The increasing connection of distributed energy resources (DERs) to low-voltage (LV) power grids challenges the operation of both connected LV grids and upstream medium-voltage (MV) grids, through power flow via the MV/LV transformers. Handling the coupling between MV and LV grids calls for combined MV-LV network operation models. This study develops various optimization-based models, built respectively on sequential, integrated, and decentralized control architectures. A new objective function is also designed to attain fairer DER curtailment strategies. For the decentralized architecture, this study explores the generalized Benders decomposition (GBD) and two augmented Lagrangian relaxation (ALR)-based approaches: the alternating direction method of multipliers (ADMM) and the auxiliary problem principle (APP). Computational results based on open-source Simbench networks show reduced power curtailment from the integrated architecture compared to the sequential one. For decentralization, GBD already shows superior convergence performance compared to ADMM and APP under moderate accuracy requirements. Under higher accuracy requirements, GBD maintains fast convergence, while ADMM and APP fail to converge in a reasonable number of iterations.