Voltage control of DC networks: robustness for unknown ZIP-loads

In this paper we propose a new passivity-based control technique for DC power networks comprising the so-called ZIP-loads, i.e., nonlinear loads with the parallel combination of unknown constant impedance (Z), current (I) and power (P) components. More precisely, we propose a novel passifying input and a storage function based on the so-called mixed potential function introduced by Brayton and Moser, leading to a novel passivity property with output port-variable equal to the first time derivative of the voltage. Differently from the existing results in the literature, where restrictive (sufficient) conditions on Z, P and the voltage reference are assumed to be satisfied, we establish a passivity property for every positive voltage reference and every type of load. Consequently, we develop a new decentralized passivity-based control scheme that is robust with respect to the uncertainty affecting the ZIP-loads.