Eigenvalue calculator for Islanded Inverter-Based Microgrids

Document Type : Research Article



The stability analysis of islanded inverter-based microgrids (IBMGs) is increasingly an important and challenging topic due to the nonlinearity of IBMGs. In this paper, a new linear model for such microgrids as well as an iterative method to correct the linear model is proposed. Using the linear model makes it easy to analyze the eigenvalues and stability of IBMGs due to the fact that it derives the eigenvalues directly and the linearization around an operating point to study the small signal stability and also use the newton-raphson method or other load flow solutions to solve these systems are no longer needed. An effective eigenvalue calculator is developed which is able to calculate the eigenvalues of IBMGs in the first few iterations of the proposed method. The proposed method provides the superior performance considering the simulation time compared to the conventional methods. The validation and comparison of the results show the performance of the proposed method.


[1] R.H.Lasseter, microgrids and distributed Generation. Journal of Energy Engineering, 133(2007),144-149.
[2]IEEE P1547 standard for Distributed Resources Interconnected with Electric power systems, IEEE P1547 std.,sep. 2002
[3] F. Katiraei, M. R. Iravani, and P. W. Lehn, Micro-grid Autonomous Operation During and Subsequent to Islanding Process, IEEE Trans. On Power Delivery, 20(2005) 248-257.
[4] Gao, M., Chen, M., Jin Ch., Guerrero, J. M., Qian, Zh. M., 2013. Analysis, design, and experimental evaluation of power calculation in digital droop-controlled parallel microgrid inverters. Journal of Zhejiang University SCIENCE C, 14(1): 50-64.
[5] B. Bahrani, H. Karimi, R. Iravani, Decentralized Control of Parallel Connection of Two Distributed Generation Units, Industrial Electronics, 2009. IECON '09. 35th Annual Conference of IEEE, 2009, 358-362.
[6] N. Cai, J. Mitra, A multi-level control architecture for master-slave organized microgrids with power electronic interfaces, Electric Power Systems Research, 109 (2014), 8–19.
[7] F. Gao and R. Iravani, “A Control Strategy for a Distributed Generation Unit in Grid-Connected and Autonomous Modes of Operation,” Power Delivery, IEEE Trans., vol. 23, no. 2, pp. 850 –859, Apr 2008.
[8] F. Katiraei, and M. R. Iravani, “Power Management Strategies for a Microgrid with Multiple Distributed Generation Units,” Power Systems IEEE Trans., vol. 21, no. 4, pp. 1821-1831, Nov. 2006.
[9] Vandoorn T. L., Renders B., Degroote L., Meersman B., Vandevelde L., “Active Load Control in Islanded Microgrids Based on the Grid Voltage” Smart Grid, IEEE Trans. Vol.2, no. 1, pp. 139-151, Mar. 2013.
[10] N. Pogaku, M. Prodanovic, and T. C. Green, “Modeling, Analysis and Testing of Autonomous Operation of an Inverter-Based Microgrid,” Power Electronics IEEE Trans., vol. 22, no. 2, pp. 613–625, Mar. 2007.
[11] N. Bottrell, M. Prodanovic, T. C. Green, “Dynamic Stability of a Microgrid with an Active Load” Power Electronics IEEE Trans., Vol. 28, no. 11, pp. 5107 – 5119, Nov. 2013.
[12] H. Ch. Chiang, Chi‐Yung Yen and K. T. Chang, “A frequency‐dependent droop scheme for parallel control of ups inverters” Journal of the Chinese Institute of Engineers, Vol. 24, No. 6, pp. 699-708, 2001
[13] E. Barklund, N. Pogaku, M. Prodanovic, C. Hernandez-Aramburo, and T. Green, “Energy Management in Autonomous Microgrid Using Stability-Constrained Droop Control of Inverters” Power Electronics, IEEE Trans., vol. 23, no. 5, pp. 2346 –2352, Sept 2008.
[14] Seidi Khorramabadi, S, Bakhshai, A, “Critic-Based Self-Tuning PI Structure for Active and Reactive Power Control of VSCs in Microgrid Systems” Smart Grid, IEEE Trans. Vol. 6, No. 1, pp. 92-103, Jan. 2015.
[15] J. Vasquez, J. Guerrero, A. Luna, P. Rodriguez, and R. Teodorescu, “Adaptive Droop Control Applied to Voltage-Source Inverters Operating in Grid-Connected and Islanded Modes,” IEEE Trans. Industrial Electronics, vol. 56, no. 10, pp. 4088 –4096, Oct 2009.
[16] Bevrani, H., Shokoohi S., “An Intelligent Droop Control for Simultaneous Voltage and Frequency Regulation in Islanded Microgrids” Smart Grid, IEEE Trans. Vol. 4, No. 3, pp. 1505-1513, Sept. 2013.
[17] Savaghebi, M., Jalilian, A., Vasquez, J.C., Guerrero, J. M., “Secondary Control Scheme for Voltage Unbalance Compensation in an Islanded Droop-Controlled Microgrid” Smart Grid, IEEE Trans. Vol. 3, No. 2, pp. 797-807, June 2012.
[18] Laghari, J. A., Mokhlis, H., Karimi, M., Bakar, A. H. A., Hasmaini M., 2015. A new technique for islanding operation of distribution network connected with mini hydro. Frontiers of Information Technology & Electronic Engineering. 16(5):418-427.
[19] J. Kim, J. Guerrero, P. Rodriguez, R. Teodorescu, and K. Nam, “Mode Adaptive Droop Control With Virtual Output Impedances for an Inverter-Based Flexible AC Microgrid,” Power Electronics, IEEE Trans on, vol. 26, no. 3, pp. 689 –701, Mar 2011.
[20] M. Hua, H. Hu, Y. Xing, and J. Guerrero, “Multilayer Control for Inverters in Parallel Operation Without Intercommunications,” IEEE Trans. Power Electronics, vol. 27, no. 8, pp. 3651 –3663, Aug 2012.
[21] Z. Zeng, H. Yang, R. Zhao, Study on small signal stability of microgrids: A review and a new approach, Renewable and Sustainable Energy Reviews, 15 (2011) 4818–4828.
[22] M. Marwali, J.-W. Jung, and A. Keyhani, Stability Analysis of Load Sharing Control for Distributed Generation Systems, Energy Conversion, IEEE Trans., 22 (2007) 737–745.
[23] S. Iyer, M. Belur, and M. Chandorkar, A Generalized Computational Method to Determine Stability of a Multi-inverter Microgrid, Power Electronics, IEEE Trans., 25 (2010) 2420–2432.
[24] N. Jayawarna, X. Wu, Y. Zhang, N. Jenkins, and M. Barnes, Stability of a Microgrid, The 3rd IET International Conference on Power Electronics, Machines and Drives, (2006) 316–320.
[25] Johnson B.B., Davoudi A., Chapman P.L., Sauer P., Microgrid dynamics characterization using the automated state model generation algorithm, Proceedings of 2010 IEEE International Symposium on Circuits and Systems (2010) 2758 – 2761.
[26] Chakraborty S., Simões M. G., Kramer, W. E., Power Electronics for Renewable and Distributed Energy Systems: A Sourcebook of Topologies, Control and Integration, Springer London, Green Energy and Technology (2013) 483-484.