Zero-carbon parks have broad prospects in carbon neutralization. As an energy hub, hydrogen energy storage plays an important role in zero-carbon parks. However, the nonlinear characteristics of hydrogen energy storage systems (HESSs) have a significant impact on the system economy. Therefore, considering the variable working condition characteristics of HESSs, a hybrid operation method is proposed for HESS, to support the efficient and economic operation of zero-carbon parks, by analyzing the operating principle of a zero-carbon park with HESS, the system structure framework and variable condition linearization model of the equipment in HESS are established. Moreover, considering the energy output characteristics of hydrogen energy storage equipment under variable working conditions, a multimodule hybrid operation strategy is proposed for electrolytic and fuel cells, effectively meeting the thermoelectric load demand of zero- carbon parks in different scenarios. Finally, the economy of the proposed hybrid operation strategy was verified in typical scenarios, using a zero-carbon park embedded with a HESS.