Deriving pack rules for hydro–photovoltaic hybrid power systems considering diminishing marginal benefit of energy

•We derive that pack rules are piecewise linear functions of available energy.•Power output may decrease with increasing available energy due to curtailment.•Two multi-point pack rules increase operating benefits by 6.92% and 18.76%.•Optimal water levels are sensitive to forecast uncertainties in non-flood seasons. The hybrid operation of multiple renewables is a promising approach to enhance energy efficiency. The benefit of energy is influenced by a specified target. The energy exceeding the target is still beneficial, while the marginal benefit is diminishing. The diminishing marginal benefit of energy can significantly influence power system performance, however, was seldom considered in hybrid operation. To address this issue, we derive operating rules considering the diminishing marginal benefit of energy, namely the pack rules, for hydro–photovoltaic hybrid systems. First, a two-period hybrid operation model is built incorporating the diminishing marginal benefit of energy. After that, the total operation benefit is maximized and the optimal pack rules are derived to balance between the current and future energy. Finally, the sensitivity analysis of the optimal pack rules is conducted. Results using China’s Ertan hydro–photovoltaic power plant indicate that: (1) the analytical pack rules illustrate that the power output is a piecewise linear function of the available energy, and the power output decreases with the increase in available energy when the power curtailment rate increases significantly; (2) the multi-point pack rules, which are based on two-point and three-point rules, outperform the standard operating policy by 6.92% and 18.76% in terms of operating benefit, respectively; and (3) the optimal water levels are more sensitive to forecast uncertainties for inflow and photovoltaic output in non-flood seasons compared with flood seasons. The derived pack rules could effectively improve the hybrid operation by considering the diminishing marginal benefit of energy.