With the large-scale integration of renewable energy and increasingly prominent inter-regional power demand differences, existing planning methods are mostly limited to single regions or local generation-grid-storage coordination, which cannot meet the requirements of cross-regional power complementation and wide-area coordinated operation. Aiming at the wide-area coordinated planning difficulty of generation-grid-storage oriented to multi-regional power peak shaving and mutual power support, a novel planning framework integrating multi-temporal-spatial scale coupled modeling, cross-regional complementary characteristic mining and collaborative optimization mechanism is proposed. Firstly, a multi-regional joint generation-grid-storage model considering climatic differences and time-series load characteristics is established. The Copula theory is adopted to generate wind-solar joint output scenario sets and quantitatively quantify the time-series peak shaving potential of each region. Secondly, a wide-area coordinated planning model with the objective of minimizing total system cost is built to realize coordinated allocation of power sources, power grids and energy storage facilities. Finally, a robust-stochastic hybrid optimization method is introduced to cope with multiple uncertainties of renewable energy output and cross-regional transmission capacity. Taking the interconnected multi-regional power grids of China's Three-North Region and East China as the example, simulation verification is carried out. The results show that after optimal planning, the proportion of renewable energy power generation of the system rises to 93.1%, among which wind and photovoltaic power account for 69.3% of total power generation. The overall system cost is reduced by 8.5%, and the cross-regional mutual power support capacity is increased by approximately 15.0%. The research provides theoretical support and technical approaches for realizing low-carbon, high-efficiency and secure coordinated development of multi-regional power systems.