

modeling task

Feedback of prediction errors

Metodology

The algorithms of the FTDNN and NARX models were implemented using MATLAB

2015a software;

Two (2) time series were used for the Sobradinho HPP reservoir, located in the

municipality of Sobradinho and Casa Nova in the state of Bahia:

Useful volume: 225 monthly records from 1999-2017;

Natural flow: 1020 monthly records 1931-2015.

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Metodology

Each data set was divided into one set for training (85%) and one for validation (15%);

Due to the complexity of the time series prediction problem, it is not possible to

construct a global prediction algorithm;

We used a heuristic search to find the hyperparameters (Menezes, 2012);

To perform the search, we define the search interval for each of the hyperparameters.

To evaluate the best neural model, we used the Normalized Mean-Squared Error

(NMSE) index:

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Metodology

The Cao method was used to estimate the best values for the immersion dimension for

each series.

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Metodology

Nonlinear autocorrelation was used to estimate the best values for the immersion delay

for each series.

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Volume útil Vazões naturais


Search algorithm and ranges

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Parâmetros Intervalo de busca

Taxa aprendizagem 0,1 - 0,3

Número de épocas 50 - 300

Dimensão imersão 2 - 12

Atraso de imersão 1 - 6

Dimensão de contexto 2 - 12Neuônios na 1ª camada 4 - 12Neuônios na 2ª camada 2 - 12


Results

The maximum of 10 search cycles was chosen due to the low variance in results and

the very high computational cost;

The table below shows the hyperparameters found for each of the series.

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FTDNN NARX

Parâm./Séries Volúme útil Vazões naturais Volúme útil Vazões naturaisTaxa aprendizagem 0,15 0,275 0,001 0,15Número máximo de épocas 50 300 25 300Dimensão imersão 6 12 2 6Atraso de imersão 6 6 3 3Dimensão de contexto - - 2 4Neurônios na 1ª camada 10 8 20 11Neurônios na 2ª camada 12 12 2 3NMSE 19,5 17,07 0,0004 0,1024


Results

Result of the prediction for the useful volume series using the NARX network

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Results

Result of the prediction for the natural flow series using the NARX network

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Conclusions

This work compared the performance of two types of neural networks, FTDNN and NARX,

in the prediction task of the influent flow and reservoir level of a hydroelectric plant. The

results demonstrated the superiority of the performance of the NARX recurrent neural

network in the application in question in relation to the dynamic network FTDNN. In

addition, it can be concluded that the performance of the NARX neural networks in the

prediction of the series chosen were satisfactory if we consider a short prediction horizon,

around 24 months. Thus, this model can be used to provide predictions that will serve as a

subsidy in the determination of the hydroelectric dispatch of the Sobradinho plant.

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Future Works

The next related works are:

Implement ELM network model and obtain results;

Implement NARX-ELM network model and obtain results; Compare results obtained with the various models implemented.

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BIBLIOGRAPHY

AGUIRRE, L. A. (2015). Introdução à identificação de sistemas: técnicas lineares e não

lineares: teoria e aplicação, 4 ed, Editora UFMG.

BAFFA, A., GOLDSCHMIDT, R., SOARES, J. and FERLIN, C. (2008). Previsão de

séries temporais utilizando redes neurais artificiais.

CHEN, S., BILLINGS, S. A. and GRANT, P. M. (2013). Nonlinear system identification

using neural networks, International Journal of Control 11(6): 1191-1214.

DE MELLO, F. M. (2013). A importância dos reservatórios formados por barragens.

Haykin, S. (2009). Neural Networks and Learning Machines, Prentice Hall.

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BIBLIOGRAPHY

LOURENÇO, J. F. I. (2015). Previsão de Producão de Energia Elétrica através de

Fontes de Energia Renováveis, PhD thesis, Universidade Nova de Lisboa.

MENEZES, J. M. P. (2012). Contribuições ao Problema de Predição Recursiva de

Séries Temporais Univariadas Usando Redes Neurais Recorrentes, PhD thesis,

Universidade Federal do Ceará.

MENEZES, J. M. P. and BARRETO, G. A. (2008). Long-term time series prediction with

the narx network: An empirical evaluation, Neurocomputing 71(16): 3335-3343.

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http://ons.org.br/pt/paginas/energiaagora/reservatorios. [Web; acessado em 14-04-

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ONS (2018b). Histórico da operação, http://www.ons.org.br/pt/paginas/resultadosda-

operacao/historico-da-operacao. [Web; acessado em 14-04-2018].

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BIBLIOGRAPHY

ONS (2018c). O sistema interligado nacional, http://ons.org.br/pt/paginas/sobre-osin/o-

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Souza, R. C., Marcato, A. L. M., Dias, B. H., Oliveira, F. L. C., Ferreira, P. G. C., da

Silva BRANDI, R. B. AND RAMOS, T. P. (2014a). Planejamento da operação de

sistemas hidrotérmicos no Brasil: geração de cenários e otimização, PUC-Rio.

TAKENS, F. (1981). Detecting strange attractors in turbulence, in D. A. Rand and L.-S.

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Mathematics, Springer, pp. 366-381.

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algorithms.

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Thank you!

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