Stability Analysis of Droop-Controlled Inverter-Based Power Grids via Timescale Separation

We consider the problem of stability analysis for distribution grids with linearized droop-controlled inverter and line dynamics. The inverters are modeled as voltage sources with controllable frequency and amplitude. This problem is very challenging for large networks as numerical simulations and detailed eigenvalue analysis are impactical. Motivated by the above limitations, we present in this paper a systematic and computationally efficient framework for stability analysis of inverter-based distribution grids. To design our framework, we use tools from singular perturbation and Lyapunov theories. Interestingly, we show that stability of the fast dynamics of the power grid depends only on the voltage droop gains of the inverters while, stability of the slow dynamics, depends on both voltage and frequency droop gains. Finally, by leveraging these timescale separation properties, we derive sufficient conditions on the frequency and voltage droop gains of the inverters that warrant stability of the full system. We illustrate our theoretical results through a numerical example on the IEEE 13-bus distribution grid.

[1]  Anuradha M. Annaswamy,et al.  Emerging research topics in control for smart infrastructures , 2016, Annu. Rev. Control..

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

[3]  Anuradha M. Annaswamy,et al.  Distributed optimal wind farm control for fatigue load minimization: A consensus approach , 2019 .

[4]  Marija D. Ilić,et al.  A Consensus Approach to Real-Time Distributed Control of Energy Storage Systems in Wind Farms , 2019, IEEE Transactions on Smart Grid.

[5]  James L. Kirtley,et al.  A framework for development of universal rules for microgrids stability and control , 2017, 2017 IEEE 56th Annual Conference on Decision and Control (CDC).

[6]  Peter W. Sauer,et al.  A Hierarchy of Models for Inverter-Based Microgrids , 2018 .

[7]  Marcello Colombino,et al.  The Effect of Transmission-Line Dynamics on Grid-Forming Dispatchable Virtual Oscillator Control , 2018, IEEE Transactions on Control of Network Systems.

[8]  Francesco Vasca,et al.  Model Order Reductions for Stability Analysis of Islanded Microgrids With Droop Control , 2015, IEEE Transactions on Industrial Electronics.

[9]  R. Adapa,et al.  Control of parallel connected inverters in stand-alone AC supply systems , 1991, Conference Record of the 1991 IEEE Industry Applications Society Annual Meeting.

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

[11]  J. Miret,et al.  A wireless controller to enhance dynamic performance of parallel inverters in distributed generation systems , 2004, IEEE Transactions on Power Electronics.

[12]  Anuradha M. Annaswamy,et al.  Integration of Automatic Generation Control and Demand Response via a Dynamic Regulation Market Mechanism , 2019, IEEE Transactions on Control Systems Technology.

[13]  Ernane Antônio Alves Coelho,et al.  Small signal stability for parallel connected inverters in stand-alone AC supply systems , 2000, Conference Record of the 2000 IEEE Industry Applications Conference. Thirty-Fifth IAS Annual Meeting and World Conference on Industrial Applications of Electrical Energy (Cat. No.00CH37129).

[14]  Anuradha M. Annaswamy,et al.  Reliability Contracts Between Renewable and Natural Gas Power Producers , 2019, IEEE Transactions on Control of Network Systems.

[15]  Hatem H. Zeineldin,et al.  Stability Evaluation of Interconnected Multi-Inverter Microgrids Through Critical Clusters , 2016, IEEE Transactions on Power Systems.

[16]  Dragoslav D. Siljak,et al.  Multiparameter singular perturbations of linear systems with multiple time scales , 1983, Autom..

[17]  Brian B. Johnson,et al.  Reduced-order Aggregate Model for Parallel-connected Single-phase Inverters , 2019, IEEE Transactions on Energy Conversion.

[18]  Hassan K. Khalil,et al.  Singular perturbation methods in control : analysis and design , 1986 .

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

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

[21]  W. Marsden.  I and J , 2012 .

[22]  Anuradha M. Annaswamy,et al.  Using natural gas reserves to mitigate intermittence of renewables in the day ahead market , 2017, 2017 IEEE 56th Annual Conference on Decision and Control (CDC).

[23]  Josep M. Guerrero,et al.  Dynamic Phasors-Based Modeling and Stability Analysis of Droop-Controlled Inverters for Microgrid Applications , 2014, IEEE Transactions on Smart Grid.

[24]  Marija D. Ilić,et al.  Distributed Torque Control of Deloaded Wind DFIGs for Wind Farm Power Output Regulation , 2017, IEEE Transactions on Power Systems.