Improving Small-Signal Stability of an MMC With CCSC by Control of the Internally Stored Energy

The dc-side dynamics of modular multilevel converters (MMCs) can be prone to poorly damped oscillations or stability problems when the second-harmonic components of the arm currents are mitigated by a circulating current suppression controller (CCSC). This paper demonstrates that the source of these oscillations is the uncontrolled interaction of the dc-side current and the internally stored energy of the MMC, as resulting from the CCSC. Stable operation and improved performance of the MMC control system can be ensured by introducing the closed-loop control of the energy and the dc-side current. The presented analysis relies on a detailed state-space model of the MMC, which is formulated to obtain constant variables in steady state. The resulting state-space equations can be linearized to achieve a linear time invariant model, allowing for eigenvalue analysis of the small-signal dynamics of the MMC. Participation factor analysis is utilized to identify the source of the poorly damped dc-side oscillations, and indicates the suitability of introducing control of the internal capacitor voltage or the corresponding stored energy. An MMC connected to a dc power source with an equivalent capacitance, and operated with dc voltage droop in the active power flow control, is used as an example for the presented analysis. The developed small-signal models and the improvement in small-signal dynamics achieved by introducing control of the internally stored energy are verified by time-domain simulations in comparison to an electro-magnetic transient (EMT) simulation model of an MMC with 400 submodules per arm.