Abstract
Sensitivities of eigen-solutions to control variables play an important role in microgrid studies, such as coordinated optimal design of controllers and parameters, robust stability analysis on control variables, oscillation modes analysis on a system, etc. Considering the importance of sensitivities and the complexity of state matrix in a microgrid, parameter perturbations are utilized in this paper to analyze the construction characteristics of state matrix. Then, the sensitivities of eigenvalues and eigenvectors to control variables are obtained based on the first-order matrix perturbation theory, which makes the complex derivations of sensitivity formulas and repeated solutions of eigenvalue problem unnecessary. Finally, the effectiveness of the matrix perturbation based approach for sensitivity calculation in a microgrid is verified by a numerical example on a low-voltage microgrid prototype.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Lasseter R, Akhil A, Marnay C, et al. The CERTS microgrid concept, white paper on integration of distributed energy resources. Consortium for Electric Reliability Technology Solutions (CERTS) Tech Rep. LBNL-50829, 2002. 1–10
Wang C S, Li X L, Guo L, et al. A seamless operation mode transition control strategy for a microgrid based on master-slave control. Sci China Tech Sci, 2012, 55(6): 1644–1654
Barklund E, Pogaku N, Prodanovic M, et al. Energy management in autonomous microgrid using stability-constrained droop control of inverters. IEEE T Power Electr, 2008, 23(5): 2346–2352
Lasseter R, Piagi, P. Control and design of microgrid components. In: Power Systems Engineering Research Center (PSERC), Final Proj Rep. Wisconsin, 2006. 1–245
Luo J. Introduction to system sensitivity theory. Beijing: Science Press, 1990
Miao X F, Guo Z Z. A survey of sensitivity technique and its application in power systems analysis and control. Relay, 2007, 35(15): 72–76
Rayleigh B. Theory of Sound. New York: Dover, 1945
Baldwin J, Hutton S. Natural modes of modified structures. AIAA, 1984, 23(11): 1737–1743
Sutter T, Adelman H, Camarda C, et al. Comparison of several methods for calculating vibration mode shape derivatives. AIAA, 1988, 26(11): 1506–1511
Assem S. Advanced Matrix Theory for Scientists and Engineers. Kent: Abacus Press, 1982
Günel S, Zoral E. Parametric history analysis of resonance problems via step-by-step eigenvalue perturbation technique. IET Microw Antennas Propag, 2010, 4(4): 466–476
Chen S H. Matrix perturbation theory in structural dynamic design. Beijing: Science Press, 2007
Wilkinson J. The algebraic eigenvalue problem. Landon: Oxford University Press, 1965
Coelho E, Cortizo P, Gracia P. Small signal stability for parallel-connected inverters in stand-alone ac supply systems. IEEE T Ind Appl, 2002, 38(2): 533–542
Chung Il-Y, Liu W X, Cartes D A, et al. Control methods of inverter-interfaced distributed generators in a microgrid system. IEEE T Ind Appl, 2010, 46(3): 1078–1088
Wang Y, Lu Z X, Min Y. Small signal analysis of microgrid with multiple micro sources based on reduced order model in islanding operation. IEEE PES General Meeting, 2011, 1–9
Peng K, Wang C S, Li Y, et al. Design of a typical medium-low voltage Microgrid network. Autom Electr Power Syst, 2011, 35(18): 31–35
Mohamed Y A-R I, El-Saadany E F. Adaptive decentral-ized droop controller to preserve power sharing stability of paralleled inverters in distributed generation microgrids. IEEE T Power Electr, 2008, 23(6): 2806–2816
Xue Q, Wang H X. Local reconstruction method for low-energy gamma-ray computed tomography system. J Instrumentation, 2011, 6: 1–12
Díaz G, Morán C, Aleixandre J, et al. Scheduling of droop coefficients for frequency and voltage regulation in isolated Microgrids. IEEE T Power Syst, 2010, 25(1): 489–496
Yang L, Xu Z, Ostergaard J, et al. Oscillatory stability and eigenvalue sensitivity analysis of a DFIG wind turbine system. IEEE T Energ Conv, 2011, 26(1): 328–339
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wang, C., Li, Y., Peng, K. et al. Matrix perturbation based approach for sensitivity analysis of eigen-solutions in a microgrid. Sci. China Technol. Sci. 56, 237–244 (2013). https://doi.org/10.1007/s11431-012-5067-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11431-012-5067-3