Análisis de estabilidad de convertidores de segundo orden con la metodología de optimización de suma de polinomios cuadráticos

  • Jhon Jairo Herrera-Pérez Universidad Tecnológica de Pereira
  • Alejandro Garcés-Ruiz Universidad Tecnológica de Pereira
Keywords: Optimization algorithms, direct current networks, Buck, Boost, DC-DC converter, DC microgrid, second order converte, Lyapunov, Sum of squares, Stability


This paper presents a non-linear method based on sum-of-squares (SOS), to determine the stability of equilibrium points for the Buck, Boost, Buck-Boost and non-inverter Buck-Boost converters. These converters share a similar structure with a PI controller to regulate the output voltage. A quadratic Lyapunov function is proposed in all cases, and the conditions for stability are evaluated using convex optimization based on SOS models. The methodology is useful for academic purposes but also in practical applications like DC microgrids. Simulation results shows the advantages of the proposed method.


A. Papachristodoulou, J. Anderson, G. V. S. P. P. S. and Parrilo, P. A. (2013). SOSTOOLS:

Sum of squares optimization toolbox for MATLAB. Available

from, and˜parrilo/sostools.

Blekherman, G., Parrilo, P. A., and Thomas, R. R. (2012). Semidefinite optimization and convex algebraic geometry. SIAM.

Garcés, A. (2019). Stability analysis of dc-microgrids: A gradient formulation. Journal of Control, Automation and

Electrical Systems, pages 1–9.

Garcés, A. and Montoya, O.-D. (2019). A potential function for the power flow in dc microgrids: An analysis of

the uniqueness and existence of the solution and convergence of the algorithms. Journal of Control, Automation and Electrical Systems, 30(5):794–801. doi:10.1007/s40313-019-00489-4.

Hale, J. (2009). Ordinary Differential Equations. Dover Books on Mathematics Series. Dover Publications.

Joseph, S. C., Ashok, S., and Dhanesh, P. (2017). Low voltage direct current (lvdc) nanogrid for home application.

In 2017 IEEE Region 10 Symposium (TENSYMP), pages 1–5. IEEE.

Li, H., Guo, Z., Ren, F., Zhang, X., and Zhang, B. (2017). A stability analysis method based on floquet theory

for multi-stage dc-dc converters system. In 2017 IEEE Energy Conversion Congress and Exposition (ECCE), pages

–3029. IEEE.

Li, H., Ren, F., Shang, J., Zhang, B., Lü, J., and Qi, H. (2016). A novel large-signal stability analysis approach based

on semi-tensor product of matrices with lyapunov stability theorem for dc-dc converters. In 2016 IEEE Energy

Conversion Congress and Exposition (ECCE), pages 1–5. IEEE.

Lopes, J. A. P., Madureira, A. G., and Moreira, C. C. L. M. (2013). A view of microgrids. Wiley Interdisciplinary

Reviews: Energy and Environment, 2(1):86–103.

Sadabadi, M. S., Shafiee, Q., and Karimi, A. (2017). Plug-and-play robust voltage control of dc microgrids. IEEE

Transactions on Smart Grid, 9(6):6886–6896.

Shang, J., Li, H., You, X., Zheng, T. Q., and Wang, S. (2015). A novel stability analysis approach based on describing function method using for dc-dc converters. In 2015 IEEE Applied Power Electronics Conference and Exposition (APEC), pages 2642–2647. IEEE.

Sira-Ramirez, H. J. and Silva-Ortigoza, R. (2006). Control design techniques in power electronics devices. Springer

Science & Business Media.

VanAntwerp, J. G. and Braatz, R. D. (2000). A tutorial on linear and bilinear matrix inequalities. Journal of Process

Control, 10(4):363 – 385. doi:

How to Cite
Herrera-Pérez, J., & Garcés-Ruiz, A. (2020). Análisis de estabilidad de convertidores de segundo orden con la metodología de optimización de suma de polinomios cuadráticos. Transactions on Energy Systems and Engineering Applications, 1(1), 49-58.
Abstract - 74