A modular design of incremental Lyapunov functions for microgrid control with power sharing

Persis, Claudio De; Monshizadeh, Nima

doi:10.1109/ecc.2016.7810502

Cited by 11 publications

(17 citation statements)

References 38 publications

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“…In addition, the Hessian condition guarantees the existence of a local storage function around the equilibrium. The following result, which establishes decentralized conditions for checking the positive definiteness of the Hessian, was proven in [28]:…”

Section: B Power Network Modelmentioning

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.

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: B Power Network Modelmentioning

confidence: 99%

“…Proof. Let (z,μ) be the equilibrium of (28). By defining the shifted HamiltonianH(x) aroundx := τz bȳ…”

Section: B Including Line Congestion and Transmission Costsmentioning

confidence: 99%

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

Stegink

Persis

Schaft

2017

IEEE Trans. Automat. Contr.

155

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“…The Lyapunov functions in this case are constructed starting from the power dissipated in the network that is further shaped to take into account the specifics of the dynamics. The presence of the loads, which shift the equilibrium of interest, is taken into account by the so-called Bregman function [16]. The level sets of the Lyapunov functions are used to estimate the excursion of the state response of these systems and therefore, combined with the preservation of the geometric average of the source voltages, can be used to obtain an estimate of the voltage at steady state.…”

Section: Main Contributionmentioning

confidence: 99%

A power consensus algorithm for DC microgrids

Persis¹,

Weitenberg²,

2018

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A novel power consensus algorithm for DC microgrids is proposed and analyzed. DC microgrids are networks composed of DC sources, loads, and interconnecting lines. They are represented by differential-algebraic equations connected over an undirected weighted graph that models the electrical circuit. A second graph represents the communication network over which the source nodes exchange information about the instantaneous powers, which is used to adjust the injected current accordingly. This give rise to a nonlinear consensus-like system of differential-algebraic equations that is analyzed via Lyapunov functions inspired by the physics of the system. We establish convergence to the set of equilibria consisting of weighted consensus power vectors as well as preservation of the weighted geometric mean of the source voltages. The results apply to networks with constant impedance, constant current and constant power loads.

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“…where M i > 0, D i > 0 are constants, and P ij is the line power from bus i to bus j. This model is suitable for both synchronous generators and inverters [37]- [39]. (28) can be rewritten as…”

Section: B Real-time Asdpdmentioning

confidence: 99%

Asynchronous Distributed Power Control of Multimicrogrid Systems

Wang

Chen

Liu

et al. 2020

IEEE Trans. Control Netw. Syst.

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Asynchrony widely exists in microgrids (MGs), such as non-identical sampling rates and communication delays, which challenges the MG control. This paper addresses the asynchronous distributed power control problem of hybrid microgrids, considering different kinds of asynchrony, such as non-identical sampling rates and random time delays. To this end, we first formulate the economic dispatch problem of MGs and devise a synchronous algorithm. Then, we analyze the impact of asynchrony and propose an asynchronous iteration algorithm based on the synchronous version. By introducing a random clock at each iteration, different types of asynchrony are fitted into a unified framework, where the asynchronous algorithm is converted into a fixed-point iteration problem with a nonexpansive operator, leading to a convergence proof. We further provide an upper bound estimation of the time delay of the communication. Moreover, the real-time implementation of the proposed algorithm in both AC and DC MGs is introduced. By measuring the frequency/voltage, the controller is simplified by reducing one order and adapt to the fast varying load demand. Finally, simulations on a benchmark MG and experiments are utilized to verify the effectiveness and advantages of the proposed algorithm. Index Terms-Asynchronous control, distributed control, multi-agent system, multi-microgrid networks, time delay. I. INTRODUCTION Multi-Microgrid systems or Microgrids (MGs) are clusters of distributed generators (DGs), energy storage systems and loads, which are generally categorized into three types: AC, DC and hybrid AC/DC MGs [1], [2]. A hybrid AC/DC MG has the advantage of reducing processes of multiple inverse conversions in the involved individual AC or DC grid [3]. Recently, the distributed power control for MGs has attracted more and more attention due to its fast response speed, privacy

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A modular design of incremental Lyapunov functions for microgrid control with power sharing

Cited by 11 publications

References 38 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

A power consensus algorithm for DC microgrids

Asynchronous Distributed Power Control of Multimicrogrid Systems

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