Robust Stability Analysis of the Interactions in Multi-Terminal HVDC Systems Using <i>ν</i>-Gap Metric

Stability analysis of multi-terminal HVDC systems is an important and challenging issue for the safety and stable operation of power systems with large-scale renewable energy generations. It is quite difficult to analyze the system stability caused by the interactions among different VSCs with the coupling of DC and AC networks. This paper aims to present a method to analyze the relative stability of different interactions in multi-terminal HVDC systems. By the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\nu $ </tex-math></inline-formula>-gap metric based robust stability theory, firstly we propose a stability index to quantify the stability margin with respect to different paths of interactions. The influence of the interactions among different VSCs on the stability margin can be analyzed quantitatively. Then we present a method to easily calculate the stable region of parameters in the interactions. Extensive examples are given to demonstrate the application and the effectiveness of the proposed method. Note to Practitioners—This paper is motivated by the problem of improving the small-signal stability of multi-terminal high voltage direct current (MTDC) systems, which are widely used to transmit large-scale renewable energy generations. In recent years, many small-signal instability accidents have occurred in actual HVDC projects. The dynamic behavior of MTDC systems is related to the complex interactions among different voltage source converters (VSCs) through the coupling of AC and DC networks. Therefore, we aim to explain the mechanism of oscillations caused by the interactions and the relation between the dynamics and the control parameters. In this paper, we employ the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\nu $ </tex-math></inline-formula>-gap metric based robust control theory to quantify the stability of an MTDC system with respect to different interactions and to calculate the stable region of a particular parameter in the interactions. The results in this paper can explain the influence of the interactions among different VSCs on the stability margin quantitatively. Moreover, the results provide new ideas for the setting and tuning of control parameters in MTDC systems and even in other multi-equipment power systems.