Enhanced high-speed electromagnetic transient simulation of MMC-MTdc grid

• This proposed models use either Backward Euler (BE) method or Trapezoidal Rules (TR).
• At most (2N-3) comparisons are required for TR model and at most (N-1) for BE model.
• The BE model is between 1 and 2 orders of magnitude faster than the previous models.

This paper introduces a very fast electromagnetic transient (EMT) simulation model for the HVdc modular multilevel converter (MMC) that maintains the identity of each switching level, but achieves computation speeds comparable to the much simplified averaged-value models (AVMs) when simulating the multi-terminal dc grid. Speedup is achieved by representing the off state of a MMC sub-module (SM) with ideal zero conductance, and representing the converter with a companion model using the A-stable Backward Euler (BE) method. Often, the user may wish to use the nearest level control (NLC) based voltage balancing algorithm. Then additional speedup can be obtained by using an efficient sorting algorithm which is integrated into the Thévenin equivalent circuit. This achieves a linear speedup (i.e. order O(N)) with system size. When compared with a fully detailed simulation (no simplifications), the method shows one to two orders of magnitude speed improvement with earlier reported fast MMC models, with negligible loss in accuracy.