In response to the multiple uncertainties such as runoff and new energy output in reservoir operation under the multi energy complementary mode, as well as key issues such as how to determine the optimal remaining storage capacity that can coordinate short-term and long-term benefits, a hydro-photovoltaic complementary stochastic optimal operation method based on the utility function of the carryover stage was studied. Firstly, combine the mathematical expectation model to derive a two-stage decision-making framework of hydro-photovoltaic complementarity, and then establish a two-stage stochastic optimization operation model of hydro-photovoltaic complementarity based on the utility function of the carryover stage to realize the dynamic decision-making of carryover storage under limited forecast information. Taking Jinping level 1 hydro-photovoltaic complementary system as an example for verification, the results show that the utility function of the carryover stage is less affected by the photovoltaic output, but positively related to the carryover storage and runoff. With the operation period from dry season to flood season, the utility function of the carryover stage gradually changes from linear surface to convex surface. Compared with the conventional operation method, the average annual power generation of the two-stage operation method has increased by 270 million kWh and 251 million kWh respectively in the periodic and inspection periods. Under the condition of relatively small predicted information on runoff and photovoltaic output, the method can effectively guide the long-term scheduling and operation of hydro-photovoltaic complementary systems.