With the large-scale integration of distributed new energy and flexible loads into new power systems, traditional approaches for balancing electric power supply and demand are increasingly inadequate in addressing the complexity characteristics of generation and load, as well as the evolving supply-demand relationships. This presents significant challenges to the coordinated operation of such systems. To harness the regulatory potential of flexible resources within distribution networks and enhance self-balancing capability of power grids, a self-balancing capability assessment method for new power systems is proposed based on multi-criteria decision analysis. First, an evaluation index system is established to quantitively assess the self-balancing level of the distribution network. Then, a self-balancing capability assessment method based on multi-criteria decision analysis is developed by constructing a evaluation model based on preference order structure. Finally, the effectiveness of the proposed method is verified by example analysis and historical data. The assessment results can guide the construction of flexible resources such as new energy and demand-side response to meet the needs of new power systems across various time scale and application scenarios.