State-Space Models of Virtual Control and Protection Systems for Stability Analysis

To address these challenges, accurate power electronics’ models and simulation are essential to de-risk future grid investments. Power electronic converters operate with fast and diverse control strategies, which can interact in complex ways – especially when sourced from multiple vendors. To study Voltage Source Converters (VSC) dominated interactions it is necessary to utilize tools and models capable to capture their complex dynamics. Thus, EMT simulation is recognized as the most suitable platform for studying these interactions. However, state-space models in Linear Time Invariant (LTI) form appear as a promising complementary alternative despite their complexity. Common approaches to derive state-space models include the DirectQuadrature (DQ) frame transformations, phasor sequence-domain models and harmonic state space models.

State-space models emerge as a complement to the traditional power system models used for time domain studies. Even though state-space models are capable of running time domain studies, they are especially useful for small-signal stability screening studies in complex converter dominated systems, e.g. offshore wind applications. State-space model’s representation in Linear Time Invariant (LTI) form allow to linearise converter dynamics around certain defined operating points, enabling to perform extended analysis.

This paper presents a methodology to automate the generation of state-space models of real

HVDC modular multilevel converters (MMC) and its control for modal analysis. The paper introduces the LTI state-space models of virtual control systems and describes the virtual

Control and Protection (vC&P) framework developed to generate a LTI state-space representation of industrial HVDC control systems, discussing their key features and limitations. Later, the role of these models in real HVDC project is discussed. Finally, results obtained by using the proposed framework are shown to illustrate the practical relevance of LTI state-space models in comparison with already available EMT simulations.