A constructive heuristic algorithm to Short Term Transmission Network Expansion Planning

In this paper a method for solving the Short Term Transmission Network Expansion Planning (STTNEP) problem is presented. The STTNEP is a very complex mixed integer nonlinear programming problem that presents a combinatorial explosion in the search space. In this work we present a constructive heuristic algorithm to find a solution of the STTNEP of excellent quality. In each step of the algorithm a sensitivity index is used to add a circuit (transmission line or transformer) to the system. This sensitivity index is obtained solving the STTNEP problem considering as a continuous variable the number of circuits to be added (relaxed problem). The relaxed problem is a large and complex nonlinear programming and was solved through an interior points method that uses a combination of the multiple predictor corrector and multiple centrality corrections methods, both belonging to the family of higher order interior points method (HOIPM). Tests were carried out using a modified Carver system and the results presented show the good performance of both the constructive heuristic algorithm to solve the STTNEP problem and the HOIPM used in each step.

Branch and bound algorithm for transmission network expansion planning using DC model

This paper presents an algorithm to solve the network transmission system expansion planning problem using the DC model which is a mixed non-linear integer programming problem. The major feature of this work is the use of a Branch-and-Bound (B&B) algorithm to directly solve mixed non-linear integer problems. An efficient interior point method is used to solve the non-linear programming problem at each node of the B&B tree. Tests with several known systems are presented to illustrate the performance of the proposed method. ©2007 IEEE.

Heuristic algorithm to solve the short term transmission network expansion planning

In this paper, a method for solving the short term transmission network expansion planning problem is presented. This is a very complex mixed integer nonlinear programming problem that presents a combinatorial explosion in the search space. In order to And a solution of excellent quality for this problem, a constructive heuristic algorithm is presented in this paper. In each step of the algorithm, a sensitivity index is used to add a circuit (transmission line or transformer) or a capacitor bank (fixed or variable) to the system. This sensitivity index is obtained solving the problem considering the numbers of circuits and capacitors banks to be added (relaxed problem), as continuous variables. The relaxed problem is a large and complex nonlinear programming and was solved through a higher order interior point method. The paper shows results of several tests that were performed using three well-known electric energy systems in order to show the possibility and the advantages of using the AC model. ©2007 IEEE.

Higher order ionospheric effects in GNSS positioning in the European region

After removal of the Selective Availability in 2000, the ionosphere became the dominant error source for Global Navigation Satellite Systems (GNSS), especially for the high-accuracy (cm-mm) demanding applications like the Precise Point Positioning (PPP) and Real Time Kinematic (RTK) positioning.The common practice of eliminating the ionospheric error, e. g. by the ionosphere free (IF) observable, which is a linear combination of observables on two frequencies such as GPS L1 and L2, accounts for about 99% of the total ionospheric effect, known as the first order ionospheric effect (Ion1). The remaining 1% residual range errors (RREs) in the IF observable are due to the higher - second and third, order ionospheric effects, Ion2 and Ion3, respectively. Both terms are related with the electron content along the signal path; moreover Ion2 term is associated with the influence of the geomagnetic field on the ionospheric refractive index and Ion3 with the ray bending effect of the ionosphere, which can cause significant deviation in the ray trajectory (due to strong electron density gradients in the ionosphere) such that the error contribution of Ion3 can exceed that of Ion2 (Kim and Tinin, 2007).The higher order error terms do not cancel out in the (first order) ionospherically corrected observable and as such, when not accounted for, they can degrade the accuracy of GNSS positioning, depending on the level of the solar activity and geomagnetic and ionospheric conditions (Hoque and Jakowski, 2007). Simulation results from early 1990s show that Ion2 and Ion3 would contribute to the ionospheric error budget by less than 1% of the Ion1 term at GPS frequencies (Datta-Barua et al., 2008). Although the IF observable may provide sufficient accuracy for most GNSS applications, Ion2 and Ion3 need to be considered for higher accuracy demanding applications especially at times of higher solar activity.This paper investigates the higher order ionospheric effects (Ion2 and Ion3, however excluding the ray bending effects associated with Ion3) in the European region in the GNSS positioning considering the precise point positioning (PPP) method. For this purpose observations from four European stations were considered. These observations were taken in four time intervals corresponding to various geophysical conditions: the active and quiet periods of the solar cycle, 2001 and 2006, respectively, excluding the effects of disturbances in the geomagnetic field (i.e. geomagnetic storms), as well as the years of 2001 and 2003, this time including the impact of geomagnetic disturbances. The program RINEX_HO (Marques et al., 2011) was used to calculate the magnitudes of Ion2 and Ion3 on the range measurements as well as the total electron content (TEC) observed on each receiver-satellite link. The program also corrects the GPS observation files for Ion2 and Ion3; thereafter it is possible to perform PPP with both the original and corrected GPS observation files to analyze the impact of the higher order ionospheric error terms excluding the ray bending effect which may become significant especially at low elevation angles (Ioannides and Strangeways, 2002) on the estimated station coordinates.

Interior point method for long-term generation scheduling of large-scale hydrothermal systems

This paper presents an interior point method for the long-term generation scheduling of large-scale hydrothermal systems. The problem is formulated as a nonlinear programming one due to the nonlinear representation of hydropower production and thermal fuel cost functions. Sparsity exploitation techniques and an heuristic procedure for computing the interior point method search directions have been developed. Numerical tests in case studies with systems of different dimensions and inflow scenarios have been carried out in order to evaluate the proposed method. Three systems were tested, with the largest being the Brazilian hydropower system with 74 hydro plants distributed in several cascades. Results show that the proposed method is an efficient and robust tool for solving the long-term generation scheduling problem.

An adaptation of the dual-affine interior point method for the surface flatness problem

This paper presents an adaptation of the dual-affine interior point method for the surface flatness problem. In order to determine how flat a surface is, one should find two parallel planes so that the surface is between them and they are as close together as possible. This problem is equivalent to the problem of solving inconsistent linear systems in terms of Tchebyshev's norm. An algorithm is proposed and results are presented and compared with others published in the literature. (C) 2006 Elsevier B.V. All rights reserved.

Multiple-time higher-order perturbation analysis of the regularized long-wavelength equation

By considering the long-wavelength limit of the regularized long wave (RLW) equation, we study its multiple-time higher-order evolution equations. As a first result, the equations of the Korteweg-de Vries hierarchy are shown to play a crucial role in providing a secularity-free perturbation theory in the specific case of a solitary-wave solution. Then, as a consequence, we show that the related perturbative series can be summed and gives exactly the solitary-wave solution of the RLW equation. Finally, some comments and considerations are made on the N-soliton solution, as well as on the limitations of applicability of the multiple-scale method in obtaining uniform perturbative series.

Optimal power flow via interior-exterior method

This paper presents a new approach to the resolution of the Optimal Power Flow problem. In this approach the inequality constraints are treated by the Modified Barrier and Primal-Dual Logarithmic Barrier methods. The inequality constraints are transformed into equalities by introducing positive auxiliary variables, which are perturbed by the barrier parameter. A Lagrangian function is associated with the modified problem. The first-order necessary conditions are applied to the Lagrangian, generating a nonlinear system which is solved by Newton's method. The perturbation of the auxiliary variables results in an expansion of the feasible set of the original problem, allowing the limits of the inequality constraints to be reached. Numerical tests on the Brazilian CESP and South-Southeast systems and a comparative test indicated that the new approach efficiently resolves of the Optimal Power Flow problem. © 2007 IEEE.

Solving the multiobjective environmental/economic dispatch problem using weighted sum and ε-constraint strategies and a predictor-corrector primal-dual interior point method

This paper proposes a technique for solving the multiobjective environmental/economic dispatch problem using the weighted sum and ε-constraint strategies, which transform the problem into a set of single-objective problems. In the first strategy, the objective function is a weighted sum of the environmental and economic objective functions. The second strategy considers one of the objective functions: in this case, the environmental function, as a problem constraint, bounded above by a constant. A specific predictor-corrector primal-dual interior point method which uses the modified log barrier is proposed for solving the set of single-objective problems generated by such strategies. The purpose of the modified barrier approach is to solve the problem with relaxation of its original feasible region, enabling the method to be initialized with unfeasible points. The tests involving the proposed solution technique indicate i) the efficiency of the proposed method with respect to the initialization with unfeasible points, and ii) its ability to find a set of efficient solutions for the multiobjective environmental/economic dispatch problem.

Resonant excitation of Mn local vibrational modes in the higher order Raman spectra of nanocrystalline Ga(1-x)Mn(x)N films

The effect of manganese on the vibrational properties of Ga(1-x)Mn(x)N (0 <= x <= 0.18) films has been investigated by Raman scattering using 488.0 and 632.8 nm photon excitations. The first-order transverse and longitudinal optical GaN vibrational bands were observed in the whole composition range using both excitations, while the corresponding overtones, as well as a prominent peak located in 1238 cm(-1) (153.5 meV) were only observed in the Mn-containing films under 488.0 nm excitation. We propose that the peak observed at 1238 cm(-1) is due to resonant Mn local vibrational modes, the excitation process being related to electronic transitions involving the Mn acceptor band.

Predictor-Corrector Primal-Dual Interior Point Method for Solving Economic Dispatch Problems: A Postoptimization Analysis

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Security constrained optimal active power flow via network model and interior point method

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Generalization of the Hamilton-Jacobi approach for higher-order singular systems

We generalize the Hamilton-Jacobi formulation for higher-order singular systems and obtain the equations of motion as total differential equations. To do this we first study the constraints structure present in such systems.

A symmetry reduction technique for higher order Painleve systems

The symmetry reduction of higher order Painleve systems is formulated in terms of Dirac procedure. A set of canonical variables that admit Dirac reduction procedure is proposed for Hamiltonian structures governing the A(2M)((1)) and A(2M-1)((1)) Painleve systems for M = 2,3,.... (C) 2012 Elsevier B.V. All rights reserved.

Gauge formulation for higher order gravity

This work is an application of the second order gauge theory for the Lorentz group, where a description of the gravitational interaction is obtained that includes derivatives of the curvature. We analyze the form of the second field strength, G=partial derivative F+fAF, in terms of geometrical variables. All possible independent Lagrangians constructed with quadratic contractions of F and quadratic contractions of G are analyzed. The equations of motion for a particular Lagrangian, which is analogous to Podolsky's term of his generalized electrodynamics, are calculated. The static isotropic solution in the linear approximation was found, exhibiting the regular Newtonian behavior at short distances as well as a meso-large distance modification.