Robustness of distributed averaging control in power systems: Time delays & dynamic communication topology

Distributed averaging-based integral (DAI) controllers are becoming increasingly popular in power system applications. The literature has thus far primarily focused on disturbance rejection, steady-state optimality and adaption to complex physical system models without considering uncertainties on the cyber and communication layer nor their effect on robustness and performance. In this paper, we derive sufficient delay-dependent conditions for robust stability of a secondary-frequency-DAI-controlled power system with respect to heterogeneous communication delays, link failures and packet losses. Our analysis takes into account both constant as well as fast-varying delays, and it is based on a common strictly decreasing Lyapunov–Krasovskii functional. The conditions illustrate an inherent trade-off between robustness and performance of DAI controllers. The effectiveness and tightness of our stability certificates are illustrated via a numerical example based on Kundur’s four-machine-two-area test system.

[1]  Peng Yang,et al.  Stability and Convergence Properties of Dynamic Average Consensus Estimators , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[2]  Claudio De Persis,et al.  An internal model approach to (optimal) frequency regulation in power grids with time-varying voltages , 2014, Autom..

[3]  Johannes Schiffer,et al.  Stability and power sharing in microgrids , 2015 .

[4]  Josep M. Guerrero,et al.  Secondary Control Strategies for Frequency Restoration in Islanded Microgrids with Consideration of Communication Delays , 2015 .

[5]  Arjan van der Schaft,et al.  A unifying energy-based approach to optimal frequency and market regulation in power grids , 2015 .

[6]  Rafael Wisniewski,et al.  Active power management in power distribution grids: Disturbance modeling and rejection , 2016, 2016 European Control Conference (ECC).

[7]  K. R. Padiyar,et al.  ENERGY FUNCTION ANALYSIS FOR POWER SYSTEM STABILITY , 1990 .

[8]  Jie Lin,et al.  Coordination of groups of mobile autonomous agents using nearest neighbor rules , 2003, IEEE Trans. Autom. Control..

[9]  Xuan Zhang,et al.  Redesigning generation control in power systems: Methodology, stability and delay robustness , 2014, 53rd IEEE Conference on Decision and Control.

[10]  Babu Narayanan,et al.  Power system stability and control , 2007 .

[11]  Alessandro Astolfi,et al.  Conditions for stability of droop-controlled inverter-based microgrids , 2014, Autom..

[12]  Karl Henrik Johansson,et al.  Distributed integral action: Stability analysis and frequency control of power systems , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[13]  Timothy C. Green,et al.  Communication Infrastructures for Distributed Control of Power Distribution Networks , 2011, IEEE Transactions on Industrial Informatics.

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

[15]  Emilia Fridman,et al.  Robust sampled-data stabilization of linear systems: an input delay approach , 2004, Autom..

[16]  Wilhelm Winter,et al.  Pushing the Limits: Europe's New Grid: Innovative Tools to Combat Transmission Bottlenecks and Reduced Inertia , 2015, IEEE Power and Energy Magazine.

[17]  Antonis Papachristodoulou,et al.  Real-time active and reactive power regulation in power systems with tap-changing transformers and controllable loads , 2016 .

[18]  Juan C. Vasquez,et al.  Small-Signal Analysis of the Microgrid Secondary Control Considering a Communication Time Delay , 2016, IEEE Transactions on Industrial Electronics.

[19]  Xinghuo Yu,et al.  Droop-Based Distributed Cooperative Control for Microgrids With Time-Varying Delays , 2016, IEEE Transactions on Smart Grid.

[20]  Gordon F. Royle,et al.  Algebraic Graph Theory , 2001, Graduate texts in mathematics.

[21]  J. Lofberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004, 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508).

[22]  Arjan van der Schaft,et al.  Optimal power dispatch in networks of high-dimensional models of synchronous machines , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

[23]  Kun Liu,et al.  Wirtinger's inequality and Lyapunov-based sampled-data stabilization , 2012, Autom..

[24]  Claudio De Persis,et al.  Agreeing in networks: Unmatched disturbances, algebraic constraints and optimality , 2017, Autom..

[25]  PooGyeon Park,et al.  Reciprocally convex approach to stability of systems with time-varying delays , 2011, Autom..

[26]  Peter Xiaoping Liu,et al.  Impact of Communication Delays on Secondary Frequency Control in an Islanded Microgrid , 2015, IEEE Transactions on Industrial Electronics.

[27]  Francesco Bullo,et al.  Breaking the Hierarchy: Distributed Control and Economic Optimality in Microgrids , 2014, IEEE Transactions on Control of Network Systems.

[28]  Reza Olfati-Saber,et al.  Consensus and Cooperation in Networked Multi-Agent Systems , 2007, Proceedings of the IEEE.

[29]  Emilia Fridman,et al.  Tutorial on Lyapunov-based methods for time-delay systems , 2014, Eur. J. Control.

[30]  A. D. Lewis,et al.  Geometric control of mechanical systems : modeling, analysis, and design for simple mechanical control systems , 2005 .

[31]  Frank L. Lewis,et al.  Distributed Control Systems for Small-Scale Power Networks: Using Multiagent Cooperative Control Theory , 2014, IEEE Control Systems.

[32]  S.D.J. McArthur,et al.  Multi-Agent Systems for Power Engineering Applications—Part I: Concepts, Approaches, and Technical Challenges , 2007, IEEE Transactions on Power Systems.

[33]  M. Balaji,et al.  CONTROL OF POWER INVERTERS IN RENEWABLE ENERGY AND SMART GRID INTEGRATION , 2013 .

[34]  Johannes Schiffer,et al.  Synchronization of droop-controlled microgrids with distributed rotational and electronic generation , 2013, 52nd IEEE Conference on Decision and Control.

[35]  Emilia Fridman,et al.  Stability of a class of delayed port-Hamiltonian systems with application to microgrids with distributed rotational and electronic generation , 2016, Autom..

[36]  Johannes Schiffer,et al.  On stability of a distributed averaging PI frequency and active power controlled differential-algebraic power system model , 2016, 2016 European Control Conference (ECC).

[37]  João Pedro Hespanha,et al.  A Survey of Recent Results in Networked Control Systems , 2007, Proceedings of the IEEE.

[38]  Qing-Guo Wang.  Necessary and sufficient conditions for stability of a matrix polytope with normal vertex matrices , 1991, Autom..

[39]  Xiaoqing Lu,et al.  Distributed power control for DERs based on networked multiagent systems with communication delays , 2016, Neurocomputing.

[40]  P. Olver.  Nonlinear Systems , 2013 .

[41]  OrtegaRomeo,et al.  A survey on modeling of microgrids-From fundamental physics to phasors and voltage sources , 2016 .

[42]  Johan Löfberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004 .

[43]  Goran Strbac,et al.  Microgrids: Enhancing the Resilience of the European Megagrid , 2015, IEEE Power and Energy Magazine.

[44]  Arjan van der Schaft,et al.  A Unifying Energy-Based Approach to Stability of Power Grids With Market Dynamics , 2016, IEEE Transactions on Automatic Control.

[45]  Enrique Mallada,et al.  Distributed frequency control for stability and economic dispatch in power networks , 2015, 2015 American Control Conference (ACC).

[46]  Johannes Schiffer,et al.  A Lyapunov approach to control of microgrids with a network-preserved differential-algebraic model , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

[47]  Mihailo R. Jovanovic,et al.  Input-Output Analysis and Decentralized Optimal Control of Inter-Area Oscillations in Power Systems , 2016, IEEE Transactions on Power Systems.

[48]  Peng Lin,et al.  Average consensus in networks of multi-agents with both switching topology and coupling time-delay , 2008 .

[49]  Francesco Bullo,et al.  Synchronization and power sharing for droop-controlled inverters in islanded microgrids , 2012, Autom..

[50]  Emilia Fridman,et al.  Introduction to Time-Delay Systems: Analysis and Control , 2014 .

[51]  Emilia Fridman,et al.  Stability of a class of delayed port-Hamiltonian systems with application to droop-controlled microgrids , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[52]  Richard M. Murray,et al.  Consensus problems in networks of agents with switching topology and time-delays , 2004, IEEE Transactions on Automatic Control.