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E-book Advances in Energy System Optimization : Proceedings of the 2nd International Symposium on Energy System Optimization

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Penilaian

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One frequently discussedconvexdistributed optimization method is the Alternat-ing Direction of Multipliers Method (ADMM)[3],whichisalsoappliedincontextofAC OPF[1,4,5].ADMMoften yields promising results even for large-scalepower systems [4]. However,ADMMsometimes requires a specific partitioningtechnique and/or a feasible initialization in combination with high consensus-violation penalization parameters to converge [1]. The requirement of feasibleinitialization seems quite limiting as it requires solving a centralized inequality-constrained power flow problem requiring full topology and load informationleading to approximately the same complexity as fullOPF.In previous works [6–8] we suggested applying the Augmented LagrangianAlternating Direction Inexact Newton (ALADIN) method to stochastic and deter-ministicOPFproblems ranging from 5 to 300 buses. In case a certain line-searchis applied [9],ALADINprovides global convergence guarantees to local minimizersfor non-convex problems without the need offeasible initialization. The results in[6] underpin thatALADINis able to outperformADMMin many cases. This comesat cost of a higher per-step information exchange compared withADMMand a morecomplicated coordination step, cf. [6].In this paper we investigate the interplay of feasible initialization with highpenalization for consensus violation inADMMfor distributedAC OPF. We illustrateour findings on theIEEE57-bus system. Furthermore, we compare the convergencebehavior ofADMMtoALADINnot suffering from the practical need for feasibleinitialization [9]. Finally, we provide theoretical results supporting our numericalobservations for the convergence behavior ofADMM.The paper is organized as follows: In Sect.2we briefly recapADMMandALADINincluding their convergence properties. Section3shows numerical results for theIEEE57-bus system focusing on the influence of the penalization parameter?onthe convergence behavior of ADMM. Section4presents an analysis of the interplaybetween high penalization and a feasible initialization. Throughout this work we assume thatfiandhiare twice continuously differentiableand that allXiare compact. Note that the objective functionsfi:Rnxi?Rand nonlinear inequality constraintshi:Rnxi?Rnhionly depend onxiand thatcoupling between them takes place in the affine consensus constraint?i?RAixi=0 only. There are several ways of formulatingOPFproblems in form of (1) differingin the coupling variables and the type of the power flow equations (polar orrectangular), cf. [4, 6, 10].Here, we are interested in solving Problem (1)viaADMMandALADINsumma-rized in Algorithms1 and2 respectively.1,2At first glance it is apparent thatADMMandALADINshare several features. For example, in Step (1) of both algorithms,local augmented Lagrangians subject to local nonlinear inequality constraintshiare minimized in parallel.3Observe that whileADMMmaintains multiple localLagrange multipliers?i,ALADINconsiders one global Lagrange multiplier vector?.InStep(2),ALADINcomputes sensitivitiesBi,giandCi(which often candirectly be obtained from the local numerical solver without additional computation)whereasADMMupdates the multiplier vectors?i.1We remark that there exist a variety of variants ofADMM,cf.[3, 11]. Here, we choose theformulation from [9] in order to highlight similarities betweenADMMandALADIN.2Note that, due to space limitations, we describe the full-step variant ofALADINhere. To obtainconvergence guarantees from a remote starting point, a globalization strategy is necessary, cf. [9].3For notational simplicity, we only consider nonlinear inequality constraints here. Nonlinearequality constraintsgican be incorporated via a reformulation in terms of two inequalityconstraints, i.e. 0?gi(xi)?0.

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Ketersediaan

Informasi Detail

Judul Seri

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No. Panggil

003.5 ENG a

Penerbit

Switzerland : Springer Nature., 2020

Deskripsi Fisik

179 hlm

Bahasa

English

ISBN/ISSN

9783030321574

Klasifikasi

003.5

Tipe Isi

text

Tipe Media

computer

Tipe Pembawa

online resource

Edisi

-

Subjek

Theory of Communication and Control

Info Detail Spesifik

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Pernyataan Tanggungjawab

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Versi lain/terkait

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