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.

Application of pi Circuits for Simulation of Corona Effect in Transmission Lines

In this article, it is represented by state variables phase a transmission line which parameters are considered frequency independently and frequency dependent. Based on previous analyses, it is used the reasonable number of p circuits and the number of blocks composed by parallel resistor and inductor for reduction of numerical oscillations. It is analyzed the influence of the increase of the RL parallel blocks in the obtained results. The RL parallel blocks are used for inclusion of the frequency influence in the transmission line longitudinal parameter. It is a simple model that is been used by undergraduate students for simulation of traveling wave phenomena in transmission lines. Considering the model without frequency influence, it is included a representation of the corona effect. Some simulations are carried considering the corona effect and they are compared to the results without this phenomenon.

Step by step analyses of Clarke's matrix correction procedure for untransposed three-phase transmission line cases

The correction procedure for Clarke's matrix, considering three-phase transmission line analyzes, is analyzed step by step in this paper, searching to improve the application of this procedure. Changing the eigenvectors as modal transformation matrices, Clarke's matrix has been applied to analyses for transposed and untransposed three-phase transmission line cases. It is based on the fact that Clarke's matrix is an eigenvector matrix for transposed three-phase transmission lines considering symmetrical and asymmetrical cases. Because of this, the application of this matrix has been analyzed considering untransposed three-phase transmission lines. In most of these cases, the errors related to the eigenvalues can be considered negligible. It is not true when it is analyzed the elements that are not in main diagonal of the quasi-mode matrix. This matrix is obtained from the application of Clarke's matrix. The quasi-mode matrix is correspondent to the eigenvalue matrix. Their off-diagonal elements represent couplings among the quasi-modes. So, the off-diagonal quasi-mode element relative values are not negligible when compared to the eigenvalues that correspond to the coupled quasi-modes. Minimizing these relative values, the correction procedure is analyzed in detail, checking some alternatives for the correction procedure application.

Analyses of the modifications in the pi circuits for inclusion of frequency influence in transmission line representation

In this article, it is represented by state variables phase a transmission line which parameters are considered frequency independently and frequency dependent. It is analyzed what is the reasonable number of pi circuits and the number of blocks composed by parallel resistor and inductor in parallel for reduction of numerical oscillations. It is simulated the numerical routine with and without the effect of frequency in the longitudinal parameters. Initially, it is used state variables and pi circuits representing the transmission line composing a linear system which is solved by numerical routines based on the trapezoidal rule. The effect of frequency on the line is synthesized by resistors and inductors in parallel and this representation is analyzed in details. It is described transmission lines and the frequency influence in these lines through the state variables.

Transmission system expansion planning by a branch-and-bound algorithm

A branch and bound (B& B) algorithm using the DC model, to solve the power system transmission expansion planning by incorporating the electrical losses in network modelling problem is presented. This is a mixed integer nonlinear programming (MINLP) problem, and in this approach, the so-called fathoming tests in the B&B algorithm were redefined and a nonlinear programming (NLP) problem is solved in each node of the B& B tree, using an interior-point method. Pseudocosts were used to manage the development of the B&B tree and to decrease its size and the processing time. There is no guarantee of convergence towards global optimisation for the MINLP problem. However, preliminary tests show that the algorithm easily converges towards the best-known solutions or to the optimal solutions for all the tested systems neglecting the electrical losses. When the electrical losses are taken into account, the solution obtained using the Garver system is better than the best one known in the literature.

A cooperative game theory analysis for transmission loss allocation

This paper presents an analysis and discussion, based on cooperative game theory, for the allocation of the cost of losses to generators and demands in transmission systems. We construct a cooperative game theory model in which the players are represented by equivalent bilateral exchanges and we search for a unique loss allocation solution, the Core. Other solution concepts, such as the Shapley Value, the Bilateral Shapley Value and the Kernel are also explored. Our main objective is to illustrate why is not possible to find an optimal solution for allocating the cost of losses to the users of a network. Results and relevant conclusions are presented for a 4-bus system and a 14-bus system. (c) 2007 Elsevier B.V. All rights reserved.

An implementation of modified scatter search algorithm to transmission expansion planning

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

Comparative studies on non-convex optimization methods for transmission network expansion planning

We have investigated and extensively tested three families of non-convex optimization approaches for solving the transmission network expansion planning problem: simulated annealing (SA), genetic algorithms (GA), and tabu search algorithms (TS). The paper compares the main features of the three approaches and presents an integrated view of these methodologies. A hybrid approach is then proposed which presents performances which are far better than the ones obtained with any of these approaches individually. Results obtained in tests performed with large scale real-life networks are summarized.

Transient stability analysis of electrical power systems using a neural network based on fuzzy ARTMAP

This work presents a methodology to analyze transient stability for electric energy systems using artificial neural networks based on fuzzy ARTMAP architecture. This architecture seeks exploring similarity with computational concepts on fuzzy set theory and ART (Adaptive Resonance Theory) neural network. The ART architectures show plasticity and stability characteristics, which are essential qualities to provide the training and to execute the analysis. Therefore, it is used a very fast training, when compared to the conventional backpropagation algorithm formulation. Consequently, the analysis becomes more competitive, compared to the principal methods found in the specialized literature. Results considering a system composed of 45 buses, 72 transmission lines and 10 synchronous machines are presented. © 2003 IEEE.

Defects location in power systems components through a dedicated genetic algorithm

In this work the problem of defects location in power systems is formulated through a binary linear programming (BLP) model based on alarms historical database of control and protection devices from the system control center, sets theory of minimal coverage (AI) and protection philosophy adopted by the electric utility. In this model, circuit breaker operations are compared to their expected states in a strictly mathematical manner. For solving this BLP problem, which presents a great number of decision variables, a dedicated Genetic Algorithm (GA), is proposed. Control parameters of the GA, such as crossing over and mutation rates, population size, iterations number and population diversification, are calibrated in order to obtain efficiency and robustness. Results for a test system found in literature, are presented and discussed. © 2004 IEEE.

Distribution line models analysis for loss calculation within three-phase three-wire power flow algorithms

Three-phase three-wire power flow algorithms, as any tool for power systems analysis, require reliable impedances and models in order to obtain accurate results. Kron's reduction procedure, which embeds neutral wire influence into phase wires, has shown good results when three-phase three-wire power flow algorithms based on current summation method were used. However, Kron's reduction can harm reliabilities of some algorithms whose iterative processes need loss calculation (power summation method). In this work, three three-phase three-wire power flow algorithms based on power summation method, will be compared with a three-phase four-wire approach based on backward-forward technique and current summation. Two four-wire unbalanced medium-voltage distribution networks will be analyzed and results will be presented and discussed. © 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.

A new procedure to derive transmission line parameters: Theoretical considerations

The objective of this paper is to show an alternative methodology to calculate transmission line parameters per unit length. With this methodology the transmission line parameters can be obtained starting from the phase currents and voltages in one terminal of the line. First, the article shows the classical methodology to calculate frequency dependent transmission line parameters by using Carson's and Pollaczeck's equations for representing the ground effect and Bessel's functions to represent the skin effect. After that, it is shown a new procedure to calculate frequency dependent transmission line parameters directly from currents and voltages of the line that is already built. Then, this procedure is applied in a two-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. ©2005 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.