The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
This first lecture describes what EMT is. Its history of evolution. Main personalities how discovered theories relating to this theory. Applications of EMT . Scalars and vectors and there algebra. Coordinate systems. Field, Coulombs law and electric field intensity.volume charge distribution, electric flux density, gauss's law and divergence
1. The document discusses mixture models and the Expectation-Maximization (EM) algorithm. It covers K-means clustering, Gaussian mixture models, and applying EM to estimate parameters for these models.
2. EM is a general technique for finding maximum likelihood solutions for probabilistic models with latent variables. It works by iteratively computing expectations of the latent variables given current parameter estimates (E-step) and maximizing the likelihood function with respect to the parameters (M-step).
3. This process is guaranteed to increase the likelihood at each iteration until convergence. EM can be applied to problems like Gaussian mixtures, Bernoulli mixtures, and Bayesian linear regression by treating certain variables as latent.
This document summarizes key concepts from Chapter 5 of the book "Pattern Recognition and Machine Learning" regarding neural networks.
1. Neural networks can overcome the curse of dimensionality by using nonlinear activation functions between layers. Common activation functions include sigmoid, tanh, and ReLU.
2. A feedforward neural network consists of an input layer, hidden layers with nonlinear activations, and an output layer. The network learns by adjusting weights in a process called backpropagation.
3. Bayesian neural networks treat the network weights as distributions and integrate them out to make predictions, avoiding overfitting. However, the posterior distribution cannot be expressed in closed form due to the nonlinear nature of neural networks.
This document summarizes key points from Chapter 3 of the book "Pattern Recognition and Machine Learning" by Christopher M. Bishop. It discusses linear regression, Bayesian linear regression, and model comparison. The main points are:
1) Linear regression finds the best fitting linear relationship between inputs and outputs. Bayesian linear regression places prior distributions over the weights and finds the posterior distribution.
2) The prior in Bayesian linear regression acts as an intrinsic regularization. As more data is added, the posterior variance decreases while the noise variance remains.
3) Model evidence can be used to perform Bayesian model comparison by finding which model best explains the data. Approximations are required to evaluate the evidence.
This chapter discusses classification methods including linear discriminant functions and probabilistic generative and discriminative models. It covers linear decision boundaries, perceptrons, Fisher's linear discriminant, logistic regression, and the use of sigmoid and softmax activation functions. The key points are:
1) Classification involves dividing the input space into decision regions using linear or nonlinear boundaries.
2) Perceptrons and Fisher's linear discriminant find linear decision boundaries by updating weights to minimize misclassification.
3) Generative models like naive Bayes estimate joint probabilities while discriminative models like logistic regression directly model posterior probabilities.
4) Sigmoid and softmax functions are used to transform linear outputs into probabilities for binary and multiclass classification respectively.
This chapter discusses continuous latent variable models including principal component analysis (PCA), probabilistic PCA, and factor analysis. PCA finds projections of data that maximize variance or minimize error through eigenvectors of the covariance matrix. Probabilistic PCA places a probabilistic treatment on PCA by modeling the data and latent variables as Gaussian distributions. Factor analysis similarly models the data as a linear combination of latent factors plus noise.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
- The document summarizes key concepts from chapters 1.1 to 1.6 of the book "Pattern Recognition and Machine Learning" by Christopher M. Bishop.
- It introduces polynomial curve fitting, Bayesian curve fitting, decision theory, and information theory concepts such as entropy, Kullback-Leibler divergence, and their applications in machine learning.
- Key algorithms covered include linear and polynomial regression, maximum likelihood estimation, and using entropy and KL divergence to model probability distributions.
This first lecture describes what EMT is. Its history of evolution. Main personalities how discovered theories relating to this theory. Applications of EMT . Scalars and vectors and there algebra. Coordinate systems. Field, Coulombs law and electric field intensity.volume charge distribution, electric flux density, gauss's law and divergence
1. The document discusses mixture models and the Expectation-Maximization (EM) algorithm. It covers K-means clustering, Gaussian mixture models, and applying EM to estimate parameters for these models.
2. EM is a general technique for finding maximum likelihood solutions for probabilistic models with latent variables. It works by iteratively computing expectations of the latent variables given current parameter estimates (E-step) and maximizing the likelihood function with respect to the parameters (M-step).
3. This process is guaranteed to increase the likelihood at each iteration until convergence. EM can be applied to problems like Gaussian mixtures, Bernoulli mixtures, and Bayesian linear regression by treating certain variables as latent.
This document summarizes key concepts from Chapter 5 of the book "Pattern Recognition and Machine Learning" regarding neural networks.
1. Neural networks can overcome the curse of dimensionality by using nonlinear activation functions between layers. Common activation functions include sigmoid, tanh, and ReLU.
2. A feedforward neural network consists of an input layer, hidden layers with nonlinear activations, and an output layer. The network learns by adjusting weights in a process called backpropagation.
3. Bayesian neural networks treat the network weights as distributions and integrate them out to make predictions, avoiding overfitting. However, the posterior distribution cannot be expressed in closed form due to the nonlinear nature of neural networks.
This document summarizes key points from Chapter 3 of the book "Pattern Recognition and Machine Learning" by Christopher M. Bishop. It discusses linear regression, Bayesian linear regression, and model comparison. The main points are:
1) Linear regression finds the best fitting linear relationship between inputs and outputs. Bayesian linear regression places prior distributions over the weights and finds the posterior distribution.
2) The prior in Bayesian linear regression acts as an intrinsic regularization. As more data is added, the posterior variance decreases while the noise variance remains.
3) Model evidence can be used to perform Bayesian model comparison by finding which model best explains the data. Approximations are required to evaluate the evidence.
This chapter discusses classification methods including linear discriminant functions and probabilistic generative and discriminative models. It covers linear decision boundaries, perceptrons, Fisher's linear discriminant, logistic regression, and the use of sigmoid and softmax activation functions. The key points are:
1) Classification involves dividing the input space into decision regions using linear or nonlinear boundaries.
2) Perceptrons and Fisher's linear discriminant find linear decision boundaries by updating weights to minimize misclassification.
3) Generative models like naive Bayes estimate joint probabilities while discriminative models like logistic regression directly model posterior probabilities.
4) Sigmoid and softmax functions are used to transform linear outputs into probabilities for binary and multiclass classification respectively.
This chapter discusses continuous latent variable models including principal component analysis (PCA), probabilistic PCA, and factor analysis. PCA finds projections of data that maximize variance or minimize error through eigenvectors of the covariance matrix. Probabilistic PCA places a probabilistic treatment on PCA by modeling the data and latent variables as Gaussian distributions. Factor analysis similarly models the data as a linear combination of latent factors plus noise.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
- The document summarizes key concepts from chapters 1.1 to 1.6 of the book "Pattern Recognition and Machine Learning" by Christopher M. Bishop.
- It introduces polynomial curve fitting, Bayesian curve fitting, decision theory, and information theory concepts such as entropy, Kullback-Leibler divergence, and their applications in machine learning.
- Key algorithms covered include linear and polynomial regression, maximum likelihood estimation, and using entropy and KL divergence to model probability distributions.
The impact of innovation on travel and tourism industries (World Travel Marke...Brian Solis
From the impact of Pokemon Go on Silicon Valley to artificial intelligence, futurist Brian Solis talks to Mathew Parsons of World Travel Market about the future of travel, tourism and hospitality.
We’re all trying to find that idea or spark that will turn a good project into a great project. Creativity plays a huge role in the outcome of our work. Harnessing the power of collaboration and open source, we can make great strides towards excellence. Not just for designers, this talk can be applicable to many different roles – even development. In this talk, Seasoned Creative Director Sara Cannon is going to share some secrets about creative methodology, collaboration, and the strong role that open source can play in our work.
Reuters: Pictures of the Year 2016 (Part 2)maditabalnco
This document contains 20 photos from news events around the world between January and November 2016. The photos show international events like the US presidential election, the conflict in Ukraine, the migrant crisis in Europe, the Rio Olympics, and more. They also depict human interest stories and natural phenomena from various countries.
The Six Highest Performing B2B Blog Post FormatsBarry Feldman
If your B2B blogging goals include earning social media shares and backlinks to boost your search rankings, this infographic lists the size best approaches.
1) The document discusses the opportunity for technology to improve organizational efficiency and transition economies into a "smart and clean world."
2) It argues that aggregate efficiency has stalled at around 22% for 30 years due to limitations of the Second Industrial Revolution, but that digitizing transport, energy, and communication through technologies like blockchain can help manage resources and increase efficiency.
3) Technologies like precision agriculture, cloud computing, robotics, and autonomous vehicles may allow for "dematerialization" and do more with fewer physical resources through effects like reduced waste and need for transportation/logistics infrastructure.
32 Ways a Digital Marketing Consultant Can Help Grow Your BusinessBarry Feldman
How can a digital marketing consultant help your business? In this resource we'll count the ways. 24 additional marketing resources are bundled for free.
Metric Projections to Identify Critical Points in Electric Power Systemstheijes
The identification of weak nodes and branches involved have been analyzed with different technical of analysis as: sensitivities, modal and of the singular minimum value, applying the Jacobian matrix of load flows. We show up a metric projections application to identify weak nodes and branches with more participation in the electric power system.
This report describes two experiments measuring equipotential lines and electric fields between parallel plate conductors and concentric cylindrical electrodes. In both experiments, equipotential lines were marked on conducting paper connected to an 8V power supply. The electric potential and estimated field were measured and plotted against the predictions of relevant equations. For parallel plates, the potential graph matched predictions linearly but the field graph was less accurate. For concentric cylinders, both graphs matched predictions closely except for points near the disc due to measurement limitations. The experiments supported the theoretical relationships between electric potential and field.
2-Dimensional and 3-Dimesional Electromagnetic Fields Using Finite element me...IOSR Journals
This document describes using the finite element method to model 2D and 3D electromagnetic fields. It discusses modeling a quarter section of a rectangular coaxial line with triangular elements. It describes constructing the matrices for each element and combining them to solve the overall matrix equation. The document outlines implementing FEM in MATLAB, including generating meshes, adding sources, and solving the resulting matrices. Several examples are presented of using a graphical user interface created in MATLAB to calculate fields from configurations like straight wires, bent wires, solenoids, and square loops using FEM techniques.
Power System State Estimation Using Weighted Least Squares (WLS) and Regulari...IJERA Editor
In this paper, a new formulation for power system state estimation is proposed. The formulation is based on
regularized least squares method which uses the principle of Thikonov’s regularization to overcome the
limitations of conventional state estimation methods. In this approach, the mathematical unfeasibility which
results from the lack of measurements in case of ill-posed problems is eliminated. This paper also deals with
comparison of conventional method of state estimation and proposed formulation. A test procedure based n the
variance of the estimated linearized power flows is proposed to identify the observable islands of the system.
The obtained results are compared with the results obtained by conventional WLS method
This paper presents a new fault location method for distribution systems that uses voltage sag calculations between two measurement points. The method is analyzed for both radial systems and systems with distributed generation. Simulation results show the method has average errors of 0.59% without distributed generation and 1.17% with distributed generation integrated. While this method aims to improve on previous techniques, its accuracy depends on the number of line sections modeled and it showed higher errors than reported in the analyzed paper when tested on a simulated system. In conclusion, fault location remains an important problem and different methods provide varying accuracy depending on the system configuration.
FellowBuddy.com is an innovative platform that brings students together to share notes, exam papers, study guides, project reports and presentation for upcoming exams.
We connect Students who have an understanding of course material with Students who need help.
Benefits:-
# Students can catch up on notes they missed because of an absence.
# Underachievers can find peer developed notes that break down lecture and study material in a way that they can understand
# Students can earn better grades, save time and study effectively
Our Vision & Mission – Simplifying Students Life
Our Belief – “The great breakthrough in your life comes when you realize it, that you can learn anything you need to learn; to accomplish any goal that you have set for yourself. This means there are no limits on what you can be, have or do.”
Like Us - https://www.facebook.com/FellowBuddycom
Linear regression [Theory and Application (In physics point of view) using py...ANIRBANMAJUMDAR18
Machine-learning models are behind many recent technological advances, including high-accuracy translations of the text and self-driving cars. They are also increasingly used by researchers to help in solving physics problems, like Finding new phases of matter, Detecting interesting outliers
in data from high-energy physics experiments, Founding astronomical objects are known as gravitational lenses in maps of the night sky etc. The rudimentary algorithm that every Machine Learning enthusiast starts with is a linear regression algorithm. In statistics, linear regression is a linear approach to modelling the relationship between a scalar response (or dependent variable) and one or more explanatory variables (or independent
variables). Linear regression analysis (least squares) is used in a physics lab to prepare the computer-aided report and to fit data. In this article, the application is made to experiment: 'DETERMINATION OF DIELECTRIC CONSTANT OF NON-CONDUCTING LIQUIDS'. The entire computation is made through Python 3.6 programming language in this article.
Distance Metric Based Multi-Attribute Seismic Facies Classification to Identi...Pioneer Natural Resources
Conventional reservoirs benefit from a long scientific history that correlates successful plays to seismic measurements through depositional, tectonic, and digenetic models. Unconventional reservoirs are less well understood, however benefit from significantly denser well control. Thus, allowing us to establish statistical rather than model-based correlations between seismic data, geology, and successful completion strategies. One of the more commonly encountered correlation techniques is based on computer assisted pattern recognition. The pattern recognition techniques have found their niche in a plethora of applications ranging from flagging suspicious credit card purchase patterns to rewarding repeating online buying patterns. Classification of a given seismic response as having a “good” or “bad” pattern requires a “distance metric”. Distance metric “learning” uses past experiences (well performance) as training data to develop a distance metric. Alternative distance metrics have demonstrated significant value in the identification and classification of repeated or anomalous behaviors in public health, security, and marketing. In this paper we examine the value of three of these alternative distance metrics of 3D seismic attributes to the identification of sweet spots in a Barnett Shale play.
Permanent Fault Location in Distribution System Using Phasor Measurement Unit...IJECEIAES
This paper proposes a new method for locating high impedance fault in distribution systems using phasor measurement units (PMUs) installed at certain locations of the system. To implement this algorithm, at first a new method is suggested for the placement of PMUs. Taking information from the units, voltage and current of the entire distribution system are calculated. Then, the two buses in which the fault has been occurred is determined, and location and type of the fault are identified. The main characteristics of the proposed method are: the use of distributed parameter line model in phase domain, considering the presence of literals, and high precision in calculating the high impedance fault location. The results obtained from simulations in EMTP-RV and MATLAB software indicate high accuracy and independence of the proposed method from the fault type, fault location and fault resistance compared to previous methods, so that the maximum observed error was less than 0.15%.
Low-complex Bayesian estimator for imperfect channels in massive muti-input ...IJECEIAES
Motivated by the fact that the complexity of the computations is one of the main challenges in large multiple input multiple output systems, known as massive multiple-input multiple-output (MIMO) systems, this article proposes a low-complex minimum mean squared error (MMSE) Bayesian channel estimator for uplink channels of such systems. First, we have discussed the necessity of the covariance information for the MMSE estimator and how their imperfection knowledge can affect its accuracy. Then, two reduction phases in dimension and floating-point operations have been suggested to reduce its complexity: in phase 1, eigenstructure reduction for channel covariance matrices is implemented based on some truncation rules, while in phase 2, arithmetic operations reduction for matrix multiplications in the MMSE equation is followed. The proposed procedure has significantly reduced the complexity of the MMSE estimator to the first order O(M), which is less than that required for the conventional MMSE with O(M3 ) in terms of matrix dimension. It has been shown that the estimated channels using our proposed procedure are asymptotically aligned and serve the same quality as the full-rank estimated channels. Our results are validated by averaging the normalized mean squared error (NMSE) over a length of 500 sample realizations through a Monte Carlo simulation using MATLAB R2020a.
Artificial Neural Networks for ON Line Assessment of Voltage Stability using ...IOSR Journals
This document describes using an artificial neural network (ANN) technique to assess voltage stability online in power transmission systems. The ANN model is trained to correlate voltage stability status with changing load patterns using two stability indices: the fast voltage stability index (FVSI) and line stability factor (LQF). Simulation results on the IEEE 30-bus test system and Indian 72-bus power grid show the ANN method can accurately calculate the stability indices without complex calculations and can effectively monitor voltage stability online.
1) Electromagnetic theory deals with the study of charges at rest and in motion and is fundamental to electrical engineering and physics. It is used in applications like RF communication, microwave engineering, antennas, electrical machines, and more.
2) Electromagnetic theory can be thought of as a generalization of circuit theory and is useful for situations that cannot be handled by circuit theory alone. It involves electric and magnetic field vectors rather than just voltages and currents.
3) Vector analysis is a useful mathematical tool for electromagnetic concepts. Important vector operations like addition, subtraction, scaling, dot product, and cross product are introduced. Common coordinate systems like Cartesian, cylindrical, and spherical polar coordinates are also discussed.
This document summarizes a method for calculating the sensitivity matrix that defines the linear relationship between circuit parameters and poles/response of an RLC network. The sensitivity matrix enables efficient statistical analysis and yield predictions. It is obtained by taking derivatives of the poles and transfer function, which are calculated from the eigenvalues and eigenvectors of the network's state equation. An example RLC circuit demonstrates calculating the sensitivity matrix and using it to predict yield based on Monte Carlo simulations.
Experimental Verification of the Kinematic Equations of Special Relativity an...Daniel Bulhosa Solórzano
The document experimentally verifies the kinematic equations of special relativity and determines the mass and charge of the electron. It describes an experiment that measures the momentum and kinetic energy of electrons over a range of speeds. The data is fitted to both the Newtonian and relativistic kinematic models. The relativistic model provides a much better fit and allows determining the electron charge to mass ratio and mass. The values found agree well with accepted values, supporting the validity of special relativity.
This document provides an overview of Module 3 which covers Maxwell's equations, electromagnetic waves, and optical fibers. It begins by introducing Maxwell's equations, including Gauss' law, Gauss' law for magnetism, Faraday's law, and Ampere's law. It then discusses electromagnetic waves and how they are transverse waves that can be polarized. Finally, it covers optical fibers and their propagation mechanism, modes of propagation, attenuation causes, and applications to point-to-point communication. The document provides definitions and explanations of important concepts in vector calculus and electromagnetism needed to understand Maxwell's equations and electromagnetic wave behavior.
The impact of innovation on travel and tourism industries (World Travel Marke...Brian Solis
From the impact of Pokemon Go on Silicon Valley to artificial intelligence, futurist Brian Solis talks to Mathew Parsons of World Travel Market about the future of travel, tourism and hospitality.
We’re all trying to find that idea or spark that will turn a good project into a great project. Creativity plays a huge role in the outcome of our work. Harnessing the power of collaboration and open source, we can make great strides towards excellence. Not just for designers, this talk can be applicable to many different roles – even development. In this talk, Seasoned Creative Director Sara Cannon is going to share some secrets about creative methodology, collaboration, and the strong role that open source can play in our work.
Reuters: Pictures of the Year 2016 (Part 2)maditabalnco
This document contains 20 photos from news events around the world between January and November 2016. The photos show international events like the US presidential election, the conflict in Ukraine, the migrant crisis in Europe, the Rio Olympics, and more. They also depict human interest stories and natural phenomena from various countries.
The Six Highest Performing B2B Blog Post FormatsBarry Feldman
If your B2B blogging goals include earning social media shares and backlinks to boost your search rankings, this infographic lists the size best approaches.
1) The document discusses the opportunity for technology to improve organizational efficiency and transition economies into a "smart and clean world."
2) It argues that aggregate efficiency has stalled at around 22% for 30 years due to limitations of the Second Industrial Revolution, but that digitizing transport, energy, and communication through technologies like blockchain can help manage resources and increase efficiency.
3) Technologies like precision agriculture, cloud computing, robotics, and autonomous vehicles may allow for "dematerialization" and do more with fewer physical resources through effects like reduced waste and need for transportation/logistics infrastructure.
32 Ways a Digital Marketing Consultant Can Help Grow Your BusinessBarry Feldman
How can a digital marketing consultant help your business? In this resource we'll count the ways. 24 additional marketing resources are bundled for free.
Metric Projections to Identify Critical Points in Electric Power Systemstheijes
The identification of weak nodes and branches involved have been analyzed with different technical of analysis as: sensitivities, modal and of the singular minimum value, applying the Jacobian matrix of load flows. We show up a metric projections application to identify weak nodes and branches with more participation in the electric power system.
This report describes two experiments measuring equipotential lines and electric fields between parallel plate conductors and concentric cylindrical electrodes. In both experiments, equipotential lines were marked on conducting paper connected to an 8V power supply. The electric potential and estimated field were measured and plotted against the predictions of relevant equations. For parallel plates, the potential graph matched predictions linearly but the field graph was less accurate. For concentric cylinders, both graphs matched predictions closely except for points near the disc due to measurement limitations. The experiments supported the theoretical relationships between electric potential and field.
2-Dimensional and 3-Dimesional Electromagnetic Fields Using Finite element me...IOSR Journals
This document describes using the finite element method to model 2D and 3D electromagnetic fields. It discusses modeling a quarter section of a rectangular coaxial line with triangular elements. It describes constructing the matrices for each element and combining them to solve the overall matrix equation. The document outlines implementing FEM in MATLAB, including generating meshes, adding sources, and solving the resulting matrices. Several examples are presented of using a graphical user interface created in MATLAB to calculate fields from configurations like straight wires, bent wires, solenoids, and square loops using FEM techniques.
Power System State Estimation Using Weighted Least Squares (WLS) and Regulari...IJERA Editor
In this paper, a new formulation for power system state estimation is proposed. The formulation is based on
regularized least squares method which uses the principle of Thikonov’s regularization to overcome the
limitations of conventional state estimation methods. In this approach, the mathematical unfeasibility which
results from the lack of measurements in case of ill-posed problems is eliminated. This paper also deals with
comparison of conventional method of state estimation and proposed formulation. A test procedure based n the
variance of the estimated linearized power flows is proposed to identify the observable islands of the system.
The obtained results are compared with the results obtained by conventional WLS method
This paper presents a new fault location method for distribution systems that uses voltage sag calculations between two measurement points. The method is analyzed for both radial systems and systems with distributed generation. Simulation results show the method has average errors of 0.59% without distributed generation and 1.17% with distributed generation integrated. While this method aims to improve on previous techniques, its accuracy depends on the number of line sections modeled and it showed higher errors than reported in the analyzed paper when tested on a simulated system. In conclusion, fault location remains an important problem and different methods provide varying accuracy depending on the system configuration.
FellowBuddy.com is an innovative platform that brings students together to share notes, exam papers, study guides, project reports and presentation for upcoming exams.
We connect Students who have an understanding of course material with Students who need help.
Benefits:-
# Students can catch up on notes they missed because of an absence.
# Underachievers can find peer developed notes that break down lecture and study material in a way that they can understand
# Students can earn better grades, save time and study effectively
Our Vision & Mission – Simplifying Students Life
Our Belief – “The great breakthrough in your life comes when you realize it, that you can learn anything you need to learn; to accomplish any goal that you have set for yourself. This means there are no limits on what you can be, have or do.”
Like Us - https://www.facebook.com/FellowBuddycom
Linear regression [Theory and Application (In physics point of view) using py...ANIRBANMAJUMDAR18
Machine-learning models are behind many recent technological advances, including high-accuracy translations of the text and self-driving cars. They are also increasingly used by researchers to help in solving physics problems, like Finding new phases of matter, Detecting interesting outliers
in data from high-energy physics experiments, Founding astronomical objects are known as gravitational lenses in maps of the night sky etc. The rudimentary algorithm that every Machine Learning enthusiast starts with is a linear regression algorithm. In statistics, linear regression is a linear approach to modelling the relationship between a scalar response (or dependent variable) and one or more explanatory variables (or independent
variables). Linear regression analysis (least squares) is used in a physics lab to prepare the computer-aided report and to fit data. In this article, the application is made to experiment: 'DETERMINATION OF DIELECTRIC CONSTANT OF NON-CONDUCTING LIQUIDS'. The entire computation is made through Python 3.6 programming language in this article.
Distance Metric Based Multi-Attribute Seismic Facies Classification to Identi...Pioneer Natural Resources
Conventional reservoirs benefit from a long scientific history that correlates successful plays to seismic measurements through depositional, tectonic, and digenetic models. Unconventional reservoirs are less well understood, however benefit from significantly denser well control. Thus, allowing us to establish statistical rather than model-based correlations between seismic data, geology, and successful completion strategies. One of the more commonly encountered correlation techniques is based on computer assisted pattern recognition. The pattern recognition techniques have found their niche in a plethora of applications ranging from flagging suspicious credit card purchase patterns to rewarding repeating online buying patterns. Classification of a given seismic response as having a “good” or “bad” pattern requires a “distance metric”. Distance metric “learning” uses past experiences (well performance) as training data to develop a distance metric. Alternative distance metrics have demonstrated significant value in the identification and classification of repeated or anomalous behaviors in public health, security, and marketing. In this paper we examine the value of three of these alternative distance metrics of 3D seismic attributes to the identification of sweet spots in a Barnett Shale play.
Permanent Fault Location in Distribution System Using Phasor Measurement Unit...IJECEIAES
This paper proposes a new method for locating high impedance fault in distribution systems using phasor measurement units (PMUs) installed at certain locations of the system. To implement this algorithm, at first a new method is suggested for the placement of PMUs. Taking information from the units, voltage and current of the entire distribution system are calculated. Then, the two buses in which the fault has been occurred is determined, and location and type of the fault are identified. The main characteristics of the proposed method are: the use of distributed parameter line model in phase domain, considering the presence of literals, and high precision in calculating the high impedance fault location. The results obtained from simulations in EMTP-RV and MATLAB software indicate high accuracy and independence of the proposed method from the fault type, fault location and fault resistance compared to previous methods, so that the maximum observed error was less than 0.15%.
Low-complex Bayesian estimator for imperfect channels in massive muti-input ...IJECEIAES
Motivated by the fact that the complexity of the computations is one of the main challenges in large multiple input multiple output systems, known as massive multiple-input multiple-output (MIMO) systems, this article proposes a low-complex minimum mean squared error (MMSE) Bayesian channel estimator for uplink channels of such systems. First, we have discussed the necessity of the covariance information for the MMSE estimator and how their imperfection knowledge can affect its accuracy. Then, two reduction phases in dimension and floating-point operations have been suggested to reduce its complexity: in phase 1, eigenstructure reduction for channel covariance matrices is implemented based on some truncation rules, while in phase 2, arithmetic operations reduction for matrix multiplications in the MMSE equation is followed. The proposed procedure has significantly reduced the complexity of the MMSE estimator to the first order O(M), which is less than that required for the conventional MMSE with O(M3 ) in terms of matrix dimension. It has been shown that the estimated channels using our proposed procedure are asymptotically aligned and serve the same quality as the full-rank estimated channels. Our results are validated by averaging the normalized mean squared error (NMSE) over a length of 500 sample realizations through a Monte Carlo simulation using MATLAB R2020a.
Artificial Neural Networks for ON Line Assessment of Voltage Stability using ...IOSR Journals
This document describes using an artificial neural network (ANN) technique to assess voltage stability online in power transmission systems. The ANN model is trained to correlate voltage stability status with changing load patterns using two stability indices: the fast voltage stability index (FVSI) and line stability factor (LQF). Simulation results on the IEEE 30-bus test system and Indian 72-bus power grid show the ANN method can accurately calculate the stability indices without complex calculations and can effectively monitor voltage stability online.
1) Electromagnetic theory deals with the study of charges at rest and in motion and is fundamental to electrical engineering and physics. It is used in applications like RF communication, microwave engineering, antennas, electrical machines, and more.
2) Electromagnetic theory can be thought of as a generalization of circuit theory and is useful for situations that cannot be handled by circuit theory alone. It involves electric and magnetic field vectors rather than just voltages and currents.
3) Vector analysis is a useful mathematical tool for electromagnetic concepts. Important vector operations like addition, subtraction, scaling, dot product, and cross product are introduced. Common coordinate systems like Cartesian, cylindrical, and spherical polar coordinates are also discussed.
This document summarizes a method for calculating the sensitivity matrix that defines the linear relationship between circuit parameters and poles/response of an RLC network. The sensitivity matrix enables efficient statistical analysis and yield predictions. It is obtained by taking derivatives of the poles and transfer function, which are calculated from the eigenvalues and eigenvectors of the network's state equation. An example RLC circuit demonstrates calculating the sensitivity matrix and using it to predict yield based on Monte Carlo simulations.
Experimental Verification of the Kinematic Equations of Special Relativity an...Daniel Bulhosa Solórzano
The document experimentally verifies the kinematic equations of special relativity and determines the mass and charge of the electron. It describes an experiment that measures the momentum and kinetic energy of electrons over a range of speeds. The data is fitted to both the Newtonian and relativistic kinematic models. The relativistic model provides a much better fit and allows determining the electron charge to mass ratio and mass. The values found agree well with accepted values, supporting the validity of special relativity.
This document provides an overview of Module 3 which covers Maxwell's equations, electromagnetic waves, and optical fibers. It begins by introducing Maxwell's equations, including Gauss' law, Gauss' law for magnetism, Faraday's law, and Ampere's law. It then discusses electromagnetic waves and how they are transverse waves that can be polarized. Finally, it covers optical fibers and their propagation mechanism, modes of propagation, attenuation causes, and applications to point-to-point communication. The document provides definitions and explanations of important concepts in vector calculus and electromagnetism needed to understand Maxwell's equations and electromagnetic wave behavior.
This document summarizes a study on the asymmetry of the Maxwell-Boltzmann distribution. It was shown that the asymmetry is an inherent property that does not depend on the distribution parameters. Analytical expressions were derived for the symmetrical and asymmetrical parts of the distribution. The asymmetry parameters were calculated quantitatively. It is concluded that the asymmetry of the Maxwell-Boltzmann distribution reflects an inherent asymmetry in nature.
In this paper person identification is done based on sets of facial images. Each facial image is considered as the scattered point of logistic regression. The vertical distance of scattered point of facial image and the regression line is considered as the parameter to determine whether the image is of same person or not. The ratio of Euclidian distance (in terms of number of pixel of gray scale image based on ‘imtool’ of Matlab 13.0) between nasal and eye points are determined. The variance of the ration is considered another parameter to identify a facial image. The concept is combined with ghost image of Principal Component Analysis; where the mean square error and signal to noise ratio (SNR) in dB is considered as the parameters of detection. The combination of three methods, enhance the degree of accuracy compared to individual one.
An Approach for Power Flow Analysis of Radial Distribution Networksresearchinventy
This paper provides an easy and effective approach to the load flow solution of Radial distribution networks. As compared to the various methods proposed in the past, this work presents a new technique consisting of load flow solution of the network, facilitated by the identification of all the nodes beyond a particular branch. The proposed method is quite accurate and reliable for the system having any number of nodes. The primary target of this work is to evaluate the results with high precision and convergence.
Casimir energy for a double spherical shell: A global mode sum approachMiltão Ribeiro
In this work we study the configuration of two perfectly conducting spherical shells. This is a problem of basic importance to make possible development of experimental apparatuses that they make possible to measure the spherical Casimir effect, an open subject. We apply the mode sum method via cutoff exponential function regularization with two independent parameters: one to regularize the infinite order sum of the Bessel functions; other, to regularize the integral that becomes related, due to the argument theorem, with the infinite zero sum of the Bessel functions. We obtain a general expression of the Casimir energy as a quadrature sum. We investigate two immediate limit cases as a consistency test of the expression obtained: that of a spherical shell and that of two parallel plates. In the approximation of a thin spherical shell we obtain an expression that allows to relate our result with that of the proximity-force approximation, supplying a correction to this result.
Similar to The International Journal of Engineering and Science (IJES) (20)
Casimir energy for a double spherical shell: A global mode sum approach
The International Journal of Engineering and Science (IJES)
1. The International Journal of Engineering
And Science (IJES)
||Volu me|| 1 ||Issue|| 2 ||Pages|| 9-18 ||2012||
ISSN: 2319 – 1813 ISBN: 2319 – 1805
Metric Projections in State Estimation in Electric Power Systems
1,
Manuel Alejando López Zepeda, 2,Yoram Astudillo Baza, 3,Sergio Baruch
Barragán Gómez
Instituto Politécnico Nacional
Escuela Superior de Ingeniería Mecánica y Eléctrica
Departamento de Ingeniería Eléctrica
Av. Instituto Politécnico Nacional s/n, Unidad Profesional “Adolfo Lópe z Mateos”
Edif. 2, Col. Lindavista, Del. Gustavo A. Madero, D.F. C .P. 07738
---------------------------------------------------------Abstract-----------------------------------------------------------------
The identification of weak nodes and participation factors in branches have been analyzed with d ifferent
technical of analysis as: sensitivities, modal and of the singular min imu m value, leaving of the Jacobian matrix
of load flo ws. In this work shows up the application of metric projections for the id entification of weak nodes
and of the branches with more part icipation.
Keywords - Euclidean distance, Jacobian matrix, metric projections, metric spaces, state estimation.
----------------------------------------------------------------------------------------------------------------------------------------
Date of Sub mission: 16, November, 2012 Date of Publication : 5, December 2012
---------------------------------------------------------------------------------------------------------------------------------------
1. INTRODUCTION
Identifying weak nodes in electric power systems is a problem o f great interest because the electrical
system can reach up voltage instability and voltage collapse [1]-[3], if no relevant action is taken. Hence the
importance of identifying the nodes of the system before contingencies or demand growth. Identifying stress
peaks of the system to different scenarios of power system. Knowing weak nodes and branches with strong
participation can take action to improve the reactive power support, the margin of stability and capacity of
transmission lines. This work involves the application of metric pro jections [4] to the pro ximity of the min imu m
and maximu m distances from a given scenario with cutoff values thus identifying weak nodes and branches with
the strong participation. Traditionally the identification of weak nodes or branches are included in techniques
such as sensitivities analysis, modal analysis and the minimu m singular value, based on the analysis of the
Jacobian mat rix [5]-[7].The proposed technique performs the Jacobian analysis but from metric distances,
presenting a faster computer processing and identifying nodes weak and branches and participation. The
analysis of the distances in matrix form has been used to calculate the distances between cities, locating the
distances in matrix form and the comparison between arrays was performed. Where the measurement of
distances is performed based on the Euclidean norm [8]. It has also been used to identify leverage points in the
state estimation in electric power systems [4], [9], [10].
It is observed that there is a relat ionship between leverage points and sensitive nodes and branches as
they are generated by electrical parameters and topology of the electrical system, [4], [11], [12]. And their
structural characteristics are related to the parameters of electrical system (transmission lines, transformers).On
one side identifying atypical natures of suspicious points and on the other side weak node s and sensitive
branches are sought. In both cases, the distance of each point with respect to the total points are calculated in an
n-dimensional system.
2. M ETRIC SPAC ES
A metric space [13]-[16] is a pair where is a nonempty set and is a nonreal function defined
on , called distance or metric, and satisfies the following axio ms:
i. Non-negative:
ii. Identity of indiscernibles:
www.theijes.com The IJES Page 9
2. Metric Projections in State Estimation in Electric Power Systems
iii. Symmetry:
iv. Triangle inequality :
For a given set may define more than one metric. When the metric of the space is required, we simply speak
about the metric space although we know that it really is a pair . The elements of the call point metric
space.
2 .A DISCRETE METRIC S PACE
Given a nonempty set , we define any discrete metric on by
It’s easily verified that is a metric space.
2.B THE R EAL LINE
Let , for every . The metric axio ms are true. The set of complex
numbers with the distance function is also a metric space.
2.C EUCLIDEAN DISTANCE
There are many different ways to define the distance between two points. The distance between two
points is the length of the path connecting them. In the plane, the distance between two points and
is given by the Pythagorean Theorem.
Let , the set of all of real numbers. If and are
elements of , we define the distance:
The above formula is known as the Euclidean Distance [25]-[28], it is the shortest distance between two points,
and it’s also known as the “standard” distance between two vectors. The first three metric axio ms are check and
it can be easily verified. The triangular inequality is described as
If we rep lace the earlier inequality and , therefore , and the
inequality is described as
This last inequality is derived fro m the Cauchy-Schwarz-Buniakovsky inequality (CBS)
www.theijes.com The IJES Page 10
3. Metric Projections in State Estimation in Electric Power Systems
Indeed, using the inequality CBS we get
2.D THE S PACE
Let , the set of all the n-pairs of real nu mbers. If and are
elements of , we define the distance between and by
where p is a fixed number greater or equal to 1. The metric axio ms are true. To verify the triangle inequality
we make the same replacement, and then we show the Minkowski inequality.
[Minko wski]
For the inequality is trivial, for the proof is based on Hölder inequality, which is a generalized
version of CBS:
[Hölder]
where the numbers and satisfy the condition
To prove (8), consider the function with . Since , is an increasing
function for positive t. For those same the inverse function is defined. If we’ll chart the function ,
choosing two positive real numbers y , and marking the corresponding points in and axes, respectively,
and drawing straight parallel lines to the axes.
We’ll obtain two "triangles", limited by the lines, the axes and the curve, whose areas are
Furthermore, it is clear that meets . We write and , then
www.theijes.com The IJES Page 11
4. Metric Projections in State Estimation in Electric Power Systems
Therefore, for any positive real and , and conjugate pair we have
Substituting in (10)
And summing over the index have Hölder inequality(8).
Now we show the Minko wski inequality. Consider the identity
Replace and add over the index
Apply to each of the sums on the right of the Hölder inequality and we consider that , we find
Div iding both sides by
We get
and fro m this it follows immediately Minko wski inequality.
If in the equation (6) we obtain the Euclidean distance.
2.E MANHATTAN DISTANCE
The Manhattan distance [17]-[19] estimate the distance to be traveled to get fro m o ne point to another as if it
were a grid map. The Manhattan distance between two points is the sum of the differences in these points. The
formula for this distance between a point and a point , it’s obtained fro m
equation (6) if :
The Manhattan distance is measured in "the streets" rather than a straight line. Instead of walking directly
fro m point A to point B, with the Manhattan distance you cannot walk through the buildings, but you walk the
streets. The Manhattan distance is also known as the distance "city-blocks" or distance "taxi-cab". It is named
www.theijes.com The IJES Page 12
5. Metric Projections in State Estimation in Electric Power Systems
because it is the shortest distance that a car would t ravel in a city mov ing through the streets , as the Manhattan’s
streets (taking into account that in Manhattan there is only one-way streets and oblique streets and the real
streets only exist in the corners of the blocks).
3. LEAS T-SQUARES STATE ES TIMATION
The least-squares state estimator [20]-[23] for alternating current (AC) is based on a nonlinear model
measurements
where:
: measurement vector of dimension ,
: state vector of dimension n, where ,
:vector of the nonlinear function that relates the measurements with state vector,
: measurement error vector of dimension m,
: nu mber of measurements and state variables respectively.
The elements of are assumed to have mean equal to zero and the corresponding variance matrix is given by
. The optimality conditions are applied to the performance of , which is expressed by
where:
: Measurement residue.
Fro m equation (17) we’ll have to find the best estimate of the state vector of the system, wh ich it consist to
resolve the weighted least squares problem, that is, min imize the amount of residuals squared measures, whose
objective function can be rewritten as:
where is the element of the covariance matrix, . The optimality condition of first order for this
model can be written as:
where
It’s the Jacobian matrix of vector , of dimension . It's about finding the value of that satisfies the
linear equation (19). The most effective way to solve this equation is using the iterative method of Newton -
Raphson. Neglecting terms where second derivatives appear fro m , the linear system of equations to be
solved at each iteration is the following:
where:
www.theijes.com The IJES Page 13
6. Metric Projections in State Estimation in Electric Power Systems
where:
the measurement error variance.
The variance provides the accuracy of a particular measurement. A larger variance indicates that the
corresponding measurement is not very accurate, so it is desirable to have small variance in measurements.
4.RES ULTS
Consolidating the results from the implementation of metrics in the Jacobian matrix of the state
estimator for a test system of 5 nodes [24], with the increase of reactive power. Voltage results. We present the
results of the behavior of the voltage of each of the nodes or the nodes with higher voltage abatement present for
each of the cases, for the increased inductive reactive power, until the last convergence point for each of the
cases. At the end the mos t sensitive nodes for each case are shown. Metrics projections results. We present
metrics projections results using the Jacobian matrix of the state estimator derived fro m power flows
measurements and power injections measurements. They show the results u sing the elements and
fro m the Jacobian matrix of the state. In the last part, we present the minimu m met rics projections (MMP) for
each case.
Fig. 1 shows the voltage behavior at each node as the increase of the inductive reac tive power in node 3.
Fig. 2 and 3 show the min imu m metrics projections by nodes of the elements and of the Jacobian
matrix state estimator considering the power flow measurements.
Fig. 4 and 5 show the min imu m metrics projections by nodes of the elements and of the Jacobian
matrix state estimator considering power injections measurements.
The results that provide metrics projections should be noted that these values are normalized with the base case.
For all cases voltage profile (VP) considered for cutoff values (CV) is 0.8. A ll metrics projections are obtained
fro m the Jacobian matrix of the state estimator.
4 .A VO LTAGE R ESULTS
It shows the variation of the magnitude of the voltage in the system with the increase of the inductive reactive
power at node 3.
www.theijes.com The IJES Page 14
7. Metric Projections in State Estimation in Electric Power Systems
V vs Q
1.2
1.1
1
0.9
V
0.8
V1
V2
0.7 V3
V4
V5
0.6
0.5
-50 0 50 100 150 200 250 300
Q
Figure 1 Vo ltage variation with the increase of the inductive reactive power inductive at node 3.
4 .B METRICS PROJECTIO NS
1. We present the results of the minimu m met rics project ions by nodes of the elements of the
Jacobian matrix state estimator considering the active power flow measurements.
ACTIVE POWER FLOW MEASUREMENTS METRICS
1.1
MMP N1,N3
MMP N2
1 MMP N4,N5
CV = 0.5946
0.9
0.8
D
0.7
0.6
0.5
0.4
-50 0 50 100 150 200 250 300
Q
Figure 2 Metrics projections by nodes behavior with the
increase of the reactive power considering active power flo w measurements.
2. We present the results of the min imu m metrics project ions by nodes of the elements of the
Jacobian matrix state estimator considering the reactive power flo w measurements.
www.theijes.com The IJES Page 15
8. Metric Projections in State Estimation in Electric Power Systems
REACTIVE POWER FLOW MEASUREMENTS METRICS
1.2
1.1
1
0.9
D
0.8
MMP N1
0.7
MMP N2
MMP N3
0.6 MMP N4
MMP N5
CV= 0.7609
0.5
-50 0 50 100 150 200 250 300
Q
Figure 3 Metrics projections by nodes behavior with the
increase of the reactive power considering reactive power flow measurements.
3. We present the results of the minimu m met rics project ions by nodes of the elements of the
Jacobian matrix state estimator considering the active power injections measurements.
ACTIVE POWER INJECTIONS MEASUREMENTS METRICS
1.1
MMP N1
MMP N2
1 MMP N3,N5
MMP N4
CV = 0.6214
0.9
0.8
D
0.7
0.6
0.5
0.4
-50 0 50 100 150 200 250 300
Q
Figure 4 Metrics projections by nodes behavior with the
increase of the reactive power considering active power injections measurements.
4. We present the results of the min imu m metrics project ions by nodes of the elements of the
Jacobian matrix state estimator considering the reactive power inject ions measurements.
www.theijes.com The IJES Page 16
9. Metric Projections in State Estimation in Electric Power Systems
REACTIVE POWER INJECTIONS MEASUREMENTS METRICS
1.05
1
0.95
0.9 MMP N1
D MMP N2,N4
MMP N3
0.85 MMP N5
CV = 0.8016
0.8
0.75
0.7
-50 0 50 100 150 200 250 300
Q
Figure 5 Metrics projections by nodes behavior with the
increase of the reactive power considering reactive power in jections measurements.
4 .C ANALYSIS
Fig. 1 shows the voltage behavior at the five nodes of the system with the increase of the inductive
reactive power in the node 3, where the point of maximu m power transfer is 280 M VA R, beyond this value the
system does not converge and hence, the program gives incorrect estimates. In this figure we can identify nodes
3 and 4 as the nodes that have higher voltage depression, being near 0.6 PU at node 4, while node 3 is the most
affected reaching a value of 0.5706 PU.
Fig. 2 shows the behavior of the minimu m met rics projections by nodes usin g flow measurements
considering the elements of the Jacobian matrix. The CV is exceeded by all metrics p roject ions, the
minimu m metrics projections are regarding nodes 4 and 5 with a value of 0.4410 for both cases, performing
these projections in line 4-5 in both nodes.
Fig.3 shows the behavior of the minimu m metrics projections by nodes using flow measurements
considering the elements of the Jacobian mat rix. The VC is exceeded at 200 M VA R, the min imu m
metrics projections are regarding nodes 1 and 2 with a value of 0.5443, performing these projections in line 1-3
in node 1 and a value of 0.5510 in line 2-3.
Fig.4 shows the behavior of the minimu m metrics projections by nodes using power inject ions
measurements considering the elements of the Jacobian matrix. The CV is 0.6214 with a VP of 0.8, the
CV is exceeded at 250 M VA R, and the minimu m metrics projections are regarding nodes 2, 3 and 5 with a
value of 0.4886 in line 5-4 at node 2 and with a value of 0.5151 in line 5-4 at nodes 3 and 5.
Fig.5 shows the behavior of the minimu m metrics projections by nodes using power inject ions
measurements considering the elements of the Jacobian matrix. The VC is exceeded at 250 M VA R, the
minimu m metric projection is regarding node 3 with a value of 0.7203, performing these projection in line 5-4.
1. CONCLUS IONS
Metric projections have a similar behavior to voltage with the increasing of reactive power in one or
more nodes; it allows us to identify weak nodes of the system in a fast and reliable way, including the branches
involved. Because of the metric project ions are obtained from the Jacobian matrix of the state estimator, this
allo ws us to take into account all the parameters of the system when metrics are calculated. The metric
projections, as the state estimator, can be calculated in real time as the computational requirements by the
metrics are min imal and therefore their calcu lation is fast.
As metric pro jections are calculated between the rows of the Jacobian matrix of the state estimator
including compensator node, it let us analyse all the nodes in the system and they may alarm us in case of a
disturbance.
www.theijes.com The IJES Page 17
10. Metric Projections in State Estimation in Electric Power Systems
REFERENCES
[1] Vargas Luis S. & Cañizares Claudio A. “T ime Dependence of Controls to Avoid Voltage Collapse”, IEEE Transactions on Power
Systems, Vol 15 No 4, November 2000.,pp 1367-1375.
[2] Moghavvemi M. & Faruque M. O. “Estimation of Voltage Collapse from Local Measurement of Line Power Flow and Bus
Voltage”. Electric Power Engineering 1999. Power Tech Budapest 99 International Conference. 1999.,pp 77.
[3] Basu K.P. “Power Transfer Capability of T ransmission Line Limited by Voltage Stability: Simple Analytical Expressions”, IE EE
Power Engineering Review. Sept. 2000, Vol 20 No. 9 pp 46-47.
[4] Robles García Jaime, Técnicas avanzadas para estimación de estado robusta en sistemas eléctricos de potencia utilizando el método
de la mediana mínima cuadrada. T esis de doctorado, Inst ituto Politécnico Nacional, SEPI ESIME, México, D.F., 1996.
[5] León-Rodriguez Daniel, Evaluación de la Estabilidad de Voltaje ante disturbios pequeños mediante la Técnica de Análisis Modal.
Tesis de maestría, Instituto Politécnico Nacional, SEPI ESIME, México, D.F, 2000.
[6] Ambriz-Perez Hugo. Cálculo de acciones correctivas en sistemas eléctricos de potencia operando en estado de emergencia. T esis
de maestría, Instituto Politécnico Nacional, SEPI ESIME, México, D.F.,1992.
[7] Galicia-Cano Guillermo, Análisis de la estabilidad de voltaje en sistemas eléctricos de potencia empleando la técnica del mínimo
valor singular. Tesis de maestría, Instituto Politécnico Nacional, SEPI ESIME, México, D.F., 1999.
[8] Instrucción MSIDV/DMSIDV de la libreria IMSL de Mathlibrery de Fortran subroutines for mathematical aplications 1990-1995.
Microsoft Corporation.
[9] D. Romero, Jaime Robles. “Identificación de puntos de apalancamiento en estimación robusta de estado utilizando la distancia de
Mahalanobis”, Octava reunión de verano de sistemas de potencia, IEEE Sección México, vol. 2, Julio de 1995, pp 222-226.
[10] Robles García Jaime, Peña Sandoval Sergio & Romero Romero David, “Estimación robusta del pronóstico de la demanda de
energía electrica”. 5° CNIES, IPN, SEPI ESIME, México, D.F.,2000.
[11] L. Mili, M.G. Cheniae, P. J. Rouseseew. “Robust state estimation based on proyections statics”. IEEE transactions Power Systems,
Jan 11, 1996.
[12] Mili L. ,Phaniraj V., & Rousseuw P. J.“Least median of squares estimation in power systems”. IEEE T ransactions on Power
Systems, Vol. 9, No. 2, May 1994, pp 979-987.
[13] Carothers, N.L. Real Analysis. Cambridge University Press, 2000.
[14] Copson, e.t. Metric Spaces. Cambridge University Press, Reprint edition 1988.
[15] Giles, J.R. Introduction to the Analysis of Metric Spaces. Cambridge University Press, 1987.
[16] Shirali, Satish. Vasudeva, Harkrishan L. Metric Spaces. Springer, 2005.
[17] Krause, Eugene F. T axicab Geometry: An Adventure in Non-Euclidean Geometry. Dover Publications, 1987.
[18] Skiena, Steven. Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Perseus Books, 1990.
[19] Willard, Stephen. General Topology. Dover Publications, 2004.
[20] Masiello, R.D. Sheweppe, F.C. A Tracking Static State Estimator.IEEE Trans.On PWRS, Vol. PAS-90, March/April 1971.
[21] Schweppe, Fred C. Handschin, Edmund J.Static State Estimation in Electric Power Systems Proceedings of the IEEE, Vol. 62, No.
7, pp. 972-982, July 1974.
[22] Schweppe, Fred C et al. Power System Static-State Estimation. IEEE Transactions on Power Apparatus and Systems. Vol. PAS-89,
No. 1, Parts I/II/III, pp. 120-135, January 1970.
[23] Schweppe, F. C. Wildes, J. Rom, D. Power System Static State Estimation.Power Syst. Eng. Group, MIT Rep. 10, Nov. 1968.
[24] Stagg, Glenn W. El-Abiad, Ahmed H. Computer Methods in Power System Analysis. McGraw-Hill, New York, 1968.
[25] Gray, Alfred. Modern differential geometry of curves and surfaces with Mathematica.CRC 2nd Edition 1997.
[26] Kelley, John L. General Topology. Springer 1975.
[27] Munkers, James. Topology.Prentice Hall 2nd Edition 1999.
[28] O’Neil, Barret.Elementary Differential Geometry.Academic Press, 1966 .
Biographies
Manuel Alejandro López Zepeda. He received BsC and Masters in Electrical Eng ineering fro m ESIM E-IPN
and SEPI-ESIM E-IPN, Mexico in 2002 and 2006. He’s currently a Co mputer Science professor at ESIM E-IPN.
His research interests span state estimation in electric power systems, intelligent control and neuronal networks.
Yoram Astudillo Baza. He’s graduated of the Instituto Tecnológico de Acapulco of Electro mechanical
Engineer in 2000. Master of Science in Electrical Eng ineering fro m the Escuela Superior de Ingeniería
Mecánica y Eléctrica del Instituto Politécnico Nacional (IPN). Currently a professor of mathematics at the
department of Electrical Engineering of the ESIM E Zacatenco del IPN. His research and interest are: Analysis
and Control of Electrical Power Systems, Electrical Machines, Intelligent Control, Adaptive and Robust, Power
Generation, Cogeneration.
Sergio Baruch Barragán Gómez. He received Masters in Electrical Engineering from SEPI-ESIM E- IPN,
Mexico in 2004. He is currently a electric power systems professor at Depart ment of Electrical Engineering of
ESIM E-IPN. His research interests: open software, analysis and optimizat ion of electrical power systems.
www.theijes.com The IJES Page 18