scholarly journals Principal Mismatch Patterns across a Simplified Highly Renewable European Electricity Network

2017 ◽  
Author(s):  
Mads Raunbak ◽  
Timo Zeyer ◽  
Kun Zhu ◽  
Martin Greiner
Keyword(s):  
Principal Components ◽  
Principal Component ◽  
Renewable Electricity ◽  
Electricity System ◽  
System A ◽  
Dipole Structure ◽  
Electricity Network ◽  
Spatio Temporal ◽  
Demand Patterns ◽  
High Share

Due to its spatio-temporal variability, the mismatch between the weather and demand patterns challenges the design of highly renewable energy systems. A principal component analysis is applied to a simplified networked European electricity system with a high share of wind and solar power generation. It reveals a small number of important mismatch patterns, which explain most of the system's required backup and transmission infrastructure. Whereas the first principal component is already able to reproduce most of the temporal mismatch variability for a solar dominated system, a few more principal components are needed for a wind dominated system. Due to its monopole structure the first principal component causes most of the system's backup infrastructure. The next few principal components have a dipole structure and dominate the transmission infrastructure of the renewable electricity network.

scholarly journals Designing terawatt scale renewable electricity system: A dynamic analysis for India

2021 ◽  
Vol 38 ◽  
pp. 100753
Author(s):  
Sourabh Jain ◽  
Nikunj Kumar Jain ◽  
Piyush Choudhary ◽  
William Vaughn
Keyword(s):  
Dynamic Analysis ◽  
Renewable Electricity ◽  
Electricity System ◽  
System A

scholarly journals A scale-dependent measure of system dimensionality

2020 ◽  
Author(s):  
Stefano Recanatesi ◽  
Serena Bradde ◽  
Vijay Balasubramanian ◽  
Nicholas A. Steinmetz ◽  
Eric Shea-Brown
Keyword(s):  
Latent Variables ◽  
Degrees Of Freedom ◽  
Fundamental Problem ◽  
Principal Component ◽  
Dependent Measure ◽  
Neural Population ◽  
System A ◽  
Spatio Temporal ◽  
Effective Dimensionality ◽  
Dynamical Degrees

A fundamental problem in science is uncovering the effective number of dynamical degrees of freedom in a complex system, a quantity that depends on the spatio-temporal scale at which the system is observed. Here, we propose a scale-dependent generalization of a classic enumeration of latent variables, the Participation Ratio. We show how this measure relates to conventional quantities such as the Correlation dimension and Principal Component Analysis, and demonstrate its properties in dynamical systems such as the Lorentz attractor. We apply the method to neural population recordings in multiple brain areas and brain states, and demonstrate fundamental differences in the effective dimensionality of neural activity in behaviorally engaged states versus spontaneous activity. Our method applies broadly to multi-variate data across fields of science.

scholarly journals Reconstruction of spatio-temporal temperature from sparse historical records using robust probabilistic principal component regression

2017 ◽  
Vol 3 (1) ◽  
pp. 1-16 ◽  
Author(s):  
John Tipton ◽  
Mevin Hooten ◽  
Simon Goring
Keyword(s):  
Principal Components ◽  
Cross Validation ◽  
Model Performance ◽  
Principal Component Regression ◽  
Principal Component ◽  
Spatially Explicit ◽  
Proxy Data ◽  
Out Of Sample ◽  
Spatio Temporal ◽  
Paleoclimate Proxy

Abstract. Scientific records of temperature and precipitation have been kept for several hundred years, but for many areas, only a shorter record exists. To understand climate change, there is a need for rigorous statistical reconstructions of the paleoclimate using proxy data. Paleoclimate proxy data are often sparse, noisy, indirect measurements of the climate process of interest, making each proxy uniquely challenging to model statistically. We reconstruct spatially explicit temperature surfaces from sparse and noisy measurements recorded at historical United States military forts and other observer stations from 1820 to 1894. One common method for reconstructing the paleoclimate from proxy data is principal component regression (PCR). With PCR, one learns a statistical relationship between the paleoclimate proxy data and a set of climate observations that are used as patterns for potential reconstruction scenarios. We explore PCR in a Bayesian hierarchical framework, extending classical PCR in a variety of ways. First, we model the latent principal components probabilistically, accounting for measurement error in the observational data. Next, we extend our method to better accommodate outliers that occur in the proxy data. Finally, we explore alternatives to the truncation of lower-order principal components using different regularization techniques. One fundamental challenge in paleoclimate reconstruction efforts is the lack of out-of-sample data for predictive validation. Cross-validation is of potential value, but is computationally expensive and potentially sensitive to outliers in sparse data scenarios. To overcome the limitations that a lack of out-of-sample records presents, we test our methods using a simulation study, applying proper scoring rules including a computationally efficient approximation to leave-one-out cross-validation using the log score to validate model performance. The result of our analysis is a spatially explicit reconstruction of spatio-temporal temperature from a very sparse historical record.

Fossil fuel and CO2 emissions savings on a high renewable electricity system – A single year case study for Ireland

Energy Policy ◽  
2015 ◽  
Vol 83 ◽  
pp. 151-164 ◽  
Author(s):  
J.M. Clancy ◽  
F. Gaffney ◽  
J.P. Deane ◽  
J. Curtis ◽  
B.P. Ó Gallachóir
Keyword(s):  
Co2 Emissions ◽  
Fossil Fuel ◽  
Renewable Electricity ◽  
Electricity System ◽  
System A

Structuring Assessments of Psychopathology

2006 ◽  
Vol 27 (2) ◽  
pp. 87-92 ◽  
Author(s):  
Willem K.B. Hofstee ◽  
Dick P.H. Barelds ◽  
Jos M.F. Ten Berge
Keyword(s):  
Principal Components ◽  
Personality Assessment ◽  
Clinical Sample ◽  
Principal Component ◽  
Normal Sample ◽  
Normative Sample ◽  
Assessment Data ◽  
Obsessive Compulsive ◽  
Oblique Rotation ◽  
Two Samples

Hofstee and Ten Berge (2004a) have proposed a new look at personality assessment data, based on a bipolar proportional (-1, .. . 0, .. . +1) scale, a corresponding coefficient of raw-scores likeness L = ΢XY/N, and raw-scores principal component analysis. In a normal sample, the approach resulted in a structure dominated by a first principal component, according to which most people are faintly to mildly socially desirable. We hypothesized that a more differentiated structure would arise in a clinical sample. We analyzed the scores of 775 psychiatric clients on the 132 items of the Dutch Personality Questionnaire (NPV). In comparison to a normative sample (N = 3140), the eigenvalue for the first principal component appeared to be 1.7 times as small, indicating that such clients have less personality (social desirability) in common. Still, the match between the structures in the two samples was excellent after oblique rotation of the loadings. We applied the abridged m-dimensional circumplex design, by which persons are typed by their two highest scores on the principal components, to the scores on the first four principal components. We identified five types: Indignant (1-), Resilient (1-2+), Nervous (1-2-), Obsessive-Compulsive (1-3-), and Introverted (1-4-), covering 40% of the psychiatric sample. Some 26% of the individuals had negligible scores on all type vectors. We discuss the potential and the limitations of our approach in a clinical context.

Comparison of Principal Component Solutions in Two Populations

Methodology ◽  
2016 ◽  
Vol 12 (1) ◽  
pp. 11-20 ◽  
Author(s):  
Gregor Sočan
Keyword(s):  
Simulation Study ◽  
Principal Components ◽  
Common Factor ◽  
Principal Component ◽  
Component Model ◽  
Bootstrap Procedure ◽  
Factor Loadings ◽  
Component Loadings ◽  
Principal Component Model ◽  
Two Populations

Abstract. When principal component solutions are compared across two groups, a question arises whether the extracted components have the same interpretation in both populations. The problem can be approached by testing null hypotheses stating that the congruence coefficients between pairs of vectors of component loadings are equal to 1. Chan, Leung, Chan, Ho, and Yung (1999) proposed a bootstrap procedure for testing the hypothesis of perfect congruence between vectors of common factor loadings. We demonstrate that the procedure by Chan et al. is both theoretically and empirically inadequate for the application on principal components. We propose a modification of their procedure, which constructs the resampling space according to the characteristics of the principal component model. The results of a simulation study show satisfactory empirical properties of the modified procedure.

Stormwater inflow prediction using radar rainfall data compressed by principal component analysis

2006 ◽  
Vol 1 (1) ◽  
Author(s):  
K. Katayama ◽  
K. Kimijima ◽  
O. Yamanaka ◽  
A. Nagaiwa ◽  
Y. Ono
Keyword(s):  
Principal Component Analysis ◽  
Prediction Model ◽  
Principal Components ◽  
Prediction Method ◽  
Principal Component ◽  
Component Analysis ◽  
Rainfall Data ◽  
Radar Rainfall ◽  
Input Variables ◽  
Inflow Prediction

This paper proposes a method of stormwater inflow prediction using radar rainfall data as the input of the prediction model constructed by system identification. The aim of the proposal is to construct a compact system by reducing the dimension of the input data. In this paper, Principal Component Analysis (PCA), which is widely used as a statistical method for data analysis and compression, is applied to pre-processing radar rainfall data. Then we evaluate the proposed method using the radar rainfall data and the inflow data acquired in a certain combined sewer system. This study reveals that a few principal components of radar rainfall data can be appropriate as the input variables to storm water inflow prediction model. Consequently, we have established a procedure for the stormwater prediction method using a few principal components of radar rainfall data.

Evaluation functions for integral mapping

2017 ◽  
Vol 921 (3) ◽  
pp. 24-29 ◽  
Author(s):  
S.I. Lesnykh ◽  
A.K. Cherkashin
Keyword(s):  
Principal Component Analysis ◽  
Environmental Factors ◽  
Principal Components ◽  
Principal Component ◽  
Evaluation Function ◽  
Final Value ◽  
Evaluation Functions ◽  
Geographical Environment ◽  
Environmental Background ◽  
Integral Mapping

The proposed procedure of integral mapping is based on calculation of evaluation functions on the integral indicators (II) taking into account the feature of the local geographical environment, when geosystems in the same states in the different environs have various estimates. Calculation of II is realized with application of a Principal Component Analysis for processing of the forest database, allowing to consider in II the weight of each indicator (attribute). The final value of II is equal to a difference of the first (condition of geosystem) and the second (condition of environmental background) principal components. The evaluation functions are calculated on this value for various problems of integral mapping. The environmental factors of variability is excluded from final value of II, therefore there is an opportunity to find the invariant evaluation function and to determine coefficients of this function. Concepts and functions of the theory of reliability for making the evaluation maps of the hazard of functioning and stability of geosystems are used.

scholarly journals EXPRESS: Exploration of Principal Component Analysis: Deriving PCA Visually Using Spectra

2021 ◽  
pp. 000370282098784
Author(s):  
James Renwick Beattie ◽  
Francis Esmonde-White
Keyword(s):  
Principal Components ◽  
Principal Component ◽  
Original Data ◽  
Specific Chemical ◽  
Successive Refinement ◽  
Minimal Loss ◽  
Components Analysis ◽  
The Mathematical Model ◽  
Application Specific ◽  
Reconstructed Data

Spectroscopy rapidly captures a large amount of data that is not directly interpretable. Principal Components Analysis (PCA) is widely used to simplify complex spectral datasets into comprehensible information by identifying recurring patterns in the data with minimal loss of information. The linear algebra underpinning PCA is not well understood by many applied analytical scientists and spectroscopists who use PCA. The meaning of features identified through PCA are often unclear. This manuscript traces the journey of the spectra themselves through the operations behind PCA, with each step illustrated by simulated spectra. PCA relies solely on the information within the spectra, consequently the mathematical model is dependent on the nature of the data itself. The direct links between model and spectra allow concrete spectroscopic explanation of PCA, such the scores representing ‘concentration’ or ‘weights’. The principal components (loadings) are by definition hidden, repeated and uncorrelated spectral shapes that linearly combine to generate the observed spectra. They can be visualized as subtraction spectra between extreme differences within the dataset. Each PC is shown to be a successive refinement of the estimated spectra, improving the fit between PC reconstructed data and the original data. Understanding the data-led development of a PCA model shows how to interpret application specific chemical meaning of the PCA loadings and how to analyze scores. A critical benefit of PCA is its simplicity and the succinctness of its description of a dataset, making it powerful and flexible.

scholarly journals Spatial Conditions Supporting Sustainable Development of Enterprises on Local Level

2021 ◽  
Vol 13 (4) ◽  
pp. 2292
Author(s):  
Aneta Ptak-Chmielewska ◽  
Agnieszka Chłoń-Domińczak
Keyword(s):  
Social Insurance ◽  
Small And Medium Enterprises ◽  
Local Level ◽  
Principal Component ◽  
Sources Of Information ◽  
Clustering Methods ◽  
Significant Information ◽  
The Status ◽  
Medium Enterprises ◽  
High Share

Micro, small and medium enterprises (MSMEs) represent more than 99% of enterprises in Europe. Therefore, knowledge about this sector, also in the spatial context is important to understand the patterns of economic and social development. The main goal of this article is an analysis of spatial conditions and the situation of MSMEs on a local level using combined sources of information. This includes data collected in the Social Insurance Institution and Tax registers in Poland, which provides information on the employment, wages, revenues and taxes paid by the MSMEs on a local level as well as contextual statistical information. The data is used for a diagnosis of spatial circumstances and discussion of conditions influencing the status of the MSMEs sector in a selected region (voivodeship) in Poland. Taxonomy methods including factor analysis and clustering methods based on k-means and SOM Kohonen were used for selecting significant information and grouping of the local units according to the situation of the MSMEs. There are eight factors revealed in principal component analysis and five clusters of local units distinguished using these factors. These include two clusters with a high share of rural local units and two clusters with a high share of rural-urban and urban local units. Additionally, there was an outstanding cluster with only two dominant urban local units. Factors show differences between clusters in the situation of MSMEs sector and infrastructure. Different spatial conditions in different regions influence the situation of MSMEs.

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