Port-Hamiltonian Formulation of the Gradient Method Applied to Smart Grids

Tjerk Stegink; Claudio De Persis; Arjan van der Schaft

doi:10.1016/j.ifacol.2015.10.207

Port-Hamiltonian Formulation of the Gradient Method Applied to Smart Grids

Tjerk Stegink, Claudio De Persis, Arjan van der Schaft

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

18 Citations (Scopus)

90 Downloads (Pure)

Abstract

The gradient method is a well-known tool for solving convex optimization problems. This paper shows that the gradient method admits a Brayton-Moser and a port-Hamiltonian
representation. In fact, its dynamics can be interpreted as a interconnection of multiple (port-Hamiltonian) passive systems, which plays a key role in proving asymptotic stability of the
method. As an application to smart grids, this paper studies the problem of frequency regulation in power grids, while maximizing the social welfare. By applying the gradient method, we obtain a real-time dynamic pricing model in port-Hamiltonian form. By coupling with the port-Hamiltonian description of the physical network we obtain a closed-loop port-Hamiltonian system, which properties are exploited to prove asymptotic stability to the set of optimal points.

Original language	English
Title of host publication	IFAC-PapersOnLine
Publisher	Elsevier
Pages	13-18
Number of pages	6
Volume	48
DOIs	https://doi.org/10.1016/j.ifacol.2015.10.207
Publication status	Published - 4-Jul-2015
Event	5th IFAC Workshop on Lagrangian and Hamiltonian Methods for Non Linear Control (Lyon, France, 4 – 7 July 2015 - Lyon, France Duration: 4-Jul-2015 → 7-Jul-2015

Conference

Conference	5th IFAC Workshop on Lagrangian and Hamiltonian Methods for Non Linear Control (Lyon, France, 4 – 7 July 2015
Country/Territory	France
City	Lyon
Period	04/07/2015 → 07/07/2015

Keywords

port-Hamiltonian
Gradient methods
Power systems

Access to Document

10.1016/j.ifacol.2015.10.207

Port-Hamiltonian Formulation of the Gradient Method Applied to Smart GridsFinal publisher's version, 440 KBLicence: Taverne

Handle.net

Persistent link

Cite this

@inproceedings{255f2a2458c444b3bd6228de94e46ace,

title = "Port-Hamiltonian Formulation of the Gradient Method Applied to Smart Grids",

abstract = "The gradient method is a well-known tool for solving convex optimization problems. This paper shows that the gradient method admits a Brayton-Moser and a port-Hamiltonianrepresentation. In fact, its dynamics can be interpreted as a interconnection of multiple (port-Hamiltonian) passive systems, which plays a key role in proving asymptotic stability of themethod. As an application to smart grids, this paper studies the problem of frequency regulation in power grids, while maximizing the social welfare. By applying the gradient method, we obtain a real-time dynamic pricing model in port-Hamiltonian form. By coupling with the port-Hamiltonian description of the physical network we obtain a closed-loop port-Hamiltonian system, which properties are exploited to prove asymptotic stability to the set of optimal points.",

keywords = "port-Hamiltonian, Gradient methods, Power systems",

author = "Tjerk Stegink and {De Persis}, Claudio and {van der Schaft}, Arjan",

year = "2015",

month = jul,

day = "4",

doi = "10.1016/j.ifacol.2015.10.207",

language = "English",

volume = "48",

pages = "13--18",

booktitle = "IFAC-PapersOnLine",

publisher = "Elsevier",

note = " 5th IFAC Workshop on Lagrangian and Hamiltonian Methods for Non Linear Control (Lyon, France, 4 – 7 July 2015 ; Conference date: 04-07-2015 Through 07-07-2015",

}

TY - GEN

T1 - Port-Hamiltonian Formulation of the Gradient Method Applied to Smart Grids

AU - Stegink, Tjerk

AU - De Persis, Claudio

AU - van der Schaft, Arjan

PY - 2015/7/4

Y1 - 2015/7/4

N2 - The gradient method is a well-known tool for solving convex optimization problems. This paper shows that the gradient method admits a Brayton-Moser and a port-Hamiltonianrepresentation. In fact, its dynamics can be interpreted as a interconnection of multiple (port-Hamiltonian) passive systems, which plays a key role in proving asymptotic stability of themethod. As an application to smart grids, this paper studies the problem of frequency regulation in power grids, while maximizing the social welfare. By applying the gradient method, we obtain a real-time dynamic pricing model in port-Hamiltonian form. By coupling with the port-Hamiltonian description of the physical network we obtain a closed-loop port-Hamiltonian system, which properties are exploited to prove asymptotic stability to the set of optimal points.

AB - The gradient method is a well-known tool for solving convex optimization problems. This paper shows that the gradient method admits a Brayton-Moser and a port-Hamiltonianrepresentation. In fact, its dynamics can be interpreted as a interconnection of multiple (port-Hamiltonian) passive systems, which plays a key role in proving asymptotic stability of themethod. As an application to smart grids, this paper studies the problem of frequency regulation in power grids, while maximizing the social welfare. By applying the gradient method, we obtain a real-time dynamic pricing model in port-Hamiltonian form. By coupling with the port-Hamiltonian description of the physical network we obtain a closed-loop port-Hamiltonian system, which properties are exploited to prove asymptotic stability to the set of optimal points.

KW - port-Hamiltonian

KW - Gradient methods

KW - Power systems

U2 - 10.1016/j.ifacol.2015.10.207

DO - 10.1016/j.ifacol.2015.10.207

M3 - Conference contribution

VL - 48

SP - 13

EP - 18

BT - IFAC-PapersOnLine

PB - Elsevier

T2 - 5th IFAC Workshop on Lagrangian and Hamiltonian Methods for Non Linear Control (Lyon, France, 4 – 7 July 2015

Y2 - 4 July 2015 through 7 July 2015

ER -

Port-Hamiltonian Formulation of the Gradient Method Applied to Smart Grids

Abstract

Conference

Keywords

Access to Document

Handle.net

Fingerprint

Cite this