Victor H. Quintana

Comparison of performance indices for detection of proximity to voltage collapse

The paper proposes a new test function to be used in an existent performance index for detection of proximity to a static voltage collapse point. This test function is based on a reduction of the load flow Jacobian with respect to the critical bus of a system. The test function is compared with known singular values and eigenvalues indices, and with other previously proposed test functions. A thorough analysis of the similarities, advantages, and disadvantages of all these indices and test functions is presented. The techniques are tested and compared on the IEEE 300 bus test system, showing the effect of system characteristics and limits in these indices and functions.

A genetic-based neuro-fuzzy approach for modeling and control of dynamical systems

Linguistic modeling of complex irregular systems constitutes the heart of many control and decision making systems, and fuzzy logic represents one of the most effective algorithms to build such linguistic models. In this paper, a linguistic (qualitative) modeling approach is proposed. The approach combines the merits of the fuzzy logic theory, neural networks, and genetic algorithms (GAs). The proposed model is presented in a fuzzy-neural network (FNN) form which can handle both quantitative (numerical) and qualitative (linguistic) knowledge. The learning algorithm of an FNN is composed of three phases. The first phase is used to find the initial membership functions of the fuzzy model. In the second phase, a new algorithm is developed and used to extract the linguistic-fuzzy rules. In the third phase, a multiresolutional dynamic genetic algorithm (MRD-GA) is proposed and used for optimized tuning of membership functions of the proposed model. Two well-known benchmarks are used to evaluate the performance of the proposed modeling approach, and compare it with other modeling approaches.

New techniques to speed up voltage collapse computations using tangent vectors

This paper discusses various methods based on power network partitioning and voltage stability indices to accelerate the computation of voltage collapse points using continuation techniques. Partitioning methods derived from right eigenvector and tangent vector information are thoroughly studied, identifying limitations and probable application areas; a mixed partition-reduction technique is then proposed to reduce computational burden. Also, tangent vectors are used to define a clustering method for the identification at any operating condition of the critical area at the collapse point, and a new voltage stability index is defined based on the identification of this critical area. Finally, a predictor-corrector methodology based on this index and the continuation method is proposed for fast computations of voltage collapse points. All the different methods are compared based on the results obtained for the IEEE 300-bus test system, and a methodology is recommended based on its prospective computational savings.

Multiobjective optimal power flows to evaluate voltage security costs in power networks

In this paper, new optimal power flow (OPF) techniques are proposed based on multiobjective methodologies to optimize active and reactive power dispatch while maximizing voltage security in power systems. The use of interior point methods together with goal programming and linearly combined objective functions as the basic optimization techniques are explained in detail. The effects of minimizing operating costs, minimizing reactive power generation, and/or maximizing loading margins are then compared in both a 57-bus system and a 118-bus system, which are based on IEEE test systems and modeled using standard power flow models. The results obtained using the proposed mixed OPFs are compared and analyzed to suggest possible ways of costing voltage security in power systems.

Improving an interior-point-based OPF by dynamic adjustments of step sizes and tolerances

This paper presents an efficient interior point algorithm for optimal power flow (OPF) problems, in particular, the real power dispatch and the reactive power dispatch problems. The nonlinear OPF problem is solved by a predictor-corrector primal-dual log-barrier (PCPDLB) method as a sequence of linearized sub-problems. Besides discussing the problem formulation, the paper offers a detailed description of the PCPDLB algorithm; it also addresses several implementation issues such as the determination of barrier parameter and the customization of initial points for OPF problems. In addition, practical issues on how to choose linear step sizes and convergence criteria are investigated to evaluate their impact on the performance of the algorithm. Some heuristics of dynamically adjusting step sizes and tolerance are proposed which significantly improve OPF solution speed. Computational results on power systems of 118 and 1062 buses are presented and discussed. Comparisons with other variants of primal-dual log-barrier methods are also provided to demonstrate the superiority of the proposed predictor-corrector interior point algorithm.

A tutorial description of an interior point method and its applications to security-constrained economic dispatch

The authors deal with the use of successive linear programming (SLP) for the solution of the security-constrained economic dispatch (SCED) problem. They tutorially describe an interior point method (IPM) for the solution of linear programming (LP) problems, discussing important implementation issues that really make this method far superior to the simplex method. A study of the convergence of the SLP technique and a practical criterion to avoid oscillatory behavior in the iteration process are also proposed. A comparison of the proposed method with an efficient simplex code (MINOS) is carried out by solving SCED problems on two standard IEEE systems. The results show that the interior point technique is reliable, accurate, and more than two times as fast as the simplex algorithm. >

Interior-point methods and their applications to power systems: a classification of publications and software codes

Since Karmarkars first successful interior-point algorithm for linear programming in 1984, the interest and consequently the number of publications in the area have increased tremendously, leaving the newcomers to the field trapped in a jungle of papers and reports. In this paper,the authors review and classify major publications on interior-point methods theory, on the practical implementation of the most successful interior-point algorithms, and on their applications to power systems optimization problems. A listing of state-of-the-art interior-point software codes and major online research resources on the Internet are included.

On a nonlinear multiple-centrality-corrections interior-point method for optimal power flow

Large scale nonlinear optimal power flow (OPF) problems have been efficiently solved by extensions from linear programming to nonlinear programming of the primal-dual logarithmic barrier interior-point method and its predictor-corrector variant. Motivated by the impressive performance of the nonlinear predictor-corrector extension, in this paper we extend from linear programming to nonlinear OPF the efficient multiple centrality corrections (MCC) technique that was developed by Gondzio. The numerical performance of the proposed MCC algorithm is evaluated on a set of power networks ranging in size from 118 buses to 2098 buses. Extensive computational results demonstrate that the MCC technique is fast and robust, and outperforms the successful predictor-corrector technique.

Generation and Transmission Expansion Under Risk Using Stochastic Programming

In this paper, a new model for generation and transmission expansion is presented. This new model considers as random events the demand, the equivalent availability of the generating plants, and the transmission capacity factor of the transmission lines. In order to incorporate these random events into an optimization model, stochastic programming and probabilistic constraints are used. A risk factor is introduced in the objective function by means of the mean-variance Markowitz theory. The solved optimization problem is a mixed integer nonlinear program. The expected value of perfect information is obtained in order to show the cost of ignoring uncertainty. The proposed model is illustrated by a six- and a 21-node network using a dc approximation.

An efficient predictor-corrector interior point algorithm for security-constrained economic dispatch

This paper deals with the application of an advanced interior point method to the security-constrained economic dispatch (SCED) problems through successive linear programming. The nonlinear SCED problem is linearized, and then solved by a predictor-corrector interior point method. Besides describing the basic algorithm, the paper focuses on several important issues that are critical to its efficient implementation, including the adjustment of barrier parameter, the determination of initial point, and so on. Computational experiments are conducted to evaluate their impact on the performance of the algorithm. Some suggestions, such as using the feasibility condition to adjust the way of computing barrier parameter /spl mu/ and customizing initial point by adopting a relative small threshold, are proposed to reduce the overall iterations required by the algorithm. The computational results on power systems of 236 to 2124 buses have shown that these suggestions are very effective, improving the performance of the algorithm by a factor of 2. Comparison with a pure primal-dual interior point method is also provided to demonstrate the superiority of the proposed predictor-corrector method.