Stability and steady state analysis of distributed cooperative droop controlled DC microgrids

Distributed cooperative droop control consisting of the primary decentralized droop control and the {secondary} distributed correction control is studied in this paper, which aims to achieve an exact current sharing between generators, worked in the voltage control mode, of DC microgrids. For the DC microgrids with the distributed cooperative droop control, the dynamic stability has not been well investigated although its steady performance has been widely reported. This paper focuses on the stability problem and shows it is equivalent to the semistability problem of a class of second-order matrix systems. Some further sufficient conditions as well followed. The steady state is analyzed deeply for some special cases. A DC microgrid of three nodes is simulated on the Matlab/Simulink platform to illustrate the efficacy of analytic results.

[1]  Juan C. Vasquez,et al.  An Improved Droop Control Method for DC Microgrids Based on Low Bandwidth Communication With DC Bus Voltage Restoration and Enhanced Current Sharing Accuracy , 2014, IEEE Transactions on Power Electronics.

[2]  Arindam Ghosh,et al.  Smart Coordination of Energy Storage Units (ESUs) for Voltage and Loading Management in Distribution Networks , 2013, IEEE Transactions on Power Systems.

[3]  Frank L. Lewis,et al.  Distributed adaptive droop control for DC distribution systems , 2016 .

[4]  Ali Mehrizi-Sani,et al.  Distributed Control Techniques in Microgrids , 2014, IEEE Transactions on Smart Grid.

[5]  Qing Hui.  Optimal semistable control for continuous-time linear systems , 2011, Syst. Control. Lett..

[6]  R. Adapa,et al.  Expandable multiterminal DC systems based on voltage droop , 1993 .

[7]  Yasser Abdel-Rady I. Mohamed,et al.  Assessment and Mitigation of Interaction Dynamics in Hybrid AC/DC Distribution Generation Systems , 2012, IEEE Transactions on Smart Grid.

[8]  B. G. Fernandes,et al.  Distributed Control to Ensure Proportional Load Sharing and Improve Voltage Regulation in Low-Voltage DC Microgrids , 2013, IEEE Transactions on Power Electronics.

[9]  Karl Henrik Johansson,et al.  Distributed Controllers for Multi-Terminal HVDC Transmission Systems , 2014 .

[10]  Juan C. Vasquez,et al.  Hierarchical Control of Droop-Controlled AC and DC Microgrids—A General Approach Toward Standardization , 2009, IEEE Transactions on Industrial Electronics.

[11]  Osama A. Mohammed,et al.  DC microgrids and distribution systems: An overview , 2013, 2013 IEEE Power & Energy Society General Meeting.

[12]  Jon Andreu,et al.  AC and DC technology in microgrids: A review , 2015 .

[13]  M. Araki.  Stability of large-scale nonlinear systems--Quadratic-order theory of composite-system method using M-matrices , 1978 .

[14]  S. Campbell,et al.  Singular Perturbation of Autonomous Linear Systems , 1979 .

[15]  Ronnie Belmans,et al.  Analysis of Power Sharing and Voltage Deviations in Droop-Controlled DC Grids , 2013, IEEE Transactions on Power Systems.

[16]  S. Bhat,et al.  Lyapunov analysis of semistability , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[17]  Ju Lee,et al.  AC-microgrids versus DC-microgrids with distributed energy resources: A review , 2013 .

[18]  S. Bhat,et al.  Lyapunov Stability, Semistability, and Asymptotic Stability of Matrix Second-Order Systems , 1995 .

[19]  Bill Rose,et al.  Microgrids , 2018, Smart Grids.

[20]  Rama K. Yedavalli,et al.  Stability of matrix second-order systems: new conditions and perspectives , 1999, IEEE Trans. Autom. Control..

[21]  Juan C. Vasquez,et al.  Supervisory Control of an Adaptive-Droop Regulated DC Microgrid With Battery Management Capability , 2014, IEEE Transactions on Power Electronics.

[22]  Frank L. Lewis,et al.  Distributed Cooperative Control of DC Microgrids , 2015, IEEE Transactions on Power Electronics.

[23]  I. Dincer.  Renewable energy and sustainable development: a crucial review , 2000 .

[24]  Wassim M. Haddad,et al.  2 optimal semistable stabilisation for linear discrete-time dynamical systems with applications to network consensus , 2009, Int. J. Control.

[25]  T. M. Haileselassie,et al.  Impact of DC Line Voltage Drops on Power Flow of MTDC Using Droop Control , 2012, IEEE Transactions on Power Systems.

[26]  Sanjay P. Bhat,et al.  Finite-Time Semistability and Consensus for Nonlinear Dynamical Networks , 2008, IEEE Transactions on Automatic Control.

[27]  Florian Dörfler,et al.  Kron Reduction of Graphs With Applications to Electrical Networks , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[28]  Xiwei Liu.  Distributed nonlinear control algorithms for network consensus , 2010 .

[29]  Florian Dörfler,et al.  Distributed control, load sharing, and dispatch in DC microgrids , 2015, 2015 American Control Conference (ACC).

[30]  B. G. Fernandes,et al.  Reduced-Order Model and Stability Analysis of Low-Voltage DC Microgrid , 2013, IEEE Transactions on Industrial Electronics.