Impedance-Based Characterization of Digital Control Delay and Its Effects on System Stability

Delay is inevitable in power converters employing digital control and/or digital pulse-width modulation (PWM), and can be modeled in different forms for different purposes. This paper presents the modeling of such delay in frequency domain by small-signal sequence impedances and examines its effects on the stability of grid-connected converter systems, such as wind and PV farms as well as onshore and offshore HVDC transmission. The method is applied to two-level voltage source converters, type-III turbines, as well as modular multilevel converters. Negative damping in the converter input or output impedance is identified as a common result of control delay and the root cause for high-frequency resonances that became widespread in recent years, especially in MMC-based HVDC transmission systems. In addition to full models that can predict the associated impedance and negative damping behavior accurately, simplified analytical models are presented to gain insights into the factors that affect such negative damping to support the development of practical solutions to system resonance problems. Possible methods to mitigate the negative damping effects and solve high-frequency resonance problems are also discussed.