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.

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)

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

Despacho ótimo de potências ativa e reativa de sistema elétricos multi-áreas considerando restrições físicas, econômicas e ambientais =: Envronmentally constrained active-reactive optimal power flow-a compromising strategy for economic-emission dispatch and a multi-area paradigm

Pós-graduação em Engenharia Elétrica - FEIS

Integrated Optimal Power Flow for Distribution Networks in Local and Urban Scales

This paper develops an integrated optimal power flow (OPF) tool for distribution networks in two spatial scales. In the local scale, the distribution network, the natural gas network, and the heat system are coordinated as a microgrid. In the urban scale, the impact of natural gas network is considered as constraints for the distribution network operation. The proposed approach incorporates unbalance three-phase electrical systems, natural gas systems, and combined cooling, heating, and power systems. The interactions among the above three energy systems are described by energy hub model combined with components capacity constraints. In order to efficiently accommodate the nonlinear constraint optimization problem, particle swarm optimization algorithm is employed to set the control variables in the OPF problem. Numerical studies indicate that by using the OPF method, the distribution network can be economically operated. Also, the tie-line power can be effectively managed.

Funções penalidade para o tratamento das variáveis discretas do problema de fluxo de potência ótimo reativo

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Funções penalidade para o tratamento das variáveis discretas do problema de fluxo de potência ótimo reativo

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Optimal reactive power flow via the modified barrier Lagrangian function approach

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Security constrained optimal active power flow via network model and interior point method

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

VAr planning using genetic algorithm and linear programming

A combined methodology consisting of successive linear programming (SLP) and a simple genetic algorithm (SGA) solves the reactive planning problem. The problem is divided into operating and planning subproblems; the operating subproblem, which is a nonlinear, ill-conditioned and nonconvex problem, consists of determining the voltage control and the adjustment of reactive sources. The planning subproblem consists of obtaining the optimal reactive source expansion considering operational, economical and physical characteristics of the system. SLP solves the optimal reactive dispatch problem related to real variables, while SGA is used to determine the necessary adjustments of both the binary and discrete variables existing in the modelling problem. Once the set of candidate busbars has been defined, the program implemented gives the location and size of the reactive sources needed, if any, to maintain the operating and security constraints.

Optimal reactive power flow via the modified barrier Lagrangian function approach

A new approach called the Modified Barrier Lagrangian Function (MBLF) to solve the Optimal Reactive Power Flow problem is presented. In this approach, the inequality constraints are treated by the Modified Barrier Function (MBF) method, which has a finite convergence property: i.e. the optimal solution in the MBF method can actually be in the bound of the feasible set. Hence, the inequality constraints can be precisely equal to zero. Another property of the MBF method is that the barrier parameter does not need to be driven to zero to attain the solution. Therefore, the conditioning of the involved Hessian matrix is greatly enhanced. In order to show this, a comparative analysis of the numeric conditioning of the Hessian matrix of the MBLF approach, by the decomposition in singular values, is carried out. The feasibility of the proposed approach is also demonstrated with comparative tests to Interior Point Method (IPM) using various IEEE test systems and two networks derived from Brazilian generation/transmission system. The results show that the MBLF method is computationally more attractive than the IPM in terms of speed, number of iterations and numerical conditioning. (C) 2011 Elsevier B.V. All rights reserved.

Data Flow Analysis and the Linear Programming Model

* The research is supported partly by INTAS: 04-77-7173 project, http://www.intas.be

Optimal scheduling of a renewable micro-grid in an isolated load area using mixed-integer linear programming

In the energy management of the isolated operation of small power system, the economic scheduling of the generation units is a crucial problem. Applying right timing can maximize the performance of the supply. The optimal operation of a wind turbine, a solar unit, a fuel cell and a storage battery is searched by a mixed-integer linear programming implemented in General Algebraic Modeling Systems (GAMS). A Virtual Power Producer (VPP) can optimal operate the generation units, assured the good functioning of equipment, including the maintenance, operation cost and the generation measurement and control. A central control at system allows a VPP to manage the optimal generation and their load control. The application of methodology to a real case study in Budapest Tech, demonstrates the effectiveness of this method to solve the optimal isolated dispatch of the DC micro-grid renewable energy park. The problem has been converged in 0.09 s and 30 iterations.