Sequential Relaxation of Unit Commitment with AC Transmission Constraints

Zohrizadeh, Fariba; Kheirandishfard, Mohsen; Nasir, Adnan; Madani, Ramtin

doi:10.1109/cdc.2018.8619609

Cited by 9 publications

(3 citation statements)

References 50 publications

(40 reference statements)

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“…The success of the sequential framework and penalization in solving bilinear matrix inequalities (BMIs) demonstrated in [36,38,39]. The incorporation of penalty terms into the objective of SDP relaxations are proven to be computationally effective for solving non-convex optimization problems in power systems [52,53,84,85]. These papers show that penalizing certain physical quantities in power network optimization problems such as reactive power loss or thermal loss facilitates the recovery of feasible points from convex relaxations.…”

Section: Comprehensive Boundary Propertymentioning

confidence: 99%

Parabolic Relaxation for Quadratically-constrained Quadratic Programming -- Part I: Definitions & Basic Properties

Madani¹,

Ashraphijuo²,

Kheirandishfard³

et al. 2022

Preprint

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For general quadratically-constrained quadratic programming (QCQP), we propose a parabolic relaxation described with convex quadratic constraints. An interesting property of the parabolic relaxation is that the original non-convex feasible set is contained on the boundary of the parabolic relaxation. Under certain assumptions, this property enables one to recover near-optimal feasible points via objective penalization. Moreover, through an appropriate change of coordinates that requires a one-time computation of an optimal basis, the easier-to-solve parabolic relaxation can be made as strong as a semidefinite programming (SDP) relaxation, which can be effective in accelerating algorithms that require solving a sequence of convex surrogates. The majority of theoretical and computational results are given in the next part of this work [57].

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Section: Comprehensive Boundary Propertymentioning

confidence: 99%

Parabolic Relaxation for Quadratically-constrained Quadratic Programming -- Part I: Definitions & Basic Properties

Madani¹,

Ashraphijuo²,

Kheirandishfard³

et al. 2022

Preprint

Self Cite

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“…Another single convex model worth citing is that proposed in the work of Fattahi et al [3] for the DC network-constrained UC problem, in which reformulation-linearization is used to introduce relaxed non-convex quadratic inequalities in order to tighten the SDP relaxation seeking to avoid local feasibility resolution. More recently, Zohrizadeh et al [26] propose a power loss penalization method based on a series of SOCP relaxations that require an initialization "sufficiently close to the feasible set" for convergence.…”

Section: Related Workmentioning

confidence: 99%

Benders' decomposition of the unit commitment problem with semidefinite relaxation of AC power flow constraints

Paredes,

Martins,

Soares

et al. 2019

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In this paper we present a formulation of the unit commitment problem with AC power flow constraints. It is solved by a Benders' decomposition in which the unit commitment master problem is formulated as a mixed-integer problem with linearization of the power generation constraints for improved convergence. Semidefinite programming relaxation of the rectangular AC optimal power flow is used in the subproblem, providing somewhat conservative cuts. Numerical case studies, including a 6-bus and the IEEE 118-bus network, are provided to test the effectiveness of our proposal. We show in our numerical experiments that the use of such strategy improves the quality of feasibility and optimality cuts generated by the solution of the convex relaxation of the subproblem, therefore reducing the number of iterations required for algorithm convergence.

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“…Researchers have proposed various methods to increase the computational tractability of the AC-UC problem using, for example, Lagrange relaxation [19], decomposition [18], [20], and convexification methods [21]. However, this is an ongoing research area without a singular superior solution technique identified yet.…”

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confidence: 99%

Modeling the AC Power Flow Equations with Optimally Compact Neural Networks: Application to Unit Commitment

Kody¹,

Chevalier²,

Chatzivasileiadis³

et al. 2021

Preprint

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Nonlinear power flow constraints render a variety of power system optimization problems computationally intractable. Emerging research shows, however, that the nonlinear AC power flow equations can be successfully modeled using Neural Networks (NNs). These NNs can be exactly transformed into Mixed Integer Linear Programs (MILPs) and embedded inside challenging optimization problems, thus replacing nonlinearities that are intractable for many applications with tractable piecewise linear approximations. Such approaches, though, suffer from an explosion of the number of binary variables needed to represent the NN. Accordingly, this paper develops a technique for training an "optimally compact" NN, i.e., one that can represent the power flow equations with a sufficiently high degree of accuracy while still maintaining a tractable number of binary variables. We show that the resulting NN model is more expressive than both the DC and linearized power flow approximations when embedded inside of a challenging optimization problem (i.e., the AC unit commitment problem). Index Terms-AC power flow, AC unit commitment (AC-UC), mixed-integer linear program (MILP), neural networks, piecewise linear model I. INTRODUCTIONThe AC power flow equations are routinely used to model network constraints in optimization problems related to the control, operation, and planning of power systems. These constraints, however, are both nonlinear and non-convex, resulting in optimization problems that can be NP-hard [1]. In practice, many power systems operation problems, like unit commitment (UC), optimal power flow (OPF), and optimal transmission switching (OTS), are solved using linearized approximations of the nonlinear AC power flow equations for the sake of computational tractability. However, linear approximations can result in suboptimal solutions or solutions that are infeasible in the original, nonlinear problem [2].Piecewise linear models offer a method of improving solution accuracy by capturing some of the nonlinearity of the † denotes an equal contribution among authors.

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Sequential Relaxation of Unit Commitment with AC Transmission Constraints

Cited by 9 publications

References 50 publications

Parabolic Relaxation for Quadratically-constrained Quadratic Programming -- Part I: Definitions & Basic Properties

Parabolic Relaxation for Quadratically-constrained Quadratic Programming -- Part I: Definitions & Basic Properties

Benders' decomposition of the unit commitment problem with semidefinite relaxation of AC power flow constraints

Modeling the AC Power Flow Equations with Optimally Compact Neural Networks: Application to Unit Commitment

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