# 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

### Abstract

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.

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