short term electric load forecasting using echo state networks and pca decomposition

In this paper, we approach the problem of forecasting a time series (TS) of an electrical load measured on the Azienda Comunale Energia e Ambiente (ACEA) power grid, the company managing the electricity distribution in Rome, Italy, with an echo state network (ESN) considering two different leading times of 10 min and 1 day. We use a standard approach for predicting the load in the next 10 min, while, for a forecast horizon of one day, we represent the data with a high-dimensional multi-variate TS, where the number of variables is equivalent to the quantity of measurements registered in a day. Through the orthogonal transformation returned by PCA decomposition, we reduce the dimensionality of the TS to a lower number $k$ of distinct variables; this allows us to cast the original prediction problem in $k$ different one-step ahead predictions. The overall forecast can be effectively managed by $k$ distinct prediction models, whose outputs are combined together to obtain the final result. We employ a genetic algorithm for tuning the parameters of the ESN and compare its prediction accuracy with a standard autoregressive integrated moving average model

Training Echo State Networks with Regularization through Dimensionality Reduction

In this paper we introduce a new framework to train an Echo State Network to predict real valued time-series. The method consists in projecting the output of the internal layer of the network on a space with lower dimensionality, before training the output layer to learn the target task. Notably, we enforce a regularization constraint that leads to better generalization capabilities. We evaluate the performances of our approach on several benchmark tests, using different techniques to train the readout of the network, achieving superior predictive performance when using the proposed framework. Finally, we provide an insight on the effectiveness of the implemented mechanics through a visualization of the trajectory in the phase space and relying on the methodologies of nonlinear time-series analysis. By applying our method on well known chaotic systems, we provide evidence that the lower dimensional embedding retains the dynamical properties of the underlying system better than the full-dimensional internal states of the network

Local Short Term Electricity Load Forecasting: Automatic Approaches

Short-Term Load Forecasting (STLF) is a fundamental component in the efficient management of power systems, which has been studied intensively over the past 50 years. The emerging development of smart grid technologies is posing new challenges as well as opportunities to STLF. Load data, collected at higher geographical granularity and frequency through thousands of smart meters, allows us to build a more accurate local load forecasting model, which is essential for local optimization of power load through demand side management. With this paper, we show how several existing approaches for STLF are not applicable on local load forecasting, either because of long training time, unstable optimization process, or sensitivity to hyper-parameters. Accordingly, we select five models suitable for local STFL, which can be trained on different time-series with limited intervention from the user. The experiment, which consists of 40 time-series collected at different locations and aggregation levels, revealed that yearly pattern and temperature information are only useful for high aggregation level STLF. On local STLF task, the modified version of double seasonal Holt-Winter proposed in this paper performs relatively well with only 3 months of training data, compared to more complex methods

Probabilistic load forecasting with Reservoir Computing

Some applications of deep learning require not only to provide accurate results but also to quantify the amount of confidence in their prediction. The management of an electric power grid is one of these cases: to avoid risky scenarios, decision-makers need both precise and reliable forecasts of, for example, power loads. For this reason, point forecasts are not enough hence it is necessary to adopt methods that provide an uncertainty quantification. This work focuses on reservoir computing as the core time series forecasting method, due to its computational efficiency and effectiveness in predicting time series. While the RC literature mostly focused on point forecasting, this work explores the compatibility of some popular uncertainty quantification methods with the reservoir setting. Both Bayesian and deterministic approaches to uncertainty assessment are evaluated and compared in terms of their prediction accuracy, computational resource efficiency and reliability of the estimated uncertainty, based on a set of carefully chosen performance metrics

Probabilistic Wind Power and Electricity Load Forecasting with Echo State Networks

With the introduction of distributed generation and the establishment of smart grids, several new challenges in energy analytics arose. These challenges can be solved with a specific type of recurrent neural networks called echo state networks, which can handle the combination of both weather and power consumption or production depending on the dataset to make predictions. Echo state networks are particularly suitable for time series forecasting tasks. Having accurate energy forecasts is paramount to assure grid operation and power provision remains reliable during peak hours when the consumption is high. The majority of load forecasting algorithms do not produce prediction intervals with coverage guarantees but rather produce simple point estimates. Information about uncer- tainty and prediction intervals is rarely useless. It helps grid operators change strategies for configuring the grid from conservative to risk-based ones and assess the reliability of operations. A popular way of producing prediction intervals in regression tasks is by applying Bayesian regression as the regression algorithm. As Bayesian regression is done by sampling, it nat- urally lends itself to generating intervals. However, Bayesian regression is not guaranteed to satisfy the designed coverage level for finite samples. This thesis aims to modify the traditional echo state network model to produce marginally valid and calibrated prediction intervals. This is done by replacing the standard linear regression method with Bayesian linear regression while simultaneously reducing the di- mensions to speed up the computation times. Afterward, a novel calibration technique for time series forecasting is applied in order to obtain said valid prediction intervals. The experiments are conducted using three different time series, two of them being a time series of electricity load. One is univariate, and the other is bivariate. The third time series is a wind power production time series. The proposed method showed promising results for all three datasets while significantly reducing computation times in the sampling ste

A review of the enabling methodologies for knowledge discovery from smart grids data

The large-scale deployment of pervasive sensors and decentralized computing in modern smart grids is expected to exponentially increase the volume of data exchanged by power system applications. In this context, the research for scalable and flexible methodologies aimed at supporting rapid decisions in a data rich, but information limited environment represents a relevant issue to address. To this aim, this paper investigates the role of Knowledge Discovery from massive Datasets in smart grid computing, exploring its various application fields by considering the power system stakeholder available data and knowledge extraction needs. In particular, the aim of this paper is dual. In the first part, the authors summarize the most recent activities developed in this field by the Task Force on “Enabling Paradigms for High-Performance Computing in Wide Area Monitoring Protective and Control Systems” of the IEEE PSOPE Technologies and Innovation Subcommittee. Differently, in the second part, the authors propose the development of a data-driven forecasting methodology, which is modeled by considering the fundamental principles of Knowledge Discovery Process data workflow. Furthermore, the described methodology is applied to solve the load forecasting problem for a complex user case, in order to emphasize the potential role of knowledge discovery in supporting post processing analysis in data-rich environments, as feedback for the improvement of the forecasting performances

Reservoir computing approaches for representation and classification of multivariate time series

Classification of multivariate time series (MTS) has been tackled with a large variety of methodologies and applied to a wide range of scenarios. Reservoir Computing (RC) provides efficient tools to generate a vectorial, fixed-size representation of the MTS that can be further processed by standard classifiers. Despite their unrivaled training speed, MTS classifiers based on a standard RC architecture fail to achieve the same accuracy of fully trainable neural networks. In this paper we introduce the reservoir model space, an unsupervised approach based on RC to learn vectorial representations of MTS. Each MTS is encoded within the parameters of a linear model trained to predict a low-dimensional embedding of the reservoir dynamics. Compared to other RC methods, our model space yields better representations and attains comparable computational performance, thanks to an intermediate dimensionality reduction procedure. As a second contribution we propose a modular RC framework for MTS classification, with an associated open-source Python library. The framework provides different modules to seamlessly implement advanced RC architectures. The architectures are compared to other MTS classifiers, including deep learning models and time series kernels. Results obtained on benchmark and real-world MTS datasets show that RC classifiers are dramatically faster and, when implemented using our proposed representation, also achieve superior classification accuracy

Industrial time series modelling by means of the neo-fuzzy neuron

Abstract—Industrial process monitoring and modelling represents a critical step in order to achieve the paradigm of Zero Defect Manufacturing. The aim of this paper is to introduce the Neo-Fuzzy Neuron method to be applied in industrial time series modelling. Its open structure and input independency provides fast learning and convergence capabilities, while assuring a proper accuracy and generalization in the modelled output. First, the auxiliary signals in the database are analyzed in order to find correlations with the target signal. Second, the Neo-Fuzzy Neuron is configured and trained according by means of the auxiliary signal, past instants and dynamics information of the target signal. The proposed method is validated by means of real data from a Spanish copper rod industrial plant, in which a critical signal regarding copper refrigeration process is modelled. The obtained results indicate the suitability of the Neo-Fuzzy Neuron method for industrial process modelling.Postprint (published version