Eigenvalue analyses of two parallel lines using a single real transformation matrix

For a typical non-symmetrical system with two parallel three phase transmission lines, modal transformation is applied using some examples of single real transformation matrices. These examples are applied searching an adequate single real transformation matrix to two parallel three phase transmission line systems. The analyses are started with the eigenvector and eigenvalue studies, using Clarke's transformation or linear combinations of Clarke's elements. The Z C and parameters are analyzed for the case that presents the smallest errors between the exact eigenvalues and the single real transformation matrix application results. The single real transformation determined for this case is based on Clarke's matrix and its main characteristic is the use of a unique homopolar reference. So, the homopolar mode becomes a connector mode between the two three-phase circuits of the analyzed system. ©2005 IEEE.

Identifying multiple interacting bad data in power system state estimation

This paper presents an intelligent search strategy for the conforming bad data errors identification in the generalized power system state estimation, by using the tabu search meta heuristic. The main objective is to detect critical errors involving both analog and topology errors. These errors are represented by conforming errors, whose nature affects measurements that actually do not present bad data and also the conventional bad data identification strategies based on the normalized residual methods. ©2005 IEEE.

Critical speed and endurance capacity in young swimmers: Effects of gender and age

This study analyzed the relationship between critical speed (CS) and maximal speed for 30 min (S30) in swimmers of ages 10-15 years. Fifty-one swimmers were divided by chronological age (10-12 years = G10-12, 13-15 years = G13-15), sexual maturation (pubic hair stages; P1-P3 and P4-P5), and gender (M = boys, F = girls). The CS was determined through the slope of the linear regression between the distances (100, 200, and 400 m) and participants' respective times. CS and S30 were similar in the younger (G10-12M = 0.97 vs. 0.97 m/s, and G10-12F = 1.01 vs. 0.97 m/s, respectively), and older swimmers (G13-15M = 1.10 vs. 1.07 m/s and G13-15F = 0.93 vs. 0.91 m/s, respectively). In conclusion, the CS can be used in young swimmers for the evaluation of aerobic capacity, independent of gender and age. © 2005 Human Kinetics, Inc.

A procedure to estimate parameters of a line segment taking into account its representation through π circuits: Theoretical development

The objective of this paper is to show an alternative methodology to estimate per unit length parameters of a line segment of a transmission line. With this methodology the line segment parameters can be obtained starting from the phase currents and voltages in receiving and sending end of the line segment. If the line segment is represented as being one or more π circuits whose frequency dependent parameters are considered lumped, its impedance and admittance can be easily expressed as functions of the currents and voltages at the sending and receiving end. Because we are supposing that voltages and currents at the sending and receiving end of the line segment (in frequency domain) are known, it is possible to obtains its impedance and admittance and consequently its per unit length longitudinal and transversal parameters. The procedure will be applied to estimate the longitudinal and transversal parameters of a small segment of a single-phase line that is already built. © 2006 IEEE.

Genetic algorithm of chu and beasley for static and multistage transmission expansion planning

In this paper the genetic algorithm of Chu and Beasley (GACB) is applied to solve the static and multistage transmission expansion planning problem. The characteristics of the GACB, and some modifications that were done, to efficiently solve the problem described above are also presented. Results using some known systems show that the GACB is very efficient. To validate the GACB, we compare the results achieved using it with the results using other meta-heuristics like tabu-search, simulated annealing, extended genetic algorithm and hibrid algorithms. © 2006 IEEE.

Modal representation of three-phase lines applying two transformation matrices: Evaluation of its eigenvectors

The objective of this paper is to show an alternative representation in time domain of a non-transposed three-phase transmission line decomposed in its exact modes by using two transformation matrices. The first matrix is Clarke's matrix that is real, frequency independent, easily represented in computational transient programs (EMTP) and separates the line into Quasi-modes α, β and zero. After that, Quasi-modes a and zero are decomposed into their exact modes by using a modal transformation matrix whose elements can be synthesized in time domain through standard curve-fitting techniques. The main advantage of this alternative representation is to reduce the processing time because a frequency dependent modal transformation matrix of a three-phase line has nine elements to be represented in time domain while a modal transformation matrix of a two-phase line has only four elements. This paper shows modal decomposition process and eigenvectors of a non-transposed three-phase line with a vertical symmetry plane whose nominal voltage is 440 kV and line length is 500 km. ©2006 IEEE.

Some considerations about a new procedure to derive transmission line parameters concerning three-phase lines

The paper shows an alternative methodology to calculate transmission line parameters per unit length and to apply it in a three-phase line with a vertical symmetry plane. This procedure is derived from a general procedure where the modal transformation matrix of the line is required. In this paper, the unknown modal transformation matrix requested by general procedure is substituted by Clarke's matrix. With the substitution that is shown in the paper, the transmission line parameters can be obtained starting from impedances measured in one terminal of the line. First, the article shows the classical methodology to calculate frequency dependent transmission line parameters by using Carson and Pollaczeck's equations for representing the ground effect and Bessel's functions to represent the skin effect. After that, a new procedure is shown to calculate frequency dependent transmission line parameters directly from currents and voltages of an existing line. Then, this procedure is applied in a non-transposed three-phase transmission line whose parameters have been previously calculated by using the classical methodology. Finally, the results obtained by using the new procedure and by using the classical methodology are compared. The article shows simulation results for typical frequency spectra of switching transients (10 Hz to 10 kHz). Results have shown that procedure has © 2006 IEEE.

Consumer behavior after the Brazilian power rationing in 2001

In June 2001, after a dry period, the level of the water reservoirs in Brazil was below their operational levels. This situation, combined with other historical factors, led the country into a period of power rationing. As expected, power consumption lowered during this period. After December 2001, when the power rationing ended, electrical utilities expected to return to their normal power consumption in a matter of months, but the level of power consumption only returned to its level around years 2004 2005. Consumer behavior went through a change during this period, and the consumers kept this behavior after, leading to electrical and economical consequences until today. This paper presents an analysis of several factors that led to these events, including historical consumption data and comparisons with similar situations. The objective of this analysis is to give helpful information to electrical utilities, that could deal with similar situations, in their load forecasting studies. © 2006 IEEE.

Investigation of the relationship between load and loss factors for a Brazilian electric utility

With the considerable increase of the losses in electric utilities of developing countries, such as Brazil, there is an investigation for loss calculation methodologies, considering both technical (inherent of the system) and non-technical (usually associated to the electricity theft) losses. In general, all distribution networks know the load factor, obtained by measuring parameters directly from the network. However, the loss factor, important for the energy loss cost calculation, can only be obtained in a laborious way. Consequently, several formulas have been developed for obtaining the loss factor. Generally, it is used the expression that relates both factors, through the use of a coefficient k. Last reviews introduce a range of factor k within 0.04 - 0.30. In this work, an analysis with real life load curves is presented, determining new values for the coefficient k in a Brazilian electric utility. © 2006 IEEE.

Substitution-newton-Raphson method for the solution of electric network equations

The power flow problem, in transmission networks, has been well solved, for most cases, using Newton-Raphson method (NR) and its decoupled versions. Generally speaking, the solution of a non-linear system of equations refers to two methods: NR and Successive Substitution. The proposal of this paper is to evaluate the potential of the Substitution-Newton-Raphson Method (SNR), which combines both methods, on the solution of the power flow problem. Simulations were performed using a two-bus test network in order to observe the characteristics of these methods. It was verified that the NR is faster than SNR, in terms of convergence, considering non-stressed scenarios. For those cases where the power flow in the network is closed to the limits (stressed system), the SNR converges faster. This paper presents the power flow formulation of the SNR and describes its potential for its application in special cases such as stressed scenarios. © 2006 IEEE.

Sensitivity analysis for overload-relief in transmission lines using an implicitly coupled method (CRIC)

The restructuring of energy markets to provide free access to the networks and the consequent increase of the number of power transactions has been causing congestions in transmission systems. As consequence, the networks suffer overloads in a more frequent way. One parameter that has strong influence on transfer capability is the reactive power flow. A sensitivity analysis can be used to find the best solution to minimize the reactive power flows and relief, the overload in one transmission line. The proposed methodology consists on the computation of two sensitivities based on the use of the Lc matrix from CRIC (Constant Reactive Implicitly Coupled) power flow method, that provide a set of actions to reduce the reactive power flow and alleviate overloads in the lines: (a) sensitivity between reactive power flow in lines and reactive power injections in the buses, (b) sensitivity between reactive power flow in lines and transformer's taps. © 2006 IEEE.

Correction procedure applied to a single real transformation matrix -Untransposed three-phase transmission line cases

Clarke's matrix has been used as an eigenvector matrix for transposed three-phase transmission lines and it can be applied as a phase-mode transformation matrix for transposed cases. Considering untransposed three-phase transmission lines, Clarke's matrix is not an exact eigenvector matrix. In this case, the errors related to the diagonal elements of the Z and Y matrices can be considered negligible, if these diagonal elements are compared to the exact elements in domain mode. The mentioned comparisons are performed based on the error and frequency scan analyses. From these analyses and considering untransposed asymmetrical three-phase transmission lines, a correction procedure is determined searching for better results from the Clarke's matrix use as a phase-mode transformation matrix. Using the Clarke's matrix, the relative errors of the eigenvalue matrix elements can be considered negligible and the relative values of the off-diagonal elements are significant. Applying the corrected transformation matrices, the relative values of the off-diagonal elements are decreased. The comparisons among the results of these analyses show that the homopolar mode is more sensitive to the frequency influence than the two other modes related to three-phase lines. © 2006 IEEE.

Artificial immune systems applied to optimal capacitor placement in radial distribution networks

The capacitor placement problem for radial distribution networks aims to determine capacitor types, sizes, locations and control scheme. This is a combinatorial problem that can be formulated as a mixed integer nonlinear program. The paper presents an algorithm inspired in artificial immune systems and developed for this specific problem. A good performance was obtained through experimental tests applied to known systems. © 2006 IEEE.

Reliability assessment of energy limited systems using sequential montecarlo simulation

This paper explains why the reliability assessment of energy limited systems requires more detailed models for primary generating resources availability, internal and external generating dispatch and customer demand than the ones commonly used for large power systems and presents a methodology based on the full sequential Montecarlo simulation technique with AC power flow for their long term reliability assessment which can properly include these detailed models. By means of a real example, it is shown how the simplified modeling traditionally used for large power systems leads to pessimistic predictions if it is applied to an energy limited system and also that it cannot predict all the load point adequacy problems. © 2006 IEEE.

Evaluating the effects of high penetrations of roof-top wind Turbines on secondary distribution circuits

Incentives for using wind power and the increasing price of energy might generate in a relatively short time a scenario where low voltage customers opt to install roof-top wind turbines. This paper focuses on evaluating the effects of such situation in terms of energy consumption, loss reduction, reverse power flow and voltage profiles. Various commercially-available roof-top wind turbines are installed in two secondary distribution circuits considering real-life wind speed data and seasonal load demand. Results are presented and discussed. © 2006 IEEE.