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

Baptista, Edméa Cássia; Belati, Edmarcio Antônio; Costa, Geraldo Roberto Martins da

doi:10.1016/j.ijepes.2005.06.004

Cited by 34 publications

(31 citation statements)

References 5 publications

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“…We can now formally state the OPF problem that we seek to solve: minimize the power loss (5), subject to power flow constraints (1), power injection constraints (2), and voltage regulation constraints (4).…”

Section: B Controllable Devices and Control Objectivementioning

confidence: 99%

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Exact convex relaxation for optimal power flow in distribution networks

Gan

Topcu

et al. 2013

SIGMETRICS Perform. Eval. Rev.

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Abstract-The optimal power flow (OPF) problem seeks to control the generation/consumption of generators/loads to optimize certain objectives such as to minimize the generation cost or power loss in the network. It is becoming increasingly important for distribution networks due to the emerging distributed generation and controllable loads. In this paper, we study the OPF problem in distribution networks. In particular, OPF is nonconvex and we study solving it through convex relaxations. We prove that after a "small" modification to the OPF problem, the solution to its second-order-cone programming (SOCP) relaxation is the global optimum of OPF, under a "mild" condition that can be checked prior to solving the relaxation. Empirical studies justify that the modification to OPF is "small" and that the "mild" condition holds for all test distribution networks, including the IEEE 13-bus test distribution network and practical distribution networks with high penetration of distributed generation.

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Section: B Controllable Devices and Control Objectivementioning

confidence: 99%

“…Various algorithms have been proposed to find local optima of OPF, e.g., successive linear/quadratic programming [2], trust-region based methods [3], Lagrangian Newton method [4], and interior-point methods [5]. However, not only is convergence of these algorithms not guaranteed, but also a local optimum can be highly suboptimal.…”

Section: Introductionmentioning

confidence: 99%

Exact convex relaxation for optimal power flow in distribution networks

Gan

Topcu

et al. 2013

SIGMETRICS Perform. Eval. Rev.

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“…Let be feasible for SOCP, and define and according to (8) and (9). It is straightforward to check that the point satisfies (10a)-(10c) and therefore Since satisfies (6f), one has and therefore for , i.e., .…”

Section: G Proof Of Corollarymentioning

confidence: 99%

“…These algorithms use nonlinear power flow equations and therefore 1) can be used in applications like voltage regulation and volt/var control; 2) have physically implementable solutions; 3) apply to both transmission and distribution networks. Representative algorithms of this kind include successive linear/ quadratic programming [6], trust-region based methods [7], Lagrangian Newton method [8], and interior-point methods [9]. Some of these algorithms, especially those based on NewtonRalphson, are quite successful empirically.…”

mentioning

confidence: 99%

Optimal power flow in direct current networks

Gan¹,

Low

2013

52nd IEEE Conference on Decision and Control

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Abstract-The optimal power flow (OPF) problem determines power generations/demands that minimize a certain objective such as generation cost or power loss. It is non-convex and NP-hard in general. In this paper, we study the OPF problem in direct current (DC) networks. A second-order cone programming (SOCP) relaxation is considered for solving the OPF problem. We prove that the SOCP relaxation is exact if either 1) voltage upper bounds do not bind; or 2) voltage upper bounds are uniform and power injection lower bounds are negative. Based on 1), a modified OPF problem is proposed, whose corresponding SOCP is guaranteed to be exact. We also prove that SOCP has at most one optimal solution if it is exact. Finally, we discuss how to improve numerical stability and how to include line constraints.Index Terms-Direct current networks, exact relaxation, optimal power flow, second-order cone relaxation.

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“…Muitos trabalhos foram desenvolvidos na tentativa de resolvê-lo utilizando diferentes técnicas de Otimização Não-Linear, Linear e Métodos Heurísticos, entre eles citam-se: GRANVILLE [12], WU et al [22] e TORRES & QUINTANA [21] os quais aplicaram um algoritmo Primal-Dual Barreira Logarítmica na resolução do problema de Fluxo de Potência Ótimo e, as condições de Karush-Kuhn-Tuker (KKT) foram satisfeitas utilizando o método de Newton, sendo a maior dificuldade do algoritmo a escolha do parâmetro de Barreira; BAPTISTA et al [1][2][3] resolveram o problema utilizando uma função Lagrangiana Aumentada-Barreira Logarítmica; BAPTISTA et al [4] e SOUSA et al [18][19][20] utilizaram uma função Lagrangiana Barreira Modificada. Mais recentemente, lembra-se de CAPITANESCU et al [5][6][7] que analisa o desempenho de três algoritmos de pontos interiores e sua aplicação ao FPO.…”

Section: Introductionunclassified

Uma Mistura De Funções Barreira E Barreira Modificada Na Resolução Do Fluxo De Potência Ótimo

Delgado¹,

Baptista²,

Soler³

et al. 2016

Anais Do XVIII Simpósio De Pesquisa Operacional &Amp; Logística Da Marinha

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Resumo Uma abordagem misturada da função barreira e a função barreira modificada é investigada neste trabalho. As restrições de desigualdade são transformadas em igualdades introduzindo variáveis de folga positivas, as quais são tratadas pelas funções Barreira Logarítmica ou Barreira Modificada Logarítmica e as demais restrições através de multiplicadores de Lagrange. Estes métodos serão utilizados em duas etapas. Inicialmente aplicamos o método baseado na função Barreira Logarítmica até que uma condição de parada seja satisfeita, depois aplicamos o método baseado na função Barreira Modificada Logarítmica até que a condição de convergência seja satisfeita. Testes numéricos utilizando o sistema elétrico teste de 3 barras indicam que o método é eficiente na resolução do problema Fluxo de Potência Ótimo.Palavras-chave: Fluxo de Potência Ótimo, Otimização não-linear, método de Newton, função Barreira, Função Barreira Modificada.Abstract An approach mixed the barrier function and modified barrier function is investigated in this paper. The inequality constraints are transformed into equalities by adding non-negative slack variables, which are handled by logarithmic barrier function or logarithmic modified barrier function, while the remaining constraints are handled by means of the Lagrange multipliers method. These methods will be used in two steps. Initially we apply the logarithmic barrier function until a stop condition is satisfied, and then we apply logarithmic modified barrier function until a convergence condition is satisfied. Numerical tests carried out with the 3 bus electrical system indicate that the proposed approach is efficient in the resolution the optimal power flow problem.

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

Cited by 34 publications

References 5 publications

Exact convex relaxation for optimal power flow in distribution networks

Exact convex relaxation for optimal power flow in distribution networks

Optimal power flow in direct current networks

Uma Mistura De Funções Barreira E Barreira Modificada Na Resolução Do Fluxo De Potência Ótimo

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