The complementary operation is a mode to effectively ensure power benefits for a hydro-photovoltaic (PV) hybrid power system. Operating rules is a classical management tool to guide the system operation that generalizes the intrinsic dynamics relationship among optimal decision making, hydrometeorology variables and hybrid power system characteristics. Conventional rules for hydro-PV hybrid power system are often established in a subjective manner. It is a challenge in their applications because the operating rules are sensitive to climatic conditions. For dealing this challenge, dominant hydro-meteorological factors for the operation decisioning in different climatic conditions are eliminated by using the variance-based sensitivity analysis method, and further identify effective operating rules form to obtain robust operation benefits. The hydro-PV hybrid power system in Longyangxia, China is used as a case study. The result shows that the major factors in decisioning are the initial total potential stored energy (SE) and the input of potential energy (IE), whereas the interaction between SE and IE is the minor factor. It is also found that higher performance is achieved when SE and IE are considered separately instead of the product factor available energy (AE). Compared to the traditional complementary operating rules, the annual power generation and reliability of the system are increased by 1.59% and 1.71% under the newly derived rules, respectively. These findings are meaningful for robustly operating hybrid power systems under changing environments. •Optimal trajectories of the hybrid energy system operation model are taken as samples for the sensitivity analysis.•The influence of hydrometeorology variables on the optimal decision-making was qualified.•The input of potential energy should be explicitly expressed in the complementary operating rules.•The performance of the proposed complementary operating rules is superior to the traditional operating rules.