Toward Distributed Stability Analytics for Power Systems with Heterogeneous Bus Dynamics

The stability issue emerges as a growing number of diverse power apparatus connecting to the power system. The stability analysis for such power systems is required to adapt to heterogeneity and scalability. This paper derives a local passivity index condition that guarantees the system-wide stability for lossless power systems with interconnected, nonlinear, heterogeneous bus dynamics. Our condition requires each bus dynamics to be output feedback passive with a large enough index w.r.t. a special supply rate. This condition fits for numerous existing models since it only constrains the input-output property rather than the detailed dynamics. Furthermore, for three typical examples of bus dynamics in power systems, we show that this condition can be reached via proper control designs. Simulations on a 3-bus heterogeneous power system verify our results in both lossless and lossy cases. The conservativeness of our condition is also demonstrated, as well as the impact on transient stability. It shows that our condition is quite tight and a larger index benefits transient stability.

[1]  Feng Liu,et al.  Towards Distributed Stability Analytics of Dynamic Power Systems: A Phasor-Circuit Theory Perspective , 2019, 2019 Chinese Control Conference (CCC).

[2]  Graziano Chesi,et al.  Consensus of Heterogeneous Multi-Agent Systems With Diffusive Couplings via Passivity Indices , 2019, IEEE Control Systems Letters.

[3]  Tao Liu,et al.  A Distributed Framework for Stability Evaluation and Enhancement of Inverter-Based Microgrids , 2017, IEEE Transactions on Smart Grid.

[4]  Yun Zhang,et al.  A Transient Stability Assessment Framework in Power Electronic-Interfaced Distribution Systems , 2016, IEEE Transactions on Power Systems.

[5]  J.M.A. Scherpen,et al.  Multidomain modeling of nonlinear networks and systems , 2009, IEEE Control Systems.

[6]  T.C. Green,et al.  Modeling, Analysis and Testing of Autonomous Operation of an Inverter-Based Microgrid , 2007, IEEE Transactions on Power Electronics.

[7]  Jacquelien M. A. Scherpen,et al.  A port-Hamiltonian approach to power network modeling and analysis , 2013, Eur. J. Control.

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

[9]  Michael Chertkov,et al.  Synchronization in complex oscillator networks and smart grids , 2012, Proceedings of the National Academy of Sciences.

[10]  Pravin Varaiya,et al.  Hierarchical stability and alert state steering control of interconnected power systems , 1980 .

[11]  Wei Hu,et al.  An energy-based method for location of power system oscillation source , 2013, IEEE Transactions on Power Systems.

[12]  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.

[13]  Shengwei Mei,et al.  Distributed Optimal Frequency Control Considering a Nonlinear Network-Preserving Model , 2017, IEEE Transactions on Power Systems.

[14]  Diana Bohm,et al.  L2 Gain And Passivity Techniques In Nonlinear Control , 2016 .

[15]  Chia-Chi Chu,et al.  Direct stability analysis of electric power systems using energy functions: theory, applications, and perspective , 1995, Proc. IEEE.

[16]  Peter L. Lee,et al.  Process Control: The Passive Systems Approach , 2010 .

[17]  Romeo Ortega,et al.  Modeling of microgrids - from fundamental physics to phasors and voltage sources , 2015, Autom..

[18]  Yun Zhang,et al.  Online Dynamic Security Assessment of Microgrid Interconnections in Smart Distribution Systems , 2015, IEEE Transactions on Power Systems.

[19]  Soumya Kundu,et al.  A sum-of-squares approach to the stability and control of interconnected systems using vector Lyapunov functions , 2015, 2015 American Control Conference (ACC).

[20]  B. Stott,et al.  Power system dynamic response calculations , 1979, Proceedings of the IEEE.

[21]  Florian Dörfler,et al.  Voltage stabilization in microgrids via quadratic droop control , 2013, 52nd IEEE Conference on Decision and Control.

[22]  A. Schaft.  Port-Hamiltonian Systems: Network Modeling and Control of Nonlinear Physical Systems , 2004 .

[23]  Feng Liu,et al.  Distributed Frequency Control with Operational Constraints, Part II: Network Power Balance , 2017, 2018 IEEE Power & Energy Society General Meeting (PESGM).

[24]  Mrdjan J. Jankovic,et al.  Constructive Nonlinear Control , 2011 .

[25]  Jacquelien M. A. Scherpen,et al.  Power shaping: a new paradigm for stabilization of nonlinear RLC circuits , 2003, IEEE Trans. Autom. Control..

[26]  Shengwei Mei,et al.  Distributed Frequency Control With Operational Constraints, Part I: Per-Node Power Balance , 2017, IEEE Transactions on Smart Grid.

[27]  Ioannis Lestas,et al.  Primary Frequency Regulation With Load-Side Participation—Part I: Stability and Optimality , 2016, IEEE Transactions on Power Systems.

[28]  Marija D. Ilic,et al.  Toward standards for model-based control of dynamic interactions in large electric power grids , 2012, Proceedings of The 2012 Asia Pacific Signal and Information Processing Association Annual Summit and Conference.

[29]  Paulo Tabuada,et al.  Compositional Transient Stability Analysis of Multimachine Power Networks , 2013, IEEE Transactions on Control of Network Systems.

[30]  Feng Liu,et al.  Distributed Load-Side Control: Coping with Variation of Renewable Generations , 2019, Autom..