Electric Time Series Research Articles

Forecasting mid-long term electric energy consumption through bagging ARIMA and exponential smoothing methods

In the last decades, the world's energy consumption has increased rapidly due to fundamental changes in the industry and economy. In such terms, accurate demand forecasts are imperative for decision makers to develop an optimal strategy that includes not only risk reduction, but also the betterment of the economy and society as a whole. This paper expands the fields of application of combined Bootstrap aggregating (Bagging) and forecasting methods to the electric energy sector, a novelty in literature, in order to obtain more accurate demand forecasts. A comparative out-of-sample analysis is conducted using monthly electric energy consumption time series from different countries. The results show that the proposed methodologies substantially improve the forecast accuracy of the demand for energy end-use services in both developed and developing countries. Findings and policy implications are further discussed.

An improved back propagation neural network based on complexity decomposition technology and modified flower pollination optimization for short-term load forecasting

Accurate short-term load forecasting (STLF) is crucial for reliable operation of a power system. Back propagation neural network (BPNN) is widely used in the forecasting field because of its powerful approximation capability. However, due to a variety of unstable factors, electrical time series often exhibit highly noisy and nonlinear characteristics. Usually, a large deviation will be produced when employing single BPNN to capture the complex data pattern. To solve this problem, this paper proposes a new hybrid forecasting approach that combines ensemble empirical mode decomposition (EEMD), chaotic self-adaptive flower pollination algorithm (CSFPA) and BPNN. EEMD is employed to decompose the original load series with the purpose of reducing the forecasting complexity. Developed CSFPA uses logistic equation to produce the chaotic initial population. In addition, aiming at providing a better optimization capability, CSFPA calculates the self-adaptive switch probability at each iteration. The best initial weights and biases of BPNN are provided by the optimization result of CSFPA. The performance of the proposed method is validated by two real-world load data sets from different electricity markets. The numerical results demonstrate that the proposed method outperforms three advanced methods; it is an effective and promising method for STLF.

Synthesis of natural electric and magnetic Time‐series using Inter‐station transfer functions and time‐series from a Neighboring site (STIN): Applications for processing MT data

AbstractSynthesis of natural electric and magnetic Time series using Interstation transfer functions and time series from a Neighboring site (STIN) is a new approach for recovering natural electric and magnetic fields and reduce the influence of anthropogenic noise. The proposed approach modifies the windows of the local electric and magnetic time series that are affected by noise with time series resulted from modifying the spectra of the magnetic time series from a neighboring site with the interstation transfer functions between the local and neighboring sites. The STIN method was tested with artificially contaminated electric and magnetic time series. Comparison between STIN‐corrected time series and original noncontaminated time series shows high similarity, both in the time and frequency domains. Differences were quantified using the normalized root‐mean‐square error, the correlation coefficient, and the signal‐to‐noise ratio. The STIN method was also applied to two sites affected by unconstrained anthropogenic noise, thus demonstrating the ability and accuracy of STIN in synthesizing natural electric and magnetic fields and reducing the influence of anthropogenic noise. The synthesized time series provided by STIN show the method to be valuable for magnetotelluric (MT) geophysical applications, by increasing the reliability when constrains the MT impedance tensor and by reducing the scatter of data points when the time series are affected by noise, particularly for longer periods. As STIN is based on interstation transfer functions, the electric and magnetic time series can be treated independently, enabling computation of the MT impedance tensor even when the electric and magnetic time series of the local site were recorded at different times.

On the Long-Term Correlations and Multifractal Properties of Electric Arc Furnace Time Series

In this paper, we study long-term correlations and multifractal properties elaborated from time series of three-phase current signals from an industrial electric arc furnace. Implicit sinusoidal trends are suitably detected by considering the scaling of the fluctuation functions. Time series are then filtered via a Fourier-based analysis to remove such strong periodicities. In the filtered time series we detected long-term, positive correlations. The presence of positive correlations is in agreement with the typical V–I characteristic (hysteresis) of the electric arc furnace, thus providing a sound physical justification for the memory effects found in the current time series. The multifractal signature is strong enough in the filtered time series to be effectively classified as multifractal.

Exploring strategies for classification of external stimuli using statistical features of the plant electrical response.

Plants sense their environment by producing electrical signals which in essence represent changes in underlying physiological processes. These electrical signals, when monitored, show both stochastic and deterministic dynamics. In this paper, we compute 11 statistical features from the raw non-stationary plant electrical signal time series to classify the stimulus applied (causing the electrical signal). By using different discriminant analysis-based classification techniques, we successfully establish that there is enough information in the raw electrical signal to classify the stimuli. In the process, we also propose two standard features which consistently give good classification results for three types of stimuli--sodium chloride (NaCl), sulfuric acid (H₂SO₄) and ozone (O₃). This may facilitate reduction in the complexity involved in computing all the features for online classification of similar external stimuli in future.

Oscillatory Electrical Response to Osmotic Stress in Soybean Plants

Oscillations in plants can occur at various levels. Their physiological processes evolve during time, presenting a variable dynamics1. Different oscillatory dynamics in different physiological processes in plants have been observed under different environmental conditions. Oscillatory dynamics allow to organisms flexibility in responses to environmental changes2. Recent studies have evidenced the role of electrical signaling in the physiological processes. At the whole-plant level, oscillations of electrical frequency-coded signals are believed to play an important role in communication between the roots and shoots3. The aim of this work was to test the hypothesis that a severe osmotic stress causes changes in the pattern of electrical signaling in soybean plants, allowing discrimination among signs under different water conditions. Two-week-old soybean seedlings were used for the experiments, carried out under constant environmental conditions and inside a Faraday cage. Electrical time series (n=30) were obtained with an electronic acquisition data system. On previous day of experiments, the plants were transferred to hydroponic cultivation and Needle electrodes were inserted into the stem, for acclimatization. Osmotic stress was applied by replacing the nutrient solution by mannitol solution at -2MPa. Power frequency analysis has confirmed differences in oscillatory characteristic of plant bioelectrical data. Both conditions showed a power spectrum following a power-law distribution, indicating a scale-free pattern of the dynamics. On the other hand, while in the time series scored before osmotic stimuli the range of frequencies from 0.15 to 16Hz followed the power-law trend, after osmotic stimuli this range was from 0.10 to 5Hz. Moreover, before stimuli it was observed a second set of frequencies ranging from 11 to 13Hz, which it was not present in the time series after stimuli. These results have indicates a decrease trend of complexity of the electrical signal to root-shoot communication of soybean seedlings under osmotic stress.

Reproducing electric field observations during magnetic storms by means of rigorous 3-D modelling and distortion matrix co-estimation

Electric fields induced in the conducting Earth by geomagnetic disturbances drive currents in power transmission grids, telecommunication lines or buried pipelines, which can cause service disruptions. A key step in the prediction of the hazard to technological systems during magnetic storms is the calculation of the geoelectric field. To address this issue for mid-latitude regions, we revisit a method that involves 3-D modelling of induction processes in a heterogeneous Earth and the construction of a magnetospheric source model described by low-degree spherical harmonics from observatory magnetic data. The actual electric field, however, is known to be perturbed by galvanic effects, arising from very local near-surface heterogeneities or topography, which cannot be included in the model. Galvanic effects are commonly accounted for with a real-valued time-independent distortion matrix, which linearly relates measured and modelled electric fields. Using data of six magnetic storms that occurred between 2000 and 2003, we estimate distortion matrices for observatory sites onshore and on the ocean bottom. Reliable estimates are obtained, and the modellings are found to explain up to 90% of the measurements. We further find that 3-D modelling is crucial for a correct separation of galvanic and inductive effects and a precise prediction of the shape of electric field time series during magnetic storms. Since the method relies on precomputed responses of a 3-D Earth to geomagnetic disturbances, which can be recycled for each storm, the required computational resources are negligible. Our approach is thus suitable for real-time prediction of geomagnetically induced currents by combining it with reliable forecasts of the source field.

MTpy: A Python toolbox for magnetotellurics

We present the software package MTpy that allows handling, processing, and imaging of magnetotelluric (MT) data sets. Written in Python, the code is open source, containing sub-packages and modules for various tasks within the standard MT data processing and handling scheme. Besides the independent definition of classes and functions, MTpy provides wrappers and convenience scripts to call standard external data processing and modelling software.In its current state, modules and functions of MTpy work on raw and pre-processed MT data. However, opposite to providing a static compilation of software, we prefer to introduce MTpy as a flexible software toolbox, whose contents can be combined and utilised according to the respective needs of the user. Just as the overall functionality of a mechanical toolbox can be extended by adding new tools, MTpy is a flexible framework, which will be dynamically extended in the future. Furthermore, it can help to unify and extend existing codes and algorithms within the (academic) MT community.In this paper, we introduce the structure and concept of MTpy. Additionally, we show some examples from an everyday work-flow of MT data processing: the generation of standard EDI data files from raw electric (E-) and magnetic flux density (B-) field time series as input, the conversion into MiniSEED data format, as well as the generation of a graphical data representation in the form of a Phase Tensor pseudosection.

Time causal operational estimation of electric fields induced in the Earth's lithosphere during magnetic storms

In support of projects for monitoring geomagnetic hazards for electric power grids, we develop a simple mathematical formalism, consistent with the time causality of deterministic physics, for estimating electric fields that are induced in the Earth's lithosphere during magnetic storms. For an idealized model of the lithosphere, an infinite half-space having uniform electrical conductivity properties described by a galvanic tensor, we work in the Laplace-transformed frequency domain to obtain a transfer function which, when convolved with measured magnetic field time series, gives an estimated electric field time series. Using data collected at the Kakioka, Japan observatory, we optimize lithospheric conductivity parameters by minimizing the discrepancy between model-estimated electric field variation and that actually measured. With our simple model, we can estimate 87% of the variance in storm time Kakioka electric field data; a more complicated model of lithospheric conductivity would be required to estimate the remaining 13% of the variance. We discuss how our estimation formalism might be implemented for geographically coordinated real-time monitoring of geoelectric fields.

Impact of a Medium-Size Wave Farm on Grids of Different Strength Levels

Power fluctuations generated by most oscillating wave energy converters may have a negative impact on the power quality of the local grid to which the wave farms will be connected. Hence, assessing their impact is an important step in the selection process of a suitable deployment location. However, site-specific grid impact assessment studies are relatively time-consuming and require a high level of detail on the local network. Both of these constraints mean that grid impact studies are usually not performed in the preliminary stages of the site selection process, despite the extremely negative consequences resulting from poor power quality. This paper details a comprehensive study based on a relatively typical wave farm design connected to networks of different strength levels. The study was performed using experimental electrical power time series of an oscillating water column (OWC) device generated under the framework of the European FP7 project “CORES”. Simulations were performed using DIgSILENT power system simulator “PowerFactory”.

Monthly Electric Energy Consumption Forecasting Using Multiwindow Moving Average and Hybrid Growth Models

Monthly electric energy consumption forecasting is important for electricity production planning and electric power engineering decision making. Multiwindow moving average algorithm is proposed to decompose the monthly electric energy consumption time series into several periodic waves and a long-term approximately exponential increasing trend. Radial basis function (RBF) artificial neural network (ANN) models are used to forecast the extracted periodic waves. A novel hybrid growth model, which includes a constant term, a linear term, and an exponential term, is proposed to forecast the extracted increasing trend. The forecasting results of the monthly electric energy consumption can be obtained by adding the forecasting values of each model. To test the performance by comparison, the proposed and other three models are used to forecast China's monthly electric energy consumption from January 2011 to December 2012. Results show that the proposed model exhibited the best performance in terms of mean absolute percentage error (MAPE) and maximal absolute percentage error (MaxAPE).

Surface electric fields for North America during historical geomagnetic storms

To better understand the impact of geomagnetic disturbances on the electric grid, we recreate surface electric fields from two historical geomagnetic storms—the 1989 “Quebec” storm and the 2003 “Halloween” storms. Using the Spherical Elementary Current Systems method, we interpolate sparsely distributed magnetometer data across North America. We find good agreement between the measured and interpolated data, with larger RMS deviations at higher latitudes corresponding to larger magnetic field variations. The interpolated magnetic field data are combined with surface impedances for 25 unique physiographic regions from the United States Geological Survey and literature to estimate the horizontal, orthogonal surface electric fields in 1 min time steps. The induced horizontal electric field strongly depends on the local surface impedance, resulting in surprisingly strong electric field amplitudes along the Atlantic and Gulf Coast. The relative peak electric field amplitude of each physiographic region, normalized to the value in the Interior Plains region, varies by a factor of 2 for different input magnetic field time series. The order of peak electric field amplitudes (largest to smallest), however, does not depend much on the input. These results suggest that regions at lower magnetic latitudes with high ground resistivities are also at risk from the effect of geomagnetically induced currents. The historical electric field time series are useful for estimating the flow of the induced currents through long transmission lines to study power flow and grid stability during geomagnetic disturbances.

Electrical power fluctuations in a network of DC/AC inverters in a large PV plant: Relationship between correlation, distance and time scale

This paper analyzes the correlation between the fluctuations of the electrical power generated by the ensemble of 70DC/AC inverters from a 45.6MW PV plant. The use of real electrical power time series from a large collection of photovoltaic inverters of a same plant is an important contribution in the context of models built upon simplified assumptions to overcome the absence of such data.This data set is divided into three different fluctuation categories with a clustering procedure which performs correctly with the clearness index and the wavelet variances. Afterwards, the time dependent correlation between the electrical power time series of the inverters is estimated with the wavelet transform. The wavelet correlation depends on the distance between the inverters, the wavelet time scales and the daily fluctuation level. Correlation values for time scales below one minute are low without dependence on the daily fluctuation level. For time scales above 20min, positive high correlation values are obtained, and the decay rate with the distance depends on the daily fluctuation level. At intermediate time scales the correlation depends strongly on the daily fluctuation level.The proposed methods have been implemented using free software. Source code is available as supplementary material.

Neural Model with Particle Swarm Optimization Kalman Learning for Forecasting in Smart Grids

This paper discusses a novel training algorithm for a neural network architecture applied to time series prediction with smart grids applications. The proposed training algorithm is based on an extended Kalman filter (EKF) improved using particle swarm optimization (PSO) to compute the design parameters. The EKF-PSO-based algorithm is employed to update the synaptic weights of the neural network. The size of the regression vector is determined by means of the Cao methodology. The proposed structure captures more efficiently the complex nature of the wind speed, energy generation, and electrical load demand time series that are constantly monitorated in a smart grid benchmark. The proposed model is trained and tested using real data values in order to show the applicability of the proposed scheme.

Interplanetary dust detection by radio antennas: Mass calibration and fluxes measured by STEREO/WAVES

We analyze dust impacts recorded by the S/WAVES radio instrument onboard the two STEREO spacecraft near 1 A.U. during the period 2007–2010. The impact of a dust particle on a spacecraft produces a plasma cloud whose associated electric field can be detected by on‐board electric antennas. For this study we use the electric potential time series recorded by the waveform sampler of the instrument. The high time resolution and long sampling times of this measurement enable us to deduce considerably more information than in previous studies based on the dynamic power spectra provided by the same instrument or by radio instruments onboard other spacecraft. The large detection area compared to conventional dust detectors provides flux data with a better statistics. We show that the dust‐generated signals are of two kinds, corresponding to impacts of dust from distinctly different mass ranges. We propose calibration formulas for these signals and show that we are able to use S/WAVES as a dust detector with convincing results both in the nanometer and micrometer size ranges. In the latter, the orbital motion of the spacecraft enables us to distinguish between interstellar and interplanetary dust components. Our measurements cover the mass intervals ∼10−22–10−20 kg and ∼10−17 − 5 × 10−16 kg. The flux of the larger dust agrees with measurements of other instruments on different spacecraft.

Observations on the dynamics of external cavity semiconductor lasers

Dynamics of external cavity semiconductor lasers is known to be a complex and uncontrollable phenomenon. Due to the lack of experimental studies on the nature of the external cavity semiconductor lasers, there is a need to theoretically clarify laser dynamics. The stability of laser dynamics in the present paper, is analyzed through plotting the Lyapunov exponent spectra, bifurcation diagrams, phase portrait and electric field intensity time series. The analysis is preformed with respect to applied feedback phase Cp, feedback strength η and the pump current of the laser. The main argument of the paper is to show that the laser dynamics can not be accounted for through simply a bifurcation diagram and single-control parameter. The comparison of the obtained results provides a very detailed picture of the qualitative changes in laser dynamics.

First and second order non-equilibrium phase transition and evidence for non-extensive Tsallis statistics in Earth’s magnetosphere

In this paper strong evidence is provided for significant far from equilibrium phase transition processes in the Earth’s magnetosphere as revealed by the nonlinear analysis of in situ observations. These results constitute the solid base for the solution of the durable controversy about the chaotic or non-chaotic character of the magnetospheric dynamics. During the last two decades the concept of low dimensional chaos was supported by theoretical and experimental methods by our group in Thrace and others scientists, as an explicative paradigm of the magnetospheric dynamics including substorm processes. In parallel, the concept of self-organized criticality (SOC) and space–time intermittency was introduced as new and opposing to low dimensional chaos concepts for modeling the magnetospheric dynamics. Novel results concerning the nonlinear analysis of in situ space plasma data (magnetic–electric field, energetic particles and bulk plasma flow time series) obtained by the Geotail spacecraft presented in this paper for the first time reveal the following: (a) Coexistence of SOC and chaos states in the magnetospheric system and global phase transition from one state to the other during substorms. (b) Strong intermittent turbulent character of the magnetospheric system at the SOC or the low dimensional chaos states. (c) Clear indications for non-extensivity and q-Gaussian statistics during periods of low dimensional and chaotic dynamics of the magnetosphere. (d) Low dimensional and nonlinear space plasma dynamics in the day side magnetopause and bow shock dynamics. The dual character of the magnetospheric dynamics including low dimensional chaotic (coherent) and high dimensional turbulent states, as supported in this paper, is in agreement and verifies previous theoretical and experimental studies.

Broadband Spectral Change: Evidence for a Macroscale Correlate of Population Firing Rate?: Figure 1.

In [1972, Brindley and Craggs][1] measured the electric potential from the surface of the baboon brain using a 1-mm-diameter electrode. They found that the power in the 80–250 Hz frequency range of the electric potential time series was dynamically increased in motor areas during movement. Sites 2

Generation of synthetic wide-band electromagnetic time series

The estimation of the earth transfer functions in MT prospecting method poses the greatest difficulty. As in the seismic prospecting method this task requires the development of advanced processing techniques. In order to assess the performance of each technique, controlled synthetic data and different noise types, which simulate the observed signals, are required. This paper presents a procedure to generate a wide-band noise-free electromagnetic field to be used both for magnetotelluric and audio-magnetotelluric studies. Furthermore, an effort was made to extend the simulation procedures to generally stratified and simple inhomogeneous earth structures. The discrete-time magnetic field values are generated through the inverse Fourier transform of a continuous amplitude spectrum and a sampling procedure. The electric field time series are obtained by the convolution of the magnetic field time series, calculated in the interested frequency band, with a non-causal impedance impulse response. Polarized fields, which are important when inhomogeneous media are considered, are also generated.

Comparison of wind power estimates from the ECMWF reanalyses with direct turbine measurements

Reanalysis data are rarely used for wind power estimates because of the limited spatial and temporal resolution. Here we report on a detailed comparison of wind speed and electric power time series recorded at a continental location in Hungary and estimates provided by the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA-40 and Interim databases at nearby grid points. The results show that the temporal behavior is adequately represented in reanalysis records with damped magnitudes, as expected. However, characteristic shape differences in the wind speed histograms for turbine measurements and reanalysis hinder a perfect match of statistics. A satisfying agreement of histograms for measured and modeled output powers is achieved by scaling up surface wind speeds to have the same long time average value as for the turbine records. The presented calibration permits us to provide wind power estimates for large geographic areas, where the wind field is similarly coherent as around the test site.