Authors

Johannes Schiffer, Romeo Ortega, Alessandro Astolfi, Jörg Raisch, Tevfik Sezi

Abstract

We consider the problem of stability analysis for droop-controlled inverter-based microgrids with meshed topologies. The inverter models include variable frequencies as well as voltage amplitudes. Conditions on the tuning gains and setpoints for frequency and voltage stability, together with desired active power sharing, are derived in the paper. First, we prove that for all practical choices of these parameters global boundedness of trajectories is ensured. Subsequently, assuming the microgrid is lossless, a port-Hamiltonian description is derived, from which sufficient conditions for stability are given. Finally, we propose for generic lossy microgrids a design criterion for the controller gains and setpoints such that a desired steady-state active power distribution is achieved. The analysis is validated via simulation on a microgrid based on the CIGRE (Conseil International des Grands Réseaux Electriques) benchmark medium voltage distribution network.

Keywords

Microgrid control; Microgrid stability; Smart grid applications; Inverters; Droop control; Port-Hamiltonian systems; Power sharing

Citation

BibTeX

@article{Schiffer_2014,
  title={{Conditions for stability of droop-controlled inverter-based microgrids}},
  volume={50},
  ISSN={0005-1098},
  DOI={10.1016/j.automatica.2014.08.009},
  number={10},
  journal={Automatica},
  publisher={Elsevier BV},
  author={Schiffer, Johannes and Ortega, Romeo and Astolfi, Alessandro and Raisch, Jörg and Sezi, Tevfik},
  year={2014},
  pages={2457--2469}
}

Download the bib file

References

  • Barklund, E., Pogaku, N., Prodanovic, M., Hernandez-Aramburo, C. & Green, T. C. Energy Management in Autonomous Microgrid Using Stability-Constrained Droop Control of Inverters. IEEE Transactions on Power Electronics vol. 23 2346–2352 (2008) – 10.1109/tpel.2008.2001910
  • Bretas, N. G. & Alberto, L. F. C. Lyapunov function for power systems with transfer conductances: extension of the invariance principle. IEEE Transactions on Power Systems vol. 18 769–777 (2003) – 10.1109/tpwrs.2003.811207
  • Chandorkar, M. C., Divan, D. M. & Adapa, R. Control of parallel connected inverters in standalone AC supply systems. IEEE Transactions on Industry Applications vol. 29 136–143 (1993) – 10.1109/28.195899
  • Coelho, E. A. A., Cortizo, P. C. & Garcia, P. F. D. Small-signal stability for parallel-connected inverters in stand-alone AC supply systems. IEEE Transactions on Industry Applications vol. 38 533–542 (2002) – 10.1109/28.993176
  • Davy, R. J. & Hiskens, I. A. Lyapunov functions for multimachine power systems with dynamic loads. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications vol. 44 796–812 (1997) – 10.1109/81.622983
  • De Brabandere, K. et al. A Voltage and Frequency Droop Control Method for Parallel Inverters. IEEE Transactions on Power Electronics vol. 22 1107–1115 (2007) – 10.1109/tpel.2007.900456
  • Diaz, G., Gonzalez-Moran, C., Gomez-Aleixandre, J. & Diez, A. Scheduling of Droop Coefficients for Frequency and Voltage Regulation in Isolated Microgrids. IEEE Transactions on Power Systems vol. 25 489–496 (2010) – 10.1109/tpwrs.2009.2030425
  • Dib, W., Ortega, R., Barabanov, A. & Lamnabhi-Lagarrigue, F. A “Globally” Convergent Controller for Multi-Machine Power Systems Using Structure-Preserving Models. IEEE Transactions on Automatic Control vol. 54 2179–2185 (2009) – 10.1109/tac.2009.2026834
  • Dörfler, F. & Bullo, F. Synchronization and Transient Stability in Power Networks and Nonuniform Kuramoto Oscillators. SIAM Journal on Control and Optimization vol. 50 1616–1642 (2012) – 10.1137/110851584
  • Engler, Applicability of droops in low voltage grids. International Journal of Distributed Energy Resources (2005)
  • Farhangi, H. The path of the smart grid. IEEE Power and Energy Magazine vol. 8 18–28 (2010) – 10.1109/mpe.2009.934876
  • Glover, (2011)
  • Godsil, (2001)
  • Guedes, R. B. L., Silva, F. H. J. R., Alberto, L. F. C. & Bretas, N. G. Large disturbance voltage stability assessment using extended lyapunov function and considering voltage dependent active loads. IEEE Power Engineering Society General Meeting, 2005 682–689 doi:10.1109/pes.2005.1489222 – 10.1109/pes.2005.1489222
  • Guerrero, J. M., GarciadeVicuna, L., Matas, J., Castilla, M. & Miret, J. Output Impedance Design of Parallel-Connected UPS Inverters With Wireless Load-Sharing Control. IEEE Transactions on Industrial Electronics vol. 52 1126–1135 (2005) – 10.1109/tie.2005.851634
  • Guerrero, J. M., Chandorkar, M., Lee, T.-L. & Loh, P. C. Advanced Control Architectures for Intelligent Microgrids—Part I: Decentralized and Hierarchical Control. IEEE Transactions on Industrial Electronics vol. 60 1254–1262 (2013) – 10.1109/tie.2012.2194969
  • Guerrero, J. M., Matas, J., Garcia de Vicuna, L., Castilla, M. & Miret, J. Decentralized Control for Parallel Operation of Distributed Generation Inverters Using Resistive Output Impedance. IEEE Transactions on Industrial Electronics vol. 54 994–1004 (2007) – 10.1109/tie.2007.892621
  • Hatziargyriou, N., Asano, H., Iravani, R. & Marnay, C. Microgrids. IEEE Power and Energy Magazine vol. 5 78–94 (2007) – 10.1109/mpae.2007.376583
  • Hernandez-Aramburo, C. A., Green, T. C. & Mugniot, N. Fuel Consumption Minimization of a Microgrid. IEEE Transactions on Industry Applications vol. 41 673–681 (2005) – 10.1109/tia.2005.847277
  • Horn, (2012)
  • Khalil, (2002)
  • Kundur, (1994)
  • Definition and Classification of Power System Stability IEEE/CIGRE Joint Task Force on Stability Terms and Definitions. IEEE Transactions on Power Systems vol. 19 1387–1401 (2004) – 10.1109/tpwrs.2004.825981
  • Lasseter, R. H. MicroGrids. 2002 IEEE Power Engineering Society Winter Meeting. Conference Proceedings (Cat. No.02CH37309) vol. 1 305–308 – 10.1109/pesw.2002.985003
  • Lasseter, R. H. Smart Distribution: Coupled Microgrids. Proceedings of the IEEE vol. 99 1074–1082 (2011) – 10.1109/jproc.2011.2114630
  • Li, Y. W. & Kao, C.-N. An Accurate Power Control Strategy for Power-Electronics-Interfaced Distributed Generation Units Operating in a Low-Voltage Multibus Microgrid. IEEE Transactions on Power Electronics vol. 24 2977–2988 (2009) – 10.1109/tpel.2009.2022828
  • Lopes, J. A. P., Moreira, C. L. & Madureira, A. G. Defining Control Strategies for MicroGrids Islanded Operation. IEEE Transactions on Power Systems vol. 21 916–924 (2006) – 10.1109/tpwrs.2006.873018
  • Transient stabilization of multimachine power systems with nontrivial transfer conductances. IEEE Transactions on Automatic Control vol. 50 60–75 (2005) – 10.1109/tac.2004.840477
  • Ortega, R., van der Schaft, A., Maschke, B. & Escobar, G. Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems. Automatica vol. 38 585–596 (2002) – 10.1016/s0005-1098(01)00278-3
  • Pogaku, N., Prodanovic, M. & Green, T. C. Modeling, Analysis and Testing of Autonomous Operation of an Inverter-Based Microgrid. IEEE Transactions on Power Electronics vol. 22 613–625 (2007) – 10.1109/tpel.2006.890003
  • Rudion, K., Orths, A., Styczynski, Z. A. & Strunz, K. Design of benchmark of medium voltage distribution network for investigation of DG integration. 2006 IEEE Power Engineering Society General Meeting (2006) doi:10.1109/pes.2006.1709447 – 10.1109/pes.2006.1709447
  • Schiffer, J., Anta, A., Trung, T. D., Raisch, J. & Sezi, T. On power sharing and stability in autonomous inverter-based microgrids. 2012 IEEE 51st IEEE Conference on Decision and Control (CDC) 1105–1110 (2012) doi:10.1109/cdc.2012.6426704 – 10.1109/cdc.2012.6426704
  • Schiffer, J., Goldin, D., Raisch, J. & Sezi, T. Synchronization of droop-controlled microgrids with distributed rotational and electronic generation. 52nd IEEE Conference on Decision and Control 2334–2339 (2013) doi:10.1109/cdc.2013.6760229 – 10.1109/cdc.2013.6760229
  • Schiffer, J., Ortega, R., Astolfi, A., Raisch, J. & Sezi, T. Stability of Synchronized Motions of Inverter–Based Microgrids Under Droop Control. IFAC Proceedings Volumes vol. 47 6361–6367 (2014) – 10.3182/20140824-6-za-1003.00863
  • Simpson-Porco, J. W., Dörfler, F. & Bullo, F. Synchronization and power sharing for droop-controlled inverters in islanded microgrids. Automatica vol. 49 2603–2611 (2013) – 10.1016/j.automatica.2013.05.018
  • Simpson-Porco, J. W., Dorfler, F. & Bullo, F. Voltage stabilization in microgrids via quadratic droop control. 52nd IEEE Conference on Decision and Control 7582–7589 (2013) doi:10.1109/cdc.2013.6761093 – 10.1109/cdc.2013.6761093
  • Soultanis, N. L., Papathanasiou, S. A. & Hatziargyriou, N. D. A Stability Algorithm for the Dynamic Analysis of Inverter Dominated Unbalanced LV Microgrids. IEEE Transactions on Power Systems vol. 22 294–304 (2007) – 10.1109/tpwrs.2006.887961
  • van der Schaft, (2000)
  • Varaiya, P., Wu, F. F. & Rong-Liang Chen. Direct methods for transient stability analysis of power systems: Recent results. Proceedings of the IEEE vol. 73 1703–1715 (1985) – 10.1109/proc.1985.13366
  • Yao, W., Chen, M., Matas, J., Guerrero, J. M. & Qian, Z.-M. Design and Analysis of the Droop Control Method for Parallel Inverters Considering the Impact of the Complex Impedance on the Power Sharing. IEEE Transactions on Industrial Electronics vol. 58 576–588 (2011) – 10.1109/tie.2010.2046001
  • Zhong, Q.-C. Robust Droop Controller for Accurate Proportional Load Sharing Among Inverters Operated in Parallel. IEEE Transactions on Industrial Electronics vol. 60 1281–1290 (2013) – 10.1109/tie.2011.2146221