Modeling MMC (Modular Multi-level Converter) using mathematical equations is not an easy task. Realistically, mathematical modeling for a complex dynamics plant like MMC is extremely challenging. If a fault is introduced, the dynamics change significantly, requiring constant adjustments, which is practically unfeasible. If the system is interconnected, the degrees of freedom will be incredibly high, leading to a complex model. In this case, it would be advisable to utilize a Plant modeling solution.
By visiting this link and using Simscape Electrical, you can relatively easily model the MMC and the system interconnection. For simulating fault conditions, you can assume fault situations by utilizing blocks like the one found here. For examples of fault situations in Simscape, you might find this example helpful.
For your information, if you need to simulate open/short situations in specific phases of MMC, you can model it using this resource.
