A geometric interpretation for transmission real losses minimization through the optimal power flow and its influence on voltage collapse

This work presents an approach for geometric solution of an optimal power flow (OPF) problem for a two bus system (a slack and a PV busses). Additionally, the geometric relationship between the losses minimization and the increase of the reactive margin and, therefore, the maximum loading point, is shown. The algebraic equations for the calculation of the Lagrange multipliers and for the minimum losses value are obtained. These equations are used to validate the results obtained using an OPF program. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Multistage and coordinated planning of the expansion of transmission systems

In this paper, an efficient genetic algorithm (GA) is presented to solve the problem of multistage and coordinated transmission expansion planning. This is a mixed integer nonlinear programming problem, difficult for systems of medium and large size and high complexity. The GA presented has a set of specialized genetic operators and an efficient form of generation of the initial population that finds high quality suboptimal topologies for large size and high complexity systems. In these systems, multistage and coordinated planning present a lower investment than static planning. Tests results are shown in one medium complexity system and one large size high complexity system.

Reactive Control for Transmission Overload Relief Based on Sensitivity Analysis and Cooperative Game Theory

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Efficient method for AC transmission network expansion planning

A combinatorial mathematical model in tandem with a metaheuristic technique for solving transmission network expansion planning (TNEP) using an AC model associated with reactive power planning (RPP) is presented in this paper. AC-TNEP is handled through a prior DC model while additional lines as well as VAr-plants are used as reinforcements to cope with real network requirements. The solution of the reinforcement stage can be obtained by assuming all reactive demands are supplied locally to achieve a solution for AC-TNEP and by neglecting the local reactive sources, a reactive power planning (RPP) will be managed to find the minimum required reactive power sources. Binary GA as well as a real genetic algorithm (RCA) are employed as metaheuristic optimization techniques for solving this combinatorial TNEP as well as the RPP problem. High quality results related with lower investment costs through case studies on test systems show the usefulness of the proposal when working directly with the AC model in transmission network expansion planning, instead of relaxed models. (C) 2010 Elsevier B.V. All rights reserved.

A Strategy to Solve the Multistage Transmission Expansion Planning Problem

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Efficient procedure to evaluate electromagnetic transients on three-phase transmission lines

This paper presents a hybrid way mixing time and frequency domain for transmission lines modelling. The proposed methodology handles steady fundamental signal mixed with fast and slow transients, including impulsive and oscillatory behaviour. A transmission line model is developed based on lumped elements representation and state-space techniques. The proposed methodology represents an easy and practical procedure to model a three-phase transmission line directly in time domain, without the explicit use of inverse transforms. The proposed methodology takes into account the frequency-dependent parameters of the line, considering the soil and skin effects. In order to include this effect in the state matrices, a fitting method is applied. Furthermore the accuracy of proposed the developed model is verified, in frequency domain, by a simple methodology based on line distributed parameters and transfer function related to the input/output signals of the lumped parameters representation. In addition, this article proposes the use of a fast and robust analytic integration procedure to solve the state equations, enabling transient and steady-state simulations. The results are compared with those obtained by the commercial software Microtran (EMTP), taking into account a three-phase transmission line, typical in the Brazilian transmission system.

Proposal of an alternative transmission line model for symmetrical and asymmetrical configurations

This article shows a transmission line model for simulation of fast and slow transients, applied to symmetrical or asymmetrical configurations. A transmission line model is developed based on lumped elements representation and state-space techniques. The proposed methodology represents a practical procedure to model three-phase transmission lines directly in time domain, without the explicit or implicit use of inverse transforms. In three-phase representation, analysis modal techniques are applied to decouple the phases in their respective propagation modes, using a correction procedure to set a real and constant matrix for untransposed lines with or without vertical symmetry plane. The proposed methodology takes into account the frequency-dependent parameters of the line and in order to include this effect in the state matrices, a fitting procedure is applied. To verify the accuracy of the proposed state-space model in frequency domain, a simple methodology is described based on line distributed parameters and transfer function associated with input/output signals of the lumped parameters representation. In addition, this article proposes the use of a fast and robust integration procedure to solve the state equations, enabling transient and steady-state simulations. The results obtained by the proposed methodology are compared with several established transmission line models in EMTP, taking into account an asymmetrical three-phase transmission line. The principal contribution of the proposed methodology is to handle a steady fundamental signal mixed with fast and slow transients, including impulsive and oscillatory behavior, by a practical procedure applied directly in time domain for symmetrical or asymmetrical representations. (C) 2011 Elsevier Ltd. All rights reserved.

Alternative Model of Three-Phase Transmission Line Theory-Based Modal Decomposition

In this paper is shown the development of a transmission line, based on discrete circuit elements that provide responses directly in the time domain and phase. This model is valid for ideally transposed rows represent the phases of each of the small line segments are separated in their modes of propagation and the voltage and current are calculated at the modal field. However, the conversion phase-mode-phase is inserted in the state equations which describe the currents and voltages along the line of which there is no need to know the user of the model representation of the theory in the field lines modal.

Corona Discharge Model for Transmission Lines by Lumped Elements

This paper shows the insertion of corona effect in a transmission line model based on lumped elements. The development is performed considering a frequency-dependent line representation by cascade of pi sections and state equations. Hence, the detailed profile of currents and voltages along the line, described from a non-homogeneous system of differential equations, can be obtained directly in time domain applying numerical or analytic solution integration methods. The corona discharge model is also based on lumped elements and is implemented from the well-know Skilling-Umoto Model.

Proposal of a Transmission Line Model Based on Lumped Elements: An Analytic Solution

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A Bilevel Approach to Transmission Expansion Planning Within a Market Environment

We present a bilevel model for transmission expansion planning within a market environment, where producers and consumers trade freely electric energy through a pool. The target of the transmission planner, modeled through the upper-level problem, is to minimize network investment cost while facilitating energy trading. This upper-level problem is constrained by a collection of lower-level market clearing problems representing pool trading, and whose individual objective functions correspond to social welfare. Using the duality theory the proposed bilevel model is recast as a mixed-integer linear programming problem, which is solvable using branch-and-cut solvers. Detailed results from an illustrative example and a case study are presented and discussed. Finally, some relevant conclusions are drawn.

Single real transformation matrices applied to double three-phase transmission lines

Single real transformation matrices are tested as phase-mode transformation matrices of typical symmetrical systems with double three-phase and two parallel double three-phase transmission lines. These single real transformation matrices are achieved from eigenvector matrices of the mentioned systems and they are based on Clarke's matrix. Using linear combinations of the Clarke's matrix elements, the techniques applied to the single three-phase lines are extended to systems with 6 or 12 phase conductors. For transposed double three-phase lines, phase Z and Y matrices are changed into diagonal matrices in mode domain. Considering non-transposed cases of double three-phase lines, the results are not exact and the error analyses are performed using the exact eigenvalues. In case of two parallel double three-phase lines, the exact single real transformation matrix has not been obtained yet. Searching for this exact matrix, the analyses are based on a single homopolar reference. For all analyses in this paper, the homopolar mode is used as the only homopolar reference for all phase conductors of the studied system. (C) 2008 Elsevier B.V. All rights reserved.

Analysis of the Electrical Characteristics of an Alternative Solution for the Brazilian-Amazon Transmission System

This article analyzes the electrical parameters of a 3-phase transmission line using a 280-m-high steel tower that has been proposed for the Amazon transmission system in Brazil. The height of the line conductors and the distance between them are intrinsically related to the longitudinal and transverse parameters of the line. Hence, an accurate study is carried out in order to show the electrical variations between a transmission line using the new technology and a conventional 3-phase 440-kV line, considering a wide range of frequencies and variable soil resistivity. First, a brief review of the fundamental theory of line parameters is presented. In addition, by using a digital line model, simulations are carried out in the time domain to analyze possible and critical over-voltage transients on the proposed line representation.

Evaluation of hybrid models for static and multistage transmission system planning

Neste trabalho é analisada a aplicação de algoritmos heurísticos para o Modelo Híbrido Linear - Hybrid Linear Model (HLM) - no problema de planejamento da expansão de sistemas de transmissão. O HLM é um modelo relaxado que ainda não foi suficientemente explorado. Assim, é realizada uma análise das características do modelo matemático e das técnicas de solução que podem ser usadas para resolver este tipo de modelo. O trabalho analisa em detalhes um algoritmo heurístico construtivo para o HLM e faz uma extensão da modelagem e da técnica de solução para o planejamento multi-estágio da expansão de sistemas de transmissão. Dentro deste contexto, também é realizada uma avaliação da qualidade das soluções encontradas pelo HLM e as possibilidades de aplicação deste modelo em planejamento de sistemas de transmissão. Finalmente, são apresentados testes com sistemas conhecidos na literatura especializada.

Alternative proposal for Modal Representation of a Non-transposed Three-Phase Transmission Line with a Vertical Symmetry Plane

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 a, b 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.