DC traction load flow including AC distribution network

In the first part some information and characterisation about an AC distribution network that feeds traction substations and their possible influences on the DC traction load flow are presented. Those influences are investigated and mathematically modelled. To corroborate the mathematical model, an example is presented and their results are confronted with real measurements.

Artificial neural networks for load flow and external equivalents studies

In this paper an artificial neural network (ANN) based methodology is proposed for (a) solving the basic load flow, (b) solving the load flow considering the reactive power limits of generation (PV) buses, (c) determining a good quality load flow starting point for ill-conditioned systems, and (d) computing static external equivalent circuits. An analysis of the input data required as well as the ANN architecture is presented. A multilayer perceptron trained with the Levenberg-Marquardt second order method is used. The proposed methodology was tested with the IEEE 30- and 57-bus, and an ill-conditioned 11-bus system. Normal operating conditions (base case) and several contingency situations including different load and generation scenarios have been considered. Simulation results show the excellent performance of the ANN for solving problems (a)-(d). (C) 2010 Elsevier B.V. All rights reserved.

Continuation load flow using automatically determined branch megawatt losses as parameters

The conventional Newton's method is considered to be inadequate for the computation of the maximum loading point (MLP) of power systems since: (i) it encounters difficulties in the vicinity of the MLP: and (ii) the load flow Jacobian matrix becomes singular at the MLP. It is well known that continuation methods are powerful and useful tools that are able to trace the solution PV curve without experiencing such diffculties. However, continuation methods require a parameterisation so that a modified, well conditioned set of load flow equations is obtained. In particular, the Jacobian matrix associated with this modified set of equations should not be singular at the MLP. The authors propose that the actual power losses in transmission branches (lines and transformers) are used to parameterise the approach. Specific procedures for the automatic determination of the most appropriate parameter (branch) are proposed. Such procedures include the utilisation of fast voltage-stability indices. Simulation results are presented to show that the proposed method is able to trace the whole solution PV curve very efficiently.

Generalised single-equation load flow method for unbalanced distribution systems

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

A Kinetostatic Formulation for Load-Flow Visualization in Compliant Mechanisms

Load flow visualization, which is an important step in structural and machine assembly design may aid in the analysis and eventual synthesis of compliant mechanisms. In this paper, we present a kineto-static formulation to visualize load flow in compliant mechanisms. This formulation uses the concept of transferred forces to quantify load flow from input to the output of a compliant mechanism. The magnitude and direction of load flow in the constituent members enables functional decomposition of the compliant mechanism into (i) Constraints (C): members that are constrained to deform in a particular direction and (ii) Transmitters (T): members that transmit load to the output. Furthermore, it is shown that a constraint member and an adjacent transmitter member can be grouped together to constitute a fundamental building block known as an CT set whose load flow behavior is maximally decoupled from the rest of the mechanism. We can thereby explain the deformation behavior of a number of compliant mechanisms from literature by visualizing load flow, and identifying building blocks.

An Improved Parameterization Technique for the Continuation Power Flow

Continuation methods have been long used in P-V curve tracing due to their efficiency in the resolution of ill-conditioned cases, with close to singular Jacobian matrices, such as the maximum loading point of power systems. Several parameterization techniques have been proposed to avoid matrix singularity and successfully solve those cases. This paper presents a simple geometric parameterization technique to overcome the singularity of the Jacobian matrix by the addition of a line equations located at the plane determined by a bus voltage magnitude and the loading factor. This technique enlarges the set of voltage variables that can be used to whole P-V curve tracing, without ill-conditioning problems and no need of parameter changes. Simulation results, obtained for large realistic Brazilian and American power systems, show that the robustness and efficiency of the conventional power flow are not only preserved but also improved.

A Parameterization Technique for the Continuation Power Flow Developed from the Analysis of Power Flow Curves

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

An efficient geometric parameterization technique for the continuation power flow

Continuation methods have been shown as efficient tools for solving ill-conditioned cases, with close to singular Jacobian matrices, such as the maximum loading point of power systems. Some parameterization techniques have been proposed to avoid matrix singularity and successfully solve those cases. This paper presents a new geometric parameterization scheme that allows the complete tracing of the P-V curves without ill-conditioning problems. The proposed technique associates robustness to simplicity and, it is of easy understanding. The Jacobian matrix singularity is avoided by the addition of a line equation, which passes through a point in the plane determined by the total real power losses and loading factor. These two parameters have clear physical meaning. The application of this new technique to the IEEE systems (14, 30, 57, 118 and 300 buses) shows that the best characteristics of the conventional Newton's method are not only preserved but also improved. (C) 2006 Elsevier B.V. All rights reserved.

A new solution to the optimal power flow problem

A new approach to solving the Optimal Power Flow problem is described, making use of some recent findings, especially in the area of primal-dual methods for complex programming. In this approach, equality constraints are handled by Newton's method inequality constraints for voltage and transformer taps by the logarithmic barrier method and the other inequality constraints by the augmented Lagrangian method. Numerical test results are presented, showing the effective performance of this algorithm. © 2001 IEEE.

Multiarea optimal power flow using multiobjective evolutionary algorithm

In this work the multiarea optimal power flow (OPF) problem is decoupled into areas creating a set of regional OPF subproblems. The objective is to solve the optimal dispatch of active and reactive power for a determined area, without interfering in the neighboring areas. The regional OPF subproblems are modeled as a large-scale nonlinear constrained optimization problem, with both continuous and discrete variables. Constraints violated are handled as objective functions of the problem. In this way the original problem is converted to a multiobjective optimization problem, and a specifically-designed multiobjective evolutionary algorithm is proposed for solving the regional OPF subproblems. The proposed approach has been examined and tested on the RTS-96 and IEEE 354-bus test systems. Good quality suboptimal solutions were obtained, proving the effectiveness and robustness of the proposed approach. ©2009 IEEE.

Parameterization technique for the continuation power flow using the trivial and tangent predictor

This paper presents efficient geometric parameterization techniques using the tangent and the trivial predictors for the continuation power flow, developed from observation of the trajectories of the load flow solution. The parameterization technique eliminates the Jacobian matrix singularity of load flow, and therefore all the consequent problems of ill-conditioning, by the addition of the line equations which pass through the points in the plane determined by the variables loading factor and the real power generated by the slack bus, two parameters with clear physical meaning. This paper also provides an automatic step size control around the maximum loading point. Thus, the resulting method enables not only the calculation of the maximum loading point, but also the complete tracing of P-V curves of electric power systems. The technique combines robustness with ease of understanding. The results to the IEEE 300-bus system and of large real systems show the effectiveness of the proposed method. © 2012 IEEE.

Load balancing for aspect ratio in adaptive finite element simulations

In parallel adaptive finite element simulations the work load on the individual processors may change frequently. To (re)distribute the load evenly over the processors a load balancing heuristic is needed. Common strategies try to minimise subdomain dependencies by optimising the cutsize of the partitioning. However for certain solvers cutsize only plays a minor role, and their convergence is highly dependent on the subdomain shapes. Degenerated subdomain shapes cause them to need significantly more iterations to converge. In this work a new parallel load balancing strategy is introduced which directly addresses the problem of generating and conserving reasonably good subdomain shapes in a dynamically changing Finite Element Simulation. Geometric data is used to formulate several cost functions to rate elements in terms of their suitability to be migrated. The well known diffusive method which calculates the necessary load flow is enhanced by weighting the subdomain edges with the help of these cost functions. The proposed methods have been tested and results are presented.

Three-phase harmonic distortion state estimation algorithm based on evolutionary strategies

This paper presents a new methodology to estimate unbalanced harmonic distortions in a power system, based on measurements of a limited number of given sites. The algorithm utilizes evolutionary strategies (ES), a development branch of evolutionary algorithms. The problem solving algorithm herein proposed makes use of data from various power quality meters, which can either be synchronized by high technology GPS devices or by using information from a fundamental frequency load flow, what makes the overall power quality monitoring system much less costly. The ES based harmonic estimation model is applied to a 14 bus network to compare its performance to a conventional Monte Carlo approach. It is also applied to a 50 bus subtransmission network in order to compare the three-phase and single-phase approaches as well as the robustness of the proposed method. (C) 2010 Elsevier B.V. All rights reserved.

Harmonic Distortion State Estimation Using an Evolutionary Strategy

This paper presents a new methodology to estimate harmonic distortions in a power system, based on measurements of a limited number of given sites. The algorithm utilizes evolutionary strategies (ES), a development branch of evolutionary algorithms. The main advantage in using such a technique relies upon its modeling facilities as well as its potential to solve fairly complex problems. The problem-solving algorithm herein proposed makes use of data from various power-quality (PQ) meters, which can either be synchronized by high technology global positioning system devices or by using information from a fundamental frequency load flow. This second approach makes the overall PQ monitoring system much less costly. The algorithm is applied to an IEEE test network, for which sensitivity analysis is performed to determine how the parameters of the ES can be selected so that the algorithm performs in an effective way. Case studies show fairly promising results and the robustness of the proposed method.