Recently, the open-circuit fault diagnosis of modular multilevel converters (MMC) faces problems such as the need to add extra hardware circuits, difficulty in determining the fault threshold, and challenges in extracting fault characteristics. This paper proposes a fault diagnosis and localization method for MMC open-circuit switch faults based on Tucker decomposition and two-dimensional extreme learning machine (2D-ELM). Through the characteristic analysis of MMC switch open-circuit faults, this paper constructs a third-order tensor using the submodule capacitor voltages, and uses Tucker decomposition to process the voltage tensor. The fault type feature and fault location feature can be extracted from the corresponding tensor projection matrices, respectively, which realizes the decoupling of the fault type feature and the fault location feature, and greatly reduces the number of fault categories. Using 2D-ELM with a simple structure and network parameters as the fault recognition method, the classifier model is greatly simplified, and the rapid and accurate diagnosis and positioning of single-tube and multi-tube open-circuit faults of the MMC submodule are finally realized through hardware-in-the-loop experiments.