Simulated annealing metaheuristic to solve the optimal power flow

The optimal power flow problem has been widely studied in order to improve power systems operation and planning. For real power systems, the problem is formulated as a non-linear and as a large combinatorial problem. The first approaches used to solve this problem were based on mathematical methods which required huge computational efforts. Lately, artificial intelligence techniques, such as metaheuristics based on biological processes, were adopted. Metaheuristics require lower computational resources, which is a clear advantage for addressing the problem in large power systems. This paper proposes a methodology to solve optimal power flow on economic dispatch context using a Simulated Annealing algorithm inspired on the cooling temperature process seen in metallurgy. The main contribution of the proposed method is the specific neighborhood generation according to the optimal power flow problem characteristics. The proposed methodology has been tested with IEEE 6 bus and 30 bus networks. The obtained results are compared with other wellknown methodologies presented in the literature, showing the effectiveness of the proposed method.

Ant colony search algorithm for the optimal power flow problem

To maintain a power system within operation limits, a level ahead planning it is necessary to apply competitive techniques to solve the optimal power flow (OPF). OPF is a non-linear and a large combinatorial problem. The Ant Colony Search (ACS) optimization algorithm is inspired by the organized natural movement of real ants and has been successfully applied to different large combinatorial optimization problems. This paper presents an implementation of Ant Colony optimization to solve the OPF in an economic dispatch context. The proposed methodology has been developed to be used for maintenance and repairing planning with 48 to 24 hours antecipation. The main advantage of this method is its low execution time that allows the use of OPF when a large set of scenarios has to be analyzed. The paper includes a case study using the IEEE 30 bus network. The results are compared with other well-known methodologies presented in the literature.

Reduced gradient method combined with augmented Lagrangian and barrier for the optimal power flow problem

A new approach for solving the optimal power flow (OPF) problem is established by combining the reduced gradient method and the augmented Lagrangian method with barriers and exploring specific characteristics of the relations between the variables of the OPF problem. Computer simulations on IEEE 14-bus and IEEE 30-bus test systems illustrate the method. (c) 2007 Elsevier Inc. All rights reserved.

A modified Primal-Dual Logarithmic-Barrier Method for solving the Optimal Power Flow problem with discrete and continuous control variables

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

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.

Multi Objective Evolutionary Algorithm Applied to the Optimal Power Flow Problem

This work presents the application of a multiobjective evolutionary algorithm (MOEA) for optimal power flow (OPF) solution. The OPF is modeled as a constrained nonlinear optimization problem, non-convex of large-scale, with continuous and discrete variables. The violated inequality constraints are treated as objective function of the problem. This strategy allows attending the physical and operational restrictions without compromise the quality of the found solutions. The developed MOEA is based on the theory of Pareto and employs a diversity-preserving mechanism to overcome the premature convergence of algorithm and local optimal solutions. Fuzzy set theory is employed to extract the best compromises of the Pareto set. Results for the IEEE-30, RTS-96 and IEEE-354 test systems are presents to validate the efficiency of proposed model and solution technique.

Logarithmic barrier-augmented Lagrangian function to the optimal power flow problem

This paper presents a new approach to solve the Optimal Power Flow problem. This approach considers the application of logarithmic barrier method to voltage magnitude and tap-changing transformer variables and the other constraints are treated by augmented Lagrangian method. Numerical test results are presented, showing the effective performance of this algorithm. (C) 2005 Elsevier Ltd. All rights reserved.

A new approach to the solution of the optimal power flow problem based on the modified Newton's method associated to an augmented Lagrangian function

This paper presents a new algorithm for optimal power flow problem. The algorithm is based on Newton's method which it works with an Augmented Lagrangian function associated with the original problem. The function aggregates all the equality and inequality constraints and is solved using the modified-Newton method. The test results have shown the effectiveness of the approach using the IEEE 30 and 638 bus systems.

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.

An analytical solution to the optimal power flow

This letter presents an approach for a geometrical solution of an optimal power flow (OPF) problem for a two-bus system (slack and PV busses). 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.

Modified barrier method for optimal power flow problem

In this paper is presented a new approach for optimal power flow problem. This approach is based on the modified barrier function and the primal-dual logarithmic barrier method. A Lagrangian function is associated with the modified problem. The first-order necessary conditions for optimality are fulfilled by Newton's method, and by updating the barrier terms. The effectiveness of the proposed approach has been examined by solving the Brazilian 53-bus, IEEE118-bus and IEEE162-bus systems.

Optimal power flow via interior-exterior method

This paper presents a new approach to the resolution of the Optimal Power Flow problem. In this approach the inequality constraints are treated by the Modified Barrier and Primal-Dual Logarithmic Barrier methods. The inequality constraints are transformed into equalities by introducing positive auxiliary variables, which are perturbed by the barrier parameter. A Lagrangian function is associated with the modified problem. The first-order necessary conditions are applied to the Lagrangian, generating a nonlinear system which is solved by Newton's method. The perturbation of the auxiliary variables results in an expansion of the feasible set of the original problem, allowing the limits of the inequality constraints to be reached. Numerical tests on the Brazilian CESP and South-Southeast systems and a comparative test indicated that the new approach efficiently resolves of the Optimal Power Flow problem. © 2007 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.

An unequivocal normalization-based paradigm to solve dynamic economic and emission active-reactive OPF (optimal power flow)

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