Sensitivity Analysis and Small-Signal Stability of Grid Following Converters

Keywords: Grid-following converters, Hopf bifurcation, sensitivity analysis, vector-oriented control, voltage source converter


This article presents a small-signal study, based on a sensitivity analysis, of a voltage source converter (VSC) operating as a grid-following device. This type of operation is standard for integrating distributed energy resources directly into a primary grid without considering the control over specific variables (e.g., voltage and frequency), thus maximizing the amount of injected active power. The present study adopted the classical vector-oriented control based on the linearization method of the averaged model; hence, this analysis is limited to linear controls. The main objective of this study is to evaluate how each controller parameter influences the system’s stability. To conduct the sensitivity analysis, an averaged model in the dq reference frame of the VSC was employed to describe the system dynamics in the equivalent state-space model. Afterward, the stability was analyzed through a sensitivity analysis of the eigenvalues of the corresponding state matrix. The numerical results demonstrate that the main problems for the stability of VSCs operating as grid-following converters are threefold: a high value of the filter inductance, a non-ideal impedance that appears depending on the connection point, and poor coordination of the parameters of the Kp controllers. These results are compared to a simple bifurcation analysis of the state matrix, which consists of a diagram that describes the variation in eigenvalues when a parameter changes, thus proving their validity.


Author Biography

Simón Sepúlveda García*, Universidad Tecnológica de Pereira, Colombia

Universidad Tecnológica de Pereira, Pereira, Colombia,


A. Kalair; N. Abas; N. Khan, “Comparative study of HVAC and HVDC transmission systems”, Renew. Sust. Energ. Rev., vol. 59, pp. 1653–1675, Jun2016.

A. Garces, “Uniqueness of the power flow solutions in low voltage direct current grids”, Electr. Power Syst. Res., vol. 151, pp. 149–153, Oct. 2017.

A. Garcés-Ruiz, “Small-signal stability analysis of dc microgrids considering electric vehicles”, Rev. Fac. de Ing., no. 89, pp. 52-58, Oct. 2018.

C. García-Ceballos; S. Pérez-Londoño; J. Mora-Flórez, “Integration of distributed energy resource models in the VSC control for microgrid applications”, Electr. Power Syst. Res., vol. 196, p. 107278, Jul. 2021.

T. Dragičević; S. Vazquez; P. Wheeler, “Advanced Control Methods for Power Converters in DG Systems and Microgrids”, IEEE Trans. Ind. Electron., vol. 68, no. 7, pp. 5847–5862, Jul. 2021.

D. López-García; A. Arango-Manrique; S. X. Carvajal-Quintero, “Integration of distributed energy resources in isolated microgrids: the Colombian paradigm”, TecnoLógicas, vol. 21, no. 42, pp. 13–30, May 2018.

Z. Shuai et al., “Microgrid stability: Classification and a review,” Renew. Sust. Energ. Rev., vol. 58, pp. 167–179, May. 2016.

M. Farrokhabadi et al., “Microgrid Stability Definitions, Analysis, and Examples”, IEEE Trans. Power Syst., vol. 35, no. 1, pp. 13–29, Jan. 2020.

W. Du; Q. Fu; X. Wang; H. F. Wang, “Small-signal stability analysis of integrated VSC-based DC/AC power systems – A review”, Int. J. Electr. Power Energy Syst., vol. 103. pp. 545–552, Dec. 2018.

T. Kalitjuka, “Control of Voltage Source Converters for Power System Applications”, (M.S. thesis), Department of Electric Power Engineering, Norwegian University of Science and Technology, Trondheim, 2011.

J. Rocabert; A. Luna; F. Blaabjerg; P. Rodríguez, “Control of power converters in AC microgrids”, IEEE Trans. Power Electron., vol. 27, no. 11, pp. 4734–4749, Nov. 2012.

M. Huang; Y. Peng; C. K. Tse; Y. Liu; J. Sun; X. Zha, “Bifurcation and Large-Signal Stability Analysis of Three-Phase Voltage Source Converter under Grid Voltage Dips”, IEEE Trans. Power Electron., vol. 32, no. 11, pp. 8868–8879, 2017.

M. Huang; C. K. Tse; S. C. Wong; C. Wan; X. Ruan, “Low-frequency hopf bifurcation and its effects on stability margin in three-phase PFC power supplies connected to non-ideal power grid”, IEEE Trans. Power Electron., vol. 60, no. 12, pp. 3328–3340, Dec. 2013.

H. Chen; W. Yu; Z. Liu; Q. Yan; I. Adamu Tasiu; Z. Han, “Low-Frequency Instability Induced by Hopf Bifurcation in a Single-Phase Converter Connected to Non-Ideal Power Grid”, IEEE Access, vol. 8, pp. 62871–62882, 2020.

S. Rezaee; A. Radwan; M. Moallem; J. Wang, “Voltage source converters connected to very weak grids: Accurate dynamic modeling, small-signal analysis, and stability improvement”, IEEE Access, vol. 8, pp. 201120–201133, 2020.

Z. Yang; R. Ma; S. Cheng; M. Zhan, “Nonlinear Modeling and Analysis of Grid-Connected Voltage-Source Converters under Voltage Dips”, IEEE Trans. Emerg. Sel. Topics Power Electron., vol. 8, no. 4, pp. 3281–3292, Dec. 2020.

K. F. Krommydas; A. T. Alexandridis, “Nonlinear Analysis Methods Applied on Grid-Connected Photovoltaic Systems Driven by Power Electronic Converters”, IEEE Trans. Emerg. Sel. Topics Power Electron., vol. 8, no. 4, pp. 3293–3306, Dec. 2020.

L. Harnefors; X. Wang; A. G. Yepes; F. Blaabjerg, “Passivity-Based Stability Assessment of Grid-Connected VSCs-An Overview”, IEEE Trans. Emerg. Sel. Topics Power Electron., vol. 4, no. 1, pp. 116–125, Mar. 2016.

Q. Geng; X. Zhou, “Small signal stability analysis of VSC based DC systems using graph theory”, Int. J. Electr. Power Energy Syst., vol. 137, p. 107830, May. 2022.

R. Yin et al., “Modeling and stability analysis of grid-tied VSC considering the impact of voltage feed-forward”, Int. J. Electr. Power Energy Syst., vol. 135, p. 107483, Feb. 2022.

H. Zhang; Z. Liu; S. Wu; Z. Li, “Input Impedance Modeling and Verification of Single-Phase Voltage Source Converters Based on Harmonic Linearization”, IEEE Trans. Power Electron., vol. 34, no. 9, pp. 8544–8554, Sep. 2019.

J. Machowski; Z. Lubosny; J. Bialek; J. Bumby, “Power System Dynamics: Stability and Control, 3rd Edition [Book News]”, IEEE Trans. Ind. Electron., vol. 14, no. 2, pp. 94-95, Jun. 2020.

R. Jadeja; A. Ved; T. Trivedi; G. Khanduja, “Control of Power Electronic Converters in AC Microgrid”, IEEE Trans. Power Electron., pp. 329–355, 2020.

L. Wu; J. Liu; S. Vazquez; S. K. Mazumder, “Sliding Mode Control in Power Converters and Drives: A Review,” IEEE/CAA Journal of Automatica Sinica, vol. 9, no. 3, pp. 392–406, Mar. 2022.

R. Teodorescu; M. Liserre; P. Rodríguez, Grid Converters for Photovoltaic and Wind Power Systems, 1st ed. 2010.

M. Bravo; A. Garcés; O. D. Montoya; C. R. Baier, “Nonlinear Analysis for the Three-Phase PLL: A New Look for a Classical Problem”, 2018 IEEE 19th Workshop on Control and Modeling for Power Electronics, COMPEL, pp. 1–6, 2018.

M. F. Bravo López, “Stability analysis on the primary control in islanded ac microgrids”, 2019.

How to Cite
S. Sepúlveda García and A. Garcés, “Sensitivity Analysis and Small-Signal Stability of Grid Following Converters”, TecnoL., vol. 25, no. 54, p. e2383, Jul. 2022.


Download data is not yet available.
Research Papers
Crossref Cited-by logo

More on this topic