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

Abstract

Abstract-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 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 (LTI) 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 EMT simulation model of an MMC with 400 sub-modules per arm.

PI Passivity-Based Control and Performance Analysis of MMC Multiterminal HVDC Systems

“…It was shown in [31] that it can be advantageous to control the aggregate capacitive energy of the MMC by acting on the circulating current reference for improved performance. Taking inspiration on this approach, we propose to include a conventional outer-loop formed by a simple PI controller acting on the error signal between the zero-sequence arm voltage sum reference v Σref Cz and its corresponding measured signal v Σ Cz , similar to the one that was used in [31] to improve the stability margins of the MMC 5 . The output of the PI, defined as i Σ * z,i in (V.1) for the i th MMC, is further added to the desired reference of the circulating current i Σref z to produce the output of the outer loop.…”

“…The output of the PI, defined as i Σ * z,i in (V.1) for the i th MMC, is further added to the desired reference of the circulating current i Σref z to produce the output of the outer loop. However, contrary to the approach in [31] where the output of the outer loop i Σref z is implemented by conventional inner current loops, i Σ * z is here added with its desired reference i Σref z,i and is instead assigned to i Σ z , as indicated in the second line of (V.1), and as sketched in Fig. 17.…”

“…Finally, this new value of i Σ z,i will be enforced by the PI-PBC method, through the calculation of the passive output (IV.4). 5 A small difference between these outer loops is that the one used in [31] acted on the equivalent energy variable error (w Σref…”

Dynamics and Stability of Meshed Multiterminal HVDC Networks

“…The direct and quadrature axes representation of the grid currents are obtained applying the Park transform to the set (7) (See the Park's transformation in [16]). The system is represented in vector form with the current grid vector…”

Simplified Modelling of the F2F MMC-Based High Power DC-DC Converter Including the Effect of Circulating Current Dynamics

“…However, as will be shown in this paper, the model is applicable only when using compensated modulation, a special method for calculating the insertion indexes [6]. When using other types of control, such as direct voltage control, there is an uncontrolled interaction between the different harmonic components in the converter, which leads to a poorly damped oscillation at the converter terminals [15]. The existing simplified model of the F2F from [14] fails to accurately capture such modes of oscillation.…”