With the increasing emphasis on environmental problems and climate change, renewable energy sources have been developed globally to push modern power systems towards sustainability. However, the weather-dependent and non-dispatchable features of renewable energy sources often hinder their integration into power grids and also pose a challenge for peak load regulation. Recently, the complementary operation of multi-energy hybrid systems has been attracting increasing attention as a promising way to overcome the mismatch between renewable energy supply and varying load demand. Multi-energy systems should be operated considering multiple uncertainties since a deterministic method only captures a fixed snapshot of a constantly changing system. In this study, the obtained short-term peak shaving operation of a hydro-wind-photovoltaic hybrid system is developed as a stochastic programming model. The uncertainties of renewable energy production and load demand are thoroughly simulated in the form of synthetic ensemble forecasts and scenario trees. To enhance the computational efficiency, a parallel particle swarm optimization algorithm is developed to solve the stochastic peak shaving model, in which a novel encoding scheme and parallel computing strategy are used. The proposed framework is applied to a hydro-wind-photovoltaic hybrid system of the East China Power Grid. The results of three numerical experiments indicate that the framework can achieve satisfactory peak shaving performance of the power system and enable decision makers to examine the robustness of operational decisions. In addition, it is acceptable for decision makers that joint complementary operation of the hybrid system greatly enhances the peak shaving capacity (with the performance metrics being improved by 95.7%, 96.4% and 30.5%) at the cost of 0.11% loss of total power generation.