A successive linear programming approach to solving the iv-acopf

Castillo, Anya; Lipka, Paula; Watson, Jean‐Paul; Oren, Shmuel S.; O’Neill, Richard P.

doi:10.1109/tpwrs.2015.2487042

Cited by 120 publications

(134 citation statements)

References 28 publications

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“…given the underlying problem data specified in the RAC-OPF problem (8). We refer the reader to Appendix A for their specification.…”

Section: A Concise Formulation Of Rac-opfmentioning

confidence: 99%

“…Remark 2 (Eliminating quadratic equality constraints). We remark that the formulation of the original RAC-OPF problem (8) assumes that there is adjustable generation at every bus in the power transmission network. The advantage of this rather limiting assumption is that it enables the elimination of all nodal power balance equality constraints in the equivalent reformulation of the RAC-OPF problem given by P. The ability to eliminate these nonconvex quadratic equality constraints will be essential to the convex inner approximation technique developed in Section IV-B.…”

Section: A Concise Formulation Of Rac-opfmentioning

confidence: 99%

“…More recently, considerable effort has been made to identify conditions under which an optimal solution to AC-OPF can be obtained from a solution to its semidefinite programming relaxation [4]- [7]. According to the US Federal Energy Regulatory Commission, a 5% increase in the efficiency of algorithms for AC-OPF will yield six billion dollars in savings per year in the United States alone [8].…”

Section: Introductionmentioning

confidence: 99%

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Robust AC Optimal Power Flow

Louca

Bitar

2019

IEEE Trans. Power Syst.

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There is a growing need for new optimization methods to facilitate the reliable and cost-effective operation of power systems with intermittent renewable energy resources. In this paper, we formulate the robust AC optimal power flow (RAC-OPF) problem as a two-stage robust optimization problem with recourse. This problem amounts to a nonconvex infinitedimensional optimization problem that is computationally intractable, in general. Under the assumption that there is adjustable generation or load at every bus in the power transmission network, we develop a technique to approximate RAC-OPF from within by a finite-dimensional semidefinite program by restricting the space of recourse policies to be affine in the uncertain problem data. We establish a sufficient condition under which the semidefinite program returns an affine recourse policy that is guaranteed to be feasible for the original RAC-OPF problem. We illustrate the effectiveness of the proposed optimization method on the WSCC 9-bus and IEEE 14-bus test systems with different levels of renewable resource penetration and uncertainty.

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“…given the underlying problem data specified in the RAC-OPF problem (8). We refer the reader to Appendix A for their specification.…”

Section: A Concise Formulation Of Rac-opfmentioning

confidence: 99%

Section: A Concise Formulation Of Rac-opfmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Robust AC Optimal Power Flow

Louca

Bitar

2019

IEEE Trans. Power Syst.

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“…Since first being formulated by Carpentier in 1962 [5], a broad range of algorithms have been applied to solve OPF problems, including Newton-Raphson, sequential quadratic programming, interior point methods, etc. [6], [7]. Convergence of many algorithms only ensures local optimality, i.e., no feasible points in the solution's immediate neighborhood have a better objective value.…”

Section: Introductionmentioning

confidence: 99%

Empirical Investigation of Non-Convexities in Optimal Power Flow Problems

Narimani

Molzahn

et al. 2018

2018 Annual American Control Conference (ACC)

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Optimal power flow (OPF) is a central problem in the operation of electric power systems. An OPF problem optimizes a specified objective function subject to constraints imposed by both the non-linear power flow equations and engineering limits. These constraints can yield non-convex feasible spaces that result in significant computational challenges. Despite these non-convexities, local solution algorithms actually find the global optima of some practical OPF problems. This suggests that OPF problems have a range of difficulty: some problems appear to have convex or "nearly convex" feasible spaces in terms of the voltage magnitudes and power injections, while other problems can exhibit significant non-convexities. Understanding this range of problem difficulty is helpful for creating new test cases for algorithmic benchmarking purposes. Leveraging recently developed computational tools for exploring OPF feasible spaces, this paper first describes an empirical study that aims to characterize non-convexities for small OPF problems. This paper then proposes and analyzes several medium-size test cases that challenge a variety of solution algorithms. * :

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“…It must also satisfy operational constraints which include narrow voltage ranges around nominal values and line ratings to keep Joule heating to acceptable levels. While many non-linear methods [19,99] have been developed to solve this difficult problem, there is a strong motivation for producing more reliable tools. First, power systems are growing in complexity due to the increase in the share of renewables, the increase in the peak load, and the expected wider use of demand response and storage.…”

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confidence: 99%

Lasserre Hierarchy for Large Scale Polynomial Optimization in Real and Complex Variables

Josz¹,

Molzahn²

2018

SIAM J. Optim.

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We propose general notions to deal with large scale polynomial optimization problems and demonstrate their efficiency on a key industrial problem of the twenty first century, namely the optimal power flow problem. These notions enable us to find global minimizers on instances with up to 4,500 variables and 14,500 constraints. First, we generalize the Lasserre hierarchy from real to complex to numbers in order to enhance its tractability when dealing with complex polynomial optimization. Complex numbers are typically used to represent oscillatory phenomena, which are omnipresent in physical systems. Using the notion of hyponormality in operator theory, we provide a finite convergence criterion which generalizes the Curto-Fialkow conditions of the real Lasserre hierarchy. Second, we introduce the multi-ordered Lasserre hierarchy in order to exploit sparsity in polynomial optimization problems (in real or complex variables) while preserving global convergence. It is based on two ideas: 1) to use a different relaxation order for each constraint, and 2) to iteratively seek a closest measure to the truncated moment data until a measure matches the truncated data. Third and last, we exhibit a block diagonal structure of the Lasserre hierarchy in the presence of commonly encountered symmetries.Key words. Multi-ordered Lasserre hierarchy, Hermitian sum-of-squares, chordal sparsity, semidefinite programming, optimal power flow.AMS subject classifications. 90C22, 90C06, 90C26, 28A99, 14Q99, 47N10.1. Introduction. Polynomial optimization encompasses NP-hard non-convex problems that arise in various applications and it includes, as special cases, integer programming and quadratically-constrained quadratic programming. The Lasserre hierarchy [59,76,77], which draws on algebraic geometry [80], enables one to solve such problems to global optimality using semidefinite programming. A big challenge today is to make it applicable to large scale real world problems. Recent approaches in this direction include the use of chordal sparsity [95], the BSOS hierarchy [57] and Sparse-BSOS hierarchy [96], the DSOS and SDSOS hierarchies [3,49,55], and ADMM for sum-of-squares [97]. The Lasserre hierarchy has two dual facets, moments and sumsof-squares, and most approaches to reduce the computational burden can be viewed as a restriction on the sum-of-squares: [95] restricts the number of variables, [57] restricts the degree, and [3] restricts the number of terms inside the square. Following this line of research, we propose to restrict sum-of-squares to Hermitian sum-of-squares [34] for optimization problems with oscillatory phenomena (e.g. power systems [11,17,65], imaging science [13,16,89], signal processing [4,21,69,70], automatic control [93], and quantum mechanics [45]). In addition, we propose to restrain the use of high degree sum-of-squares to only some constraints by using a different degree for each constraint. Finally, we show that if the polynomials defining the objective and the constraints are even (i.e. all the monomials have ...

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A successive linear programming approach to solving the iv-acopf

Cited by 120 publications

References 28 publications

Robust AC Optimal Power Flow

Robust AC Optimal Power Flow

Empirical Investigation of Non-Convexities in Optimal Power Flow Problems

Lasserre Hierarchy for Large Scale Polynomial Optimization in Real and Complex Variables

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