Observing the state of a smart grid using bilevel programming

Sonia Toubaline; Pierre Louis Poirion; Claudia D’Ambrosio; Leo Liberti

doi:10.1007/978-3-319-26626-8_27

Observing the state of a smart grid using bilevel programming

Sonia Toubaline
, Pierre Louis Poirion
, Claudia D’Ambrosio
, Leo Liberti

Laboratoire d'Informatique (LIX)

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Monitoring an electrical network is an important and challenging task. Phasor measurement units are measurement devices that can be used for a state estimation of this network. In this paper we consider a PMU placement problem without conventional measurements and with zero injection nodes for a full observability of the network. We propose two new approaches to model this problem, which take into account a propagation rule based on Ohm’s and Kirchoff’s law. The natural binary linear programming description models an iterative observability process. We remove the iteration by reformulating its fixed point conditions to a bilevel program, which we then further reformulate to a single-level mixed-integer linear program. We also present a bilevel algorithm to solve directly the proposed bilevel model. We implemented and tested our models and algorithm: the results show that the bilevel algorithm is better in terms of running time and size of instances which can be solved.

Original language	English
Title of host publication	Combinatorial Optimization and Applications - 9th International Conference, COCOA 2015, Proceedings
Editors	Donghyun Kim, Weili Wu, Ding-Zhu Du, Zaixin Lu, Wei Li
Publisher	Springer Verlag
Pages	364-376
Number of pages	13
ISBN (Print)	9783319266251
DOIs	https://doi.org/10.1007/978-3-319-26626-8_27
Publication status	Published - 1 Jan 2015
Event	9th International Conference on Combinatorial Optimization and Applications, COCOA 2015 - Houston, United States Duration: 18 Dec 2015 → 20 Dec 2015

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9486
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	9th International Conference on Combinatorial Optimization and Applications, COCOA 2015
Country/Territory	United States
City	Houston
Period	18/12/15 → 20/12/15

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 7 Affordable and Clean Energy

Keywords

Bilevel program
Mixed integer linear program
Monitoring electrical network
PMU placement problem

Access to Document

10.1007/978-3-319-26626-8_27

Cite this

Toubaline, S., Poirion, P. L., D’Ambrosio, C., & Liberti, L. (2015). Observing the state of a smart grid using bilevel programming. In D. Kim, W. Wu, D.-Z. Du, Z. Lu, & W. Li (Eds.), Combinatorial Optimization and Applications - 9th International Conference, COCOA 2015, Proceedings (pp. 364-376). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9486). Springer Verlag. https://doi.org/10.1007/978-3-319-26626-8_27

Toubaline, Sonia ; Poirion, Pierre Louis ; D’Ambrosio, Claudia et al. / Observing the state of a smart grid using bilevel programming. Combinatorial Optimization and Applications - 9th International Conference, COCOA 2015, Proceedings. editor / Donghyun Kim ; Weili Wu ; Ding-Zhu Du ; Zaixin Lu ; Wei Li. Springer Verlag, 2015. pp. 364-376 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Observing the state of a smart grid using bilevel programming",

abstract = "Monitoring an electrical network is an important and challenging task. Phasor measurement units are measurement devices that can be used for a state estimation of this network. In this paper we consider a PMU placement problem without conventional measurements and with zero injection nodes for a full observability of the network. We propose two new approaches to model this problem, which take into account a propagation rule based on Ohm{\textquoteright}s and Kirchoff{\textquoteright}s law. The natural binary linear programming description models an iterative observability process. We remove the iteration by reformulating its fixed point conditions to a bilevel program, which we then further reformulate to a single-level mixed-integer linear program. We also present a bilevel algorithm to solve directly the proposed bilevel model. We implemented and tested our models and algorithm: the results show that the bilevel algorithm is better in terms of running time and size of instances which can be solved.",

keywords = "Bilevel program, Mixed integer linear program, Monitoring electrical network, PMU placement problem",

author = "Sonia Toubaline and Poirion, \{Pierre Louis\} and Claudia D{\textquoteright}Ambrosio and Leo Liberti",

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doi = "10.1007/978-3-319-26626-8\_27",

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series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

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Toubaline, S, Poirion, PL, D’Ambrosio, C & Liberti, L 2015, Observing the state of a smart grid using bilevel programming. in D Kim, W Wu, D-Z Du, Z Lu & W Li (eds), Combinatorial Optimization and Applications - 9th International Conference, COCOA 2015, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9486, Springer Verlag, pp. 364-376, 9th International Conference on Combinatorial Optimization and Applications, COCOA 2015, Houston, United States, 18/12/15. https://doi.org/10.1007/978-3-319-26626-8_27

Observing the state of a smart grid using bilevel programming. / Toubaline, Sonia; Poirion, Pierre Louis; D’Ambrosio, Claudia et al.
Combinatorial Optimization and Applications - 9th International Conference, COCOA 2015, Proceedings. ed. / Donghyun Kim; Weili Wu; Ding-Zhu Du; Zaixin Lu; Wei Li. Springer Verlag, 2015. p. 364-376 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9486).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Observing the state of a smart grid using bilevel programming

AU - Toubaline, Sonia

AU - Poirion, Pierre Louis

AU - D’Ambrosio, Claudia

AU - Liberti, Leo

N1 - Publisher Copyright: © Springer International Publishing Switzerland 2015.

PY - 2015/1/1

Y1 - 2015/1/1

N2 - Monitoring an electrical network is an important and challenging task. Phasor measurement units are measurement devices that can be used for a state estimation of this network. In this paper we consider a PMU placement problem without conventional measurements and with zero injection nodes for a full observability of the network. We propose two new approaches to model this problem, which take into account a propagation rule based on Ohm’s and Kirchoff’s law. The natural binary linear programming description models an iterative observability process. We remove the iteration by reformulating its fixed point conditions to a bilevel program, which we then further reformulate to a single-level mixed-integer linear program. We also present a bilevel algorithm to solve directly the proposed bilevel model. We implemented and tested our models and algorithm: the results show that the bilevel algorithm is better in terms of running time and size of instances which can be solved.

AB - Monitoring an electrical network is an important and challenging task. Phasor measurement units are measurement devices that can be used for a state estimation of this network. In this paper we consider a PMU placement problem without conventional measurements and with zero injection nodes for a full observability of the network. We propose two new approaches to model this problem, which take into account a propagation rule based on Ohm’s and Kirchoff’s law. The natural binary linear programming description models an iterative observability process. We remove the iteration by reformulating its fixed point conditions to a bilevel program, which we then further reformulate to a single-level mixed-integer linear program. We also present a bilevel algorithm to solve directly the proposed bilevel model. We implemented and tested our models and algorithm: the results show that the bilevel algorithm is better in terms of running time and size of instances which can be solved.

KW - Bilevel program

KW - Mixed integer linear program

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KW - PMU placement problem

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DO - 10.1007/978-3-319-26626-8_27

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AN - SCOPUS:84951949810

SN - 9783319266251

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 364

EP - 376

BT - Combinatorial Optimization and Applications - 9th International Conference, COCOA 2015, Proceedings

A2 - Kim, Donghyun

A2 - Wu, Weili

A2 - Du, Ding-Zhu

A2 - Lu, Zaixin

A2 - Li, Wei

PB - Springer Verlag

T2 - 9th International Conference on Combinatorial Optimization and Applications, COCOA 2015

Y2 - 18 December 2015 through 20 December 2015

ER -

Toubaline S, Poirion PL, D’Ambrosio C , Liberti L. Observing the state of a smart grid using bilevel programming. In Kim D, Wu W, Du DZ, Lu Z, Li W, editors, Combinatorial Optimization and Applications - 9th International Conference, COCOA 2015, Proceedings. Springer Verlag. 2015. p. 364-376. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-26626-8_27

Observing the state of a smart grid using bilevel programming

Abstract

Publication series

Conference

UN SDGs

Keywords

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