Programação linear por partes: revisão teórica e aplicações

Procura-se resgatar a importância de uma subárea da Programação Matemática conhecida como Programação Linear Por Partes - PLP. de fato a PLP tem inúmeras aplicações tanto na área teórica como em situações reais. Este trabalho apresenta os resultados de uma pesquisa bibliográfica, efetuada nas principais revistas técnicas e livros disponíveis relacionados com Pesquisa Operacional, que visou situar o estado da'arte da Programação Linear por Partes, bem como a abrangência de sua aplicabilidade. Particularmente, no contexto da PLP, este texto deslaca a Programação em Redes Lineares por Partes devido a sua relevância em muitas situações práticas.

Test systems and mathematical models for transmission network expansion planning

The data of four networks that can be used in carrying out comparative studies with methods for transmission network expansion planning are given. These networks are of various types and different levels of complexity. The main mathematical formulations used in transmission expansion studies-transportation models, hybrid models, DC power flow models, and disjunctive models are also summarised and compared. The main algorithm families are reviewed-both analytical, combinatorial and heuristic approaches. Optimal solutions are not yet known for some of the four networks when more accurate models (e.g. The DC model) are used to represent the power flow equations-the state of the art with regard to this is also summarised. This should serve as a challenge to authors searching for new, more efficient methods.

Accountability in Smart Microgrids Based on Conservative Power Theory

Smart microgrids offer a new challenging domain for power theories and metering techniques because they include a variety of intermittent power sources which positively impact on power flow and distribution losses but may cause voltage asymmetry and frequency variation. In smart microgrids, the voltage distortion and asymmetry in presence of poly-phase nonlinear loads can be also greater than in usual distribution lines fed by the utility, thus affecting measurement accuracy and possibly causing tripping of protections. In such a context, a reconsideration of power theories is required since they form the basis for supply and load characterization. A revision of revenue metering techniques is also suggested to ensure a correct penalization of the loads for their responsibility in generating reactive power, voltage asymmetry, and distortion. This paper shows that the conservative power theory provides a suitable background to cope with smart grids characterization and metering needs. Simulation and experimental results show the properties of the proposed approach.

An implementation of modified scatter search algorithm to transmission expansion planning

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

Algorithms for network piecewise-linear programs: A comparative study

Piecewise-Linear Programming (PLP) is an important area of Mathematical Programming and concerns the minimisation of a convex separable piecewise-linear objective function, subject to linear constraints. In this paper a subarea of PLP called Network Piecewise-Linear Programming (NPLP) is explored. The paper presents four specialised algorithms for NPLP: (Strongly Feasible) Primal Simplex, Dual Method, Out-of-Kilter and (Strongly Polynomial) Cost-Scaling and their relative efficiency is studied. A statistically designed experiment is used to perform a computational comparison of the algorithms. The response variable observed in the experiment is the CPU time to solve randomly generated network piecewise-linear problems classified according to problem class (Transportation, Transshipment and Circulation), problem size, extent of capacitation, and number of breakpoints per arc. Results and conclusions on performance of the algorithms are reported.

Optimized allocation of sectionalizing switches and control and protection devices for reliability indices improvement in distribution systems

Reliability of power supply is related, among other factors, to the control and protection devices allocation in feeders of distribution systems. In this way, optimized allocation of sectionalizing switches and protection devices in strategic points of distribution circuits, improves the quality of power supply and the system reliability indices. In this work, it is presented a mixed integer non-linear programming (MINLP) model, with real and binary variables, for the sectionalizing switches and protection devices allocation problem, in strategic sectors, aimed at improving reliability indices, increasing the utilities billing and fulfilling exigencies of regulatory agencies for the power supply. Optimized allocation of protection devices and switches for restoration, allows that those faulted sectors of the system can be isolated and repaired, re-managing loads of the analyzed feeder into the set of neighbor feeders. Proposed solution technique is a Genetic Algorithm (GA) developed exploiting the physical characteristics of the problem. Results obtained through simulations for a real-life circuit, are presented. © 2004 IEEE.

Comparison of algorithms for loss allocation in transmission networks considering power redispatch

An analysis of the performances of three important methods for generators and loads loss allocation is presented. The discussed methods are: based on pro-rata technique; based on the incremental technique; and based on matrices of circuit. The algorithms are tested considering different generation conditions, using a known electric power system: IEEE 14 bus. Presented and discussed results verify: the location and the magnitude of generators and loads; the possibility to have agents well or poorly located in each network configuration; the discriminatory behavior considering variations in the power flow in the transmission lines. © 2004 IEEE.

Effects of the thyristor controlled serie capacitor on the electric power system

This work deals with the effects of the series compensation on the electric power system for small-signal stability studies. Therefore, the system is modeled admitting the existence of the compensation and then, the equations are linearized and a linear model is obtained for a single machine-infinite bus power system with a compensator installed. The resulting model with nine defined constants is very similar to the Heffron & Phillips linear model widely used on the existent literature. Finally, simulations are executed for an example system, to analyze the behavior of these constants when loading the system. © 2004 IEEE.

Planning of secondary distribution circuits through evolutionary algorithms

In this work, the planning of secondary distribution circuits is approached as a mixed integer nonlinear programming problem (MINLP). In order to solve this problem, a dedicated evolutionary algorithm (EA) is proposed. This algorithm uses a codification scheme, genetic operators, and control parameters, projected and managed to consider the specific characteristics of the secondary network planning. The codification scheme maps the possible solutions that satisfy the requirements in order to obtain an effective and low-cost projected system-the conductors' adequate dimensioning, load balancing among phases, and the transformer placed at the center of the secondary system loads. An effective algorithm for three-phase power flow is used as an auxiliary methodology of the EA for the calculation of the fitness function proposed for solutions of each topology. Results for two secondary distribution circuits are presented, whereas one presents radial topology and the other a weakly meshed topology. © 2005 IEEE.

Optimal Boussinesq model for shallow-water waves interacting with a microstructure

In this paper, we consider the propagation of water waves in a long-wave asymptotic regime, when the bottom topography is periodic on a short length scale. We perform a multiscale asymptotic analysis of the full potential theory model and of a family of reduced Boussinesq systems parametrized by a free parameter that is the depth at which the velocity is evaluated. We obtain explicit expressions for the coefficients of the resulting effective Korteweg-de Vries (KdV) equations. We show that it is possible to choose the free parameter of the reduced model so as to match the KdV limits of the full and reduced models. Hence the reduced model is optimal regarding the embedded linear weakly dispersive and weakly nonlinear characteristics of the underlying physical problem, which has a microstructure. We also discuss the impact of the rough bottom on the effective wave propagation. In particular, nonlinearity is enhanced and we can distinguish two regimes depending on the period of the bottom where the dispersion is either enhanced or reduced compared to the flat bottom case. © 2007 The American Physical Society.

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.

Planeamiento de la expansión de sistemas de transmisión considerando contingencias y demanda incierta

This paper presents a methodology and a mathematical model to solve the expansion planning problem that takes into account the effect of contingencies in the planning stage, and considers the demand as a stochastic variable within a specified range. In this way, it is possible to find a solution that minimizes the investment costs guarantying reliability and minimizing future load shedding. The mathematical model of the expansion planning can be represented by a mixed integer nonlinear programming problem. To solve this problem a specialized Genetic Algorithm combined with Linear Programming was implemented.

Integrated planning of electric power distribution networks

In this work, a heuristic model for integrated planning of primary distribution network and secondary distribution circuits is proposed. A Tabu Search (TS) algorithm is employed to solve the planning of primary distribution networks. Evolutionary Algorithms (EA) are used to solve the planning model of secondary networks. The planning integration of both networks is carried out by means a constructive heuristic taking into account a set of integration alternatives between these networks. These integration alternatives are treated in a hierarchical way. The planning of primary networks and secondary distribution circuits is carried out based on assessment of the effects of the alternative solutions in the expansion costs of both networks simultaneously. In order to evaluate this methodology, tests were performed for a real-life distribution system taking into account the primary and secondary networks.

Flujo de potencia AC descentralizado para sistemas de potencia multi-área usando un método de descomposición basado en relajación Lagrangiana

A decentralized solution method to the AC power flow problem in power systems with interconnected areas is presented. The proposed methodology allows finding the operation point of a particular area without explicit knowledge of network data of adjacent areas, being only necessary to exchange border information related to the interconnection lines between areas. The methodology is based on the decomposition of the first-order optimality conditions of the AC power flow, which is formulated as a nonlinear programming problem. A 9-bus didactic system, the IEEE Three Area RTS-96 and the IEEE 118 bus test systems are used in order to show the operation and effectiveness of the distributed AC power flow.

Power Oscillation index - A tool for investigation into unbalance phenomena in the distribution Networks

Unbalance and harmonics are two major distortions in the three-phase distribution systems. In this paper an investigation into unbalance phenomena in the distribution networks using instantaneous space vector theory, is presented. Power oscillation index (POI) and effective power factor (PFe) are calculated in the network nodes for several unbalance loading conditions. For system analysis a general power flow algorithm for three-phase four-wire radial distribution networks, based on backward-forward technique, is applied. Results obtained from several case studies using medium and low voltage test feeder with unbalanced load, are presented and discussed. © 2010 Praise Worthy Prize S.r.l. - All rights reserved.