Frequency-Domain Modeling and Assessment of AC and DC Electromagnetic Stability in MMC-Based VSC HVDC Links

Abstract

In this paper, an analysis of electromagnetic instability is presented for Voltage Source Converter High Voltage Direct Current (VSC HVDC) systems. In recent years, the interaction between electromagnetic modes of the system and the converter dynamics has shown to give rise to instability problems in the AC network, up to the kHz range. This paper extends the analysis of the problem to the DC side and investigates to what extent similar problems can be expected in future HVDC installations.

Generalized impedance-based AC/DC power system modeling for harmonic stability analysis

“…Such a transfer function has an infinite number of poles, which cannot be represented in a finitedimensional state-space model, such as the MMC model considered in this paper. Thus, the transfer function T delay (s) is represented as a rational transfer function by applying a Padé approximation as represented in (14), where m and n are the numerator and denominator orders of the approximation.…”

“…contains the timedelayed insertion indices, which are used in the differential and algebraic equations in (4). In this work, m = n = 3 is chosen for the transfer function in (14), which results in 15 additional state variables. The accuracy of a third-order Padé approximation in representing a time delay of 150 µs is depicted in Fig.…”

“…The implicit assumption behind such studies is that there is an inherent decoupling of the AC and DC sides provided by the converter. It has been shown in [14], that both the AC and DC sides have similar properties when high-frequency interactions are concerned, and as such, it becomes ever more clear that a thorough stability analysis should ideally account for both sides at the same time. This was shown in [15] by including the DC bus dynamics in the sequence impedance models of a type III wind turbine.…”

Modeling and Shaping of the DC-Side Admittance of a Modular Multilevel Converter Under Closed-Loop Voltage Control

“…As seen in the figure, the control system time delay has negligible effect on the magnitude of the admittance, but affects the phase in the high-frequency region. For instance, with a 200µs time delay, the phase drops below -90 degrees at approximately 2000 Hz, implying non-passivity of Y dc (s) which may indicate closedloop system instability [11], [40].…”