Optimal reactive power flow via the modified barrier Lagrangian function approach

Sousa, V.A. de; Baptista, Edméa Cássia; Costa, Geraldo Roberto Martins da

doi:10.1016/j.epsr.2011.11.001

Cited by 43 publications

(24 citation statements)

References 22 publications

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“…Da mesma forma que o método descrito em [11], neste trabalho as variáveis de folga são tratadas pela função barreira logarítmica modificada de [4] e incorporadas à função objetivo por meio do parâmetro de barreira 0 μ > , conforme descrito em (4):…”

Section: O Problema De Fluxo De Potência óTimo Reativounclassified

“…Em relação aos métodos previamente propostos na literatura para a solução do FPOR [3], [7], [10] e [11] podem ser destacadas as seguintes contribuições do método proposto neste trabalho: i) o método proposto busca reduzir o tempo computacional para a solução do problema de FPOR, ao utilizar na verificação da positividade da matriz hessiana k θ , um procedimento que exige menor esforço computacional em relação ao procedimento de Cholesky, tradicionalmente utilizado na literatura; ii) as estratégias de definição das novas direções de busca propostas, as quais não desprezam as direções associadas ao passo previsor, por meio de um teste de complementaridade, tornam o método mais eficiente para a determinação das soluções ótimas, buscando reduzir o número de iterações para a solução do problema.…”

Section: Introductionunclassified

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A primal-dual interior/exterior point method, with combined directions and quadratic test in reactive optimal power flow problems

Souza

Balbo

Nepomuceno

et al. 2017

IEEE Latin Am. Trans.

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In this paper, we propose a primal-dual interior/exterior point method that uses the modified logarithmic barrier function together with a quadratic test strategy and new search direction procedures for solving the reactive optimal power flow problem. The quadratic test is proposed as an alternative strategy for the Cholesky procedure for calculating the positivity of the Hessian matrix of the problem. The new search directions investigated in the paper are determined by combining the search directions calculated in the predictor and corrector steps, and also by using information associated with the complementarity conditions. The method is implemented in Matlab and applied to solving the reactive optimal power flow problem for 9 and 39 bus systems, as well as for the IEEE 14, 30, 57 and 118 test systems. The results reinforce the efficiency of the method proposed for solving the problem.

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Section: O Problema De Fluxo De Potência óTimo Reativounclassified

Section: Introductionunclassified

A primal-dual interior/exterior point method, with combined directions and quadratic test in reactive optimal power flow problems

Souza

Balbo

Nepomuceno

et al. 2017

IEEE Latin Am. Trans.

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“…As a subproblem of OPF, the aim of optimal reactive power flow (ORPF) is to make the objectives (e.g., power loss) minimal by regulating the reactive power compensation devices and choosing the positions of transformer taps reasonably to change the distribution of power flow, under the premise of satisfying network security constraints. Compared to the traditional OPF [2,3], ORPF [4][5][6] is more complicated because of the transformer ratios. However, it also provides controllable measures to ensure power quality and reduce power losses.…”

Section: Introductionmentioning

confidence: 99%

The optimal reactive power flow model in mixed polar form based on transformer dummy nodes

Wang

Chen

Wang

2017

IEEJ Transactions Elec Engng

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This paper proposes a simple optimal reactive power flow (ORPF) model in mixed polar form based on the dummy nodes transformer model. By introducing voltage magnitude variables at the dummy nodes to express the transformation relationships of the power and the voltages of ideal transformers, the proposed model does not need to consider the variables of transformer ratios directly. So the power equations of the transformer branches do not contain complex items multiplied by the squares of variables, but drop from four-dimensional variables of the transformer equivalent circuits to three-dimensional variables. It simplifies the ORPF model efficiently and solves the problem of the traditional model which is a little complicated and hard to calculate. The calculation results of IEEE-30, -57, -118, and -300 bus systems show that the proposed model converges quickly and the number of iterations reduce by more than half compared to the traditional model. With higher computational efficiency and more stable numerical property, the proposed model is suitable for practical application in large-scale power systems.Hua Wei (Non-member) received the M.S. degree from Guangxi University (GU), Nanning, China, and the PhD. degree from Hiroshima University, both in power engineering. Now he is a Professor of electrical engineering, GU. His research interests include power system operation and planning, in particular the application of optimization methods to power systems. Prof. Wei is a member of the CSEE and IEEE.Chunmei Lin (Non-member) received the B.E. degree in electrical engineering and automation from Guangxi University (GU), Nanning, China, in 2014. Currently, she is a postgraduate student at the Guangxi Key Laboratory of Power System Optimization and Energy Technology, GU. Her current research interests include power system optimization.Yufei Wang (Non-member) received the B.E. degree in technique and instrumentation of measurements

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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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Optimal reactive power flow via the modified barrier Lagrangian function approach

Cited by 43 publications

References 22 publications

A primal-dual interior/exterior point method, with combined directions and quadratic test in reactive optimal power flow problems

A primal-dual interior/exterior point method, with combined directions and quadratic test in reactive optimal power flow problems

The optimal reactive power flow model in mixed polar form based on transformer dummy nodes

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

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