zbMATH — the first resource for mathematics

Conditions for stability of droop-controlled inverter-based microgrids. (English) Zbl 1301.93145
Summary: 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.

93D99 Stability of control systems
93C95 Application models in control theory
37L15 Stability problems for infinite-dimensional dissipative dynamical systems
Full Text: DOI
[1] Barklund, E.; Pogaku, N.; Prodanovic, M.; Hernandez-Aramburo, C.; Green, T., Energy management in autonomous microgrid using stability-constrained droop control of inverters, IEEE Transactions on Power Electronics, 23, 2346-2352, (2008)
[2] Bretas, N.; Alberto, L. F.C., Lyapunov function for power systems with transfer conductances: extension of the invariance principle, IEEE Transactions on Power Systems, 18, 769-777, (2003)
[3] Chandorkar, M.; Divan, D.; Adapa, R., Control of parallel connected inverters in standalone AC supply systems, IEEE Transactions on Industry Applications, 29, 136-143, (1993)
[4] Coelho, E.; Cortizo, P.; Garcia, P., Small-signal stability for parallel-connected inverters in stand-alone AC supply systems, IEEE Transactions on Industry Applications, 38, 533-542, (2002)
[5] 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, 44, 796-812, (1997)
[6] De Brabandere, K.; Bolsens, B.; Van den Keybus, J.; Woyte, A.; Driesen, J.; Belmans, R., A voltage and frequency droop control method for parallel inverters, IEEE Transactions on Power Electronics, 22, 1107-1115, (2007)
[7] 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, 25, 489-496, (2010)
[8] 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, 54, 2179-2185, (2009) · Zbl 1367.93495
[9] Dörfler, F.; Bullo, F., Synchronization and transient stability in power networks and non-uniform Kuramoto oscillators, SIAM Journal on Control and Optimization, 50, 1616-1642, (2012) · Zbl 1264.34105
[10] Engler, A., Applicability of droops in low voltage grids, International Journal of Distributed Energy Resources, 1, 1-6, (2005)
[11] Farhangi, H., The path of the smart grid, IEEE Power and Energy Magazine, 8, 18-28, (2010)
[12] Glover, J. D.; Sarma, M. S.; Overbye, T. J., Power system analysis and design, (2011), Cengage Learning
[13] Godsil, C.; Royle, G., Algebraic graph theory, (2001), Springer · Zbl 0968.05002
[14] Guedes, R., Silva, F., Alberto, L., & Bretas, N. (2005). Large disturbance voltage stability assessment using extended Lyapunov function and considering voltage dependent active loads. In IEEE PESGM (pp. 1760-1767).
[15] Guerrero, J.; Garcia de Vicuna, 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, 52, 1126-1135, (2005)
[16] Guerrero, J.; Loh, P.; Chandorkar, M.; Lee, T., Advanced control architectures for intelligent microgrids—part I: decentralized and hierarchical control, IEEE Transactions on Industrial Electronics, 60, 1254-1262, (2013)
[17] Guerrero, J.; Matas, J.; de Vicuna, L. G.; Castilla, M.; Miret, J., Decentralized control for parallel operation of distributed generation inverters using resistive output impedance, IEEE Transactions on Industrial Electronics, 54, 994-1004, (2007)
[18] Hatziargyriou, N.; Asano, H.; Iravani, R.; Marnay, C., Microgrids, IEEE Power and Energy Magazine, 5, 78-94, (2007)
[19] Hernandez-Aramburo, C.; Green, T.; Mugniot, N., Fuel consumption minimization of a microgrid, IEEE Transactions on Industry Applications, 41, 673-681, (2005)
[20] Horn, R. A.; Johnson, C. R., Matrix analysis, (2012), Cambridge University Press
[21] IEEE (1998). IEEE recommended practice for industrial and commercial power systems analysis (brown book). IEEE standard 399-1997 (pp. 1-488).
[22] Khalil, H. K., Nonlinear systems. vol. 3, (2002), Prentice Hall
[23] Kundur, P., Power system stability and control, (1994), McGraw-Hill
[24] Kundur, P.; Paserba, J.; Ajjarapu, V.; Andersson, G.; Bose, A.; Canizares, C., Definition and classification of power system stability IEEE/CIGRE joint task force on stability terms and definitions, IEEE Transactions on Power Systems, 19, 1387-1401, (2004)
[25] Lasseter, R. (2002). Microgrids. In IEEE power engineering society winter meeting, 2002. Vol. 1 (pp. 305-308).
[26] Lasseter, R. H., Smart distribution: coupled microgrids, Proceedings of the IEEE, 99, 1074-1082, (2011)
[27] 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, 24, 2977-2988, (2009)
[28] Lopes, J.; Moreira, C.; Madureira, A., Defining control strategies for microgrids islanded operation, IEEE Transactions on Power Systems, 21, 916-924, (2006)
[29] Ortega, R.; Galaz, M.; Astolfi, A.; Sun, Y.; Shen, T., Transient stabilization of multimachine power systems with nontrivial transfer conductances, IEEE Transactions on Automatic Control, 50, 60-75, (2005) · Zbl 1365.93413
[30] Ortega, R.; van der Schaft, A.; Maschke, B.; Escobar, G., Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems, Automatica, 38, 585-596, (2002) · Zbl 1009.93063
[31] Plexim GmbH (2013). Plecs software. www.plexim.com.
[32] Pogaku, N.; Prodanovic, M.; Green, T., Modeling, analysis and testing of autonomous operation of an inverter-based microgrid, IEEE Transactions on Power Electronics, 22, 613-625, (2007)
[33] Rudion, K., Orths, A., Styczynski, Z., & Strunz, K. (2006). Design of benchmark of medium voltage distribution network for investigation of DG integration. In IEEE PESGM.
[34] Schiffer, J., Anta, A., Trung, T. D., Raisch, J., & Sezi, T. (2012). On power sharing and stability in autonomous inverter-based microgrids. In Proc. 51st IEEE CDC. Maui, HI, USA (pp. 1105-1110).
[35] Schiffer, J., Goldin, D., Raisch, J., & Sezi, T. (2013). Synchronization of droop-controlled microgrids with distributed rotational and electronic generation. In Proc. 52nd IEEE CDC. Florence, Italy (pp. 2334-2339).
[36] Schiffer, J., Ortega, R., Astolfi, A., Raisch, J., & Sezi, T. (2014). Stability of synchronized motions of inverter-based microgrids under droop control. In Proc. of 19th IFAC World Congress. August 24-29, Cape Town, South Africa. · Zbl 1301.93145
[37] Simpson-Porco, J. W.; Dörfler, F.; Bullo, F., Synchronization and power sharing for droop-controlled inverters in islanded microgrids, Automatica, 49, 2603-2611, (2013) · Zbl 1364.93544
[38] Simpson-Porco, J. W., Dörfler, F., & Bullo, F. (2013b). Voltage stabilization in microgrids using quadratic droop control. In Proc. 52nd IEEE CDC. Florence, Italy (pp. 7582-7589).
[39] 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, 22, 294-304, (2007)
[40] van der Schaft, A., L2-gain and passivity techniques in nonlinear control, (2000), Springer · Zbl 0937.93020
[41] Varaiya, P.; Wu, F. F.; Chen, R.-L., Direct methods for transient stability analysis of power systems: recent results, Proceedings of the IEEE, 73, 1703-1715, (1985)
[42] Yao, W.; Chen, M.; Matas, J.; Guerrero, J.; 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, 58, 576-588, (2011)
[43] Zhong, Q.-C., Robust droop controller for accurate proportional load sharing among inverters operated in parallel, IEEE Transactions on Industrial Electronics, 60, 1281-1290, (2013)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.