As a multi-energy flow coupled microgrid system, optimized equipment capacity allocation for the micro energy grid is required, considering the uncertainties of internal distributed renewable energy and loads. A scenario probability-driven distributed robust planning method for the micro energy grid under comprehensive norm constraints was proposed, aiming to address the uncertainties of distributed renewable energy sources and electric-thermal-hydrogen loads. Historical data of wind-photovoltaic outputs and multi-energy loads were clustered to extract typical scenarios. An uncertainty set for scenario probability distributions was constructed based on 1-norm and ∞-norm constraints to characterize source-load uncertainties. A triple-layer min-max-min distributed robust optimization model was established with the objective of minimizing annual comprehensive costs, and the model was solved using the column and constraint generation (C & CG) algorithm. It is demonstrated by simulation results that a 1.33% reduction in annual comprehensive costs is achieved by the proposed uncertainty set and robust model compared to conventional approaches. Superior balance between economic efficiency and robustness is exhibited by the model over traditional stochastic and robust optimization methods, while fewer iterations are required for the model to converge. Decision-making adaptability against multi-dimensional uncertainties in renewable-dominated energy systems is effectively enhanced by this framework.