Stability of Synchronized Motions of Inverter–Based Microgrids Under Droop Control

Abstract

ReuseUnless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version -refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher's website. TakedownIf you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request. Rome, Italy (e-mail: a.astolfi@ic.ac.uk) * * * * Max-Planck-Institut für Dynamik komplexer technischer Systeme, Germany (e-mail: raisch@control.tu-berlin.de) 3 Siemens AG, Germany (e-mail: tevfik.sezi@siemens.com) Stability of Synchronized Motions of Abstract:We consider the problems of frequency stability, voltage stability and power sharing in droop-controlled inverter-based microgrids with meshed topologies and dominantly inductive power lines. Assuming that the conductances in the microgrid can be neglected, a portHamiltonian description of a droop-controlled microgrid is derived. The model is used to establish sufficient conditions for local stability. Furthermore, we propose a condition for the controller parameters such that a desired steady-state active power distribution is achieved. The robustness of the stability condition with respect to the presence of conductances is analyzed via a simulation example based on the CIGRE benchmark medium voltage distribution network.

Conditions for stability of droop-controlled inverter-based microgrids

“…The present work extends our results in [37] in several regards: first, conditions for global boundedness are given for lossy microgrids; second, we relate the spectral properties of the local network couplings between the phase angles and the active power flows of the microgrid in portHamiltonian form (which has a reduced state vector in relative coordinates) to those of the microgrid in absolute coordinates; third, making use of the global boundedness result, a relaxed stability condition for a lossless microgrid under a specific parameter selection of the controller gains and setpoints of the frequency droop control is derived; finally, the theoretical analysis is illustrated via detailed simulation scenarios.…”

“…and in analogy to (37) it holds that the invariant set wherė H(z(t)) ≡ 0 is an equilibrium set. Moreover, it follows from Proposition 4.2 that the state z = col(θ,ω, V ) ∈ Γ is globally bounded.…”

“…Instead, we adopt a classical Lyapunov-like approach for analysis of stability of equilibria and boundedness of trajectories. Following the interconnection and damping assignment passivity-based control approach [30,37], we represent the lossless microgrid system in portHamiltonian form [34] to identify the energy-Lyapunov function and give conditions for stability of the frequency synchronization equilibrium state.…”

Decentralised control of parallel inverters connected to microgrid using the derivative‐free non‐linear Kalman filter

“…This synchronisation enables better integration of DC renewable energy units to the grid. The functioning of the ith inverter is shown to be equivalent to a synchronous generator with turn speed denoted as ω i [15][16][17][18][19]44]. In this modelling approach one has…”

“…where J i is the virtual inertia, D p i is the virtual damping coefficient, P d i is the desirable active power of the ith unit and P i and the measured active power, G ij is a coupling coefficient between the ith and the jth power generation unit and sin(δ i − δ j ) is a synchronisation index between the ith and the jth power generation unit [15][16][17][18][19]44]. The electrical part has been defined in Section 2 and is given by (see (77)) The synchronising control approach for the ith inverter makes use of (76) and of the linearised inverter model given in (77).…”