On existence and stability of equilibria of DC Microgrid with constant power loads

TL;DR

This paper investigates the existence and stability of equilibria in DC microgrids with constant power loads, proposing control methods and analytical conditions to ensure system stability and reliable operation.

Contribution

It introduces a novel control approach using virtual resistance and inductance, and derives explicit conditions for equilibrium existence and local stability.

Findings

Proposed a control method based on virtual resistance and inductance.

Derived analytical sufficient conditions for equilibrium existence.

Established stability conditions using quadratic eigenvalue problem theorem.

Abstract

The problem of existence and stability of equilibria of DC microgirds with constant power loads methods is addressed in this paper. Constant power loads (CPLs) often cause instability due to its negative impedance characteristics. What is the worse, CPLs may cause that the system admits no equilibria for its nonlinearity. The purpose of paper can be summarized as: A) designing a controller to overcome CPLs instability; B) obtaining the sufficient conditions to guarantee the existence of the equilibria; C) Under the conditions of equilibria existing, obtaining the sufficient conditions of local stability. For the first objective, the method based on virtual resistance and virtual inductance is proposed. For the second objective, we transform the problem of solvability of quadratic equations into the existence of the fixed point of a mapping. Thus, the analytical sufficient conditions is obtained based on Tarski fixed point theorem. Moreover, a numerical method is also provided to reduce conservatism. For the third objective, the small-signal model is established to predict the system qualitative behavior around equilibria. The stability conditions are obtained by using quadratic eigenvalue problem (GEP) theorem. These explicit conditions are obtained as a function of system parameters and it lead to build reliable microgrid.