Nuclear power plants (NPPs) have recently undergone rapid development in China. To improve the performance of both NPPs and grids during adverse conditions, a precise understanding of the coordination between NPPs and grids is required. Therefore, a new mathematical model with reasonable accuracy and reduced computational complexity is developed. This model is applicable to the short, mid, and long-term dynamic simulation of large-scale power systems. The effectiveness of the model is verified by using an actual NPP full-scope simulator as a reference. Based on this model, the interaction and coordination between NPPs and grids under the conditions of over-frequency, under-frequency and under-voltage are analyzed, with special stress applied to the effect of protection systems on the safe operation of both NPPs and power grids. Finally, the coordinated control principles and schemes, together with the recommended protection system values, are proposed for both NPPs and grids. These results show that coordination between the protection systems of NPPs and power networks is a crucial factor in ensuring the safe and stable operation of both NPPs and grids. The results can be used as a reference for coordination between NPPs and grids, as well as for parameter optimization of grid-related generator protection of NPPs.