A “Globally” Convergent Controller for Multi-Machine Power Systems Using Structure-Preserving Models

Dib, Wissam; Ortega, Roméo; Barabanov, Andrey E.; Lamnabhi-Lagarrigue, F.

doi:10.1109/tac.2009.2026834

Cited by 37 publications

(27 citation statements)

References 17 publications

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“…The inclusion of this term destroys the natural topology of the system, e.g., with θ ∈ S n−1 , and we have to look at the system with θ evolving in R n−1 -which is not a bounded set. See Remark 7 of [8] for further discussion on this point that, unfortunately, is often overlooked in the literature.…”

Section: A Relaxed Stability Conditionmentioning

confidence: 99%

Conditions for stability of droop-controlled inverter-based microgrids

Schiffer¹,

Ortega²,

Astolfi³

et al. 2014

Automatica

384

367

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We consider the problem of stability analysis for droop-controlled inverter-based microgrids with meshed topologies. The inverter models include variable frequencies as well as voltage amplitudes. Conditions on the tuning gains and setpoints for frequency and voltage stability, together with desired active power sharing, are derived in the paper. First, we prove that for all practical choices of these parameters global boundedness of trajectories is ensured. Subsequently, assuming the microgrid is lossless, a port-Hamiltonian description is derived, from which sufficient conditions for stability are given. Finally, we propose for generic lossy microgrids a design criterion for the controller gains and setpoints such that a desired steady-state active power distribution is achieved. The analysis is validated via simulation on a microgrid based on the CIGRE (Conseil International des Grands Réseaux Electriques) benchmark medium voltage distribution network.

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Section: A Relaxed Stability Conditionmentioning

confidence: 99%

Conditions for stability of droop-controlled inverter-based microgrids

Schiffer¹,

Ortega²,

Astolfi³

et al. 2014

Automatica

384

367

View full text Add to dashboard Cite

show abstract

“…The objective of control design is to guarantee the decay of Lyapunov function V e whether ς-saturation happens or not. Thus, from equation (14) and Lemma 2, one can conclude this proof. □□ Remark 1.…”

Section: )mentioning

confidence: 55%

“…: Tech. XX(Y) 2016 (14) where A k = A when there is no saturation, and A k = A kς = A + + (ς ¡ 1)br when there is ς-saturation, ε is disturbance attenuation constant.…”

Section: Some Discussionmentioning

confidence: 99%

“…Thus, on the basis of the classical SMIB model [17,18] and the above statements, the system dynamic model considered in this paper is proposed as follows: model [13,14], the SMIB model does not directly reflect the influences of power network components and loads, instead of aggregated node containing the information of these elements. Furthermore, the reduced-order model also neglects the flux linkages dynamics by using the singular perturbation technique.…”

Section: Problem Statement and System Modelmentioning

confidence: 99%

“…(1) model [13,14], the SMIB model does not directly reflect the influences of power network components and loads, instead of aggregated node containing the information of these elements. Furthermore, the reduced-order model also neglects the flux linkages dynamics by using the singular perturbation technique.…”

Section: Is Equivalent To Q(x) Q(x) Q(x) − S(x) S(x) S(x)r(x) R(x) R(mentioning

confidence: 99%

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Nonlinear robust control for single-machine infinite-bus power systems with input saturation

Wan

2017

Bulletin of the Polish Academy of Sciences Technical Sciences

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Abstract. In this paper, a new control scheme is proposed to achieve stability for a single-machine infinite-bus power system. A power system model simultaneously considering input saturation and time-varying uncertainties is presented. A sufficient condition for the system convergence is given and based on this result, a switching excitation control law with auxiliary system is designed. The stability analysis and simulation results all show that the developed controller is effective.Key words: nonlinear robust control, input saturation, generator excitation, single-machine infinite-bus power systems (SMIB).Nonlinear robust control for single-machine infinite-bus power systems with input saturation Y. WAN * College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China tion to the control problem of nonlinear systems with input saturation. In [9], an auxiliary system is employed to address input constraints, but only boundedness of the "last modified virtual error" is obtained. If the desired value of control input greatly exceeds the constraints, then the auxiliary system will be unstable and thus the convergence of the "last virtual error" to the origin cannot be ensured. In [10], the tanh function and the mean-value theorem are used to deal with the saturation function, and then the redial basis function i.e. neural network is employed to approximate the unknown control gain. However, since the tanh function is also a kind of bounded function, when there are large disturbances and the desired value of control input goes beyond the range of tanh, the efficacy of the designed control law may be limited. In [11], dynamic surface control is used to equivalently transform a class of nonlinear system into a linear system, and then the region of attraction which is enlarged to allow some degree of input saturation is estimated via a linear matrix inequality method [12]. But this approach does not give a solution for a case when the initial condition is out of this region of attraction. This article proposes a new nonlinear robust control framework to tackle the stabilization problem for a class of nonlinear system with time-varying uncertainties and input saturation. Compared with the prior works, the proposed method ensures not only the boundedness of state variables but the global stability of the closed-loop system. Furthermore, the approach proposed processes the saturation phenomenon directly and does not require approximating the saturation function by a smooth function, which is often not invertible outside its range.The paper is organized as follows: the preliminaries and a SMIB power system model are described in Section 2. In Section 3, a sufficient condition for the convergence of states to the origin under saturation is shown in a Theorem, and then on the basis of this result, a switching excitation control law with auxiliary system (SAEC) is designed, as well as stability analysis for the closed-loop system with the designed controller. The simulation resul...

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Transient Stability Enhancement of Multi–Machine Power Systems: Synchronization via Immersion of a Pendular System

Dib

Ortega

Hill³

2012

Asian Journal of Control

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International audienceIn this paper the problem of designing excitation controllers to improve the transient stability of multi-machine power systems is addressed adopting two new perspectives. First, instead of the standard formulation of stabilization of an equilibrium point, we aim here at the more realistic objective of keeping the difference between the generators rotor angles bounded and their speeds equal—which is called synchronization in the power literature—and translates into a problem of stabilization of a set. Second, we adopt the classical viewpoint of power systems as a set of coupled nonlinear pendula, and express our control objective as ensuring that some suitable defined pendula dynamics are (asymptotically) immersed into the power system dynamics. Our main contribution is the explicit computation of a control law for the two–machine system that achieves global synchronization. The same procedure is applicable to the n–machine case, for which the existence of a locally stabilizing solution is established

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A “Globally” Convergent Controller for Multi-Machine Power Systems Using Structure-Preserving Models

Cited by 37 publications

References 17 publications

Conditions for stability of droop-controlled inverter-based microgrids

Conditions for stability of droop-controlled inverter-based microgrids

Nonlinear robust control for single-machine infinite-bus power systems with input saturation

Transient Stability Enhancement of Multi–Machine Power Systems: Synchronization via Immersion of a Pendular System

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