Improved geometric parameterisation techniques for continuation power flow

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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.

Evaluation of economic impact of external eauivalent models used in reactive OPF studies for interconnected systems

Reactive-optimisation procedures are responsible for the minimisation of online power losses in interconnected systems. These procedures are performed separately at each control centre and involve external network representations. If total losses can be minimised by the implementation of calculated local control actions, the entire system benefits economically, but such control actions generally result in a certain degree of inaccuracy, owing to errors in the modelling of the external system. Since these errors are inevitable, they must at least be maintained within tolerable limits by external-modelling approaches. Care must be taken to avoid unrealistic loss minimisation, as the local-control actions adopted can lead the system to points of operation which will be less economical for the interconnected system as a whole. The evaluation of the economic impact of the external modelling during reactive-optimisation procedures in interconnected systems, in terms of both the amount of losses and constraint violations, becomes important in this context. In the paper, an analytical approach is proposed for such an evaluation. Case studies using data from the Brazilian South-Southeast system (810 buses) have been carried out to compare two different external-modelling approaches, both derived from the equivalent-optimal-power-flow (EOPF) model. Results obtained show that, depending on the external-model representation adopted, the loss representation can be flawed. Results also suggest some modelling features that should be adopted in the EOPF model to enhance the economy of the overall system.

Short term hydroelectric scheduling combining network flow and interior point approaches

In this paper, short term hydroelectric scheduling is formulated as a network flow optimization model and solved by interior point methods. The primal-dual and predictor-corrector versions of such interior point methods are developed and the resulting matrix structure is explored. This structure leads to very fast iterations since it avoids computation and factorization of impedance matrices. For each time interval, the linear algebra reduces to the solution of two linear systems, either to the number of buses or to the number of independent loops. Either matrix is invariant and can be factored off-line. As a consequence of such matrix manipulations, a linear system which changes at each iteration has to be solved, although its size is reduced to the number of generating units and is not a function of time intervals. These methods were applied to IEEE and Brazilian power systems, and numerical results were obtained using a MATLAB implementation. Both interior point methods proved to be robust and achieved fast convergence for all instances tested. (C) 2004 Elsevier Ltd. All rights reserved.

Study of alternative schemes for the parameterization step of the continuation power flow method based on physical parameters, part I: Mathematical modeling

The conventional power flow method is considered to be inadequate to obtain the maximum loading point because of the singularity of Jacobian matrix. Continuation methods are efficient tools for solving this kind of problem since different parameterization schemes can be used to avoid such ill-conditioning problems. This paper presents the details of new schemes for the parameterization step of the continuation power flow method. The new parameterization options are based on physical parameters, namely, the total power losses (real and reactive), the power at the slack bus (real or reactive), the reactive power at generation buses, and transmission line power losses (real and reactive). The simulation results obtained with the new approach for the IEEE test systems (14, 30, 57, and 118 buses) are presented and discussed in the companion paper. The results show that the characteristics of the conventional method are not only preserved but also improved.

Study of alternative schemes for the parameterization step of the continuation power flow method based on physical parameters, part II: Performance evaluation

New parameterization schemes have been proposed by the authors in Part I of this paper. In this part these new options for the parameterization of power flow equations are tested, namely, the total power losses (real and reactive), the power at the slack bus (real or reactive), the reactive power at generation buses, and the transmission line power losses (real and reactive). These different parameterization schemes can be used to obtain the maximum loading point without ill-conditioning problems, once the singularity of Jacobian matrix is avoided. The results obtained with the new approach for the IEEE test systems (14, 30, 57, and 118 buses) show that the characteristics of the conventional method are not only preserved but also improved. In addition, it is shown that the proposed method and the conventional one can be switched during the tracing of PV curves to determine, with few iterations, all points of the PV curve. Several tests were also carried out to compare the performance of the proposed parameterization schemes for the continuation power flow method with the use of both the secant and tangent predictors.

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 heuristic method for reactive power planning

An approach for solving reactive power planning problems is presented, which is based on binary search techniques and the use of a special heuristic to obtain a discrete solution. Two versions were developed, one to run on conventional (sequential) computers and the other to run on a distributed memory (hypercube) machine. This latter parallel processing version employs an asynchronous programming model. Once the set of candidate buses has been defined, the program gives the location and size of the reactive sources needed(if any) in keeping with operating and security constraints.

Electric power systems transient stability analysis by neural networks

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Solucao de sistemas lineares com matrizes e vetores esparsos em computadores vetoriais

This paper presents a methodology for solving a set of linear sparse equations on vector computers. The new methodology is able to exploit the matrix and vector sparsities. The implementation was made on a CRAY Y-MP 2E/232 computer and the results were taken from electric power systems with 118, 320, 725 and 1729 buses. The proposed methodology was compared with three previous methods and the results show the superior performance of the new one.

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.

Utilização de índices de estabilidade transitória para a avaliação de segurança dinâmica

Indices that report how much a contingency is stable or unstable in an electrical power system have been the object of several studies in the last decades. In some approaches, indices are obtained from time-domain simulation; others explore the calculation of the stability margin from the so-called direct methods, or even by neural networks.The goal is always to obtain a fast and reliable way of analysing large disturbance that might occur on the power systems. A fast classification in stable and unstable, as a function of transient stability is crucial for a dynamic security analysis. All good propositions as how to analyse contingencies must present some important features: classification of contingencies; precision and reliability; and efficiency computation. Indices obtained from time-domain simulations have been used to classify the contingencies as stable or unstable. These indices are based on the concepts of coherence, transient energy conversion between kinetic energy and potential energy, and three dot products of state variable. The classification of the contingencies using the indices individually is not reliable, since the performance of these indices varies with each simulated condition. However, collapsing these indices into a single one can improve the analysis significantly. In this paper, it is presented the results of an approach to filter the contingencies, by a simple classification of them into stable, unstable or marginal. This classification is performed from the composite indices obtained from step by step simulation with a time period of the clearing time plus 0.5 second. The contingencies originally classified as stable or unstable do not require this extra simulation. The methodology requires an initial effort to obtain the values of the intervals for classification, and the weights. This is performed once for each power system and can be used in different operating conditions and for different contingencies. No misplaced classification o- - ccurred in any of the tests, i.e., we detected no stable case classified as unstable or otherwise. The methodology is thus well fitted for it allows for a rapid conclusion about the stability of th system, for the majority of the contingencies (Stable or Unstable Cases). The tests, results and discussions are presented using two power systems: (1) the IEEE17 system, composed of 17 generators, 162 buses and 284 transmission lines; and (2) a South Brazilian system configuration, with 10 generators, 45 buses and 71 lines.

Alternative continuation method for loading margin improvement and transmission losses reduction

This paper presents an alternative methodology for loading margin improvement and total real power losses reduction by using a continuation method. In order to attain this goal, a parameterizing equation based on the total real power losses and the equations of the reactive power at the slack and generation buses are added to the conventional power flow equations. The voltages at these buses are considered as control variables and a new parameter is chosen to reduce the real power losses in the transmission lines. The results show that this procedure leads to maximum loading point increase and consequently, in static voltage stability margin improvement. Besides, this procedure also takes to a reduction in the operational costs and, simultaneously, to voltage profile improvement. Another important result of this methodology is that the resulting operating points are close to that provided by an optimal power flow program. © 2004 IEEE.

PMUs optimized allocation using a tabu search algorithm for fault location in electric power distribution system

Phasor Measurement Units (PMUs) optimized allocation allows control, monitoring and accurate operation of electric power distribution systems, improving reliability and service quality. Good quality and considerable results are obtained for transmission systems using fault location techniques based on voltage measurements. Based on these techniques and performing PMUs optimized allocation it is possible to develop an electric power distribution system fault locator, which provides accurate results. The PMUs allocation problem presents combinatorial features related to devices number that can be allocated, and also probably places for allocation. Tabu search algorithm is the proposed technique to carry out PMUs allocation. This technique applied in a 141 buses real-life distribution urban feeder improved significantly the fault location results. © 2004 IEEE.

Influence of the supply of reactive power in the calculation of the transfer capability

This paper presents some initial concepts for including reactive power in linear methods for computing Available Transfer Capability (ATC). It is proposed an approximation for the reactive power flows computation that uses the exact circle equations for the transmission line complex flow, and then it is determined the ATC using active power distribution factors. The transfer capability can be increased using the sensitivities of flow that show the best group of buses which can have their reactive power injection modified in order to remove the overload in the transmission lines. The results of the ATC computation and of the use of the sensitivities of flow are presented using the Cigré 32-bus system. © 2004 IEEE.