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

Persis, Claudio De; Schaft, A.J. van der

doi:10.1016/j.ifacol.2015.10.207

Cited by 17 publications

(26 citation statements)

References 10 publications

(9 reference statements)

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“…= τ c z c and note that, in the sequel, we interchangeably write the system dynamics in terms of both x c and z c for ease of notation. In these new variables the dynamics (9) admits a natural port-Hamiltonian representation [20], which is given bẏ…”

Section: Basic Primal-dual Gradient Controllermentioning

confidence: 99%

See 1 more Smart Citation

A Unifying Energy-Based Approach to Stability of Power Grids With Market Dynamics

Stegink

Persis

Schaft

2017

IEEE Trans. Automat. Contr.

154

155

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In this paper a unifying energy-based approach is provided to the modeling and stability analysis of power systems coupled with market dynamics. We consider a standard model of the power network with a third-order model for the synchronous generators involving voltage dynamics. By applying the primal-dual gradient method to a social welfare optimization, a distributed dynamic pricing algorithm is obtained, which can be naturally formulated in port-Hamiltonian form. By interconnection with the physical model a closed-loop port-Hamiltonian system is obtained, whose properties are exploited to prove asymptotic stability to the set of optimal points. This result is extended to the case that also general nodal power constraints are included into the social welfare problem. Additionally, the case of line congestion and power transmission costs in acyclic networks is covered. Finally, a dynamic pricing algorithm is proposed that does not require knowledge about the power supply and demand.

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Section: Basic Primal-dual Gradient Controllermentioning

confidence: 99%

“…The subsystems (19) have the following passivity property [20]. 20]). Let i ∈ I, (μ i ,w i ) ∈ Z µi and definē y µi := ∇g i (w i )μ i .…”

Section: (18)mentioning

confidence: 99%

A Unifying Energy-Based Approach to Stability of Power Grids With Market Dynamics

Stegink

Persis

Schaft

2017

IEEE Trans. Automat. Contr.

154

155

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“…Since energy is the main quantity of interest, the port-Hamiltonian framework is a natural approach to deal with the problem [1]. Moreover, it lends itself to deal with large-scale nonlinear multi-physics systems like power networks [2][3][4][5].…”

Section: Problem Statement/motivationmentioning

confidence: 99%

“…Note that in a purely inductive network G = 0 and B ik ≤ 0 for all i, k. The resulting multi-machine network, commonly referred to as the swing equations, is often used in power network stability studies, see e.g. [4,11,13,31].…”

Section: The Classical Multi-machine Networkmentioning

confidence: 99%

An energy-based analysis of reduced-order models of (networked) synchronous machines

Persis

Schaft

2019

Mathematical and Computer Modelling of Dynamical Systems

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Stability of power networks is an increasingly important topic because of the high penetration of renewable distributed generation units. This requires the development of advanced (typically model-based) techniques for the analysis and controller design of power networks. Although there are widely accepted reduced-order models to describe the dynamic behavior of power networks, they are commonly presented without details about the reduction procedure, hampering the understanding of the physical phenomena behind them. The present paper aims to provide a modular model derivation of multi-machine power networks. Starting from first-principle fundamental physics, we present detailed dynamical models of synchronous machines and clearly state the underlying assumptions which lead to some of the standard reduced-order multi-machine models, including the classical second-order swing equations. In addition, the energy functions for the reduced-order multi-machine models are derived, which allows to represent the multi-machine systems as port-Hamiltonian systems. Moreover, the systems are proven to be passive with respect to its steady states, which permits for a power-preserving interconnection with other passive components, including passive controllers. As a result, the corresponding energy function or Hamiltonian can be used to provide a rigorous stability analysis of advanced models for the power network without having to linearize the system.

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“…Alternatively, the LaSalle Invariance Principle can be used to guarantee the stability for a certain combination of cost functions and constraints in [21], [25]. Recently, the continuous-time port-Hamiltonian description of the gradient method has been proposed in [20] [27], which results have motivated this work.…”

Section: Introductionmentioning

confidence: 99%

Port-Hamiltonian based Optimal Power Flow algorithm for multi-terminal DC networks

Benedito

Puerto-Flores

Dòria‐Cerezo

et al. 2019

Control Engineering Practice

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In this paper an algorithm for solving the Optimal Power Flow problem for multi-terminal DC networks based on the gradient method is proposed. The aim is seeking the optimal point subject to voltage, current and power constraints. The algorithm is described by a continuous-time port-Hamiltonian model, and the inequality constrains are included by the use of barrier functions. The dynamics of the algorithm is studied and stability conditions are obtained. Finally, the method is used for the offshore wind integration grid in the North Sea and the interconnection with the network dynamics is tested by means of numerical simulations.

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

Cited by 17 publications

References 10 publications

A Unifying Energy-Based Approach to Stability of Power Grids With Market Dynamics

A Unifying Energy-Based Approach to Stability of Power Grids With Market Dynamics

An energy-based analysis of reduced-order models of (networked) synchronous machines

Port-Hamiltonian based Optimal Power Flow algorithm for multi-terminal DC networks

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