Impact of stability conditions on protective relaying

This paper proposes a state-feedback controller using the linear matrix inequality (LMI) approach for the robust position control of a 1-DoF, periodically forced, impact mechanical oscillator subject to asymmetric two-sided rigid end-stops. The periodic forcing input is considered as a persistent external disturbance. The motion of the impacting oscillator is modeled by an impulsive hybrid dynamics. Thus, the control problem of the impact oscillator is recast as a problem of the robust control of such disturbed impulsive hybrid system. To synthesize stability conditions, we introduce the S-procedure and the Finsler lemmas by only considering the region within which the state evolves. We show that the stability conditions are first expressed in terms of bilinear matrix inequalities (BMIs). Using some technical lemmas, we convert these BMIs into LMIs. Finally, some numerical results and simulations are given. We show the effectiveness of the designed state-feedback controller in the robust stabilization of the position of the impact mechanical oscillator under the disturbance.

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PROTECTIVE RELAYING

Arc Flash Hazard Analysis and Mitigation ◽

10.1002/9781119709787.ch7 ◽

2020 ◽

pp. 206-266

Keyword(s):

Protective Relaying

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Stability conditions for thermodiffusion Timoshenko system with second sound

Zeitschrift für angewandte Mathematik und Physik ◽

10.1007/s00033-021-01580-0 ◽

2021 ◽

Vol 72 (4) ◽

Author(s):

Moncef Aouadi ◽

Anderson Ramos ◽

Alberto Castejón

Keyword(s):

Stability Conditions ◽

Second Sound ◽

Timoshenko System

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An extension of the Levy-Desplanque theorem and some stability conditions for matrices with uncertain entries

IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications ◽

10.1109/81.554337 ◽

1997 ◽

Vol 44 (2) ◽

pp. 167-170 ◽

Cited By ~ 6

Author(s):

L. Naimark ◽

E. Zeheb

Keyword(s):

Stability Conditions

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Optimization-Based Formulations for Short-Circuit Studies with Inverter-Interfaced Generation in PowerModelsProtection.jl

Energies ◽

10.3390/en14082160 ◽

2021 ◽

Vol 14 (8) ◽

pp. 2160

Author(s):

Arthur K. Barnes ◽

Jose E. Tabarez ◽

Adam Mate ◽

Russell W. Bent

Keyword(s):

Optimization Problem ◽

Short Circuit ◽

Problem Formulation ◽

Power Delivery ◽

Fault Current ◽

Protective Device ◽

Protective Relaying ◽

Overcurrent Protection ◽

Short Circuits ◽

Optimization Problem Formulation

Protecting inverter-interfaced microgrids is challenging as conventional time-overcurrent protection becomes unusable due to the lack of fault current. There is a great need for novel protective relaying methods that enable the application of protection coordination on microgrids, thereby allowing for microgrids with larger areas and numbers of loads while not compromising reliable power delivery. Tools for modeling and analyzing such microgrids under fault conditions are necessary in order to help design such protective relaying and operate microgrids in a configuration that can be protected, though there is currently a lack of tools applicable to inverter-interfaced microgrids. This paper introduces the concept of applying an optimization problem formulation to the topic of inverter-interfaced microgrid fault modeling, and discusses how it can be employed both for simulating short-circuits and as a set of constraints for optimal microgrid operation to ensure protective device coordination.

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