The convective-scale numerical weather prediction (NWP) is sensitive to the initial minor perturbation and the evolution of initial perturbation (hereafter IP) is model-dependent, flow-dependent, and scale-dependent. And it has always been difficult to construct a reasonable initial perturbation for the convection-permitting ensemble prediction systems. Based on the GRAPES 3km convective-scale model of Center for Earth System Modeling and Prediction of CMA, we use a two-dimensional random function and background error of assimilation system in GRAPES 3km to construct the large, meso, and small scale stochastic initial perturbation field. Based on the constructed different scale initial perturbations, three convective-scale ensemble forecast experiments are conducted for a typical weather process of multi-regional heavy precipitation in summer in China. The spatial-temporal evolution and spectral decomposition characteristics of perturbation energy for three IP experiments are analyzed to understand the evolution characteristics of different scale initial perturbations in a convective scale model, to provide a reference for constructing an optimal initial perturbation in GRAPES convection-permitting ensemble prediction systems. Results show that: in the GRAPES 3km convective-scale model, (1) There are significant differences in the evolution of difference total energy (DTE) in three IP experiments. The DTE of large-scale IP increases with model integration, especially in the middle and upper troposphere. However, the DTE evolution of meso and small-scale IP experiments shows an apparent diurnal cycle characteristic. Specifically, it exhibits a significant increase (decrease) from afternoon to evening (from night to morning) when the convection is active (passive), and the diurnal cycle is mainly caused by the diurnal cycle of the small-scale component of DTE. The diurnal cycle of DTE may be due to the surface heating caused by solar short wave radiation, which makes the convection more active during the day than at night, and the convection directly affects the small-scale component of the DTE. In addition, the DTE of three IP experiments increases mainly by the development of difference kinetic energy (DKE), and the difference potential energy (DPE) cannot be neglected in the lower troposphere. (2) The DTE evolution of large, meso, and small-scale IP experiments is flow-dependent. Specifically, in the mid-high latitudes, the DTE increases of large-scale IP is dominant in the region where the baroclinic instability is strong (e.g., trough region), and the DTE of large, meso, and small-scale IP experiments does not develop in the region with relatively weak baroclinic instability (e.g., the northwest flow behind trough). In the confluence region of the north and south airflow, the DTE increases of large-scale IP is still dominant. However, the DTE of all three IP experiments hardly develops in the region affected by the South China Sea summer monsoon, and there is a relatively consistent relationship between the DPE(difference potential energy) development and the ratio of large precipitation rate in this region. (4) The DTE spectrum shows that the multi-scale cascade characteristics of DTE change with integration periods. The downscaling cascade of DTE from the large-scale component to the small-scale component in the first 3 hours is powerful. However, for lead times after 6 hours, the upscale DTE growth from meso and small-scale components becomes the main characteristic of the DTE spectrum. In conclusion, it is necessary to construct a scale-dependent and flow-dependent initial perturbation structure for different unstable weather regions, especially when we build the convection-permitting ensemble prediction in regions with complex weather systems and non-uniform spatial-temporal distribution dynamic instability (such as China).