On the existence and uniqueness of equilibria in meshed DC microgrids with CPLs

In this paper, we analyse the existence and uniqueness of equilibria of constant power loads (CPLs) in meshed DC microgrid architectures. Given the CPLs’ nonlinear characteristic and negative impedance behaviour, they are commonly known to introduce a destabilising effect into the system, effect intuitively coined as negative impedance instability. In the present approach, we start by deriving the characteristic polynomial from the power balance equation aiming to observe the nature of the CPLs voltage solutions, and assess their feasibility. Then, the algebraic expression is transformed into a problem of existence and uniqueness of a fixed point, and further tested by means of contraction mapping theory. A sufficient condition for the sources’ voltage references is obtained to guarantee the existence and uniqueness of equilibria. This provides a useful guidance in selecting the voltage references in the control design process. A numerical investigation on a meshed DC microgrid is carried out to verify the acquired sufficient condition and its underlying developed theory.